%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL033-1 : 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 : n008.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 59.30s 59.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL033-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 18:51:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.24/0.53 start to proof:theBenchmark
% 59.30/59.40 %-------------------------------------------
% 59.30/59.40 % File :CSE---1.7
% 59.30/59.40 % Problem :theBenchmark
% 59.30/59.40 % Transform :cnf
% 59.30/59.40 % Format :tptp:raw
% 59.30/59.40 % Command :java -jar mcs_scs.jar %d %s
% 59.30/59.40
% 59.30/59.40 % Result :Theorem 58.885034s
% 59.30/59.40 % Output :CNFRefutation 58.885034s
% 59.30/59.40 %-------------------------------------------
% 59.30/59.40 %--------------------------------------------------------------------------
% 59.30/59.40 % File : LCL033-1 : TPTP v9.3.1. Released v1.0.0.
% 59.30/59.40 % Domain : Logic Calculi (Implication/Falsehood 2 valued sentential)
% 59.30/59.40 % Problem : C0-2 depends on the Meredith axiom
% 59.30/59.40 % Version : [McC92] axioms.
% 59.30/59.40 % English : Axiomatisations for the Implication/Falsehood 2 valued
% 59.30/59.40 % sentential calculus are {C0-1,C0-2,C0-3,C0-4}
% 59.30/59.40 % by Tarski-Bernays, {C0-2,C0-5,C0-6} by Church, and the single
% 59.30/59.40 % Meredith axioms. Show that C0-2 can be derived from the
% 59.30/59.40 % single Meredith axiom.
% 59.30/59.40
% 59.30/59.40 % Refs : [Mer53] Meredith (1953), Single Axioms for the Systems (C,N),
% 59.30/59.40 % : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 59.30/59.40 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 59.30/59.40 % Source : [McC92]
% 59.30/59.40 % Names : C0-45 [MW92]
% 59.30/59.40
% 59.30/59.40 % Status : Unsatisfiable
% 59.30/59.40 % 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 v2.6.0, 0.14 v2.5.0, 0.00 v2.4.0, 0.00 v2.3.0, 0.14 v2.2.1, 0.11 v2.1.0, 0.13 v2.0.0
% 59.30/59.40 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 59.30/59.40 % Number of literals : 5 ( 0 equ; 3 neg)
% 59.30/59.40 % Maximal clause size : 3 ( 1 avg)
% 59.30/59.40 % Maximal term depth : 6 ( 2 avg)
% 59.30/59.40 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 59.30/59.40 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 59.30/59.40 % Number of variables : 7 ( 2 sgn)
% 59.30/59.40 % SPC : CNF_UNS_RFO_NEQ_HRN
% 59.30/59.40
% 59.30/59.40 % Comments :
% 59.30/59.40 %--------------------------------------------------------------------------
% 59.30/59.40 cnf(condensed_detachment,axiom,
% 59.30/59.40 ( ~ is_a_theorem(implies(X,Y))
% 59.30/59.40 | ~ is_a_theorem(X)
% 59.30/59.40 | is_a_theorem(Y) ) ).
% 59.30/59.40
% 59.30/59.40 cnf(c0_CAMeredith,axiom,
% 59.30/59.40 is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))) ).
% 59.30/59.40
% 59.30/59.40 cnf(prove_c0_2,negated_conjecture,
% 59.30/59.40 ~ is_a_theorem(implies(a,implies(b,a))) ).
% 59.30/59.40
% 59.30/59.40 %--------------------------------------------------------------------------
% 59.30/59.40 %-------------------------------------------
% 59.30/59.40 % Proof found
% 59.30/59.40 % SZS status Theorem for theBenchmark
% 59.30/59.40 % SZS output start Proof
% 59.30/59.40 %ClaNum:3(EqnAxiom:0)
% 59.30/59.41 %VarNum:13(SingletonVarNum:7)
% 59.30/59.41 %MaxLitNum:3
% 59.30/59.41 %MaxfuncDepth:3
% 59.30/59.41 %SharedTerms:6
% 59.30/59.41 %goalClause: 2
% 59.30/59.41 %singleGoalClaCount:1
% 59.30/59.41 [2]~P1(f1(a3,f1(a4,a3)))
% 59.30/59.41 [1]P1(f1(f1(f1(f1(f1(x11,x12),f1(x13,a2)),x14),x15),f1(f1(x15,x11),f1(x13,x11))))
% 59.30/59.41 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 59.30/59.41 %EqnAxiom
% 59.30/59.41
% 59.30/59.41 %-------------------------------------------
% 59.30/59.41 cnf(4,plain,
% 59.30/59.41 (P1(f1(f1(x41,x42),f1(x43,x42)))+~P1(f1(f1(f1(f1(x42,x44),f1(x43,a2)),x45),x41))),
% 59.30/59.41 inference(scs_inference,[],[1,3])).
% 59.30/59.41 cnf(6,plain,
% 59.30/59.41 (P1(f1(f1(f1(f1(x61,x62),f1(x63,x62)),f1(x62,x64)),f1(x65,f1(x62,x64))))),
% 59.30/59.41 inference(scs_inference,[],[1,4])).
% 59.30/59.41 cnf(7,plain,
% 59.30/59.41 (P1(f1(f1(f1(f1(f1(x71,x72),f1(x73,a2)),x74),x75),f1(f1(x75,x71),f1(x73,x71))))),
% 59.30/59.41 inference(rename_variables,[],[1])).
% 59.30/59.41 cnf(9,plain,
% 59.30/59.41 (P1(f1(f1(f1(x91,f1(a2,x92)),x93),f1(x94,x93)))),
% 59.30/59.41 inference(scs_inference,[],[1,7,4,3])).
% 59.30/59.41 cnf(12,plain,
% 59.30/59.41 (P1(f1(f1(f1(x121,x122),x123),f1(a2,x123)))),
% 59.30/59.41 inference(scs_inference,[],[9,4])).
% 59.30/59.41 cnf(18,plain,
% 59.30/59.41 (P1(f1(f1(f1(a2,x181),x182),f1(x183,x182)))),
% 59.30/59.41 inference(scs_inference,[],[12,4])).
% 59.30/59.41 cnf(110,plain,
% 59.30/59.41 (~P1(f1(f1(f1(f1(x1101,f1(a2,x1102)),x1103),f1(x1104,x1103)),f1(a3,f1(a4,a3))))),
% 59.30/59.41 inference(scs_inference,[],[2,9,3])).
% 59.30/59.41 cnf(130,plain,
% 59.30/59.41 ($false),
% 59.30/59.41 inference(scs_inference,[],[110,6,18,3]),
% 59.30/59.41 ['proof']).
% 59.30/59.41 % SZS output end Proof
% 59.30/59.41 % Total time :58.885034s
%------------------------------------------------------------------------------