%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL079-1 : 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 : n013.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 33.79s 33.92s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL079-1 : 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
% 0.07/0.34 % Computer : n013.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
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 6 01:04:35 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.24/0.52 start to proof:theBenchmark
% 33.79/33.92 %-------------------------------------------
% 33.79/33.92 % File :CSE---1.7
% 33.79/33.92 % Problem :theBenchmark
% 33.79/33.92 % Transform :cnf
% 33.79/33.92 % Format :tptp:raw
% 33.79/33.92 % Command :java -jar mcs_scs.jar %d %s
% 33.79/33.92
% 33.79/33.92 % Result :Theorem 33.420720s
% 33.79/33.92 % Output :CNFRefutation 33.420720s
% 33.79/33.92 %-------------------------------------------
% 33.79/33.92 %--------------------------------------------------------------------------
% 33.79/33.92 % File : LCL079-1 : TPTP v9.3.1. Released v1.0.0.
% 33.79/33.92 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 33.79/33.92 % Problem : Transitivity can be derived from Church's system
% 33.79/33.92 % Version : [ANL] axioms.
% 33.79/33.92 % English : An axiomatisation of the Implication/Negation 2 valued
% 33.79/33.92 % sentential calculus is {CN-18,CN-35,CN-49} by Church. Show
% 33.79/33.92 % that transitivity of implies can be derived from the Church
% 33.79/33.92 % system.
% 33.79/33.92
% 33.79/33.92 % Refs :
% 33.79/33.92 % Source : [ANL]
% 33.79/33.92 % Names : morgan.one.ver2.in [ANL]
% 33.79/33.92
% 33.79/33.92 % Status : Unsatisfiable
% 33.79/33.92 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.05 v5.2.0, 0.00 v2.1.0, 0.00 v2.0.0
% 33.79/33.92 % Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 4 RR)
% 33.79/33.92 % Number of literals : 9 ( 0 equ; 3 neg)
% 33.79/33.92 % Maximal clause size : 3 ( 1 avg)
% 33.79/33.92 % Maximal term depth : 4 ( 2 avg)
% 33.79/33.92 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 33.79/33.92 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% 33.79/33.92 % Number of variables : 9 ( 1 sgn)
% 33.79/33.92 % SPC : CNF_UNS_RFO_NEQ_HRN
% 33.79/33.92
% 33.79/33.92 % Comments : Contributed to the ANL library by Charles Morgan.
% 33.79/33.92 %--------------------------------------------------------------------------
% 33.79/33.92 cnf(condensed_detachment,axiom,
% 33.79/33.92 ( ~ is_a_theorem(implies(X,Y))
% 33.79/33.92 | ~ is_a_theorem(X)
% 33.79/33.92 | is_a_theorem(Y) ) ).
% 33.79/33.92
% 33.79/33.92 cnf(cn_18,axiom,
% 33.79/33.92 is_a_theorem(implies(X,implies(Y,X))) ).
% 33.79/33.92
% 33.79/33.92 cnf(cn_35,axiom,
% 33.79/33.92 is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
% 33.79/33.92
% 33.79/33.92 cnf(cn_49_reversed,axiom,
% 33.79/33.92 is_a_theorem(implies(implies(Y,X),implies(not(X),not(Y)))) ).
% 33.79/33.92
% 33.79/33.92 cnf(a_implies_b,hypothesis,
% 33.79/33.92 is_a_theorem(implies(a,b)) ).
% 33.79/33.92
% 33.79/33.92 cnf(b_implies_c,hypothesis,
% 33.79/33.92 is_a_theorem(implies(b,c)) ).
% 33.79/33.92
% 33.79/33.92 cnf(prove_transitivity,negated_conjecture,
% 33.79/33.92 ~ is_a_theorem(implies(a,c)) ).
% 33.79/33.92
% 33.79/33.92 %--------------------------------------------------------------------------
% 33.79/33.92 %-------------------------------------------
% 33.79/33.92 % Proof found
% 33.79/33.92 % SZS status Theorem for theBenchmark
% 33.79/33.92 % SZS output start Proof
% 33.79/33.92 %ClaNum:7(EqnAxiom:0)
% 33.79/33.92 %VarNum:18(SingletonVarNum:9)
% 33.79/33.92 %MaxLitNum:3
% 33.79/33.92 %MaxfuncDepth:3
% 33.79/33.92 %SharedTerms:9
% 33.79/33.92 %goalClause: 6
% 33.79/33.92 %singleGoalClaCount:1
% 33.79/33.92 [1]P1(f3(a1,a2))
% 33.79/33.92 [2]P1(f3(a2,a4))
% 33.79/33.92 [6]~P1(f3(a1,a4))
% 33.79/33.92 [3]P1(f3(x31,f3(x32,x31)))
% 33.79/33.92 [4]P1(f3(f3(x41,x42),f3(f5(x42),f5(x41))))
% 33.79/33.92 [5]P1(f3(f3(x51,f3(x52,x53)),f3(f3(x51,x52),f3(x51,x53))))
% 33.79/33.92 [7]P1(x71)+~P1(x72)+~P1(f3(x72,x71))
% 33.79/33.92 %EqnAxiom
% 33.79/33.92
% 33.79/33.92 %-------------------------------------------
% 33.79/33.93 cnf(32,plain,
% 33.79/33.93 (P1(f3(f3(x321,x322),f3(x321,x321)))),
% 33.79/33.93 inference(scs_inference,[],[3,5,7])).
% 33.79/33.93 cnf(36,plain,
% 33.79/33.93 (P1(f3(x361,x361))),
% 33.79/33.93 inference(scs_inference,[],[3,32,7])).
% 33.79/33.93 cnf(72,plain,
% 33.79/33.93 (P1(f3(f3(f3(x721,x722),x721),f3(f3(x721,x722),x722)))),
% 33.79/33.93 inference(scs_inference,[],[36,5,7])).
% 33.79/33.93 cnf(453,plain,
% 33.79/33.93 (P1(f3(x4531,f3(a1,a2)))),
% 33.79/33.93 inference(scs_inference,[],[1,3,7])).
% 33.79/33.93 cnf(457,plain,
% 33.79/33.93 (P1(f3(f3(f3(a1,a2),x4571),x4571))),
% 33.79/33.93 inference(scs_inference,[],[72,453,7])).
% 33.79/33.93 cnf(462,plain,
% 33.79/33.93 (P1(f3(x4621,f3(a2,a4)))),
% 33.79/33.93 inference(scs_inference,[],[2,3,7])).
% 33.79/33.93 cnf(522,plain,
% 33.79/33.93 (P1(f3(f3(x5221,a2),f3(x5221,a4)))),
% 33.79/33.93 inference(scs_inference,[],[462,5,7])).
% 33.79/33.93 cnf(682,plain,
% 33.79/33.93 ($false),
% 33.79/33.93 inference(scs_inference,[],[522,457,6,7]),
% 33.79/33.93 ['proof']).
% 33.79/33.93 % SZS output end Proof
% 33.79/33.93 % Total time :33.420720s
%------------------------------------------------------------------------------