%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL007-1 : 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 : n005.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 11:18:31 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL007-1 : 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
% 0.06/0.33 % Computer : n005.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Fri Sep 4 17:51:05 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.24/0.50 start to proof:theBenchmark
% 0.24/0.50 %-------------------------------------------
% 0.24/0.50 % File :CSE---1.7
% 0.24/0.50 % Problem :theBenchmark
% 0.24/0.50 % Transform :cnf
% 0.24/0.50 % Format :tptp:raw
% 0.24/0.50 % Command :java -jar mcs_scs.jar %d %s
% 0.24/0.50
% 0.24/0.50 % Result :Theorem 0.002810s
% 0.24/0.50 % Output :CNFRefutation 0.002810s
% 0.24/0.50 %-------------------------------------------
% 0.24/0.50 %--------------------------------------------------------------------------
% 0.24/0.50 % File : LCL007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.24/0.50 % Domain : Logic Calculi (Equivalential)
% 0.24/0.50 % Problem : EC-2 depends on the Wajsberg system
% 0.24/0.50 % Version : [McC92] axioms.
% 0.24/0.50 % English : Two axiomatisations of the equivalential calculus are
% 0.24/0.50 % {EC-1,EC-2} by Lesniewski, and {EC-4,EC-5} by Wajsburg. Show
% 0.24/0.50 % that EC-2 can be derived from the Wajsburg system.
% 0.24/0.50
% 0.24/0.50 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 0.24/0.50 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 0.24/0.50 % Source : [McC92]
% 0.24/0.50 % Names : EC-70 [MW92]
% 0.24/0.50
% 0.24/0.50 % Status : Unsatisfiable
% 0.24/0.50 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.0.0
% 0.24/0.50 % Syntax : Number of clauses : 4 ( 3 unt; 0 nHn; 2 RR)
% 0.24/0.50 % Number of literals : 6 ( 0 equ; 3 neg)
% 0.24/0.50 % Maximal clause size : 3 ( 1 avg)
% 0.24/0.50 % Maximal term depth : 4 ( 2 avg)
% 0.24/0.50 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 0.24/0.50 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 0.24/0.50 % Number of variables : 7 ( 0 sgn)
% 0.24/0.50 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.24/0.50
% 0.24/0.50 % Comments :
% 0.24/0.50 %--------------------------------------------------------------------------
% 0.24/0.50 cnf(condensed_detachment,axiom,
% 0.24/0.50 ( ~ is_a_theorem(equivalent(X,Y))
% 0.24/0.50 | ~ is_a_theorem(X)
% 0.24/0.50 | is_a_theorem(Y) ) ).
% 0.24/0.50
% 0.24/0.50 %----Axiom of symmetry
% 0.24/0.50 cnf(ec_4,axiom,
% 0.24/0.50 is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))) ).
% 0.24/0.50
% 0.24/0.50 %----Axiom of associativity
% 0.24/0.50 cnf(ec_5,axiom,
% 0.24/0.50 is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z)))) ).
% 0.24/0.50
% 0.24/0.50 cnf(prove_ec_2,negated_conjecture,
% 0.24/0.51 ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))) ).
% 0.24/0.51
% 0.24/0.51 %--------------------------------------------------------------------------
% 0.24/0.51 %-------------------------------------------
% 0.24/0.51 % Proof found
% 0.24/0.51 % SZS status Theorem for theBenchmark
% 0.24/0.51 % SZS output start Proof
% 0.24/0.51 %ClaNum:4(EqnAxiom:0)
% 0.24/0.51 %VarNum:14(SingletonVarNum:7)
% 0.24/0.51 %MaxLitNum:3
% 0.24/0.51 %MaxfuncDepth:3
% 0.24/0.51 %SharedTerms:9
% 0.24/0.51 %goalClause: 3
% 0.24/0.51 %singleGoalClaCount:1
% 0.24/0.51 [3]~P1(f1(f1(a2,f1(a3,a4)),f1(f1(a2,a3),a4)))
% 0.24/0.51 [1]P1(f1(f1(x11,x12),f1(x12,x11)))
% 0.24/0.51 [2]P1(f1(f1(f1(x21,x22),x23),f1(x21,f1(x22,x23))))
% 0.24/0.51 [4]P1(x41)+~P1(x42)+~P1(f1(x42,x41))
% 0.24/0.51 %EqnAxiom
% 0.24/0.51
% 0.24/0.51 %-------------------------------------------
% 0.24/0.51 cnf(5,plain,
% 0.24/0.51 ($false),
% 0.24/0.51 inference(scs_inference,[],[3,1,2,4]),
% 0.24/0.51 ['proof']).
% 0.24/0.51 % SZS output end Proof
% 0.24/0.51 % Total time :0.002810s
%------------------------------------------------------------------------------