%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 11:18:31 AM UTC 2026
% Result : Unsatisfiable 242.18s 242.15s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n011.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 : Fri Sep 4 22:42:43 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.25/0.52 start to proof:theBenchmark
% 242.07/242.15 %-------------------------------------------
% 242.07/242.15 % File :CSE---1.7
% 242.07/242.15 % Problem :theBenchmark
% 242.07/242.15 % Transform :cnf
% 242.07/242.15 % Format :tptp:raw
% 242.07/242.15 % Command :java -jar mcs_scs.jar %d %s
% 242.07/242.15
% 242.07/242.15 % Result :Theorem 241.641112s
% 242.07/242.15 % Output :CNFRefutation 241.641112s
% 242.07/242.15 %-------------------------------------------
% 242.07/242.15 %--------------------------------------------------------------------------
% 242.07/242.15 % File : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% 242.07/242.15 % Domain : Logic Calculi (Equivalential)
% 242.07/242.15 % Problem : EC-4 depends on YQL
% 242.07/242.15 % Version : [McC92] axioms.
% 242.07/242.15 % English : An axiomatisation of the equivalential calculus is {EC-4,
% 242.07/242.15 % EC-5} by Wajsburg. Show that EC-4 can be derived from the
% 242.07/242.15 % single Lukasiewicz axiom YQL.
% 242.07/242.15
% 242.07/242.15 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 242.07/242.15 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 242.07/242.15 % Source : [McC92]
% 242.07/242.15 % Names : EC-71 [MW92]
% 242.07/242.15
% 242.07/242.15 % Status : Unsatisfiable
% 242.07/242.15 % Rating : 0.00 v9.3.0, 0.06 v9.1.0, 0.00 v5.4.0, 0.06 v5.3.0, 0.05 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.07 v4.0.1, 0.00 v2.1.0, 0.00 v2.0.0
% 242.07/242.15 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 242.07/242.15 % Number of literals : 5 ( 0 equ; 3 neg)
% 242.07/242.15 % Maximal clause size : 3 ( 1 avg)
% 242.07/242.15 % Maximal term depth : 4 ( 2 avg)
% 242.07/242.15 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 242.07/242.15 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 242.07/242.15 % Number of variables : 5 ( 0 sgn)
% 242.07/242.15 % SPC : CNF_UNS_RFO_NEQ_HRN
% 242.07/242.15
% 242.07/242.15 % Comments :
% 242.07/242.15 %--------------------------------------------------------------------------
% 242.07/242.15 cnf(condensed_detachment,axiom,
% 242.07/242.15 ( ~ is_a_theorem(equivalent(X,Y))
% 242.07/242.15 | ~ is_a_theorem(X)
% 242.07/242.15 | is_a_theorem(Y) ) ).
% 242.07/242.15
% 242.07/242.15 %----Axiom by Lukasiewicz
% 242.07/242.15 cnf(yql,axiom,
% 242.07/242.15 is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
% 242.07/242.15
% 242.07/242.15 %----Axiom of symmetry
% 242.07/242.15 cnf(prove_ec_4,negated_conjecture,
% 242.07/242.15 ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))) ).
% 242.07/242.15
% 242.07/242.15 %--------------------------------------------------------------------------
% 242.18/242.15 %-------------------------------------------
% 242.18/242.15 % Proof found
% 242.18/242.15 % SZS status Theorem for theBenchmark
% 242.18/242.15 % SZS output start Proof
% 242.18/242.15 %ClaNum:3(EqnAxiom:0)
% 242.18/242.15 %VarNum:10(SingletonVarNum:5)
% 242.18/242.15 %MaxLitNum:3
% 242.18/242.15 %MaxfuncDepth:3
% 242.18/242.15 %SharedTerms:6
% 242.18/242.15 %goalClause: 2
% 242.18/242.15 %singleGoalClaCount:1
% 242.18/242.15 [2]~P1(f1(f1(a2,a3),f1(a3,a2)))
% 242.18/242.15 [1]P1(f1(f1(x11,x12),f1(f1(x13,x12),f1(x11,x13))))
% 242.18/242.15 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 242.18/242.15 %EqnAxiom
% 242.18/242.15
% 242.18/242.15 %-------------------------------------------
% 242.18/242.15 cnf(4,plain,
% 242.18/242.15 (~P1(f1(a3,a3))),
% 242.18/242.15 inference(scs_inference,[],[2,1,3])).
% 242.18/242.15 cnf(9,plain,
% 242.18/242.15 (~P1(f1(f1(f1(x91,x92),f1(f1(x93,x92),f1(x91,x93))),f1(a3,a3)))),
% 242.18/242.15 inference(scs_inference,[],[1,4,3])).
