%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL035-1 : 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 : n017.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 11:18:33 AM UTC 2026
% Result : Unsatisfiable 0.47s 0.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL035-1 : 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
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 06:01:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.24/0.51 start to proof:theBenchmark
% 0.47/0.65 %-------------------------------------------
% 0.47/0.65 % File :CSE---1.7
% 0.47/0.65 % Problem :theBenchmark
% 0.47/0.65 % Transform :cnf
% 0.47/0.65 % Format :tptp:raw
% 0.47/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.47/0.65
% 0.47/0.65 % Result :Theorem 0.156249s
% 0.47/0.65 % Output :CNFRefutation 0.156249s
% 0.47/0.65 %-------------------------------------------
% 0.47/0.65 %--------------------------------------------------------------------------
% 0.47/0.65 % File : LCL035-1 : TPTP v9.3.1. Released v1.0.0.
% 0.47/0.65 % Domain : Logic Calculi (Implication/Falsehood 2 valued sentential)
% 0.47/0.65 % Problem : C0-4 depends on the Meredith axiom
% 0.47/0.65 % Version : [McC92] axioms.
% 0.47/0.65 % English : Axiomatisations for the Implication/Falsehood 2 valued
% 0.47/0.65 % sentential calculus are {C0-1,C0-2,C0-3,C0-4}
% 0.47/0.65 % by Tarski-Bernays, {C0-2,C0-5,C0-6} by Church, and the single
% 0.47/0.65 % Meredith axioms. Show that C0-4 can be derived from the
% 0.47/0.65 % single Meredith axiom.
% 0.47/0.65
% 0.47/0.65 % Refs : [Mer53] Meredith (1953), Single Axioms for the Systems (C,N),
% 0.47/0.65 % : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 0.47/0.65 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 0.47/0.65 % Source : [McC92]
% 0.47/0.65 % Names : C0-47 [MW92]
% 0.47/0.65
% 0.47/0.65 % Status : Unsatisfiable
% 0.47/0.65 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 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
% 0.47/0.65 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 0.47/0.65 % Number of literals : 5 ( 0 equ; 3 neg)
% 0.47/0.65 % Maximal clause size : 3 ( 1 avg)
% 0.47/0.65 % Maximal term depth : 6 ( 2 avg)
% 0.47/0.65 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 0.47/0.65 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 0.47/0.65 % Number of variables : 7 ( 2 sgn)
% 0.47/0.65 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.47/0.65
% 0.47/0.65 % Comments :
% 0.47/0.65 %--------------------------------------------------------------------------
% 0.47/0.65 cnf(condensed_detachment,axiom,
% 0.47/0.65 ( ~ is_a_theorem(implies(X,Y))
% 0.47/0.65 | ~ is_a_theorem(X)
% 0.47/0.65 | is_a_theorem(Y) ) ).
% 0.47/0.65
% 0.47/0.65 cnf(c0_CAMeredith,axiom,
% 0.47/0.65 is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))) ).
% 0.47/0.65
% 0.47/0.65 cnf(prove_c0_4,negated_conjecture,
% 0.47/0.65 ~ is_a_theorem(implies(falsehood,a)) ).
% 0.47/0.65
% 0.47/0.65 %--------------------------------------------------------------------------
% 0.47/0.65 %-------------------------------------------
% 0.47/0.65 % Proof found
% 0.47/0.65 % SZS status Theorem for theBenchmark
% 0.47/0.65 % SZS output start Proof
% 0.47/0.65 %ClaNum:3(EqnAxiom:0)
% 0.47/0.65 %VarNum:13(SingletonVarNum:7)
% 0.47/0.65 %MaxLitNum:3
% 0.47/0.65 %MaxfuncDepth:3
% 0.47/0.65 %SharedTerms:4
% 0.47/0.65 %goalClause: 2
% 0.47/0.65 %singleGoalClaCount:1
% 0.47/0.65 [2]~P1(f1(a2,a3))
% 0.47/0.65 [1]P1(f1(f1(f1(f1(f1(x11,x12),f1(x13,a2)),x14),x15),f1(f1(x15,x11),f1(x13,x11))))
% 0.47/0.65 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 0.47/0.65 %EqnAxiom
% 0.47/0.65
% 0.47/0.65 %-------------------------------------------
% 0.47/0.66 cnf(4,plain,
% 0.47/0.66 (P1(f1(f1(x41,x42),f1(x43,x42)))+~P1(f1(f1(f1(f1(x42,x44),f1(x43,a2)),x45),x41))),
% 0.47/0.66 inference(scs_inference,[],[1,3])).
