%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL196-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 11:18:47 AM UTC 2026
% Result : Unsatisfiable 285.40s 285.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL196-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.32 % Computer : n002.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Sat Sep 5 12:20:50 UTC 2026
% 0.07/0.32 % CPUTime :
% 0.25/0.49 start to proof:theBenchmark
% 285.40/285.50 %-------------------------------------------
% 285.40/285.50 % File :CSE---1.7
% 285.40/285.50 % Problem :theBenchmark
% 285.40/285.50 % Transform :cnf
% 285.40/285.50 % Format :tptp:raw
% 285.40/285.50 % Command :java -jar mcs_scs.jar %d %s
% 285.40/285.50
% 285.40/285.50 % Result :Theorem 284.945624s
% 285.40/285.50 % Output :CNFRefutation 284.945624s
% 285.40/285.50 %-------------------------------------------
% 285.40/285.50 %--------------------------------------------------------------------------
% 285.40/285.50 % File : LCL196-3 : TPTP v9.3.1. Released v2.3.0.
% 285.40/285.50 % Domain : Logic Calculi (Propositional)
% 285.40/285.50 % Problem : Principia Mathematica 2.4
% 285.40/285.50 % Version : [WR27] axioms.
% 285.40/285.50 % English :
% 285.40/285.50
% 285.40/285.50 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 285.40/285.50 % Source : [WR27]
% 285.40/285.50 % Names : Problem 2.4 [WR27]
% 285.40/285.50
% 285.40/285.50 % Status : Unsatisfiable
% 285.40/285.50 % Rating : 0.00 v9.3.0, 0.17 v9.1.0, 0.08 v9.0.0, 0.25 v8.2.0, 0.17 v8.1.0, 0.11 v7.5.0, 0.20 v7.4.0, 0.33 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.57 v6.3.0, 0.50 v6.2.0, 0.00 v6.1.0, 0.40 v6.0.0, 0.44 v5.5.0, 0.31 v5.4.0, 0.27 v5.3.0, 0.17 v5.2.0, 0.38 v5.1.0, 0.29 v5.0.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.00 v4.0.0, 0.17 v3.5.0, 0.00 v3.4.0, 0.17 v3.3.0, 0.29 v3.2.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.00 v2.3.0
% 285.40/285.50 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 285.40/285.50 % Number of literals : 12 ( 1 equ; 4 neg)
% 285.40/285.50 % Maximal clause size : 3 ( 1 avg)
% 285.40/285.50 % Maximal term depth : 4 ( 2 avg)
% 285.40/285.50 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 285.40/285.50 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 285.40/285.50 % Number of variables : 16 ( 1 sgn)
% 285.40/285.51 % SPC : CNF_UNS_RFO_SEQ_HRN
% 285.40/285.51
% 285.40/285.51 % Comments :
% 285.40/285.51 %--------------------------------------------------------------------------
% 285.40/285.51 %----Include axioms of propositional logic
% 285.40/285.51 include('Axioms/LCL004-0.ax').
% 285.40/285.51 %--------------------------------------------------------------------------
% 285.40/285.51 cnf(prove_this,negated_conjecture,
% 285.40/285.51 ~ theorem(implies(or(p,or(p,q)),or(p,q))) ).
% 285.40/285.51
% 285.40/285.51 %--------------------------------------------------------------------------
% 285.40/285.51 %-------------------------------------------
% 285.40/285.51 % Proof found
% 285.40/285.51 % SZS status Theorem for theBenchmark
% 285.40/285.51 % SZS output start Proof
% 285.40/285.51 %ClaNum:8(EqnAxiom:0)
% 285.40/285.51 %VarNum:28(SingletonVarNum:14)
% 285.40/285.51 %MaxLitNum:3
% 285.40/285.51 %MaxfuncDepth:3
% 285.40/285.51 %SharedTerms:7
% 285.40/285.51 %goalClause: 6
% 285.40/285.51 %singleGoalClaCount:1
% 285.40/285.51 [6]~P2(f2(f1(f2(a3,f2(a3,a4))),f2(a3,a4)))
% 285.40/285.51 [2]P1(f2(f1(f2(x21,x21)),x21))
% 285.40/285.51 [1]P1(f2(f1(x11),f2(x12,x11)))
% 285.40/285.51 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 285.40/285.51 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 285.40/285.51 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 285.40/285.51 [7]~P1(x71)+P2(x71)
% 285.40/285.51 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 285.40/285.51 %EqnAxiom
% 285.40/285.51
% 285.40/285.51 %-------------------------------------------
% 285.72/285.85 cnf(344851,plain,
% 285.72/285.85 (P2(f2(f1(x3448511),f2(x3448512,x3448511)))),
% 285.72/285.85 inference(scs_inference,[],[1,7])).
