%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL027-1 : 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 : n031.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 11:18:32 AM UTC 2026
% Result : Unsatisfiable 60.01s 60.16s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL027-1 : 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
% 0.08/0.35 % Computer : n031.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 : Sat Sep 5 17:15:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.24/0.52 start to proof:theBenchmark
% 60.01/60.15 %-------------------------------------------
% 60.01/60.15 % File :CSE---1.7
% 60.01/60.15 % Problem :theBenchmark
% 60.01/60.15 % Transform :cnf
% 60.01/60.15 % Format :tptp:raw
% 60.01/60.16 % Command :java -jar mcs_scs.jar %d %s
% 60.01/60.16
% 60.01/60.16 % Result :Theorem 59.653538s
% 60.01/60.16 % Output :CNFRefutation 59.653538s
% 60.01/60.16 %-------------------------------------------
% 60.01/60.16 %--------------------------------------------------------------------------
% 60.01/60.16 % File : LCL027-1 : TPTP v9.3.1. Released v1.0.0.
% 60.01/60.16 % Domain : Logic Calculi (Implication/Falsehood 2 valued sentential)
% 60.01/60.16 % Problem : C0-4 depends on the Church system
% 60.01/60.16 % Version : [McC92] axioms.
% 60.01/60.16 % English : Axiomatisations for the Implication/Falsehood 2 valued
% 60.01/60.16 % sentential calculus are {C0-1,C0-2,C0-3,C0-4}
% 60.01/60.16 % by Tarski-Bernays, {C0-2,C0-5,C0-6} by Church, and the single
% 60.01/60.16 % Meredith axioms. Show that C0-4 can be derived from the
% 60.01/60.16 % Church system.
% 60.01/60.16
% 60.01/60.16 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 60.01/60.16 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 60.01/60.16 % Source : [McC92]
% 60.01/60.16 % Names : C0-39 [MW92]
% 60.01/60.16
% 60.01/60.16 % Status : Unsatisfiable
% 60.01/60.16 % 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, 0.00 v2.1.0, 0.00 v2.0.0
% 60.01/60.16 % Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 2 RR)
% 60.01/60.16 % Number of literals : 7 ( 0 equ; 3 neg)
% 60.01/60.16 % Maximal clause size : 3 ( 1 avg)
% 60.01/60.16 % Maximal term depth : 4 ( 2 avg)
% 60.01/60.16 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 60.01/60.16 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 60.01/60.16 % Number of variables : 8 ( 1 sgn)
% 60.01/60.16 % SPC : CNF_UNS_RFO_NEQ_HRN
% 60.01/60.16
% 60.01/60.16 % Comments :
% 60.01/60.16 %--------------------------------------------------------------------------
% 60.01/60.16 cnf(condensed_detachment,axiom,
% 60.01/60.16 ( ~ is_a_theorem(implies(X,Y))
% 60.01/60.16 | ~ is_a_theorem(X)
% 60.01/60.16 | is_a_theorem(Y) ) ).
% 60.01/60.16
% 60.01/60.16 cnf(c0_2,axiom,
% 60.01/60.16 is_a_theorem(implies(X,implies(Y,X))) ).
% 60.01/60.16
% 60.01/60.16 cnf(c0_5,axiom,
% 60.01/60.16 is_a_theorem(implies(implies(implies(X,falsehood),falsehood),X)) ).
% 60.01/60.16
% 60.01/60.16 cnf(c0_6,axiom,
% 60.01/60.16 is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
% 60.01/60.16
% 60.01/60.16 cnf(prove_c0_4,negated_conjecture,
% 60.01/60.16 ~ is_a_theorem(implies(falsehood,a)) ).
% 60.01/60.16
% 60.01/60.16 %--------------------------------------------------------------------------
% 60.01/60.16 %-------------------------------------------
% 60.01/60.16 % Proof found
% 60.01/60.16 % SZS status Theorem for theBenchmark
% 60.01/60.16 % SZS output start Proof
% 60.01/60.16 %ClaNum:5(EqnAxiom:0)
% 60.01/60.16 %VarNum:16(SingletonVarNum:8)
% 60.01/60.16 %MaxLitNum:3
% 60.01/60.16 %MaxfuncDepth:3
% 60.01/60.16 %SharedTerms:4
% 60.01/60.16 %goalClause: 4
% 60.01/60.16 %singleGoalClaCount:1
% 60.01/60.16 [4]~P1(f1(a2,a3))
% 60.01/60.16 [2]P1(f1(f1(f1(x21,a2),a2),x21))
% 60.01/60.16 [1]P1(f1(x11,f1(x12,x11)))
% 60.01/60.16 [3]P1(f1(f1(x31,f1(x32,x33)),f1(f1(x31,x32),f1(x31,x33))))
% 60.01/60.16 [5]P1(x51)+~P1(x52)+~P1(f1(x52,x51))
% 60.01/60.16 %EqnAxiom
% 60.01/60.16
% 60.01/60.16 %-------------------------------------------
% 60.01/60.16 cnf(215,plain,
% 60.01/60.16 (P1(f1(x2151,f1(f1(f1(x2152,a2),a2),x2152)))),
% 60.01/60.16 inference(scs_inference,[],[2,1,5])).
% 60.01/60.16 cnf(220,plain,
% 60.01/60.16 (P1(f1(f1(x2201,f1(f1(x2202,a2),a2)),f1(x2201,x2202)))),
% 60.01/60.16 inference(scs_inference,[],[215,3,5])).
% 60.01/60.16 cnf(334,plain,
% 60.01/60.16 ($false),
% 60.01/60.16 inference(scs_inference,[],[220,4,1,5]),
% 60.01/60.16 ['proof']).
% 60.01/60.16 % SZS output end Proof
% 60.01/60.16 % Total time :59.653538s
%------------------------------------------------------------------------------