%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 11:18:32 AM UTC 2026
% Result : Unsatisfiable 59.21s 59.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.01 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 5 18:41:57 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.09/0.38 start to proof:theBenchmark
% 59.12/59.39 %-------------------------------------------
% 59.12/59.39 % File :CSE---1.7
% 59.12/59.39 % Problem :theBenchmark
% 59.12/59.39 % Transform :cnf
% 59.12/59.40 % Format :tptp:raw
% 59.12/59.40 % Command :java -jar mcs_scs.jar %d %s
% 59.12/59.40
% 59.12/59.40 % Result :Theorem 59.023929s
% 59.12/59.40 % Output :CNFRefutation 59.023929s
% 59.12/59.40 %-------------------------------------------
% 59.21/59.40 %--------------------------------------------------------------------------
% 59.21/59.40 % File : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% 59.21/59.40 % Domain : Logic Calculi (Equivalential)
% 59.21/59.40 % Problem : EC-2 depends on YQL
% 59.21/59.40 % Version : [OTTER] axioms.
% 59.21/59.40 % English : An axiomatisation of the equivalential calculus is {EC-1,
% 59.21/59.40 % EC-2} by Lesniewski. Show that EC-2 can be derived from the
% 59.21/59.40 % single Lukasiewicz axiom YQL.
% 59.21/59.40
% 59.21/59.40 % Refs :
% 59.21/59.40 % Source : [OTTER]
% 59.21/59.40 % Names : ec.in part 2 [OTTER]
% 59.21/59.40
% 59.21/59.40 % Status : Unsatisfiable
% 59.21/59.40 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 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
% 59.21/59.40 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 59.21/59.40 % Number of literals : 5 ( 0 equ; 3 neg)
% 59.21/59.40 % Maximal clause size : 3 ( 1 avg)
% 59.21/59.40 % Maximal term depth : 4 ( 2 avg)
% 59.21/59.40 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 59.21/59.40 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 59.21/59.40 % Number of variables : 5 ( 0 sgn)
% 59.21/59.40 % SPC : CNF_UNS_RFO_NEQ_HRN
% 59.21/59.40
% 59.21/59.40 % Comments :
% 59.21/59.40 %--------------------------------------------------------------------------
% 59.21/59.40 cnf(condensed_detachment,axiom,
% 59.21/59.40 ( ~ is_a_theorem(equivalent(X,Y))
% 59.21/59.40 | ~ is_a_theorem(X)
% 59.21/59.40 | is_a_theorem(Y) ) ).
% 59.21/59.40
% 59.21/59.40 %----Axiom by Lukasiewicz
% 59.21/59.40 cnf(yql,axiom,
% 59.21/59.40 is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
% 59.21/59.40
% 59.21/59.40 %----Axiom of symmetry
% 59.21/59.40 cnf(prove_ec_2,negated_conjecture,
% 59.21/59.40 ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))) ).
% 59.21/59.40
% 59.21/59.40 %--------------------------------------------------------------------------
% 59.21/59.40 %-------------------------------------------
% 59.21/59.40 % Proof found
% 59.21/59.40 % SZS status Theorem for theBenchmark
% 59.21/59.40 % SZS output start Proof
% 59.21/59.40 %ClaNum:3(EqnAxiom:0)
% 59.21/59.40 %VarNum:10(SingletonVarNum:5)
% 59.21/59.40 %MaxLitNum:3
% 59.21/59.40 %MaxfuncDepth:3
% 59.21/59.40 %SharedTerms:9
% 59.21/59.40 %goalClause: 2
% 59.21/59.40 %singleGoalClaCount:1
% 59.21/59.40 [2]~P1(f1(f1(a2,f1(a3,a4)),f1(f1(a2,a3),a4)))
% 59.21/59.40 [1]P1(f1(f1(x11,x12),f1(f1(x13,x12),f1(x11,x13))))
% 59.21/59.40 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 59.21/59.40 %EqnAxiom
% 59.21/59.40
% 59.21/59.40 %-------------------------------------------
% 59.21/59.40 cnf(4,plain,
% 59.21/59.40 (P1(f1(f1(x41,x42),f1(x43,x41)))+~P1(f1(x43,x42))),
% 59.21/59.40 inference(scs_inference,[],[1,3])).
% 59.21/59.40 cnf(6,plain,
% 59.21/59.40 (P1(f1(f1(x61,f1(f1(x62,x63),f1(x64,x62))),f1(f1(x64,x63),x61)))),
% 59.21/59.40 inference(scs_inference,[],[1,4])).
