%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL187-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:18:45 AM UTC 2026
% Result : Unsatisfiable 58.59s 58.70s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL187-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.34 % Computer : n018.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 5 04:43:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.24/0.51 start to proof:theBenchmark
% 58.49/58.69 %-------------------------------------------
% 58.49/58.69 % File :CSE---1.7
% 58.49/58.69 % Problem :theBenchmark
% 58.49/58.69 % Transform :cnf
% 58.49/58.69 % Format :tptp:raw
% 58.49/58.69 % Command :java -jar mcs_scs.jar %d %s
% 58.49/58.69
% 58.49/58.69 % Result :Theorem 58.196530s
% 58.49/58.69 % Output :CNFRefutation 58.196530s
% 58.49/58.69 %-------------------------------------------
% 58.59/58.70 %--------------------------------------------------------------------------
% 58.59/58.70 % File : LCL187-1 : TPTP v9.3.1. Released v1.1.0.
% 58.59/58.70 % Domain : Logic Calculi (Propositional)
% 58.59/58.70 % Problem : Principia Mathematica 2.24
% 58.59/58.70 % Version : [WR27] axioms : Reduced & Augmented.
% 58.59/58.70 % English :
% 58.59/58.70
% 58.59/58.70 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 58.59/58.70 % : [NSS63] Newell et al. (1963), Empirical Explorations with the
% 58.59/58.70 % : [ORo89] O'Rourke (1989), LT Revisited: Explanation-Based Learn
% 58.59/58.70 % : [SE94] Segre & Elkan (1994), A High-Performance Explanation-B
% 58.59/58.70 % Source : [SE94]
% 58.59/58.70 % Names : Problem 2.24 [WR27]
% 58.59/58.70
% 58.59/58.70 % Status : Unsatisfiable
% 58.59/58.70 % Rating : 0.00 v5.5.0, 0.12 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.07 v4.0.1, 0.00 v2.2.1, 0.11 v2.1.0, 0.13 v2.0.0
% 58.59/58.70 % Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 4 RR)
% 58.59/58.70 % Number of literals : 14 ( 0 equ; 6 neg)
% 58.59/58.70 % Maximal clause size : 3 ( 1 avg)
% 58.59/58.70 % Maximal term depth : 5 ( 2 avg)
% 58.59/58.70 % Number of predicates : 2 ( 2 usr; 0 prp; 1-1 aty)
% 58.59/58.70 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 58.59/58.70 % Number of variables : 17 ( 1 sgn)
% 58.59/58.70 % SPC : CNF_UNS_RFO_NEQ_HRN
% 58.59/58.70
% 58.59/58.70 % Comments : Reduced to use only or and not, and includes a redundant rule
% 58.59/58.70 % of transitivity of implication, and a reduced rule of
% 58.59/58.70 % detachment.
% 58.59/58.70 %--------------------------------------------------------------------------
% 58.59/58.70 %----Include axioms of propositional logic
% 58.59/58.70 include('Axioms/LCL003-0.ax').
% 58.59/58.70 %--------------------------------------------------------------------------
% 58.59/58.70 cnf(prove_this,negated_conjecture,
% 58.59/58.70 ~ theorem(or(not(p),or(not(not(p)),q))) ).
% 58.59/58.70
% 58.59/58.70 %--------------------------------------------------------------------------
% 58.59/58.70 %-------------------------------------------
% 58.59/58.70 % Proof found
% 58.59/58.70 % SZS status Theorem for theBenchmark
% 58.59/58.70 % SZS output start Proof
% 58.59/58.70 %ClaNum:9(EqnAxiom:0)
% 58.59/58.70 %VarNum:34(SingletonVarNum:17)
% 58.59/58.70 %MaxLitNum:3
% 58.59/58.70 %MaxfuncDepth:4
% 58.59/58.70 %SharedTerms:7
% 58.59/58.70 %goalClause: 6
% 58.59/58.70 %singleGoalClaCount:1
% 58.59/58.70 [6]~P2(f2(f1(a3),f2(f1(f1(a3)),a4)))
% 58.59/58.70 [2]P1(f2(f1(f2(x21,x21)),x21))
% 58.59/58.70 [1]P1(f2(f1(x11),f2(x12,x11)))
% 58.59/58.70 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 58.59/58.70 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 58.59/58.70 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 58.59/58.70 [7]~P1(x71)+P2(x71)
% 58.59/58.70 [8]P2(x81)+~P2(x82)+~P1(f2(f1(x82),x81))
% 58.59/58.70 [9]~P2(f2(f1(x93),x92))+P2(f2(f1(x91),x92))+~P1(f2(f1(x91),x93))
% 58.59/58.70 %EqnAxiom
% 58.59/58.70
% 58.59/58.70 %-------------------------------------------
% 58.59/58.72 cnf(22,plain,
% 58.59/58.72 (~P2(f2(f1(f1(a3)),f2(f1(a3),a4)))),
% 58.59/58.72 inference(scs_inference,[],[6,4,7,8])).
