============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 99361 was started by root on a2204b2d3c4a,
Thu Nov 20 17:07:12 2025
The command was "/content/drive/MyDrive/Colab-Notebooks/PIP_Packages/pyprover9_package/pyprover9/prover9-64 -t 10".
============================== end of head ===========================

============================== INPUT =================================
set(ignore_option_dependencies).
if(Prover9).
% Conditional input included.
clear(auto).
clear(auto_setup).
clear(auto_limits).
clear(auto_denials).
clear(auto_inference).
clear(auto_process).
assign(eq_defs,pass).
assign(max_seconds,10).
assign(max_weight,2147483647).
assign(sos_limit,-1).
clear(predicate_elim).
set(binary_resolution).
set(paramodulation).
set(factor).
end_if.
if(Mace4).
% Conditional input omitted.
end_if.

formulas(assumptions).
A -> B.
B -> C.
end_of_list.

formulas(goals).
A -> C.
end_of_list.

============================== end of input ==========================

% From the command line: assign(max_seconds, 10).

% Enabling option dependencies (ignore applies only on input).

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:
1 A -> B # label(non_clause).  [assumption].
2 B -> C # label(non_clause).  [assumption].
3 A -> C # label(non_clause) # label(goal).  [goal].

============================== end of process non-clausal formulas ===

============================== PROCESS INITIAL CLAUSES ===============

% Clauses before input processing:

formulas(usable).
end_of_list.

formulas(sos).
-A | B.  [clausify(1)].
-B | C.  [clausify(2)].
A.  [deny(3)].
-C.  [deny(3)].
end_of_list.

formulas(demodulators).
end_of_list.

Term ordering decisions:
Predicate symbol precedence:  predicate_order([ A, B, C ]).
Function symbol precedence:  function_order([ ]).
After inverse_order:  (no changes).

kept:      4 -A | B.  [clausify(1)].
kept:      5 -B | C.  [clausify(2)].
kept:      6 A.  [deny(3)].
kept:      7 -C.  [deny(3)].

============================== end of process initial clauses ========

============================== CLAUSES FOR SEARCH ====================

% Clauses after input processing:

formulas(usable).
end_of_list.

formulas(sos).
4 -A | B.  [clausify(1)].
5 -B | C.  [clausify(2)].
6 A.  [deny(3)].
7 -C.  [deny(3)].
end_of_list.

formulas(demodulators).
end_of_list.

============================== end of clauses for search =============

============================== SEARCH ================================

% Starting search at 0.00 seconds.

given #1 (I,wt=2): 4 -A | B.  [clausify(1)].

given #2 (I,wt=2): 5 -B | C.  [clausify(2)].

given #3 (I,wt=1): 6 A.  [deny(3)].

given #4 (I,wt=1): 7 -C.  [deny(3)].

given #5 (A,wt=1): 8 B.  [resolve(6,a,4,a)].

============================== PROOF =================================

% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 10.
% Level of proof is 4.
% Maximum clause weight is 2.000.
% Given clauses 5.

1 A -> B # label(non_clause).  [assumption].
2 B -> C # label(non_clause).  [assumption].
3 A -> C # label(non_clause) # label(goal).  [goal].
4 -A | B.  [clausify(1)].
5 -B | C.  [clausify(2)].
6 A.  [deny(3)].
7 -C.  [deny(3)].
8 B.  [resolve(6,a,4,a)].
9 C.  [resolve(8,a,5,a)].
10 $F.  [resolve(9,a,7,a)].

============================== end of proof ==========================

============================== STATISTICS ============================

Given=5. Generated=6. Kept=6. proofs=1.
Usable=4. Sos=0. Demods=0. Limbo=0, Disabled=5. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=0. Back_subsumed=1.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=0. Demod_rewrites=0.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=3.
Megabytes=0.03.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 99361 exit (max_proofs) Thu Nov 20 17:07:12 2025
