%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL009-1 : 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 : n017.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 58.81s 58.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.34 % Computer : n017.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 : Sat Sep 5 02:55:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.26/0.51 start to proof:theBenchmark
% 58.81/58.97 %-------------------------------------------
% 58.81/58.97 % File :CSE---1.7
% 58.81/58.97 % Problem :theBenchmark
% 58.81/58.97 % Transform :cnf
% 58.81/58.97 % Format :tptp:raw
% 58.81/58.97 % Command :java -jar mcs_scs.jar %d %s
% 58.81/58.97
% 58.81/58.97 % Result :Theorem 58.472392s
% 58.81/58.97 % Output :CNFRefutation 58.472392s
% 58.81/58.97 %-------------------------------------------
% 58.81/58.97 %--------------------------------------------------------------------------
% 58.81/58.97 % File : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% 58.81/58.97 % Domain : Logic Calculi (Equivalential)
% 58.81/58.97 % Problem : EC-5 depends on YQL
% 58.81/58.97 % Version : [McC92] axioms.
% 58.81/58.97 % English : An axiomatisation of the equivalential calculus is {EC-4,
% 58.81/58.97 % EC-5} by Wajsburg. Show that EC-5 can be derived from the
% 58.81/58.97 % single Lukasiewicz axiom YQL.
% 58.81/58.97
% 58.81/58.97 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 58.81/58.97 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 58.81/58.97 % Source : [McC92]
% 58.81/58.97 % Names : EC-72 [MW92]
% 58.81/58.97
% 58.81/58.97 % Status : Unsatisfiable
% 58.81/58.97 % Rating : 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 v2.2.1, 0.11 v2.1.0, 0.13 v2.0.0
% 58.81/58.97 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 58.81/58.97 % Number of literals : 5 ( 0 equ; 3 neg)
% 58.81/58.97 % Maximal clause size : 3 ( 1 avg)
% 58.81/58.97 % Maximal term depth : 4 ( 2 avg)
% 58.81/58.97 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 58.81/58.97 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 58.81/58.97 % Number of variables : 5 ( 0 sgn)
% 58.81/58.97 % SPC : CNF_UNS_RFO_NEQ_HRN
% 58.81/58.97
% 58.81/58.97 % Comments :
% 58.81/58.97 %--------------------------------------------------------------------------
% 58.81/58.97 cnf(condensed_detachment,axiom,
% 58.81/58.97 ( ~ is_a_theorem(equivalent(X,Y))
% 58.81/58.98 | ~ is_a_theorem(X)
% 58.81/58.98 | is_a_theorem(Y) ) ).
% 58.81/58.98
% 58.81/58.98 %----Axiom by Lukasiewicz
% 58.81/58.98 cnf(yql,axiom,
% 58.81/58.98 is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
% 58.81/58.98
% 58.81/58.98 %----Axiom of associativity
% 58.81/58.98 cnf(prove_ec_5,negated_conjecture,
% 58.81/58.98 ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))) ).
% 58.81/58.98
% 58.81/58.98 %--------------------------------------------------------------------------
% 58.81/58.98 %-------------------------------------------
% 58.81/58.98 % Proof found
% 58.81/58.98 % SZS status Theorem for theBenchmark
% 58.81/58.98 % SZS output start Proof
% 58.81/58.98 %ClaNum:3(EqnAxiom:0)
% 58.81/58.98 %VarNum:10(SingletonVarNum:5)
% 58.81/58.98 %MaxLitNum:3
% 58.81/58.98 %MaxfuncDepth:3
% 58.81/58.98 %SharedTerms:9
% 58.81/58.98 %goalClause: 2
% 58.81/58.98 %singleGoalClaCount:1
% 58.81/58.98 [2]~P1(f1(f1(f1(a2,a3),a4),f1(a2,f1(a3,a4))))
% 58.81/58.98 [1]P1(f1(f1(x11,x12),f1(f1(x13,x12),f1(x11,x13))))
% 58.81/58.98 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 58.81/58.98 %EqnAxiom
% 58.81/58.98
% 58.81/58.98 %-------------------------------------------
% 58.81/58.98 cnf(4,plain,
% 58.81/58.98 (P1(f1(f1(x41,x42),f1(x43,x41)))+~P1(f1(x43,x42))),
% 58.81/58.98 inference(scs_inference,[],[1,3])).
