%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL358-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 11:19:01 AM UTC 2026
% Result : Unsatisfiable 0.32s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL358-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.08/0.33 % Computer : n001.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sat Sep 5 02:59:00 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.32/0.48 start to proof:theBenchmark
% 0.32/0.54 %-------------------------------------------
% 0.32/0.54 % File :CSE---1.7
% 0.32/0.54 % Problem :theBenchmark
% 0.32/0.54 % Transform :cnf
% 0.32/0.54 % Format :tptp:raw
% 0.32/0.54 % Command :java -jar mcs_scs.jar %d %s
% 0.32/0.54
% 0.32/0.54 % Result :Theorem 0.075964s
% 0.32/0.54 % Output :CNFRefutation 0.075964s
% 0.32/0.54 %-------------------------------------------
% 0.32/0.54 %--------------------------------------------------------------------------
% 0.32/0.54 % File : LCL358-1 : TPTP v9.3.1. Released v2.3.0.
% 0.32/0.54 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 0.32/0.54 % Problem : CN-07 depends on the Lukasiewicz system
% 0.32/0.54 % Version : [McC92] axioms.
% 0.32/0.54 % English : An axiomatisation of the Implication/Negation 2 valued
% 0.32/0.54 % sentential calculus is {CN-1,CN-2,CN-3} by Lukasiewicz.
% 0.32/0.54 % Show that CN-07 depends on the Lukasiewicz system.
% 0.32/0.54
% 0.32/0.54 % Refs : [Wos96] Wos (1996), Combining Resonance with Heat
% 0.32/0.54 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 0.32/0.54 % Source : [Wos96]
% 0.32/0.54 % Names : thesis_07 [Wos96]
% 0.32/0.54
% 0.32/0.54 % Status : Unsatisfiable
% 0.32/0.54 % Rating : 0.00 v9.3.0, 0.06 v9.1.0, 0.07 v9.0.0, 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v5.5.0, 0.06 v5.4.0, 0.17 v5.3.0, 0.25 v5.2.0, 0.23 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, 0.00 v2.5.0, 0.14 v2.4.0, 0.00 v2.3.0
% 0.32/0.54 % Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 2 RR)
% 0.32/0.55 % Number of literals : 7 ( 0 equ; 3 neg)
% 0.32/0.55 % Maximal clause size : 3 ( 1 avg)
% 0.32/0.55 % Maximal term depth : 6 ( 2 avg)
% 0.32/0.55 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 0.32/0.55 % Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% 0.32/0.55 % Number of variables : 8 ( 1 sgn)
% 0.32/0.55 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.32/0.55
% 0.32/0.55 % Comments :
% 0.32/0.55 %--------------------------------------------------------------------------
% 0.32/0.55 cnf(condensed_detachment,axiom,
% 0.32/0.55 ( ~ is_a_theorem(implies(X,Y))
% 0.32/0.55 | ~ is_a_theorem(X)
% 0.32/0.55 | is_a_theorem(Y) ) ).
% 0.32/0.55
% 0.32/0.55 cnf(cn_1,axiom,
% 0.32/0.55 is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
% 0.32/0.55
% 0.32/0.55 cnf(cn_2,axiom,
% 0.32/0.55 is_a_theorem(implies(implies(not(X),X),X)) ).
% 0.32/0.55
% 0.32/0.55 cnf(cn_3,axiom,
% 0.32/0.55 is_a_theorem(implies(X,implies(not(X),Y))) ).
% 0.32/0.55
% 0.32/0.55 cnf(prove_cn_07,negated_conjecture,
% 0.32/0.55 ~ is_a_theorem(implies(implies(x,implies(implies(y,z),u)),implies(implies(y,v),implies(x,implies(implies(v,z),u))))) ).
% 0.32/0.55
% 0.32/0.55 %--------------------------------------------------------------------------
% 0.32/0.55 %-------------------------------------------
% 0.32/0.55 % Proof found
% 0.32/0.55 % SZS status Theorem for theBenchmark
% 0.32/0.55 % SZS output start Proof
% 0.32/0.55 %ClaNum:5(EqnAxiom:0)
% 0.32/0.55 %VarNum:16(SingletonVarNum:8)
% 0.32/0.55 %MaxLitNum:3
% 0.32/0.55 %MaxfuncDepth:5
% 0.32/0.55 %SharedTerms:15
% 0.32/0.55 %goalClause: 4
% 0.32/0.55 %singleGoalClaCount:1
% 0.32/0.55 [4]~P1(f2(f2(a3,f2(f2(a6,a7),a4)),f2(f2(a6,a5),f2(a3,f2(f2(a5,a7),a4)))))
% 0.32/0.55 [2]P1(f2(f2(f1(x21),x21),x21))
% 0.32/0.55 [1]P1(f2(x11,f2(f1(x11),x12)))
% 0.32/0.55 [3]P1(f2(f2(x31,x32),f2(f2(x32,x33),f2(x31,x33))))
% 0.32/0.55 [5]P1(x51)+~P1(x52)+~P1(f2(x52,x51))
% 0.32/0.55 %EqnAxiom
% 0.32/0.55
% 0.32/0.55 %-------------------------------------------
% 0.32/0.55 cnf(6,plain,
% 0.32/0.55 (P1(f2(f2(x61,x62),f2(f2(f1(x61),x61),x62)))),
% 0.32/0.55 inference(scs_inference,[],[2,3,5])).
% 0.32/0.55 cnf(31,plain,
% 0.32/0.55 (P1(f2(f2(f1(f2(x311,x312)),f2(x311,x312)),f2(f2(x312,x313),f2(x311,x313))))),
% 0.32/0.55 inference(scs_inference,[],[3,6,5])).
% 0.32/0.55 cnf(34,plain,
% 0.32/0.55 (P1(f2(f1(f2(f2(x341,x342),f2(f2(x342,x343),f2(x341,x343)))),x344))),
% 0.32/0.55 inference(scs_inference,[],[3,1,5])).
% 0.32/0.55 cnf(37,plain,
% 0.32/0.55 (P1(f2(f2(f2(f2(x371,x372),f2(x373,x372)),x374),f2(f2(x373,x371),x374)))),
% 0.32/0.55 inference(scs_inference,[],[31,34,5])).
% 0.32/0.55 cnf(43,plain,
% 0.32/0.55 (~P1(f2(x431,x432))+P1(x432)+~P1(x431)),
% 0.32/0.55 inference(rename_variables,[],[5])).
% 0.32/0.55 cnf(44,plain,
% 0.32/0.55 (~P1(f2(f2(a6,a5),f2(f2(f2(a6,a7),a4),f2(f2(a5,a7),a4))))),
% 0.32/0.55 inference(scs_inference,[],[3,37,4,5,43])).
% 0.32/0.55 cnf(83,plain,
% 0.32/0.55 ($false),
% 0.32/0.55 inference(scs_inference,[],[44,37,3,5]),
% 0.32/0.55 ['proof']).
% 0.32/0.55 % SZS output end Proof
% 0.32/0.55 % Total time :0.075964s
%------------------------------------------------------------------------------