%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 12:41:47 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 17 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
cnf(extra_lemma,axiom,
is_a_theorem(implies(not(not(X1)),X1)) ).
cnf(prove_cn_40,negated_conjecture,
~ is_a_theorem(implies(a,not(not(a)))) ).
cnf(refute_0_0,plain,
is_a_theorem(implies(not(not(not(X_23))),not(X_23))),
inference(subst,[],[extra_lemma:[bind(X1,$fot(not(X_23)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(not(not(not(X_23))),not(X_23)))
| is_a_theorem(implies(X_23,not(not(X_23)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(not(X_23)))),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(X_23,not(not(X_23)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(X_23))),not(X_23))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(a,not(not(a)))),
inference(subst,[],[refute_0_4:[bind(X_23,$fot(a))]]) ).
cnf(refute_0_6,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,not(not(a)))) )],[refute_0_5,prove_cn_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 4 19:42:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------