% 285.72/285.85 cnf(344855,plain,
% 285.72/285.85 (P2(f2(f1(f2(x3448551,x3448552)),f2(x3448552,x3448551)))),
% 285.72/285.85 inference(scs_inference,[],[3,7])).
% 285.72/285.85 cnf(344857,plain,
% 285.72/285.85 (~P2(f2(f1(f2(f1(f2(x3448571,x3448572)),f2(x3448572,x3448571))),f2(f1(f2(a3,f2(a3,a4))),f2(a3,a4))))),
% 285.72/285.85 inference(scs_inference,[],[6,3,7,8])).
% 285.72/285.85 cnf(344859,plain,
% 285.72/285.85 (P2(f2(f1(f2(x3448591,x3448591)),x3448591))),
% 285.72/285.85 inference(scs_inference,[],[2,7])).
% 285.72/285.85 cnf(344863,plain,
% 285.72/285.85 (P2(f2(f1(f2(x3448631,f2(x3448632,x3448633))),f2(x3448632,f2(x3448631,x3448633))))),
% 285.72/285.85 inference(scs_inference,[],[4,7])).
% 285.72/285.85 cnf(344865,plain,
% 285.72/285.85 (P2(f2(f1(f2(f1(x3448651),x3448652)),f2(f1(f2(x3448653,x3448651)),f2(x3448653,x3448652))))),
% 285.72/285.85 inference(scs_inference,[],[5,7])).
% 285.72/285.85 cnf(350171,plain,
% 285.72/285.85 (P2(f2(x3501711,f2(f1(f2(x3501712,x3501711)),x3501712)))),
% 285.72/285.85 inference(scs_inference,[],[344855,344863,8])).
% 285.72/285.85 cnf(350184,plain,
% 285.72/285.85 (P2(f2(f2(f1(f2(x3501841,x3501842)),x3501841),x3501842))),
% 285.72/285.85 inference(scs_inference,[],[350171,344855,8])).
% 285.72/285.85 cnf(350208,plain,
% 285.72/285.85 (~P2(f2(f1(f2(f2(a3,a4),a3)),f2(a3,a4)))),
% 285.72/285.85 inference(scs_inference,[],[344857,344865,8])).
% 285.72/285.85 cnf(350252,plain,
% 285.72/285.85 (P2(f2(x3502521,f2(f2(f1(f2(x3502522,x3502523)),x3502522),x3502523)))),
% 285.72/285.85 inference(scs_inference,[],[344851,350184,8])).
% 285.72/285.85 cnf(350360,plain,
% 285.72/285.85 (P2(f2(f2(f1(f2(x3503601,x3503602)),x3503601),f2(x3503603,x3503602)))),
% 285.72/285.85 inference(scs_inference,[],[344863,350252,8])).
% 285.72/285.85 cnf(350447,plain,
% 285.72/285.85 (~P2(f2(f2(f1(f2(f2(a3,a4),a3)),f2(a3,a4)),f2(f1(f2(f2(a3,a4),a3)),f2(a3,a4))))),
% 285.72/285.85 inference(scs_inference,[],[350208,344859,8])).
% 285.72/285.85 cnf(350463,plain,
% 285.72/285.85 (~P2(f2(f1(f2(f2(a3,a4),a3)),f2(f2(f1(f2(f2(a3,a4),a3)),f2(a3,a4)),f2(a3,a4))))),
% 285.72/285.85 inference(scs_inference,[],[350447,344863,8])).
% 285.72/285.85 cnf(350476,plain,
% 285.72/285.85 (~P2(f2(f2(f1(f2(f2(a3,a4),a3)),f2(a3,a4)),f2(a3,a4)))),
% 285.72/285.85 inference(scs_inference,[],[350463,344851,8])).
% 285.72/285.86 cnf(354864,plain,
% 285.72/285.86 (~P2(f2(f1(f2(f2(f1(f2(x3548641,x3548642)),x3548641),f2(x3548643,x3548642))),f2(f2(f1(f2(f2(a3,a4),a3)),f2(a3,a4)),f2(a3,a4))))),
% 285.72/285.86 inference(scs_inference,[],[350476,350360,8])).
% 285.72/285.86 cnf(356576,plain,
% 285.72/285.86 ($false),
% 285.72/285.86 inference(scs_inference,[],[344855,344865,354864,8]),
% 285.72/285.86 ['proof']).
% 285.84/285.97 % SZS output end Proof
% 285.84/285.97 % Total time :284.945624s
%------------------------------------------------------------------------------