% 59.21/59.40 cnf(8,plain,
% 59.21/59.40 (~P1(f1(f1(f1(a2,a3),a4),f1(f1(x81,f1(a3,a4)),f1(a2,x81))))),
% 59.21/59.40 inference(scs_inference,[],[1,2,4,3])).
% 59.21/59.40 cnf(10,plain,
% 59.21/59.40 (~P1(f1(f1(a3,f1(a3,a4)),a4))),
% 59.21/59.40 inference(scs_inference,[],[1,8,3])).
% 59.21/59.40 cnf(14,plain,
% 59.21/59.40 (~P1(f1(a4,f1(f1(x141,f1(a3,a4)),f1(a3,x141))))),
% 59.21/59.40 inference(scs_inference,[],[10,6,3])).
% 59.21/59.40 cnf(17,plain,
% 59.21/59.40 (P1(f1(f1(x171,x172),f1(x171,x172)))),
% 59.21/59.40 inference(scs_inference,[],[1,6,3])).
% 59.21/59.40 cnf(21,plain,
% 59.21/59.40 (P1(f1(f1(x211,f1(x212,x213)),f1(f1(x212,x213),x211)))),
% 59.21/59.40 inference(scs_inference,[],[17,4])).
% 59.21/59.40 cnf(25,plain,
% 59.21/59.40 (P1(f1(f1(f1(x251,x252),x253),f1(x253,f1(f1(x254,x252),f1(x251,x254)))))),
% 59.21/59.40 inference(scs_inference,[],[21,6,3])).
% 59.21/59.40 cnf(34,plain,
% 59.21/59.40 (P1(f1(f1(f1(x341,x342),x343),f1(f1(x344,f1(x341,x342)),f1(x343,x344))))),
% 59.21/59.40 inference(scs_inference,[],[21,25,3])).
% 59.21/59.40 cnf(37,plain,
% 59.21/59.40 (P1(f1(f1(x371,f1(x372,x373)),f1(f1(f1(x374,x373),f1(x372,x374)),x371)))),
% 59.21/59.40 inference(scs_inference,[],[34,1,3])).
% 59.21/59.40 cnf(55,plain,
% 59.21/59.40 (P1(f1(f1(f1(x551,f1(x552,x553)),f1(x554,x551)),f1(f1(x552,x553),x554)))),
% 59.21/59.40 inference(scs_inference,[],[34,21,3])).
% 59.21/59.40 cnf(64,plain,
% 59.21/59.40 (P1(f1(f1(f1(f1(x641,x642),f1(x643,x641)),x644),f1(x644,f1(x643,x642))))),
% 59.21/59.40 inference(scs_inference,[],[21,37,3])).
% 59.21/59.40 cnf(71,plain,
% 59.21/59.40 (P1(f1(f1(f1(x711,x712),f1(f1(x713,x714),x711)),f1(f1(x715,f1(x713,x714)),f1(x712,x715))))),
% 59.21/59.40 inference(scs_inference,[],[37,55,3])).
% 59.21/59.40 cnf(79,plain,
% 59.21/59.40 (P1(f1(f1(f1(x791,x792),x793),f1(x793,f1(x791,x792))))),
% 59.21/59.40 inference(scs_inference,[],[55,64,3])).
% 59.21/59.40 cnf(86,plain,
% 59.21/59.40 (P1(f1(f1(f1(x861,x862),f1(x863,x861)),f1(x863,x862)))),
% 59.21/59.40 inference(scs_inference,[],[79,1,3])).
% 59.21/59.40 cnf(93,plain,
% 59.21/59.40 (P1(f1(f1(x931,f1(x932,f1(x933,x932))),f1(x933,x931)))),
% 59.21/59.40 inference(scs_inference,[],[71,34,3])).
% 59.21/59.40 cnf(97,plain,
% 59.21/59.40 (~P1(f1(f1(x971,f1(f1(x972,f1(a3,a4)),f1(a3,x972))),f1(a4,x971)))),
% 59.21/59.40 inference(scs_inference,[],[86,14,3])).
% 59.21/59.40 cnf(100,plain,
% 59.21/59.40 ($false),
% 59.21/59.40 inference(scs_inference,[],[93,97,55,3]),
% 59.21/59.40 ['proof']).
% 59.21/59.40 % SZS output end Proof
% 59.21/59.40 % Total time :59.023929s
%------------------------------------------------------------------------------