%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL076-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 0.42s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL076-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.34 % Computer : n029.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 : Fri Sep 4 23:09:54 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.25/0.51 start to proof:theBenchmark
% 0.25/0.56 %-------------------------------------------
% 0.25/0.56 % File :CSE---1.7
% 0.25/0.56 % Problem :theBenchmark
% 0.25/0.56 % Transform :cnf
% 0.25/0.56 % Format :tptp:raw
% 0.25/0.56 % Command :java -jar mcs_scs.jar %d %s
% 0.25/0.56
% 0.25/0.56 % Result :Theorem 0.066371s
% 0.25/0.56 % Output :CNFRefutation 0.066371s
% 0.25/0.56 %-------------------------------------------
% 0.25/0.56 %--------------------------------------------------------------------------
% 0.25/0.56 % File : LCL076-3 : TPTP v9.3.1. Released v1.0.0.
% 0.25/0.56 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 0.25/0.56 % Problem : CN-40 depends on the Church system
% 0.25/0.56 % Version : [ANL] axioms : Augmented.
% 0.25/0.56 % English : Axiomatisations of the Implication/Negation 2 valued
% 0.42/0.56 % sentential calculus are {CN-1,CN-2,CN-3} by Lukasiewicz,
% 0.42/0.56 % {CN-18,CN-21,CN-35,CN-39,CN-39,CN-40,CN-46} by Frege,
% 0.42/0.56 % {CN-3,CN-18,CN-21,CN-22,CN-30,CN-54} by Hilbert, {CN-18,
% 0.42/0.56 % CN-35,CN-49} by Church, {CN-19,CN-37,CN-59} by Lukasiewicz,
% 0.42/0.56 % {CN-19,CN-37,CN-60} by Wos, and the single Meredith axiom.
% 0.42/0.56 % Show that CN-40 depends on the Church system.
% 0.42/0.56
% 0.42/0.56 % Refs :
% 0.42/0.56 % Source : [ANL]
% 0.42/0.56 % Names : morgan.four.ver1.in [ANL]
% 0.42/0.56
% 0.42/0.56 % Status : Unsatisfiable
% 0.42/0.56 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.15 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
% 0.42/0.56 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 3 RR)
% 0.42/0.56 % Number of literals : 10 ( 0 equ; 5 neg)
% 0.42/0.56 % Maximal clause size : 3 ( 1 avg)
% 0.42/0.56 % Maximal term depth : 4 ( 2 avg)
% 0.42/0.56 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 0.42/0.56 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.42/0.56 % Number of variables : 12 ( 1 sgn)
% 0.42/0.56 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.42/0.56
% 0.42/0.56 % Comments : Transitivity of implies is supplied as a lemma
% 0.42/0.56 % : Contributed to the ANL library by Charles Morgan.
% 0.42/0.56 %--------------------------------------------------------------------------
% 0.42/0.56 cnf(condensed_detachment,axiom,
% 0.42/0.56 ( ~ is_a_theorem(implies(X,Y))
% 0.42/0.56 | ~ is_a_theorem(X)
% 0.42/0.56 | is_a_theorem(Y) ) ).
% 0.42/0.56
% 0.42/0.56 cnf(cn_18,axiom,
% 0.42/0.56 is_a_theorem(implies(X,implies(Y,X))) ).
% 0.42/0.56
% 0.42/0.56 cnf(cn_35,axiom,
% 0.42/0.56 is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
% 0.42/0.56
% 0.42/0.56 cnf(cn_49,axiom,
% 0.42/0.56 is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
% 0.42/0.56
% 0.42/0.56 cnf(transitivity,axiom,
% 0.42/0.56 ( ~ is_a_theorem(implies(X1,X2))
% 0.42/0.56 | ~ is_a_theorem(implies(X2,X3))
% 0.42/0.56 | is_a_theorem(implies(X1,X3)) ) ).
% 0.42/0.56
% 0.42/0.56 cnf(prove_cn_40,negated_conjecture,
% 0.42/0.56 ~ is_a_theorem(implies(a,not(not(a)))) ).
