%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL356-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:42:29 PM UTC 2026
% Result : Unsatisfiable 2.16s 2.48s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 15 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 25 ( 0 equ; 11 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(prove_cn_05,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(u,y),implies(x,implies(u,z))))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_25),implies(implies(X,Y),X_25))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_3,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_25),implies(implies(X,Y),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_2]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X_1490,implies(X,Z))),implies(implies(X,Y),implies(X_1490,implies(X,Z))))),
inference(subst,[],[refute_0_3:[bind(X_25,$fot(implies(X_1490,implies(X,Z))))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(X_84,X_85),implies(X_83,X_85)),X_86))
| ~ is_a_theorem(implies(implies(implies(implies(X_84,X_85),implies(X_83,X_85)),X_86),implies(implies(X_83,X_84),X_86)))
| is_a_theorem(implies(implies(X_83,X_84),X_86)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_84,X_85),implies(X_83,X_85)),X_86))),bind(Y,$fot(implies(implies(X_83,X_84),X_86)))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(implies(X_84,X_85),implies(X_83,X_85)),X_86),implies(implies(X_83,X_84),X_86))),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_83)),bind(Y,$fot(X_84)),bind(Z,$fot(X_85)),bind(X_25,$fot(X_86))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(X_84,X_85),implies(X_83,X_85)),X_86))
| is_a_theorem(implies(implies(X_83,X_84),X_86)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_84,X_85),implies(X_83,X_85)),X_86),implies(implies(X_83,X_84),X_86))) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X_1490,implies(X,Z))),implies(implies(X,Y),implies(X_1490,implies(X,Z)))))
| is_a_theorem(implies(implies(X_1490,implies(Y,Z)),implies(implies(X,Y),implies(X_1490,implies(X,Z))))) ),
inference(subst,[],[refute_0_7:[bind(X_83,$fot(X_1490)),bind(X_84,$fot(implies(Y,Z))),bind(X_85,$fot(implies(X,Z))),bind(X_86,$fot(implies(implies(X,Y),implies(X_1490,implies(X,Z)))))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(X_1490,implies(Y,Z)),implies(implies(X,Y),implies(X_1490,implies(X,Z))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X_1490,implies(X,Z))),implies(implies(X,Y),implies(X_1490,implies(X,Z))))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(u,y),implies(x,implies(u,z))))),
inference(subst,[],[refute_0_9:[bind(X,$fot(u)),bind(Y,$fot(y)),bind(Z,$fot(z)),bind(X_1490,$fot(x))]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(u,y),implies(x,implies(u,z))))) )],[refute_0_10,prove_cn_05]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL356-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n026.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 : Sat Sep 5 09:20:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.16/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.16/2.48
% 2.16/2.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.16/2.49
%------------------------------------------------------------------------------