%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL082-1 : 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 : n005.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 117.54s 117.68s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL082-1 : 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 : n005.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 16:31:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.25/0.52 start to proof:theBenchmark
% 117.54/117.68 %-------------------------------------------
% 117.54/117.68 % File :CSE---1.7
% 117.54/117.68 % Problem :theBenchmark
% 117.54/117.68 % Transform :cnf
% 117.54/117.68 % Format :tptp:raw
% 117.54/117.68 % Command :java -jar mcs_scs.jar %d %s
% 117.54/117.68
% 117.54/117.68 % Result :Theorem 117.170429s
% 117.54/117.68 % Output :CNFRefutation 117.170429s
% 117.54/117.68 %-------------------------------------------
% 117.54/117.68 %--------------------------------------------------------------------------
% 117.54/117.68 % File : LCL082-1 : TPTP v9.3.1. Released v1.0.0.
% 117.54/117.68 % Domain : Logic Calculi (Implicational propositional)
% 117.54/117.68 % Problem : IC-2 depends on the 1st Lukasiewicz axiom
% 117.54/117.68 % Version : [McC92] axioms.
% 117.54/117.68 % English : Axiomatisations of the Implicational propositional calculus
% 117.54/117.68 % are {IC-2,IC-3,IC-4} by Tarski-Bernays and single Lukasiewicz
% 117.54/117.68 % axioms.Show that IC-2 depends on the first Lukasiewicz axiom.
% 117.54/117.68
% 117.54/117.68 % Refs : [Luk48] Lukasiewicz (1948), The Shortest Axiom of the Implicat
% 117.54/117.68 % : [Pfe88] Pfenning (1988), Single Axioms in the Implicational Pr
% 117.54/117.68 % : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to
% 117.54/117.68 % : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 117.54/117.68 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 117.54/117.68 % Source : [McC92]
% 117.54/117.68 % Names : S1 [Pfe88]
% 117.54/117.68 % : IC-1.1 [WW+90]
% 117.54/117.68 % : IC-65 [MW92]
% 117.54/117.68 % : ls2 [SETHEO]
% 117.54/117.68
% 117.54/117.68 % Status : Unsatisfiable
% 117.54/117.68 % 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 v2.6.0, 0.14 v2.5.0, 0.00 v2.1.0, 0.00 v2.0.0
% 117.54/117.68 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 117.54/117.68 % Number of literals : 5 ( 0 equ; 3 neg)
% 117.54/117.68 % Maximal clause size : 3 ( 1 avg)
% 117.54/117.68 % Maximal term depth : 4 ( 2 avg)
% 117.54/117.68 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 117.54/117.68 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 117.54/117.68 % Number of variables : 6 ( 2 sgn)
% 117.54/117.68 % SPC : CNF_UNS_RFO_NEQ_HRN
% 117.54/117.68
% 117.54/117.68 % Comments :
% 117.54/117.68 %--------------------------------------------------------------------------
% 117.54/117.68 cnf(condensed_detachment,axiom,
% 117.54/117.68 ( ~ is_a_theorem(implies(X,Y))
% 117.54/117.68 | ~ is_a_theorem(X)
% 117.54/117.68 | is_a_theorem(Y) ) ).
% 117.54/117.68
% 117.54/117.68 cnf(ic_JLukasiewicz,axiom,
% 117.54/117.68 is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))) ).
% 117.54/117.68
% 117.54/117.68 cnf(prove_ic_2,negated_conjecture,
% 117.54/117.68 ~ is_a_theorem(implies(a,implies(b,a))) ).
% 117.54/117.68
% 117.54/117.68 %--------------------------------------------------------------------------
% 117.54/117.68 %-------------------------------------------
% 117.54/117.68 % Proof found
% 117.54/117.68 % SZS status Theorem for theBenchmark
% 117.54/117.68 % SZS output start Proof
% 117.54/117.68 %ClaNum:3(EqnAxiom:0)
% 117.54/117.68 %VarNum:11(SingletonVarNum:6)
% 117.54/117.68 %MaxLitNum:3
% 117.54/117.68 %MaxfuncDepth:3
% 117.54/117.68 %SharedTerms:5
% 117.54/117.68 %goalClause: 2
% 117.54/117.68 %singleGoalClaCount:1
% 117.54/117.68 [2]~P1(f1(a2,f1(a3,a2)))
% 117.54/117.68 [1]P1(f1(f1(f1(x11,x12),x13),f1(f1(x13,x11),f1(x14,x11))))
% 117.54/117.68 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 117.54/117.68 %EqnAxiom
% 117.54/117.68
% 117.54/117.68 %-------------------------------------------
% 117.54/117.69 cnf(4,plain,
% 117.54/117.69 (P1(f1(f1(x41,x42),f1(x43,x42)))+~P1(f1(f1(x42,x44),x41))),
% 117.54/117.69 inference(scs_inference,[],[1,3])).
% 117.54/117.69 cnf(6,plain,
% 117.54/117.69 (P1(f1(f1(f1(f1(x61,x62),f1(x63,x62)),f1(x62,x64)),f1(x65,f1(x62,x64))))),
% 117.54/117.69 inference(scs_inference,[],[1,4])).
% 117.54/117.69 cnf(11,plain,
% 117.54/117.69 (P1(f1(f1(f1(x111,f1(x112,x113)),f1(f1(x114,x112),f1(x115,x112))),f1(x116,f1(f1(x114,x112),f1(x115,x112)))))),
% 117.54/117.69 inference(scs_inference,[],[6,1,3])).
% 117.54/117.69 cnf(14,plain,
% 117.54/117.69 (P1(f1(x141,f1(f1(x142,x143),f1(x143,x143))))),
% 117.54/117.69 inference(scs_inference,[],[11,6,3])).
% 117.54/117.69 cnf(18,plain,
% 117.54/117.69 (P1(f1(f1(x181,x182),f1(x182,x182)))),
% 117.54/117.69 inference(scs_inference,[],[14,11,3])).
% 117.54/117.69 cnf(21,plain,
% 117.54/117.69 (P1(f1(f1(f1(x211,x211),x212),f1(x213,x212)))),
% 117.54/117.69 inference(scs_inference,[],[18,1,3])).
% 117.54/117.69 cnf(62,plain,
% 117.54/117.69 (~P1(f1(f1(f1(f1(x621,x622),x623),f1(f1(x623,x621),f1(x624,x621))),f1(a2,f1(a3,a2))))),
% 117.54/117.69 inference(scs_inference,[],[1,2,14,4,3])).
% 117.54/117.69 cnf(283,plain,
% 117.54/117.69 ($false),
% 117.54/117.69 inference(scs_inference,[],[21,6,62,3]),
% 117.54/117.69 ['proof']).
% 117.54/117.69 % SZS output end Proof
% 117.54/117.69 % Total time :117.170429s
%------------------------------------------------------------------------------