% 0.47/0.66 cnf(6,plain,
% 0.47/0.66 (P1(f1(f1(f1(f1(x61,x62),f1(x63,x62)),f1(x62,x64)),f1(x65,f1(x62,x64))))),
% 0.47/0.66 inference(scs_inference,[],[1,4])).
% 0.47/0.66 cnf(7,plain,
% 0.47/0.66 (P1(f1(f1(f1(f1(f1(x71,x72),f1(x73,a2)),x74),x75),f1(f1(x75,x71),f1(x73,x71))))),
% 0.47/0.66 inference(rename_variables,[],[1])).
% 0.47/0.66 cnf(9,plain,
% 0.47/0.66 (P1(f1(f1(f1(x91,f1(a2,x92)),x93),f1(x94,x93)))),
% 0.47/0.66 inference(scs_inference,[],[1,7,4,3])).
% 0.47/0.66 cnf(12,plain,
% 0.47/0.66 (P1(f1(f1(f1(x121,x122),x123),f1(a2,x123)))),
% 0.47/0.66 inference(scs_inference,[],[9,4])).
% 0.47/0.66 cnf(25,plain,
% 0.47/0.66 (P1(f1(f1(f1(a2,x251),x252),f1(x253,x252)))),
% 0.47/0.66 inference(scs_inference,[],[12,4])).
% 0.47/0.66 cnf(44,plain,
% 0.47/0.66 (P1(f1(x441,f1(a2,f1(x442,a2))))),
% 0.47/0.66 inference(scs_inference,[],[12,6,3])).
% 0.47/0.66 cnf(48,plain,
% 0.47/0.66 (P1(f1(a2,f1(x481,a2)))),
% 0.47/0.66 inference(scs_inference,[],[12,44,3])).
% 0.47/0.66 cnf(72,plain,
% 0.47/0.66 (P1(f1(x721,f1(x722,f1(x723,x722))))),
% 0.47/0.66 inference(scs_inference,[],[25,6,3])).
% 0.47/0.66 cnf(78,plain,
% 0.47/0.66 (P1(f1(x781,f1(x782,x781)))),
% 0.47/0.66 inference(scs_inference,[],[48,72,3])).
% 0.47/0.66 cnf(86,plain,
% 0.47/0.66 (P1(f1(x861,f1(x862,f1(f1(x863,x862),f1(x864,x862)))))),
% 0.47/0.66 inference(scs_inference,[],[78,6,3])).
% 0.47/0.66 cnf(108,plain,
% 0.47/0.66 (P1(f1(x1081,f1(x1082,f1(x1083,f1(a2,x1084)))))),
% 0.47/0.66 inference(scs_inference,[],[78,9,3])).
% 0.47/0.66 cnf(122,plain,
% 0.47/0.66 (P1(f1(x1221,f1(x1222,f1(a2,x1223))))),
% 0.47/0.66 inference(scs_inference,[],[78,108,3])).
% 0.47/0.66 cnf(125,plain,
% 0.47/0.66 (P1(f1(x1251,f1(a2,x1252)))),
% 0.47/0.66 inference(scs_inference,[],[78,122,3])).
% 0.47/0.66 cnf(129,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(scs_inference,[],[86,125,2,3]),
% 0.47/0.66 ['proof']).
% 0.47/0.66 % SZS output end Proof
% 0.47/0.66 % Total time :0.156249s
%------------------------------------------------------------------------------