%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL258-3 : 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 : n006.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 11:18:54 AM UTC 2026
% Result : Unsatisfiable 242.36s 242.59s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL258-3 : 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
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 19:57:46 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.12/0.45 start to proof:theBenchmark
% 242.36/242.59 %-------------------------------------------
% 242.36/242.59 % File :CSE---1.7
% 242.36/242.59 % Problem :theBenchmark
% 242.36/242.59 % Transform :cnf
% 242.36/242.59 % Format :tptp:raw
% 242.36/242.59 % Command :java -jar mcs_scs.jar %d %s
% 242.36/242.59
% 242.36/242.59 % Result :Theorem 242.026790s
% 242.36/242.59 % Output :CNFRefutation 242.026790s
% 242.36/242.59 %-------------------------------------------
% 242.36/242.59 %--------------------------------------------------------------------------
% 242.36/242.59 % File : LCL258-3 : TPTP v9.3.1. Released v2.3.0.
% 242.36/242.59 % Domain : Logic Calculi (Propositional)
% 242.36/242.59 % Problem : Principia Mathematica 2.27
% 242.36/242.59 % Version : [WR27] axioms.
% 242.36/242.59 % English :
% 242.36/242.59
% 242.36/242.59 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 242.36/242.59 % Source : [WR27]
% 242.36/242.59 % Names : Problem 2.27 [WR27]
% 242.36/242.59
% 242.36/242.59 % Status : Unsatisfiable
% 242.36/242.59 % Rating : 0.00 v7.0.0, 0.14 v6.3.0, 0.17 v6.2.0, 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 v4.1.0, 0.22 v4.0.1, 0.00 v3.3.0, 0.14 v3.2.0, 0.00 v2.3.0
% 242.36/242.59 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 242.36/242.59 % Number of literals : 12 ( 1 equ; 4 neg)
% 242.36/242.59 % Maximal clause size : 3 ( 1 avg)
% 242.36/242.59 % Maximal term depth : 4 ( 2 avg)
% 242.36/242.59 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 242.36/242.59 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 242.36/242.59 % Number of variables : 16 ( 1 sgn)
% 242.36/242.59 % SPC : CNF_UNS_RFO_SEQ_HRN
% 242.36/242.59
% 242.36/242.59 % Comments :
% 242.36/242.59 %--------------------------------------------------------------------------
% 242.36/242.59 %----Include axioms of propositional logic
% 242.36/242.59 include('Axioms/LCL004-0.ax').
% 242.36/242.59 %--------------------------------------------------------------------------
% 242.36/242.59 cnf(prove_this,negated_conjecture,
% 242.36/242.59 ~ theorem(implies(p,implies(implies(p,q),q))) ).
% 242.36/242.59
% 242.36/242.59 %--------------------------------------------------------------------------
% 242.36/242.59 %-------------------------------------------
% 242.36/242.59 % Proof found
% 242.36/242.59 % SZS status Theorem for theBenchmark
% 242.36/242.59 % SZS output start Proof
% 242.36/242.60 %ClaNum:8(EqnAxiom:0)
% 242.36/242.60 %VarNum:28(SingletonVarNum:14)
% 242.36/242.60 %MaxLitNum:3
% 242.36/242.60 %MaxfuncDepth:5
% 242.36/242.60 %SharedTerms:8
% 242.36/242.60 %goalClause: 6
% 242.36/242.60 %singleGoalClaCount:1
% 242.36/242.60 [6]~P2(f2(f1(a3),f2(f1(f2(f1(a3),a4)),a4)))
% 242.36/242.60 [2]P1(f2(f1(f2(x21,x21)),x21))
% 242.48/242.60 [1]P1(f2(f1(x11),f2(x12,x11)))
% 242.48/242.60 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 242.48/242.60 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 242.48/242.60 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 242.48/242.60 [7]~P1(x71)+P2(x71)
% 242.48/242.60 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 242.48/242.60 %EqnAxiom
% 242.48/242.60
% 242.48/242.60 %-------------------------------------------
% 242.90/243.04 cnf(456559,plain,
% 242.90/243.04 (P2(f2(f1(x4565591),f2(x4565592,x4565591)))),
% 242.90/243.04 inference(scs_inference,[],[1,7])).
% 242.90/243.04 cnf(456567,plain,
% 242.90/243.04 (P2(f2(f1(f2(x4565671,f2(x4565672,x4565673))),f2(x4565672,f2(x4565671,x4565673))))),
% 242.90/243.04 inference(scs_inference,[],[4,7])).
% 242.90/243.04 cnf(456650,plain,
% 242.90/243.04 (P2(f2(x4566501,f2(f1(f2(x4566502,f2(x4566501,x4566503))),f2(x4566502,x4566503))))),
% 242.90/243.04 inference(scs_inference,[],[4,456567,7,8])).
% 242.90/243.04 cnf(456655,plain,
% 242.90/243.04 (P2(f2(f2(f1(f2(x4566551,f2(x4566552,x4566553))),f2(x4566551,x4566553)),x4566552))),
% 242.90/243.04 inference(scs_inference,[],[3,456650,7,8])).
% 242.90/243.04 cnf(459635,plain,
% 242.90/243.04 (~P2(f2(f1(f2(f1(a3),a4)),f2(f1(a3),a4)))),
% 242.90/243.04 inference(scs_inference,[],[6,456567,7,8])).
% 242.90/243.04 cnf(464774,plain,
% 242.90/243.04 (~P2(f2(f1(f2(f2(f1(f2(x4647741,f2(x4647742,x4647743))),f2(x4647741,x4647743)),x4647742)),f2(f1(f2(f1(a3),a4)),f2(f1(a3),a4))))),
% 242.90/243.04 inference(scs_inference,[],[456655,459635,8])).
% 242.90/243.04 cnf(468578,plain,
% 242.90/243.04 ($false),
% 242.90/243.04 inference(scs_inference,[],[456559,464774,456567,8]),
% 242.90/243.04 ['proof']).
% 243.09/243.20 % SZS output end Proof
% 243.09/243.20 % Total time :242.026790s
%------------------------------------------------------------------------------