%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:41:39 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.35s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 16 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(ec_4,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))) ).
cnf(ec_5,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z)))) ).
cnf(prove_ec_2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X)))
| is_a_theorem(equivalent(Y,X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(Y,X)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(Y,X)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))) )],[ec_4,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(equivalent(X,Y),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(equivalent(X,Y),Z))),bind(Y,$fot(equivalent(X,equivalent(Y,Z))))]]) ).
cnf(refute_0_3,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(equivalent(X,Y),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z)))) )],[ec_5,refute_0_2]) ).
cnf(refute_0_4,plain,
is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
inference(subst,[],[refute_0_3:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).
cnf(refute_0_5,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))) )],[refute_0_4,prove_ec_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.08/0.34 % Computer : n027.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 17:54:12 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.08/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35
% 0.08/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.08/0.35
%------------------------------------------------------------------------------