% 58.81/58.98 cnf(6,plain,
% 58.81/58.98 (P1(f1(f1(x61,f1(f1(x62,x63),f1(x64,x62))),f1(f1(x64,x63),x61)))),
% 58.81/58.98 inference(scs_inference,[],[1,4])).
% 58.81/58.98 cnf(20,plain,
% 58.81/58.98 (P1(f1(f1(x201,x202),f1(x201,x202)))),
% 58.81/58.98 inference(scs_inference,[],[6,1,3])).
% 58.81/58.98 cnf(24,plain,
% 58.81/58.98 (P1(f1(f1(x241,f1(x242,x243)),f1(f1(x242,x243),x241)))),
% 58.81/58.98 inference(scs_inference,[],[6,1,3,4])).
% 58.81/58.98 cnf(32,plain,
% 58.81/58.98 (~P1(f1(f1(a2,f1(a3,a4)),f1(f1(a2,a3),a4)))),
% 58.81/58.98 inference(scs_inference,[],[2,24,3])).
% 58.81/58.98 cnf(38,plain,
% 58.81/58.98 (~P1(f1(f1(f1(a2,a3),a4),f1(f1(x381,f1(a3,a4)),f1(a2,x381))))),
% 58.81/58.98 inference(scs_inference,[],[32,6,3])).
% 58.81/58.98 cnf(41,plain,
% 58.81/58.98 (~P1(f1(f1(a3,f1(a3,a4)),a4))),
% 58.81/58.98 inference(scs_inference,[],[38,4])).
% 58.81/58.98 cnf(49,plain,
% 58.81/58.98 (P1(f1(f1(f1(x491,x492),x493),f1(x493,f1(f1(x494,x492),f1(x491,x494)))))),
% 58.81/58.98 inference(scs_inference,[],[6,24,3])).
% 58.81/58.98 cnf(52,plain,
% 58.81/58.98 (P1(f1(f1(f1(x521,x522),x523),f1(f1(x524,f1(x521,x522)),f1(x523,x524))))),
% 58.81/58.98 inference(scs_inference,[],[49,24,3])).
% 58.81/58.98 cnf(59,plain,
% 58.81/58.98 (P1(f1(f1(f1(x591,f1(x592,x593)),f1(x594,x591)),f1(f1(x592,x593),x594)))),
% 58.81/58.98 inference(scs_inference,[],[24,52,3])).
% 58.81/58.98 cnf(62,plain,
% 58.81/58.98 (P1(f1(f1(x621,x622),f1(x623,f1(f1(x621,x622),x623))))),
% 58.81/58.98 inference(scs_inference,[],[59,52,3])).
% 58.81/58.98 cnf(70,plain,
% 58.81/58.98 (P1(f1(x701,f1(f1(f1(x702,x703),f1(x702,x703)),x701)))),
% 58.81/58.98 inference(scs_inference,[],[62,20,3])).
% 58.81/58.98 cnf(73,plain,
% 58.81/58.98 (P1(f1(f1(x731,f1(f1(f1(x732,x733),f1(x732,x733)),x734)),f1(x734,x731)))),
% 58.81/58.98 inference(scs_inference,[],[62,20,3,4])).
% 58.81/58.98 cnf(78,plain,
% 58.81/58.98 (P1(f1(x781,x781))),
% 58.81/58.98 inference(scs_inference,[],[70,73,3])).
% 58.81/58.98 cnf(82,plain,
% 58.81/58.98 (P1(f1(f1(x821,x822),f1(x822,x821)))),
% 58.81/58.98 inference(scs_inference,[],[70,73,3,4])).
% 58.81/58.98 cnf(84,plain,
% 58.81/58.98 (~P1(f1(f1(x841,f1(a3,f1(a3,a4))),f1(a4,x841)))),
% 58.81/58.98 inference(scs_inference,[],[59,41,3])).
% 58.81/58.98 cnf(89,plain,
% 58.81/58.98 (P1(f1(f1(x891,f1(x892,x893)),f1(f1(x893,x892),x891)))),
% 58.81/58.98 inference(scs_inference,[],[82,4])).