% 242.18/242.15 cnf(19,plain,
% 242.18/242.15 (~P1(f1(f1(f1(x191,x192),f1(f1(x193,x192),f1(x191,x193))),f1(f1(f1(x194,x195),f1(f1(x196,x195),f1(x194,x196))),f1(a3,a3))))),
% 242.18/242.16 inference(scs_inference,[],[1,9,3])).
% 242.18/242.16 cnf(21,plain,
% 242.18/242.16 (~P1(f1(f1(f1(x211,x212),f1(f1(x213,x212),f1(x211,x213))),f1(f1(f1(x214,x215),f1(f1(x216,x215),f1(x214,x216))),f1(f1(f1(x217,x218),f1(f1(x219,x218),f1(x217,x219))),f1(a3,a3)))))),
% 242.18/242.16 inference(scs_inference,[],[1,19,3])).
% 242.18/242.16 cnf(65,plain,
% 242.18/242.16 (~P1(f1(f1(f1(x651,x652),f1(f1(x653,x652),f1(x651,x653))),f1(f1(x654,f1(a3,a3)),f1(f1(f1(x655,x656),f1(f1(x657,x656),f1(x655,x657))),x654))))),
% 242.18/242.16 inference(scs_inference,[],[21,1,3])).
% 242.18/242.16 cnf(99,plain,
% 242.18/242.16 (~P1(f1(f1(f1(x991,x992),f1(f1(x993,x992),f1(x991,x993))),f1(f1(f1(x994,x995),f1(f1(x996,x995),f1(x994,x996))),f1(f1(x997,f1(a3,a3)),f1(f1(f1(x998,x999),f1(f1(x9910,x999),f1(x998,x9910))),x997)))))),
% 242.18/242.16 inference(scs_inference,[],[65,1,3])).
% 242.18/242.16 cnf(137,plain,
% 242.18/242.16 (~P1(f1(f1(f1(x1371,x1372),f1(f1(x1373,x1372),f1(x1371,x1373))),f1(f1(x1374,f1(f1(f1(x1375,x1376),f1(f1(x1377,x1376),f1(x1375,x1377))),x1378)),f1(f1(x1378,f1(a3,a3)),x1374))))),
% 242.18/242.16 inference(scs_inference,[],[99,1,3])).
% 242.18/242.16 cnf(211,plain,
% 242.18/242.16 (~P1(f1(f1(x2111,f1(f1(f1(x2112,x2113),f1(f1(x2114,x2113),f1(x2112,x2114))),x2115)),f1(f1(x2116,x2111),f1(f1(x2115,f1(a3,a3)),x2116))))),
% 242.18/242.16 inference(scs_inference,[],[137,1,3])).
% 242.18/242.16 cnf(341,plain,
% 242.18/242.16 (~P1(f1(f1(x3411,f1(f1(x3412,f1(a3,a3)),x3411)),f1(f1(f1(x3413,x3414),f1(f1(x3415,x3414),f1(x3413,x3415))),x3412)))),
% 242.18/242.16 inference(scs_inference,[],[211,1,3])).
% 242.18/242.16 cnf(425,plain,
% 242.18/242.16 (~P1(f1(f1(f1(x4251,x4252),f1(f1(x4253,x4252),f1(x4251,x4253))),f1(f1(x4254,f1(a3,a3)),x4254)))),
% 242.18/242.16 inference(scs_inference,[],[341,1,3])).
% 242.18/242.16 cnf(431,plain,
% 242.18/242.16 (~P1(f1(f1(f1(x4311,x4312),f1(a3,a3)),f1(f1(x4313,x4312),f1(x4311,x4313))))),
% 242.18/242.16 inference(scs_inference,[],[425,1,3])).
% 242.18/242.16 cnf(471,plain,
% 242.18/242.16 (~P1(f1(f1(x4711,x4711),f1(a3,a3)))),
% 242.18/242.16 inference(scs_inference,[],[431,1,3])).
% 242.18/242.16 cnf(775,plain,
% 242.18/242.16 (~P1(f1(f1(f1(x7751,x7752),f1(f1(x7753,x7752),f1(x7751,x7753))),f1(f1(x7754,x7754),f1(a3,a3))))),
% 242.18/242.16 inference(scs_inference,[],[471,1,3])).
% 242.18/242.16 cnf(871,plain,
% 242.18/242.16 (~P1(f1(f1(x8711,x8711),f1(f1(x8712,a3),f1(a3,x8712))))),
% 242.18/242.16 inference(scs_inference,[],[775,1,3])).
% 242.18/242.16 cnf(875,plain,
% 242.18/242.16 ($false),
% 242.18/242.16 inference(scs_inference,[],[871,1]),
% 242.18/242.16 ['proof']).
% 242.18/242.16 % SZS output end Proof
% 242.18/242.16 % Total time :241.641112s
%------------------------------------------------------------------------------