%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL212-3 : 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 : n031.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 11:18:48 AM UTC 2026
% Result : Unsatisfiable 58.35s 58.54s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL212-3 : 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
% 0.09/0.35 % Computer : n031.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 20:18:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.22/0.52 start to proof:theBenchmark
% 58.35/58.53 %-------------------------------------------
% 58.35/58.53 % File :CSE---1.7
% 58.35/58.53 % Problem :theBenchmark
% 58.35/58.53 % Transform :cnf
% 58.35/58.53 % Format :tptp:raw
% 58.35/58.53 % Command :java -jar mcs_scs.jar %d %s
% 58.35/58.53
% 58.35/58.53 % Result :Theorem 58.008335s
% 58.35/58.54 % Output :CNFRefutation 58.008335s
% 58.35/58.54 %-------------------------------------------
% 58.35/58.54 %--------------------------------------------------------------------------
% 58.35/58.54 % File : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 58.35/58.54 % Domain : Logic Calculi (Propositional)
% 58.35/58.54 % Problem : Principia Mathematica 2.6
% 58.35/58.54 % Version : [WR27] axioms.
% 58.35/58.54 % English :
% 58.35/58.54
% 58.35/58.54 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 58.35/58.54 % Source : [WR27]
% 58.35/58.54 % Names : Problem 2.6 [WR27]
% 58.35/58.54
% 58.35/58.54 % Status : Unsatisfiable
% 58.35/58.54 % Rating : 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
% 58.35/58.54 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 58.35/58.54 % Number of literals : 12 ( 1 equ; 4 neg)
% 58.35/58.54 % Maximal clause size : 3 ( 1 avg)
% 58.35/58.54 % Maximal term depth : 5 ( 2 avg)
% 58.35/58.54 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 58.35/58.54 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 58.35/58.54 % Number of variables : 16 ( 1 sgn)
% 58.35/58.54 % SPC : CNF_UNS_RFO_SEQ_HRN
% 58.35/58.54
% 58.35/58.54 % Comments :
% 58.35/58.54 %--------------------------------------------------------------------------
% 58.35/58.54 %----Include axioms of propositional logic
% 58.35/58.54 include('Axioms/LCL004-0.ax').
% 58.35/58.54 %--------------------------------------------------------------------------
% 58.35/58.54 cnf(prove_this,negated_conjecture,
% 58.35/58.54 ~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))) ).
% 58.35/58.54
% 58.35/58.54 %--------------------------------------------------------------------------
% 58.35/58.54 %-------------------------------------------
% 58.35/58.54 % Proof found
% 58.35/58.54 % SZS status Theorem for theBenchmark
% 58.35/58.54 % SZS output start Proof
% 58.35/58.54 %ClaNum:8(EqnAxiom:0)
% 58.35/58.54 %VarNum:28(SingletonVarNum:14)
% 58.35/58.54 %MaxLitNum:3
% 58.35/58.54 %MaxfuncDepth:6
% 58.35/58.54 %SharedTerms:11
% 58.35/58.54 %goalClause: 6
% 58.35/58.54 %singleGoalClaCount:1
% 58.35/58.54 [6]~P2(f2(f1(f1(a3)),f2(f1(a4),f2(f1(f2(f1(a3),a4)),a4))))
% 58.35/58.54 [2]P1(f2(f1(f2(x21,x21)),x21))
% 58.35/58.54 [1]P1(f2(f1(x11),f2(x12,x11)))
% 58.35/58.54 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 58.35/58.54 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 58.35/58.54 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 58.35/58.54 [7]~P1(x71)+P2(x71)
% 58.35/58.54 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 58.35/58.54 %EqnAxiom
% 58.35/58.54
% 58.35/58.54 %-------------------------------------------
% 58.65/58.84 cnf(319059,plain,
% 58.65/58.84 (P2(f2(f1(x3190591),f2(x3190592,x3190591)))),
% 58.65/58.84 inference(scs_inference,[],[1,7])).
% 58.65/58.84 cnf(319069,plain,
% 58.65/58.84 ($false),
% 58.65/58.84 inference(scs_inference,[],[6,319059,1,8,7]),
% 58.65/58.84 ['proof']).
% 58.75/58.93 % SZS output end Proof
% 58.75/58.93 % Total time :58.008335s
%------------------------------------------------------------------------------