% 58.81/58.98 cnf(91,plain,
% 58.81/58.98 (P1(f1(x911,f1(f1(x912,f1(f1(x913,x914),f1(x913,x914))),f1(x911,x912))))),
% 58.81/58.98 inference(scs_inference,[],[59,82,73,4,3])).
% 58.81/58.98 cnf(102,plain,
% 58.81/58.98 (P1(f1(f1(x1021,x1022),f1(f1(x1023,f1(x1024,x1022)),f1(f1(x1021,x1024),x1023))))),
% 58.81/58.98 inference(scs_inference,[],[59,6,3])).
% 58.81/58.98 cnf(106,plain,
% 58.81/58.98 (~P1(f1(f1(x1061,x1061),f1(f1(x1062,f1(a3,f1(a3,a4))),f1(a4,x1062))))),
% 58.81/58.98 inference(scs_inference,[],[84,78,3])).
% 58.81/58.98 cnf(111,plain,
% 58.81/58.98 (P1(f1(f1(f1(x1111,x1112),f1(x1112,x1113)),f1(x1111,x1113)))),
% 58.81/58.98 inference(scs_inference,[],[73,102,3])).
% 58.81/58.98 cnf(118,plain,
% 58.81/58.98 (P1(f1(f1(x1181,f1(x1182,x1183)),f1(f1(f1(x1182,x1184),f1(x1184,x1183)),x1181)))),
% 58.81/58.98 inference(scs_inference,[],[111,106,82,3,4])).
% 58.81/58.98 cnf(122,plain,
% 58.81/58.98 (P1(f1(f1(x1221,f1(f1(x1222,x1223),f1(x1222,x1223))),f1(f1(x1224,x1224),x1221)))),
% 58.81/58.98 inference(scs_inference,[],[78,91,3])).
% 58.81/58.98 cnf(125,plain,
% 58.81/58.98 (~P1(f1(f1(f1(x1251,x1252),f1(x1252,x1251)),f1(f1(x1253,f1(a3,f1(a3,a4))),f1(a4,x1253))))),
% 58.81/58.98 inference(scs_inference,[],[84,82,3])).
% 58.81/58.98 cnf(127,plain,
% 58.81/58.98 (~P1(f1(f1(x1271,f1(a3,f1(a3,a4))),f1(x1271,a4)))),
% 58.81/58.98 inference(scs_inference,[],[125,4])).
% 58.81/58.98 cnf(134,plain,
% 58.81/58.98 (P1(f1(f1(f1(x1341,x1342),f1(x1342,x1343)),f1(f1(x1341,x1344),f1(x1344,x1343))))),
% 58.81/58.98 inference(scs_inference,[],[118,111,3])).
% 58.81/58.98 cnf(139,plain,
% 58.81/58.98 (~P1(f1(f1(f1(a3,f1(a3,a4)),x1391),f1(x1391,a4)))),
% 58.81/58.98 inference(scs_inference,[],[127,134,3])).
% 58.81/58.98 cnf(146,plain,
% 58.81/58.98 (P1(f1(f1(f1(x1461,x1462),f1(x1463,x1461)),f1(f1(x1463,x1464),f1(x1464,x1462))))),
% 58.81/58.98 inference(scs_inference,[],[89,134,3])).
% 58.81/58.98 cnf(149,plain,
% 58.81/58.98 (P1(f1(f1(x1491,x1491),f1(f1(x1492,x1493),f1(x1493,x1492))))),
% 58.81/58.98 inference(scs_inference,[],[146,122,3])).
% 58.81/58.98 cnf(155,plain,
% 58.81/58.98 (~P1(f1(f1(x1551,a4),f1(f1(a3,f1(a3,a4)),x1551)))),
% 58.81/58.98 inference(scs_inference,[],[149,139,146,4,3])).
% 58.81/58.98 cnf(158,plain,
% 58.81/58.98 ($false),
% 58.81/58.98 inference(scs_inference,[],[89,155,49,3]),
% 58.81/58.98 ['proof']).
% 58.81/58.98 % SZS output end Proof
% 58.81/58.98 % Total time :58.472392s
%------------------------------------------------------------------------------