% 58.59/58.72 cnf(27,plain,
% 58.59/58.72 (P2(f2(f1(f2(x271,x272)),f2(x271,x273)))+~P2(f2(f1(x272),x273))),
% 58.59/58.72 inference(scs_inference,[],[6,5,7,8])).
% 58.59/58.72 cnf(316,plain,
% 58.59/58.72 (P2(f2(f1(f2(x3161,x3162)),f2(x3161,f2(x3163,x3162))))),
% 58.59/58.72 inference(scs_inference,[],[1,27,7])).
% 58.59/58.72 cnf(319,plain,
% 58.59/58.72 (P2(f2(f1(x3191),f2(x3192,f2(x3193,x3191))))),
% 58.59/58.72 inference(scs_inference,[],[1,6,316,7,9])).
% 58.59/58.72 cnf(836,plain,
% 58.59/58.72 (P2(f2(f1(f2(x8361,x8362)),f2(x8363,f2(x8364,f2(x8362,x8361)))))),
% 58.59/58.72 inference(scs_inference,[],[3,6,319,7,9])).
% 58.59/58.72 cnf(955,plain,
% 58.59/58.72 (P2(f2(x9551,f2(f1(f2(x9552,x9553)),f2(x9554,f2(x9553,x9552)))))),
% 58.59/58.72 inference(scs_inference,[],[6,836,4,7,8])).
% 58.59/58.72 cnf(1066,plain,
% 58.59/58.72 (P2(f2(f2(f1(f2(x10661,x10662)),f2(x10663,f2(x10662,x10661))),x10664))),
% 58.59/58.72 inference(scs_inference,[],[3,6,955,7,8])).
% 58.59/58.72 cnf(1167,plain,
% 58.59/58.72 (P2(f2(f1(f2(x11671,x11672)),f2(x11673,f2(x11672,x11671))))),
% 58.59/58.72 inference(scs_inference,[],[6,1066,2,7,8])).
% 58.59/58.72 cnf(1173,plain,
% 58.59/58.72 (P2(f2(x11731,f2(f1(f2(x11732,x11733)),f2(x11733,x11732))))),
% 58.59/58.72 inference(scs_inference,[],[4,6,1167,7,8])).
% 58.59/58.72 cnf(1180,plain,
% 58.59/58.72 (P2(f2(f1(f2(x11801,x11802)),f2(x11802,x11801)))),
% 58.59/58.72 inference(scs_inference,[],[6,1173,2,7,8])).
% 58.59/58.72 cnf(2708,plain,
% 58.59/58.72 (P2(f2(f1(f2(x27081,f2(x27082,x27082))),f2(x27081,x27082)))),
% 58.59/58.72 inference(scs_inference,[],[5,2,8,7])).
% 58.59/58.72 cnf(7904,plain,
% 58.59/58.72 (P2(f2(x79041,f2(f1(x79042),f2(x79043,x79042))))),
% 58.59/58.72 inference(scs_inference,[],[319,6,4,2708,7,9,8])).
% 58.59/58.72 cnf(7920,plain,
% 58.59/58.72 (P2(f2(f1(x79201),f2(x79202,x79201)))),
% 58.59/58.72 inference(scs_inference,[],[6,7904,2,2708,7,9,8])).
% 58.59/58.72 cnf(34284,plain,
% 58.59/58.72 ($false),
% 58.59/58.72 inference(scs_inference,[],[6,1,22,7920,1180,8,9]),
% 58.59/58.72 ['proof']).
% 58.59/58.73 % SZS output end Proof
% 58.59/58.73 % Total time :58.196530s
%------------------------------------------------------------------------------