%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL187-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 80.42s 80.66s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL187-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.33 % Computer : n028.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % 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 13:33:43 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.14/0.44 start to proof:theBenchmark
% 80.42/80.66 %-------------------------------------------
% 80.42/80.66 % File :CSE---1.7
% 80.42/80.66 % Problem :theBenchmark
% 80.42/80.66 % Transform :cnf
% 80.42/80.66 % Format :tptp:raw
% 80.42/80.66 % Command :java -jar mcs_scs.jar %d %s
% 80.42/80.66
% 80.42/80.66 % Result :Theorem 80.140121s
% 80.42/80.66 % Output :CNFRefutation 80.140121s
% 80.42/80.66 %-------------------------------------------
% 80.42/80.66 %--------------------------------------------------------------------------
% 80.42/80.66 % File : LCL187-3 : TPTP v9.3.1. Released v2.3.0.
% 80.42/80.66 % Domain : Logic Calculi (Propositional)
% 80.42/80.66 % Problem : Principia Mathematica 2.24
% 80.42/80.66 % Version : [WR27] axioms.
% 80.42/80.66 % English :
% 80.42/80.66
% 80.42/80.66 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 80.42/80.66 % Source : [WR27]
% 80.42/80.66 % Names : Problem 2.24 [WR27]
% 80.42/80.66
% 80.42/80.66 % Status : Unsatisfiable
% 80.42/80.66 % Rating : 0.00 v9.3.0, 0.17 v9.1.0, 0.08 v9.0.0, 0.12 v8.2.0, 0.08 v8.1.0, 0.11 v7.5.0, 0.10 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.29 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, 0.14 v4.1.0, 0.22 v4.0.1, 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 v2.5.0, 0.20 v2.4.0, 0.00 v2.3.0
% 80.42/80.66 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 80.42/80.66 % Number of literals : 12 ( 1 equ; 4 neg)
% 80.42/80.66 % Maximal clause size : 3 ( 1 avg)
% 80.42/80.66 % Maximal term depth : 4 ( 2 avg)
% 80.42/80.66 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 80.42/80.66 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 80.42/80.66 % Number of variables : 16 ( 1 sgn)
% 80.42/80.66 % SPC : CNF_UNS_RFO_SEQ_HRN
% 80.42/80.66
% 80.42/80.66 % Comments :
% 80.42/80.66 %--------------------------------------------------------------------------
% 80.42/80.66 %----Include axioms of propositional logic
% 80.42/80.66 include('Axioms/LCL004-0.ax').
% 80.42/80.66 %--------------------------------------------------------------------------
% 80.42/80.66 cnf(prove_this,negated_conjecture,
% 80.42/80.66 ~ theorem(implies(p,implies(not(p),q))) ).
% 80.42/80.66
% 80.42/80.66 %--------------------------------------------------------------------------
% 80.42/80.66 %-------------------------------------------
% 80.42/80.66 % Proof found
% 80.42/80.66 % SZS status Theorem for theBenchmark
% 80.42/80.66 % SZS output start Proof
% 80.42/80.66 %ClaNum:8(EqnAxiom:0)
% 80.42/80.66 %VarNum:28(SingletonVarNum:14)
% 80.42/80.67 %MaxLitNum:3
% 80.42/80.67 %MaxfuncDepth:4
% 80.42/80.67 %SharedTerms:7
% 80.42/80.67 %goalClause: 6
% 80.42/80.67 %singleGoalClaCount:1
% 80.42/80.67 [6]~P2(f2(f1(a3),f2(f1(f1(a3)),a4)))
% 80.42/80.67 [2]P1(f2(f1(f2(x21,x21)),x21))
% 80.42/80.67 [1]P1(f2(f1(x11),f2(x12,x11)))
% 80.42/80.67 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 80.42/80.67 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 80.42/80.67 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 80.42/80.67 [7]~P1(x71)+P2(x71)
% 80.42/80.67 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 80.42/80.67 %EqnAxiom
% 80.42/80.67
% 80.42/80.67 %-------------------------------------------
% 80.74/80.99 cnf(345135,plain,
% 80.74/80.99 (~P2(f2(f1(f2(f1(x3451351),f2(x3451352,x3451351))),f2(f1(a3),f2(f1(f1(a3)),a4))))),
% 80.74/80.99 inference(scs_inference,[],[6,1,7,8])).
% 80.74/80.99 cnf(345137,plain,
% 80.74/80.99 (P2(f2(f1(f2(x3451371,x3451372)),f2(x3451372,x3451371)))),
% 80.74/80.99 inference(scs_inference,[],[3,7])).
% 80.74/80.99 cnf(345143,plain,
% 80.74/80.99 (P2(f2(f1(f2(f1(x3451431),x3451432)),f2(f1(f2(x3451433,x3451431)),f2(x3451433,x3451432))))),
% 80.74/80.99 inference(scs_inference,[],[5,7])).
% 80.74/80.99 cnf(345161,plain,
% 80.74/80.99 (~P2(f2(f1(a3),f2(f1(f2(f1(x3451611),f2(x3451612,x3451611))),f2(f1(f1(a3)),a4))))),
% 80.74/80.99 inference(scs_inference,[],[4,345135,7,8])).
% 80.74/80.99 cnf(346627,plain,
% 80.74/80.99 (P2(f2(f1(f2(x3466271,f2(f1(x3466272),x3466273))),f2(x3466271,f2(f1(f2(x3466274,x3466272)),f2(x3466274,x3466273)))))),
% 80.74/80.99 inference(scs_inference,[],[5,345143,7,8])).
% 80.74/80.99 cnf(347170,plain,
% 80.74/80.99 (P2(f2(x3471701,f2(f1(f2(x3471702,x3471701)),x3471702)))),
% 80.74/80.99 inference(scs_inference,[],[4,345137,7,8])).
% 80.74/80.99 cnf(347177,plain,
% 80.74/80.99 ($false),
% 80.74/80.99 inference(scs_inference,[],[345161,347170,346627,8]),
% 80.74/80.99 ['proof']).
% 80.87/81.10 % SZS output end Proof
% 80.87/81.10 % Total time :80.140121s
%------------------------------------------------------------------------------