%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 116.64s 116.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 13:57:06 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.26/0.51 start to proof:theBenchmark
% 116.64/116.73 %-------------------------------------------
% 116.64/116.73 % File :CSE---1.7
% 116.64/116.73 % Problem :theBenchmark
% 116.64/116.73 % Transform :cnf
% 116.64/116.73 % Format :tptp:raw
% 116.64/116.73 % Command :java -jar mcs_scs.jar %d %s
% 116.64/116.73
% 116.64/116.73 % Result :Theorem 116.223055s
% 116.64/116.73 % Output :CNFRefutation 116.223055s
% 116.64/116.73 %-------------------------------------------
% 116.64/116.73 %--------------------------------------------------------------------------
% 116.64/116.73 % File : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 116.64/116.73 % Domain : Logic Calculi (Implicational propositional)
% 116.64/116.73 % Problem : IC-3 depends on the 1st Lukasiewicz axiom
% 116.64/116.73 % Version : [ANL] axioms : Augmented.
% 116.64/116.73 % English : Axiomatisations of the Implicational propositional calculus
% 116.64/116.73 % are {IC-2,IC-3,IC-4} by Tarski-Bernays and single Lukasiewicz
% 116.64/116.73 % axioms. Show that IC-3 depends on the first Lukasiewicz
% 116.64/116.73 % axiom.
% 116.64/116.73
% 116.64/116.73 % Refs : [Luk48] Lukasiewicz (1948), The Shortest Axiom of the Implicat
% 116.64/116.73 % : [Pfe88] Pfenning (1988), Single Axioms in the Implicational Pr
% 116.64/116.73 % Source : [Pfe88]
% 116.64/116.73 % Names : IP1 [Pfe88]
% 116.64/116.73 % : ls4 [SETHEO]
% 116.64/116.73
% 116.64/116.73 % Status : Unsatisfiable
% 116.64/116.73 % Rating : 0.00 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.12 v5.4.0, 0.17 v5.3.0, 0.20 v5.2.0, 0.08 v5.1.0, 0.19 v5.0.0, 0.27 v4.1.0, 0.20 v4.0.1, 0.00 v2.7.0, 0.12 v2.6.0, 0.29 v2.5.0, 0.00 v2.4.0, 0.00 v2.3.0, 0.14 v2.2.1, 0.17 v2.1.0, 0.33 v2.0.0
% 116.64/116.73 % Syntax : Number of clauses : 4 ( 3 unt; 0 nHn; 2 RR)
% 116.64/116.73 % Number of literals : 6 ( 0 equ; 3 neg)
% 116.64/116.73 % Maximal clause size : 3 ( 1 avg)
% 116.64/116.73 % Maximal term depth : 4 ( 2 avg)
% 116.64/116.73 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 116.64/116.74 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 116.64/116.74 % Number of variables : 7 ( 2 sgn)
% 116.64/116.74 % SPC : CNF_UNS_RFO_NEQ_HRN
% 116.64/116.74
% 116.64/116.74 % Comments : Supplies IC-1 as an extra axiom
% 116.64/116.74 % Bugfixes : v1.2.0 - Clause ic_1 fixed.
% 116.64/116.74 %--------------------------------------------------------------------------
% 116.64/116.74 cnf(condensed_detachment,axiom,
% 116.64/116.74 ( ~ is_a_theorem(implies(X,Y))
% 116.64/116.74 | ~ is_a_theorem(X)
% 116.64/116.74 | is_a_theorem(Y) ) ).
% 116.64/116.74
% 116.64/116.74 cnf(ic_JLukasiewicz,axiom,
% 116.64/116.74 is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))) ).
% 116.64/116.74
% 116.64/116.74 cnf(ic_1,axiom,
% 116.64/116.74 is_a_theorem(implies(X,X)) ).
% 116.64/116.74
% 116.64/116.74 cnf(prove_ic_3,negated_conjecture,
% 116.64/116.74 ~ is_a_theorem(implies(implies(implies(a,b),a),a)) ).
