%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL077-1 : 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 : 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 68.37s 68.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL077-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.06/0.33 % Computer : n009.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sat Sep 5 16:27:07 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.25/0.49 start to proof:theBenchmark
% 68.37/68.51 %-------------------------------------------
% 68.37/68.51 % File :CSE---1.7
% 68.37/68.51 % Problem :theBenchmark
% 68.37/68.51 % Transform :cnf
% 68.37/68.51 % Format :tptp:raw
% 68.37/68.51 % Command :java -jar mcs_scs.jar %d %s
% 68.37/68.51
% 68.37/68.51 % Result :Theorem 68.035342s
% 68.37/68.51 % Output :CNFRefutation 68.035342s
% 68.37/68.51 %-------------------------------------------
% 68.37/68.52 %--------------------------------------------------------------------------
% 68.37/68.52 % File : LCL077-1 : TPTP v9.3.1. Released v1.0.0.
% 68.37/68.52 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 68.37/68.52 % Problem : CN-39 depends on the Church system
% 68.37/68.52 % Version : [Pel86] axioms.
% 68.37/68.52 % English : Axiomatisations of the Implication/Negation 2 valued
% 68.37/68.52 % sentential calculus are {CN-1,CN-2,CN-3} by Lukasiewicz,
% 68.37/68.52 % {CN-18,CN-21,CN-35,CN-39,CN-39,CN-40,CN-46} by Frege,
% 68.37/68.52 % {CN-3,CN-18,CN-21,CN-22,CN-30,CN-54} by Hilbert, {CN-18,
% 68.37/68.52 % CN-35,CN-49} by Church, {CN-19,CN-37,CN-59} by Lukasiewicz,
% 68.37/68.52 % {CN-19,CN-37,CN-60} by Wos, and the single Meredith axiom.
% 68.37/68.52 % Show that CN-39 depends on the Church system.
% 68.37/68.52
% 68.37/68.52 % Refs : [Mor84] Morgan (1984), Logic Problems
% 68.37/68.52 % : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 68.37/68.52 % Source : [Pel86]
% 68.37/68.52 % Names : Pelletier 67 [Pel86]
% 68.37/68.52 % : morgan.five.ver1.in [ANL]
% 68.37/68.52
% 68.37/68.52 % Status : Unsatisfiable
% 68.37/68.52 % Rating : 0.00 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.06 v5.4.0, 0.11 v5.3.0, 0.20 v5.2.0, 0.15 v5.1.0, 0.12 v5.0.0, 0.07 v4.1.0, 0.13 v4.0.1, 0.00 v2.7.0, 0.12 v2.6.0, 0.00 v2.1.0, 0.00 v2.0.0
% 68.37/68.52 % Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 2 RR)
% 68.37/68.52 % Number of literals : 7 ( 0 equ; 3 neg)
% 68.37/68.52 % Maximal clause size : 3 ( 1 avg)
% 68.37/68.52 % Maximal term depth : 4 ( 2 avg)
% 68.37/68.52 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 68.37/68.52 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 68.37/68.52 % Number of variables : 9 ( 1 sgn)
% 68.37/68.52 % SPC : CNF_UNS_RFO_NEQ_HRN
% 68.37/68.52
% 68.37/68.52 % Comments :
% 68.37/68.52 %--------------------------------------------------------------------------
% 68.37/68.52 cnf(condensed_detachment,axiom,
% 68.37/68.52 ( ~ is_a_theorem(implies(X,Y))
% 68.37/68.52 | ~ is_a_theorem(X)
% 68.37/68.52 | is_a_theorem(Y) ) ).
% 68.37/68.52
% 68.37/68.52 cnf(cn_18,axiom,
% 68.37/68.52 is_a_theorem(implies(X,implies(Y,X))) ).
% 68.37/68.52
% 68.37/68.52 cnf(cn_35,axiom,
% 68.37/68.52 is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
% 68.37/68.52
% 68.37/68.52 cnf(cn_49,axiom,
% 68.37/68.52 is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
% 68.37/68.52
% 68.37/68.52 cnf(prove_cn_39,negated_conjecture,
% 68.37/68.52 ~ is_a_theorem(implies(not(not(a)),a)) ).
% 68.37/68.52
% 68.37/68.52 %--------------------------------------------------------------------------
% 68.37/68.52 %-------------------------------------------
% 68.37/68.52 % Proof found
% 68.37/68.52 % SZS status Theorem for theBenchmark
% 68.37/68.52 % SZS output start Proof
% 68.37/68.52 %ClaNum:5(EqnAxiom:0)
% 68.37/68.52 %VarNum:18(SingletonVarNum:9)
% 68.37/68.52 %MaxLitNum:3
% 68.37/68.52 %MaxfuncDepth:3
% 68.37/68.52 %SharedTerms:5
% 68.37/68.52 %goalClause: 4
% 68.37/68.52 %singleGoalClaCount:1
% 68.37/68.52 [4]~P1(f1(f3(f3(a2)),a2))
% 68.37/68.52 [1]P1(f1(x11,f1(x12,x11)))
% 68.37/68.52 [2]P1(f1(f1(f3(x21),f3(x22)),f1(x22,x21)))
% 68.37/68.52 [3]P1(f1(f1(x31,f1(x32,x33)),f1(f1(x31,x32),f1(x31,x33))))
% 68.37/68.52 [5]P1(x51)+~P1(x52)+~P1(f1(x52,x51))
% 68.37/68.52 %EqnAxiom
% 68.37/68.52
% 68.37/68.52 %-------------------------------------------
% 68.37/68.52 cnf(9,plain,
% 68.37/68.52 (P1(f1(f1(x91,x92),f1(x91,x91)))),
% 68.37/68.52 inference(scs_inference,[],[1,3,5])).
% 68.37/68.52 cnf(12,plain,
% 68.37/68.52 (P1(f1(x121,x121))),
% 68.37/68.52 inference(scs_inference,[],[1,9,5])).
% 68.37/68.52 cnf(83,plain,
% 68.37/68.52 (~P1(f1(f1(x831,x831),f1(f3(f3(a2)),a2)))),
% 68.37/68.52 inference(scs_inference,[],[4,12,5])).
% 68.37/68.52 cnf(91,plain,
% 68.37/68.52 (P1(f1(x911,f1(f1(f3(x912),f3(x913)),f1(x913,x912))))),
% 68.37/68.52 inference(scs_inference,[],[1,2,5])).
% 68.37/68.52 cnf(105,plain,
% 68.37/68.52 (~P1(f1(f3(f3(a2)),f1(f3(f3(a2)),a2)))),
% 68.37/68.52 inference(scs_inference,[],[3,83,5])).
% 68.37/68.52 cnf(146,plain,
% 68.37/68.52 (P1(f1(f1(x1461,f1(f3(x1462),f3(x1463))),f1(x1461,f1(x1463,x1462))))),
% 68.37/68.52 inference(scs_inference,[],[3,91,5])).
% 68.37/68.52 cnf(274,plain,
% 68.37/68.52 (P1(f1(f3(x2741),f1(x2741,x2742)))),
% 68.37/68.52 inference(scs_inference,[],[146,1,5])).
% 68.37/68.52 cnf(314,plain,
% 68.37/68.52 ($false),
% 68.37/68.52 inference(scs_inference,[],[274,105,146,5]),
% 68.37/68.52 ['proof']).
% 68.37/68.52 % SZS output end Proof
% 68.37/68.52 % Total time :68.035342s
%------------------------------------------------------------------------------