%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL186-1 : 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 : n010.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 2.45s 2.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-1 : 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
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 23:44:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.23/0.54 start to proof:theBenchmark
% 2.45/2.65 %-------------------------------------------
% 2.45/2.65 % File :CSE---1.7
% 2.45/2.65 % Problem :theBenchmark
% 2.45/2.65 % Transform :cnf
% 2.45/2.65 % Format :tptp:raw
% 2.45/2.65 % Command :java -jar mcs_scs.jar %d %s
% 2.45/2.65
% 2.45/2.65 % Result :Theorem 2.125113s
% 2.45/2.65 % Output :CNFRefutation 2.125113s
% 2.45/2.65 %-------------------------------------------
% 2.45/2.65 %--------------------------------------------------------------------------
% 2.45/2.65 % File : LCL186-1 : TPTP v9.3.1. Released v1.1.0.
% 2.45/2.65 % Domain : Logic Calculi (Propositional)
% 2.45/2.65 % Problem : Principia Mathematica 2.21
% 2.45/2.65 % Version : [WR27] axioms : Reduced & Augmented.
% 2.45/2.65 % English :
% 2.45/2.65
% 2.45/2.65 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 2.45/2.65 % : [NSS63] Newell et al. (1963), Empirical Explorations with the
% 2.45/2.65 % : [ORo89] O'Rourke (1989), LT Revisited: Explanation-Based Learn
% 2.45/2.65 % : [SE94] Segre & Elkan (1994), A High-Performance Explanation-B
% 2.45/2.65 % Source : [SE94]
% 2.45/2.65 % Names : Problem 2.21 [WR27]
% 2.45/2.65
% 2.45/2.65 % Status : Unsatisfiable
% 2.45/2.65 % Rating : 0.00 v5.5.0, 0.06 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.00 v2.0.0
% 2.45/2.65 % Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 4 RR)
% 2.45/2.65 % Number of literals : 14 ( 0 equ; 6 neg)
% 2.45/2.65 % Maximal clause size : 3 ( 1 avg)
% 2.45/2.65 % Maximal term depth : 5 ( 2 avg)
% 2.45/2.65 % Number of predicates : 2 ( 2 usr; 0 prp; 1-1 aty)
% 2.45/2.65 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 2.45/2.65 % Number of variables : 17 ( 1 sgn)
% 2.45/2.65 % SPC : CNF_UNS_RFO_NEQ_HRN
% 2.45/2.65
% 2.45/2.65 % Comments : Reduced to use only or and not, and includes a redundant rule
% 2.45/2.65 % of transitivity of implication, and a reduced rule of
% 2.45/2.65 % detachment.
% 2.45/2.65 %--------------------------------------------------------------------------
% 2.45/2.65 %----Include axioms of propositional logic
% 2.45/2.65 include('Axioms/LCL003-0.ax').
% 2.45/2.65 %--------------------------------------------------------------------------
% 2.45/2.65 cnf(prove_this,negated_conjecture,
% 2.45/2.65 ~ theorem(or(not(not(p)),or(not(p),q))) ).
% 2.45/2.65
% 2.45/2.65 %--------------------------------------------------------------------------
% 2.45/2.65 %-------------------------------------------
% 2.45/2.65 % Proof found
% 2.45/2.65 % SZS status Theorem for theBenchmark
% 2.45/2.65 % SZS output start Proof
% 2.45/2.65 %ClaNum:9(EqnAxiom:0)
% 2.45/2.65 %VarNum:34(SingletonVarNum:17)
% 2.45/2.65 %MaxLitNum:3
% 2.45/2.65 %MaxfuncDepth:3
% 2.45/2.65 %SharedTerms:7
% 2.45/2.65 %goalClause: 6
% 2.45/2.65 %singleGoalClaCount:1
% 2.45/2.65 [6]~P2(f2(f1(f1(a3)),f2(f1(a3),a4)))
% 2.45/2.65 [2]P1(f2(f1(f2(x21,x21)),x21))
% 2.45/2.65 [1]P1(f2(f1(x11),f2(x12,x11)))
% 2.45/2.65 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 2.45/2.65 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 2.45/2.65 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 2.45/2.65 [7]~P1(x71)+P2(x71)
% 2.45/2.65 [8]P2(x81)+~P2(x82)+~P1(f2(f1(x82),x81))
% 2.45/2.65 [9]~P2(f2(f1(x93),x92))+P2(f2(f1(x91),x92))+~P1(f2(f1(x91),x93))
% 2.45/2.65 %EqnAxiom
% 2.45/2.65
% 2.45/2.65 %-------------------------------------------
% 2.45/2.66 cnf(27,plain,
% 2.45/2.66 (P2(f2(f1(f2(x271,x272)),f2(x271,x273)))+~P2(f2(f1(x272),x273))),
% 2.45/2.66 inference(scs_inference,[],[6,5,7,8])).
% 2.45/2.66 cnf(316,plain,
% 2.45/2.66 (P2(f2(f1(f2(x3161,x3162)),f2(x3161,f2(x3163,x3162))))),
% 2.45/2.66 inference(scs_inference,[],[1,27,7])).
% 2.45/2.66 cnf(319,plain,
% 2.45/2.66 (P2(f2(f1(x3191),f2(x3192,f2(x3193,x3191))))),
% 2.45/2.66 inference(scs_inference,[],[1,6,316,7,9])).
% 2.45/2.66 cnf(836,plain,
% 2.45/2.66 (P2(f2(f1(f2(x8361,x8362)),f2(x8363,f2(x8364,f2(x8362,x8361)))))),
% 2.45/2.66 inference(scs_inference,[],[3,6,319,7,9])).
% 2.45/2.66 cnf(955,plain,
% 2.45/2.66 (P2(f2(x9551,f2(f1(f2(x9552,x9553)),f2(x9554,f2(x9553,x9552)))))),
% 2.45/2.66 inference(scs_inference,[],[6,836,4,7,8])).
% 2.45/2.66 cnf(1185,plain,
% 2.45/2.66 (P2(f2(f2(f1(f2(x11851,x11852)),f2(x11853,f2(x11852,x11851))),x11854))),
% 2.45/2.66 inference(scs_inference,[],[3,6,955,7,8])).
% 2.45/2.66 cnf(1412,plain,
% 2.45/2.66 (P2(f2(f1(f2(x14121,x14122)),f2(x14123,f2(x14122,x14121))))),
% 2.45/2.66 inference(scs_inference,[],[6,1185,2,7,8])).
% 2.45/2.66 cnf(1421,plain,
% 2.45/2.66 (P2(f2(x14211,f2(f1(f2(x14212,x14213)),f2(x14213,x14212))))),
% 2.45/2.66 inference(scs_inference,[],[4,6,1412,7,8])).
% 2.45/2.66 cnf(1431,plain,
% 2.45/2.66 (P2(f2(f1(f2(x14311,x14312)),f2(x14312,x14311)))),
% 2.45/2.66 inference(scs_inference,[],[6,1421,2,7,8])).
% 2.45/2.66 cnf(1445,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(scs_inference,[],[4,6,1431,1,7,8,9]),
% 2.45/2.66 ['proof']).
% 2.45/2.66 % SZS output end Proof
% 2.45/2.66 % Total time :2.125113s
%------------------------------------------------------------------------------