% 116.64/116.74
% 116.64/116.74 %--------------------------------------------------------------------------
% 116.64/116.74 %-------------------------------------------
% 116.64/116.74 % Proof found
% 116.64/116.74 % SZS status Theorem for theBenchmark
% 116.64/116.74 % SZS output start Proof
% 116.64/116.74 %ClaNum:4(EqnAxiom:0)
% 116.64/116.74 %VarNum:13(SingletonVarNum:7)
% 116.64/116.74 %MaxLitNum:3
% 116.64/116.74 %MaxfuncDepth:3
% 116.64/116.74 %SharedTerms:6
% 116.64/116.74 %goalClause: 3
% 116.64/116.74 %singleGoalClaCount:1
% 116.64/116.74 [3]~P1(f1(f1(f1(a2,a3),a2),a2))
% 116.64/116.74 [1]P1(f1(x11,x11))
% 116.64/116.74 [2]P1(f1(f1(f1(x21,x22),x23),f1(f1(x23,x21),f1(x24,x21))))
% 116.64/116.74 [4]P1(x41)+~P1(x42)+~P1(f1(x42,x41))
% 116.64/116.74 %EqnAxiom
% 116.64/116.74
% 116.64/116.74 %-------------------------------------------
% 116.64/116.74 cnf(5,plain,
% 116.64/116.74 (P1(f1(f1(f1(x51,x52),x51),f1(x53,x51)))),
% 116.64/116.74 inference(scs_inference,[],[1,2,4])).
% 116.64/116.74 cnf(12,plain,
% 116.64/116.74 (P1(f1(f1(f1(x121,x122),f1(x122,x123)),f1(x124,f1(x122,x123))))),
% 116.64/116.74 inference(scs_inference,[],[5,2,4])).
% 116.64/116.74 cnf(43,plain,
% 116.64/116.74 (P1(f1(f1(f1(x431,f1(x432,x433)),f1(x434,x432)),f1(x435,f1(x434,x432))))),
% 116.64/116.74 inference(scs_inference,[],[12,2,4])).
% 116.64/116.74 cnf(46,plain,
% 116.64/116.74 (P1(f1(x461,f1(f1(f1(f1(x462,x463),x464),x463),f1(x462,x463))))),
% 116.64/116.74 inference(scs_inference,[],[2,43,4])).
% 116.64/116.74 cnf(50,plain,
% 116.64/116.74 (P1(f1(f1(f1(f1(f1(f1(x501,x502),x503),x502),f1(x501,x502)),x504),f1(x505,x504)))),
% 116.64/116.74 inference(scs_inference,[],[2,46,4])).
% 116.64/116.74 cnf(98,plain,
% 116.64/116.74 (~P1(f1(f1(x981,x981),f1(f1(f1(a2,a3),a2),a2)))),
% 116.64/116.74 inference(scs_inference,[],[1,3,4])).
% 116.64/116.74 cnf(481,plain,
% 116.64/116.74 (P1(f1(x4811,f1(f1(f1(x4812,x4813),f1(f1(x4812,x4813),x4814)),f1(x4815,f1(f1(x4812,x4813),x4814)))))),
% 116.64/116.74 inference(scs_inference,[],[2,50,4])).
% 116.64/116.74 cnf(511,plain,
% 116.64/116.74 (P1(f1(f1(f1(x5111,x5112),f1(f1(x5111,x5112),x5113)),f1(x5114,f1(f1(x5111,x5112),x5113))))),
% 116.64/116.74 inference(scs_inference,[],[2,481,4])).
% 116.64/116.74 cnf(524,plain,
% 116.64/116.74 ($false),
% 116.64/116.74 inference(scs_inference,[],[5,511,98,4]),
% 116.64/116.74 ['proof']).
% 116.64/116.74 % SZS output end Proof
% 116.64/116.74 % Total time :116.223055s
%------------------------------------------------------------------------------