%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL022-1 : 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 : n003.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 115.92s 116.11s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL022-1 : 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
% 0.06/0.33 % Computer : n003.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Fri Sep 4 23:32:05 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.24/0.50 start to proof:theBenchmark
% 115.92/116.10 %-------------------------------------------
% 115.92/116.10 % File :CSE---1.7
% 115.92/116.10 % Problem :theBenchmark
% 115.92/116.10 % Transform :cnf
% 115.92/116.10 % Format :tptp:raw
% 115.92/116.10 % Command :java -jar mcs_scs.jar %d %s
% 115.92/116.10
% 115.92/116.10 % Result :Theorem 115.610910s
% 115.92/116.10 % Output :CNFRefutation 115.610910s
% 115.92/116.10 %-------------------------------------------
% 115.92/116.10 %--------------------------------------------------------------------------
% 115.92/116.10 % File : LCL022-1 : TPTP v9.3.1. Released v1.0.0.
% 115.92/116.10 % Domain : Logic Calculi (Equivalential)
% 115.92/116.10 % Problem : EC-1 depends on YQL
% 115.92/116.10 % Version : [OTTER] axioms.
% 115.92/116.10 % English : An axiomatisation of the equivalential calculus is {EC-1,
% 115.92/116.10 % EC-2} by Lesniewski. Show that EC-1 can be derived from the
% 115.92/116.10 % single Lukasiewicz axiom YQL.
% 115.92/116.10
% 115.92/116.10 % Refs :
% 115.92/116.10 % Source : [OTTER]
% 115.92/116.10 % Names : ec.in part 1 [OTTER]
% 115.92/116.10
% 115.92/116.10 % Status : Unsatisfiable
% 115.92/116.11 % 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
% 115.92/116.11 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 115.92/116.11 % Number of literals : 5 ( 0 equ; 3 neg)
% 115.92/116.11 % Maximal clause size : 3 ( 1 avg)
% 115.92/116.11 % Maximal term depth : 4 ( 2 avg)
% 115.92/116.11 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 115.92/116.11 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 115.92/116.11 % Number of variables : 5 ( 0 sgn)
% 115.92/116.11 % SPC : CNF_UNS_RFO_NEQ_HRN
% 115.92/116.11
% 115.92/116.11 % Comments :
% 115.92/116.11 %--------------------------------------------------------------------------
% 115.92/116.11 cnf(condensed_detachment,axiom,
% 115.92/116.11 ( ~ is_a_theorem(equivalent(X,Y))
% 115.92/116.11 | ~ is_a_theorem(X)
% 115.92/116.11 | is_a_theorem(Y) ) ).
% 115.92/116.11
% 115.92/116.11 %----Axiom by Lukasiewicz
% 115.92/116.11 cnf(yql,axiom,
% 115.92/116.11 is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
% 115.92/116.11
% 115.92/116.11 %----Axiom of symmetry
% 115.92/116.11 cnf(prove_ec_1,negated_conjecture,
% 115.92/116.11 ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))) ).
% 115.92/116.11
% 115.92/116.11 %--------------------------------------------------------------------------
% 115.92/116.11 %-------------------------------------------
% 115.92/116.11 % Proof found
% 115.92/116.11 % SZS status Theorem for theBenchmark
% 115.92/116.11 % SZS output start Proof
% 115.92/116.11 %ClaNum:3(EqnAxiom:0)
% 115.92/116.11 %VarNum:10(SingletonVarNum:5)
% 115.92/116.11 %MaxLitNum:3
% 115.92/116.11 %MaxfuncDepth:3
% 115.92/116.11 %SharedTerms:9
% 115.92/116.11 %goalClause: 2
% 115.92/116.11 %singleGoalClaCount:1
% 115.92/116.11 [2]~P1(f1(f1(f1(a2,a3),f1(a4,a2)),f1(a3,a4)))
% 115.92/116.11 [1]P1(f1(f1(x11,x12),f1(f1(x13,x12),f1(x11,x13))))
% 115.92/116.11 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 115.92/116.11 %EqnAxiom
% 115.92/116.11
% 115.92/116.11 %-------------------------------------------
% 115.92/116.11 cnf(4,plain,
% 115.92/116.11 (P1(f1(f1(x41,x42),f1(x43,x41)))+~P1(f1(x43,x42))),
% 115.92/116.11 inference(scs_inference,[],[1,3])).
% 115.92/116.11 cnf(6,plain,
% 115.92/116.11 (P1(f1(f1(x61,f1(f1(x62,x63),f1(x64,x62))),f1(f1(x64,x63),x61)))),
% 115.92/116.11 inference(scs_inference,[],[1,4])).
% 115.92/116.11 cnf(8,plain,
% 115.92/116.11 (~P1(f1(f1(a3,a4),f1(f1(x81,f1(a4,a2)),f1(f1(a2,a3),x81))))),
% 115.92/116.11 inference(scs_inference,[],[1,2,4,3])).
% 115.92/116.11 cnf(14,plain,
% 115.92/116.11 (~P1(f1(x141,x142))+P1(x142)+~P1(x141)),
% 115.92/116.11 inference(rename_variables,[],[3])).
% 115.92/116.11 cnf(15,plain,
% 115.92/116.11 (~P1(f1(f1(f1(a4,a2),a4),f1(f1(a2,a3),a3)))),
% 115.92/116.11 inference(scs_inference,[],[1,6,8,4,3,14])).
% 115.92/116.11 cnf(22,plain,
% 115.92/116.11 (~P1(f1(f1(f1(a2,a3),a3),f1(f1(x221,a4),f1(f1(a4,a2),x221))))),
% 115.92/116.11 inference(scs_inference,[],[15,6,3])).
% 115.92/116.11 cnf(25,plain,
% 115.92/116.11 (~P1(f1(f1(f1(x251,a4),f1(f1(a4,a2),x251)),f1(f1(x252,a3),f1(f1(a2,a3),x252))))),
% 115.92/116.11 inference(scs_inference,[],[22,6,3])).
% 115.92/116.11 cnf(28,plain,
% 115.92/116.11 (~P1(f1(f1(a4,a3),f1(f1(a4,a2),f1(a2,a3))))),
% 115.92/116.11 inference(scs_inference,[],[1,25,3])).
% 115.92/116.11 cnf(32,plain,
% 115.92/116.11 (~P1(f1(f1(f1(a4,a2),f1(a2,a3)),f1(f1(x321,a3),f1(a4,x321))))),
% 115.92/116.11 inference(scs_inference,[],[28,6,3])).
% 115.92/116.11 cnf(35,plain,
% 115.92/116.11 (~P1(f1(f1(a2,a3),f1(a2,a3)))),
% 115.92/116.11 inference(scs_inference,[],[1,32,3])).
% 115.92/116.11 cnf(39,plain,
% 115.92/116.11 ($false),
% 115.92/116.11 inference(scs_inference,[],[1,35,6,3]),
% 115.92/116.11 ['proof']).
% 115.92/116.11 % SZS output end Proof
% 115.92/116.11 % Total time :115.610910s
%------------------------------------------------------------------------------