%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL186-3 : 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 : n009.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 58.37s 58.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL186-3 : 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
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 19:10:51 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.24/0.51 start to proof:theBenchmark
% 58.37/58.62 %-------------------------------------------
% 58.37/58.62 % File :CSE---1.7
% 58.37/58.62 % Problem :theBenchmark
% 58.37/58.62 % Transform :cnf
% 58.37/58.62 % Format :tptp:raw
% 58.37/58.62 % Command :java -jar mcs_scs.jar %d %s
% 58.37/58.62
% 58.37/58.62 % Result :Theorem 58.009489s
% 58.37/58.62 % Output :CNFRefutation 58.009489s
% 58.37/58.62 %-------------------------------------------
% 58.37/58.62 %--------------------------------------------------------------------------
% 58.37/58.62 % File : LCL186-3 : TPTP v9.3.1. Released v2.3.0.
% 58.37/58.62 % Domain : Logic Calculi (Propositional)
% 58.37/58.62 % Problem : Principia Mathematica 2.21
% 58.37/58.62 % Version : [WR27] axioms.
% 58.37/58.62 % English :
% 58.37/58.62
% 58.37/58.62 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 58.37/58.62 % Source : [WR27]
% 58.37/58.62 % Names : Problem 2.21 [WR27]
% 58.37/58.62
% 58.37/58.62 % Status : Unsatisfiable
% 58.37/58.62 % Rating : 0.00 v9.3.0, 0.17 v9.1.0, 0.08 v9.0.0, 0.06 v8.2.0, 0.00 v7.5.0, 0.10 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.0.0, 0.33 v5.5.0, 0.25 v5.4.0, 0.20 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 v2.3.0
% 58.37/58.62 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 58.37/58.62 % Number of literals : 12 ( 1 equ; 4 neg)
% 58.37/58.62 % Maximal clause size : 3 ( 1 avg)
% 58.37/58.62 % Maximal term depth : 4 ( 2 avg)
% 58.37/58.62 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 58.37/58.62 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 58.37/58.62 % Number of variables : 16 ( 1 sgn)
% 58.37/58.62 % SPC : CNF_UNS_RFO_SEQ_HRN
% 58.37/58.62
% 58.37/58.62 % Comments :
% 58.37/58.62 %--------------------------------------------------------------------------
% 58.37/58.62 %----Include axioms of propositional logic
% 58.37/58.62 include('Axioms/LCL004-0.ax').
% 58.37/58.62 %--------------------------------------------------------------------------
% 58.37/58.62 cnf(prove_this,negated_conjecture,
% 58.37/58.62 ~ theorem(implies(not(p),implies(p,q))) ).
% 58.37/58.62
% 58.37/58.62 %--------------------------------------------------------------------------
% 58.37/58.62 %-------------------------------------------
% 58.37/58.62 % Proof found
% 58.37/58.62 % SZS status Theorem for theBenchmark
% 58.37/58.62 % SZS output start Proof
% 58.37/58.63 %ClaNum:8(EqnAxiom:0)
% 58.37/58.63 %VarNum:28(SingletonVarNum:14)
% 58.37/58.63 %MaxLitNum:3
% 58.37/58.63 %MaxfuncDepth:3
% 58.37/58.63 %SharedTerms:7
% 58.37/58.63 %goalClause: 6
% 58.37/58.63 %singleGoalClaCount:1
% 58.37/58.63 [6]~P2(f2(f1(f1(a3)),f2(f1(a3),a4)))
% 58.37/58.63 [2]P1(f2(f1(f2(x21,x21)),x21))
% 58.37/58.63 [1]P1(f2(f1(x11),f2(x12,x11)))
% 58.37/58.63 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 58.37/58.63 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 58.37/58.63 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 58.37/58.63 [7]~P1(x71)+P2(x71)
% 58.37/58.63 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 58.37/58.63 %EqnAxiom
% 58.37/58.63
% 58.37/58.63 %-------------------------------------------
% 58.67/58.95 cnf(821125,plain,
% 58.67/58.95 (~P2(f2(f1(f2(f1(x8211251),f2(x8211252,x8211251))),f2(f1(f1(a3)),f2(f1(a3),a4))))),
% 58.67/58.95 inference(scs_inference,[],[6,1,7,8])).
% 58.67/58.95 cnf(821127,plain,
% 58.67/58.95 (P2(f2(f1(f2(x8211271,x8211272)),f2(x8211272,x8211271)))),
% 58.67/58.95 inference(scs_inference,[],[3,7])).
% 58.67/58.95 cnf(821137,plain,
% 58.67/58.96 (P2(f2(f1(f2(f1(x8211371),x8211372)),f2(f1(f2(x8211373,x8211371)),f2(x8211373,x8211372))))),
% 58.67/58.96 inference(scs_inference,[],[5,7])).
% 58.67/58.96 cnf(821142,plain,
% 58.67/58.96 ($false),
% 58.67/58.96 inference(scs_inference,[],[821127,821137,821125,8]),
% 58.67/58.96 ['proof']).
% 58.91/59.15 % SZS output end Proof
% 58.91/59.15 % Total time :58.009489s
%------------------------------------------------------------------------------