%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL178-3 : 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 : n013.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 11:18:44 AM UTC 2026
% Result : Unsatisfiable 67.90s 68.06s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL178-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 01:06:19 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.26/0.50 start to proof:theBenchmark
% 67.90/68.06 %-------------------------------------------
% 67.90/68.06 % File :CSE---1.7
% 67.90/68.06 % Problem :theBenchmark
% 67.90/68.06 % Transform :cnf
% 67.90/68.06 % Format :tptp:raw
% 67.90/68.06 % Command :java -jar mcs_scs.jar %d %s
% 67.90/68.06
% 67.90/68.06 % Result :Theorem 67.552115s
% 67.90/68.06 % Output :CNFRefutation 67.552115s
% 67.90/68.06 %-------------------------------------------
% 67.90/68.06 %--------------------------------------------------------------------------
% 67.90/68.06 % File : LCL178-3 : TPTP v9.3.1. Released v2.3.0.
% 67.90/68.06 % Domain : Logic Calculi (Propositional)
% 67.90/68.06 % Problem : Principia Mathematica 2.12
% 67.90/68.06 % Version : [WR27] axioms.
% 67.90/68.06 % English :
% 67.90/68.06
% 67.90/68.06 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 67.90/68.06 % Source : [WR27]
% 67.90/68.06 % Names : Problem 2.12 [WR27]
% 67.90/68.06
% 67.90/68.06 % Status : Unsatisfiable
% 67.90/68.06 % Rating : 0.00 v9.3.0, 0.17 v9.1.0, 0.00 v7.0.0, 0.14 v6.3.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.00 v4.1.0, 0.11 v4.0.1, 0.00 v3.3.0, 0.14 v3.2.0, 0.00 v2.3.0
% 67.90/68.06 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 67.90/68.06 % Number of literals : 12 ( 1 equ; 4 neg)
% 67.90/68.06 % Maximal clause size : 3 ( 1 avg)
% 67.90/68.06 % Maximal term depth : 4 ( 2 avg)
% 67.90/68.06 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 67.90/68.06 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 67.90/68.06 % Number of variables : 16 ( 1 sgn)
% 67.90/68.06 % SPC : CNF_UNS_RFO_SEQ_HRN
% 67.90/68.06
% 67.90/68.06 % Comments :
% 67.90/68.06 %--------------------------------------------------------------------------
% 67.90/68.06 %----Include axioms of propositional logic
% 67.90/68.06 include('Axioms/LCL004-0.ax').
% 67.90/68.06 %--------------------------------------------------------------------------
% 67.90/68.06 cnf(prove_this,negated_conjecture,
% 67.90/68.06 ~ theorem(implies(p,not(not(p)))) ).
% 67.90/68.06
% 67.90/68.06 %--------------------------------------------------------------------------
% 67.90/68.06 %-------------------------------------------
% 67.90/68.06 % Proof found
% 67.90/68.06 % SZS status Theorem for theBenchmark
% 67.90/68.06 % SZS output start Proof
% 67.90/68.06 %ClaNum:8(EqnAxiom:0)
% 67.90/68.06 %VarNum:28(SingletonVarNum:14)
% 67.90/68.06 %MaxLitNum:3
% 67.90/68.06 %MaxfuncDepth:3
% 67.90/68.06 %SharedTerms:5
% 67.90/68.06 %goalClause: 6
% 67.90/68.06 %singleGoalClaCount:1
% 67.90/68.06 [6]~P2(f2(f1(a3),f1(f1(a3))))
% 67.90/68.06 [2]P1(f2(f1(f2(x21,x21)),x21))
% 67.90/68.06 [1]P1(f2(f1(x11),f2(x12,x11)))
% 67.90/68.06 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 67.90/68.06 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 67.90/68.06 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 67.90/68.06 [7]~P1(x71)+P2(x71)
% 67.90/68.06 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 67.90/68.06 %EqnAxiom
% 67.90/68.06
% 67.90/68.06 %-------------------------------------------
% 68.29/68.41 cnf(365897,plain,
% 68.29/68.41 (P2(f2(f1(x3658971),f2(x3658972,x3658971)))),
% 68.29/68.41 inference(scs_inference,[],[1,7])).
% 68.29/68.41 cnf(365901,plain,
% 68.29/68.41 (P2(f2(f1(f2(x3659011,x3659012)),f2(x3659012,x3659011)))),
% 68.29/68.41 inference(scs_inference,[],[3,7])).
% 68.29/68.41 cnf(365905,plain,
% 68.29/68.41 (P2(f2(f1(f2(x3659051,x3659051)),x3659051))),
% 68.29/68.41 inference(scs_inference,[],[2,7])).
% 68.29/68.41 cnf(365909,plain,
% 68.29/68.41 (P2(f2(f1(f2(x3659091,f2(x3659092,x3659093))),f2(x3659092,f2(x3659091,x3659093))))),
% 68.29/68.41 inference(scs_inference,[],[4,7])).
% 68.29/68.41 cnf(365911,plain,
% 68.29/68.41 (P2(f2(f1(f2(f1(x3659111),x3659112)),f2(f1(f2(x3659113,x3659111)),f2(x3659113,x3659112))))),
% 68.29/68.41 inference(scs_inference,[],[5,7])).
% 68.29/68.41 cnf(371784,plain,
% 68.29/68.41 (P2(f2(f1(f2(x3717841,x3717842)),f2(x3717841,f2(x3717843,x3717842))))),
% 68.29/68.41 inference(scs_inference,[],[365897,365911,8])).
% 68.29/68.41 cnf(371794,plain,
% 68.29/68.41 (~P2(f2(f1(f2(f1(f2(x3717941,x3717942)),f2(x3717941,f2(x3717943,x3717942)))),f2(f1(a3),f1(f1(a3)))))),
% 68.29/68.41 inference(scs_inference,[],[371784,6,8])).
% 68.29/68.41 cnf(371820,plain,
% 68.29/68.41 (P2(f2(f1(f2(x3718201,x3718202)),f2(x3718203,f2(x3718202,x3718201))))),
% 68.29/68.41 inference(scs_inference,[],[365901,371784,8])).
% 68.29/68.41 cnf(371824,plain,
% 68.29/68.41 (~P2(f2(f1(f1(a3)),f1(a3)))),
% 68.29/68.41 inference(scs_inference,[],[371820,371794,8])).
% 68.29/68.41 cnf(371831,plain,
% 68.29/68.41 (P2(f2(x3718311,f2(f2(x3718312,x3718313),f1(f2(x3718313,x3718312)))))),
% 68.29/68.41 inference(scs_inference,[],[365901,371820,8])).
% 68.29/68.41 cnf(371853,plain,
% 68.29/68.41 (P2(f2(f2(x3718531,x3718532),f1(f2(x3718532,x3718531))))),
% 68.29/68.41 inference(scs_inference,[],[365905,371831,8])).
% 68.29/68.41 cnf(371862,plain,
% 68.29/68.41 (~P2(f2(f1(f2(f2(x3718621,x3718622),f1(f2(x3718622,x3718621)))),f2(f1(f1(a3)),f1(a3))))),
% 68.29/68.41 inference(scs_inference,[],[371853,371824,8])).
% 68.29/68.41 cnf(371869,plain,
% 68.29/68.41 ($false),
% 68.29/68.41 inference(scs_inference,[],[371862,365909,1,8,7]),
% 68.29/68.41 ['proof']).
% 68.39/68.52 % SZS output end Proof
% 68.39/68.52 % Total time :67.552115s
%------------------------------------------------------------------------------