% 0.42/0.56
% 0.42/0.56 %--------------------------------------------------------------------------
% 0.42/0.56 %-------------------------------------------
% 0.42/0.56 % Proof found
% 0.42/0.56 % SZS status Theorem for theBenchmark
% 0.42/0.56 % SZS output start Proof
% 0.42/0.56 %ClaNum:6(EqnAxiom:0)
% 0.42/0.56 %VarNum:24(SingletonVarNum:12)
% 0.42/0.56 %MaxLitNum:3
% 0.42/0.56 %MaxfuncDepth:3
% 0.42/0.56 %SharedTerms:5
% 0.42/0.56 %goalClause: 4
% 0.42/0.56 %singleGoalClaCount:1
% 0.42/0.56 [4]~P1(f1(a2,f3(f3(a2))))
% 0.42/0.56 [1]P1(f1(x11,f1(x12,x11)))
% 0.42/0.56 [2]P1(f1(f1(f3(x21),f3(x22)),f1(x22,x21)))
% 0.42/0.56 [3]P1(f1(f1(x31,f1(x32,x33)),f1(f1(x31,x32),f1(x31,x33))))
% 0.42/0.56 [5]P1(x51)+~P1(x52)+~P1(f1(x52,x51))
% 0.42/0.56 [6]~P1(f1(x61,x63))+P1(f1(x61,x62))+~P1(f1(x63,x62))
% 0.42/0.56 %EqnAxiom
% 0.42/0.56
% 0.42/0.56 %-------------------------------------------
% 0.42/0.57 cnf(8,plain,
% 0.42/0.57 (P1(f1(f1(f3(x81),f3(x82)),f1(x82,x81)))),
% 0.42/0.57 inference(rename_variables,[],[2])).
% 0.42/0.57 cnf(10,plain,
% 0.42/0.57 (P1(f1(f3(x101),f1(x101,x102)))),
% 0.42/0.57 inference(scs_inference,[],[4,2,8,1,5,6])).
% 0.42/0.57 cnf(14,plain,
% 0.42/0.57 (P1(f1(f3(x141),f1(x141,x142)))),
% 0.42/0.57 inference(rename_variables,[],[10])).
% 0.42/0.57 cnf(16,plain,
% 0.42/0.57 (P1(f1(f3(x161),f1(f1(x161,x162),f1(x161,x163))))),
% 0.42/0.57 inference(scs_inference,[],[4,10,14,3,5,6])).
% 0.42/0.57 cnf(23,plain,
% 0.42/0.57 (P1(f1(f3(f3(x231)),f1(x232,x231)))),
% 0.42/0.57 inference(scs_inference,[],[4,10,2,1,5,6])).
% 0.42/0.57 cnf(41,plain,
% 0.42/0.57 (~P1(f1(x411,f3(x412)))+P1(f1(x411,f1(x412,x413)))),
% 0.42/0.57 inference(scs_inference,[],[16,10,3,5,6])).
% 0.42/0.57 cnf(43,plain,
% 0.42/0.57 (P1(f1(f1(x431,x432),f1(x431,x431)))),
% 0.42/0.57 inference(scs_inference,[],[1,3,5])).
% 0.42/0.57 cnf(51,plain,
% 0.42/0.57 (P1(f1(x511,x511))),
% 0.42/0.57 inference(scs_inference,[],[1,43,5])).
% 0.42/0.57 cnf(52,plain,
% 0.42/0.57 (P1(f1(f1(x521,x522),f1(x521,x521)))),
% 0.42/0.57 inference(rename_variables,[],[43])).
% 0.42/0.57 cnf(54,plain,
% 0.42/0.57 (P1(f1(f1(x541,x542),f1(x543,f1(x541,x541))))),
% 0.42/0.57 inference(scs_inference,[],[1,43,52,5,6])).
% 0.42/0.57 cnf(68,plain,
% 0.42/0.57 (P1(f1(x681,f1(x682,x682)))),
% 0.42/0.57 inference(scs_inference,[],[1,54,5])).
% 0.42/0.57 cnf(89,plain,
% 0.42/0.57 (P1(f1(f1(f1(x891,x892),x891),f1(f1(x891,x892),x892)))),
% 0.42/0.57 inference(scs_inference,[],[2,51,3,6,5])).
% 0.42/0.57 cnf(92,plain,
% 0.42/0.57 (P1(f1(f1(f1(x921,x921),x922),x922))),
% 0.42/0.57 inference(scs_inference,[],[89,68,5])).
% 0.42/0.57 cnf(100,plain,
% 0.42/0.57 (P1(f1(f1(f1(x1001,x1001),x1002),x1002))),
% 0.42/0.57 inference(rename_variables,[],[92])).
% 0.42/0.57 cnf(104,plain,
% 0.42/0.57 (P1(f1(f1(f1(x1041,x1041),f1(f3(x1042),f3(x1043))),f1(x1043,x1042)))),
% 0.42/0.57 inference(scs_inference,[],[2,92,100,4,41,5,6])).
% 0.42/0.57 cnf(123,plain,
% 0.42/0.57 ($false),
% 0.42/0.57 inference(scs_inference,[],[3,4,23,104,6,5]),
% 0.42/0.57 ['proof']).
% 0.42/0.57 % SZS output end Proof
% 0.42/0.57 % Total time :0.066371s
%------------------------------------------------------------------------------