%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL041-1 : 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 : n026.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 11:18:33 AM UTC 2026
% Result : Unsatisfiable 240.79s 240.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL041-1 : 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
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 08:38:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.25/0.52 start to proof:theBenchmark
% 240.79/240.74 %-------------------------------------------
% 240.79/240.74 % File :CSE---1.7
% 240.79/240.74 % Problem :theBenchmark
% 240.79/240.74 % Transform :cnf
% 240.79/240.74 % Format :tptp:raw
% 240.79/240.74 % Command :java -jar mcs_scs.jar %d %s
% 240.79/240.74
% 240.79/240.74 % Result :Theorem 240.199141s
% 240.79/240.74 % Output :CNFRefutation 240.199141s
% 240.79/240.74 %-------------------------------------------
% 240.79/240.74 %--------------------------------------------------------------------------
% 240.79/240.74 % File : LCL041-1 : TPTP v9.3.1. Released v1.0.0.
% 240.79/240.74 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 240.79/240.74 % Problem : CN-30 depends on the rest of Hilbert's system
% 240.79/240.74 % Version : [McC92] axioms.
% 240.79/240.74 % English : An early axiomatisation of Implication/Negation 2 valued
% 240.79/240.74 % sentential calculus was {CN-3,CN-18,CN-21,CN-22,CN-30, CN-54}
% 240.79/240.74 % by Hilbert. Show, like Lukasiewicz did, that CN-30 depends
% 240.79/240.74 % on the rest of this axiomatisation.
% 240.79/240.74
% 240.79/240.74 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 240.79/240.74 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 240.79/240.74 % Source : [McC92]
% 240.79/240.74 % Names : CN-2 [MW92]
% 240.79/240.74
% 240.79/240.74 % Status : Unsatisfiable
% 240.79/240.74 % 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 v2.1.0, 0.00 v2.0.0
% 240.79/240.74 % Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 2 RR)
% 240.79/240.74 % Number of literals : 9 ( 0 equ; 3 neg)
% 240.79/240.74 % Maximal clause size : 3 ( 1 avg)
% 240.79/240.74 % Maximal term depth : 5 ( 2 avg)
% 240.79/240.74 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 240.79/240.74 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 240.79/240.74 % Number of variables : 14 ( 2 sgn)
% 240.79/240.74 % SPC : CNF_UNS_RFO_NEQ_HRN
% 240.79/240.74
% 240.79/240.74 % Comments :
% 240.79/240.74 %--------------------------------------------------------------------------
% 240.79/240.74 cnf(condensed_detachment,axiom,
% 240.79/240.74 ( ~ is_a_theorem(implies(X,Y))
% 240.79/240.74 | ~ is_a_theorem(X)
% 240.79/240.74 | is_a_theorem(Y) ) ).
% 240.79/240.74
% 240.79/240.74 cnf(cn_3,axiom,
% 240.79/240.74 is_a_theorem(implies(X,implies(not(X),Y))) ).
% 240.79/240.74
% 240.79/240.74 cnf(cn_18,axiom,
% 240.79/240.74 is_a_theorem(implies(X,implies(Y,X))) ).
% 240.79/240.74
% 240.79/240.74 cnf(cn_21,axiom,
% 240.79/240.74 is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))) ).
% 240.79/240.74
% 240.79/240.74 cnf(cn_22,axiom,
% 240.79/240.74 is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),implies(X,Z)))) ).
% 240.79/240.74
% 240.79/240.74 cnf(cn_54,axiom,
% 240.79/240.74 is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))) ).
% 240.79/240.74
% 240.79/240.74 cnf(prove_cn_30,negated_conjecture,
% 240.79/240.74 ~ is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))) ).
% 240.79/240.74
% 240.79/240.74 %--------------------------------------------------------------------------
% 240.79/240.74 %-------------------------------------------
% 240.79/240.74 % Proof found
% 240.79/240.74 % SZS status Theorem for theBenchmark
% 240.79/240.75 % SZS output start Proof
% 240.79/240.75 %ClaNum:7(EqnAxiom:0)
% 240.79/240.75 %VarNum:27(SingletonVarNum:14)
% 240.79/240.75 %MaxLitNum:3
% 240.79/240.75 %MaxfuncDepth:4
% 240.79/240.75 %SharedTerms:6
% 240.79/240.75 %goalClause: 6
% 240.79/240.75 %singleGoalClaCount:1
% 240.79/240.75 [6]~P1(f1(f1(a2,f1(a2,a3)),f1(a2,a3)))
% 240.79/240.75 [1]P1(f1(x11,f1(x12,x11)))
% 240.79/240.75 [2]P1(f1(x21,f1(f4(x21),x22)))
% 240.79/240.75 [3]P1(f1(f1(x31,x32),f1(f1(f4(x31),x32),x32)))
% 240.79/240.75 [4]P1(f1(f1(x41,x42),f1(f1(x43,x41),f1(x43,x42))))
% 240.79/240.75 [5]P1(f1(f1(x51,f1(x52,x53)),f1(x52,f1(x51,x53))))
% 240.79/240.75 [7]P1(x71)+~P1(x72)+~P1(f1(x72,x71))
% 240.79/240.75 %EqnAxiom
% 240.79/240.75
% 240.79/240.75 %-------------------------------------------
% 240.79/240.75 cnf(1419,plain,
% 240.79/240.75 (P1(f1(f4(x14191),f1(x14191,x14192)))),
% 240.79/240.75 inference(scs_inference,[],[2,5,7])).
% 240.79/240.75 cnf(1466,plain,
% 240.79/240.75 (P1(f1(f1(f4(x14661),x14662),f1(f1(x14661,x14662),x14662)))),
% 240.79/240.75 inference(scs_inference,[],[3,5,7])).
% 240.79/240.75 cnf(2958,plain,
% 240.79/240.75 ($false),
% 240.79/240.75 inference(scs_inference,[],[6,1419,1466,7]),
% 240.79/240.75 ['proof']).
% 240.79/240.75 % SZS output end Proof
% 240.79/240.75 % Total time :240.199141s
%------------------------------------------------------------------------------