%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL076-2 : 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 : n016.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 0.26s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL076-2 : 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
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 19:46:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.26/0.51 start to proof:theBenchmark
% 0.26/0.51 %-------------------------------------------
% 0.26/0.51 % File :CSE---1.7
% 0.26/0.51 % Problem :theBenchmark
% 0.26/0.51 % Transform :cnf
% 0.26/0.51 % Format :tptp:raw
% 0.26/0.51 % Command :java -jar mcs_scs.jar %d %s
% 0.26/0.51
% 0.26/0.51 % Result :Theorem 0.003541s
% 0.26/0.51 % Output :CNFRefutation 0.003541s
% 0.26/0.52 %-------------------------------------------
% 0.26/0.52 %--------------------------------------------------------------------------
% 0.26/0.52 % File : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% 0.26/0.52 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 0.26/0.52 % Problem : CN-40 depends on the Church system
% 0.26/0.52 % Version : [ANL] axioms : Augmented.
% 0.26/0.52 % English : Axiomatisations of the Implication/Negation 2 valued
% 0.26/0.52 % sentential calculus are {CN-1,CN-2,CN-3} by Lukasiewicz,
% 0.26/0.52 % {CN-18,CN-21,CN-35,CN-39,CN-39,CN-40,CN-46} by Frege,
% 0.26/0.52 % {CN-3,CN-18,CN-21,CN-22,CN-30,CN-54} by Hilbert, {CN-18,
% 0.26/0.52 % CN-35,CN-49} by Church, {CN-19,CN-37,CN-59} by Lukasiewicz,
% 0.26/0.52 % {CN-19,CN-37,CN-60} by Wos, and the single Meredith axiom.
% 0.26/0.52 % Show that CN-40 depends on the Church system.
% 0.26/0.52
% 0.26/0.52 % Refs :
% 0.26/0.52 % Source : [ANL]
% 0.26/0.52 % Names : morgan.three.ver1.in [ANL]
% 0.26/0.52 % : morgan.three.ver2.in [ANL]
% 0.26/0.52
% 0.26/0.52 % Status : Unsatisfiable
% 0.26/0.52 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.0.0
% 0.26/0.52 % Syntax : Number of clauses : 6 ( 5 unt; 0 nHn; 2 RR)
% 0.26/0.52 % Number of literals : 8 ( 0 equ; 3 neg)
% 0.26/0.52 % Maximal clause size : 3 ( 1 avg)
% 0.26/0.52 % Maximal term depth : 4 ( 2 avg)
% 0.26/0.52 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 0.26/0.52 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.26/0.52 % Number of variables : 10 ( 1 sgn)
% 0.26/0.52 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.26/0.52
% 0.26/0.52 % Comments : Contributed to the ANL library by Charles Morgan.
% 0.26/0.52 %--------------------------------------------------------------------------
% 0.26/0.52 cnf(condensed_detachment,axiom,
% 0.26/0.52 ( ~ is_a_theorem(implies(X,Y))
% 0.26/0.52 | ~ is_a_theorem(X)
% 0.26/0.52 | is_a_theorem(Y) ) ).
% 0.26/0.52
% 0.26/0.52 cnf(cn_18,axiom,
% 0.26/0.52 is_a_theorem(implies(X,implies(Y,X))) ).
% 0.26/0.52
% 0.26/0.52 cnf(cn_35,axiom,
% 0.26/0.52 is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
% 0.26/0.52
% 0.26/0.52 cnf(cn_49,axiom,
% 0.26/0.52 is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
% 0.26/0.52
% 0.26/0.52 cnf(extra_lemma,axiom,
% 0.26/0.52 is_a_theorem(implies(not(not(X1)),X1)) ).
% 0.26/0.52
% 0.26/0.52 cnf(prove_cn_40,negated_conjecture,
% 0.26/0.52 ~ is_a_theorem(implies(a,not(not(a)))) ).
% 0.26/0.52
% 0.26/0.52 %--------------------------------------------------------------------------
% 0.26/0.52 %-------------------------------------------
% 0.26/0.52 % Proof found
% 0.26/0.52 % SZS status Theorem for theBenchmark
% 0.26/0.52 % SZS output start Proof
% 0.26/0.52 %ClaNum:6(EqnAxiom:0)
% 0.26/0.52 %VarNum:20(SingletonVarNum:10)
% 0.26/0.52 %MaxLitNum:3
% 0.26/0.52 %MaxfuncDepth:3
% 0.26/0.52 %SharedTerms:5
% 0.26/0.52 %goalClause: 5
% 0.26/0.52 %singleGoalClaCount:1
% 0.26/0.52 [5]~P1(f2(a3,f1(f1(a3))))
% 0.26/0.52 [1]P1(f2(f1(f1(x11)),x11))
% 0.26/0.52 [2]P1(f2(x21,f2(x22,x21)))
% 0.26/0.52 [3]P1(f2(f2(f1(x31),f1(x32)),f2(x32,x31)))
% 0.26/0.52 [4]P1(f2(f2(x41,f2(x42,x43)),f2(f2(x41,x42),f2(x41,x43))))
% 0.26/0.52 [6]P1(x61)+~P1(x62)+~P1(f2(x62,x61))
% 0.26/0.52 %EqnAxiom
% 0.26/0.52
% 0.26/0.52 %-------------------------------------------
% 0.26/0.52 cnf(7,plain,
% 0.26/0.52 ($false),
% 0.26/0.52 inference(scs_inference,[],[5,3,1,6]),
% 0.26/0.52 ['proof']).
% 0.26/0.52 % SZS output end Proof
% 0.26/0.52 % Total time :0.003541s
%------------------------------------------------------------------------------