%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL081-1 : 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 : 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 11:18:36 AM UTC 2026
% Result : Unsatisfiable 116.02s 116.15s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n003.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 12:58:51 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.23/0.52 start to proof:theBenchmark
% 116.02/116.14 %-------------------------------------------
% 116.02/116.14 % File :CSE---1.7
% 116.02/116.14 % Problem :theBenchmark
% 116.02/116.14 % Transform :cnf
% 116.02/116.14 % Format :tptp:raw
% 116.02/116.14 % Command :java -jar mcs_scs.jar %d %s
% 116.02/116.14
% 116.02/116.14 % Result :Theorem 115.602104s
% 116.02/116.14 % Output :CNFRefutation 115.602104s
% 116.02/116.14 %-------------------------------------------
% 116.02/116.15 %--------------------------------------------------------------------------
% 116.02/116.15 % File : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% 116.02/116.15 % Domain : Logic Calculi (Implicational propositional)
% 116.02/116.15 % Problem : IC-1 depends on the 1st Lukasiewicz axiom
% 116.02/116.15 % Version : [McC92] axioms.
% 116.02/116.15 % English : Axiomatisations of the Implicational propositional calculus
% 116.02/116.15 % are {IC-2,IC-3,IC-4} by Tarski-Bernays and single Lukasiewicz
% 116.02/116.15 % axioms.Show that IC-1 depends on the first Lukasiewicz axiom.
% 116.02/116.15
% 116.02/116.15 % Refs : [Luk48] Lukasiewicz (1948), The Shortest Axiom of the Implicat
% 116.02/116.15 % : [Pfe88] Pfenning (1988), Single Axioms in the Implicational Pr
% 116.02/116.15 % : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 116.02/116.15 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 116.02/116.15 % Source : [McC92]
% 116.02/116.15 % Names : I1 [Pfe88]
% 116.02/116.15 % : IC-64 [MW92]
% 116.02/116.15 % : ls1 [SETHEO]
% 116.02/116.15
% 116.02/116.15 % Status : Unsatisfiable
% 116.02/116.15 % 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, 0.00 v2.0.0
% 116.02/116.15 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 116.02/116.15 % Number of literals : 5 ( 0 equ; 3 neg)
% 116.02/116.15 % Maximal clause size : 3 ( 1 avg)
% 116.02/116.15 % Maximal term depth : 4 ( 2 avg)
% 116.02/116.15 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 116.02/116.15 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 116.02/116.15 % Number of variables : 6 ( 2 sgn)
% 116.02/116.15 % SPC : CNF_UNS_RFO_NEQ_HRN
% 116.02/116.15
% 116.02/116.15 % Comments :
% 116.02/116.15 %--------------------------------------------------------------------------
% 116.02/116.15 cnf(condensed_detachment,axiom,
% 116.02/116.15 ( ~ is_a_theorem(implies(X,Y))
% 116.02/116.15 | ~ is_a_theorem(X)
% 116.02/116.15 | is_a_theorem(Y) ) ).
% 116.02/116.15
% 116.02/116.15 cnf(ic_JLukasiewicz,axiom,
% 116.02/116.15 is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))) ).
% 116.02/116.15
% 116.02/116.15 cnf(prove_ic_1,negated_conjecture,
% 116.02/116.15 ~ is_a_theorem(implies(a,a)) ).
% 116.02/116.15
% 116.02/116.15 %--------------------------------------------------------------------------
% 116.02/116.15 %-------------------------------------------
% 116.02/116.15 % Proof found
% 116.02/116.15 % SZS status Theorem for theBenchmark
% 116.02/116.15 % SZS output start Proof
% 116.02/116.15 %ClaNum:3(EqnAxiom:0)
% 116.02/116.15 %VarNum:11(SingletonVarNum:6)
% 116.02/116.15 %MaxLitNum:3
% 116.02/116.15 %MaxfuncDepth:3
% 116.02/116.15 %SharedTerms:3
% 116.02/116.15 %goalClause: 2
% 116.02/116.15 %singleGoalClaCount:1
% 116.02/116.15 [2]~P1(f1(a2,a2))
% 116.02/116.15 [1]P1(f1(f1(f1(x11,x12),x13),f1(f1(x13,x11),f1(x14,x11))))
% 116.02/116.15 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 116.02/116.15 %EqnAxiom
% 116.02/116.15
% 116.02/116.15 %-------------------------------------------
% 116.02/116.15 cnf(4,plain,
% 116.02/116.15 (P1(f1(f1(x41,x42),f1(x43,x42)))+~P1(f1(f1(x42,x44),x41))),
% 116.02/116.15 inference(scs_inference,[],[1,3])).
% 116.02/116.15 cnf(6,plain,
% 116.02/116.15 (P1(f1(f1(f1(f1(x61,x62),f1(x63,x62)),f1(x62,x64)),f1(x65,f1(x62,x64))))),
% 116.02/116.15 inference(scs_inference,[],[1,4])).
% 116.02/116.15 cnf(8,plain,
% 116.02/116.15 (~P1(f1(f1(f1(f1(x81,x82),x83),f1(f1(x83,x81),f1(x84,x81))),f1(a2,a2)))),
% 116.02/116.15 inference(scs_inference,[],[2,1,4,3])).
% 116.02/116.15 cnf(13,plain,
% 116.02/116.15 (P1(f1(f1(f1(x131,f1(x132,x133)),f1(f1(x134,x132),f1(x135,x132))),f1(x136,f1(f1(x134,x132),f1(x135,x132)))))),
% 116.02/116.15 inference(scs_inference,[],[6,1,3])).
% 116.02/116.15 cnf(16,plain,
% 116.02/116.15 (P1(f1(x161,f1(f1(x162,x163),f1(x163,x163))))),
% 116.02/116.15 inference(scs_inference,[],[6,13,3])).
% 116.02/116.15 cnf(20,plain,
% 116.02/116.15 (P1(f1(f1(x201,x202),f1(x202,x202)))),
% 116.02/116.15 inference(scs_inference,[],[6,16,3])).
% 116.02/116.15 cnf(26,plain,
% 116.02/116.15 (P1(f1(f1(f1(x261,x261),x262),f1(x263,x262)))),
% 116.02/116.15 inference(scs_inference,[],[20,1,3])).
% 116.02/116.15 cnf(29,plain,
% 116.02/116.15 ($false),
% 116.02/116.15 inference(scs_inference,[],[8,26,20,3]),
% 116.02/116.15 ['proof']).
% 116.02/116.15 % SZS output end Proof
% 116.02/116.15 % Total time :115.602104s
%------------------------------------------------------------------------------