%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL041-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:41:42 PM UTC 2026
% Result : Unsatisfiable 0.47s 0.73s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 21 ( 13 unt; 0 nHn; 11 RR)
% Number of literals : 32 ( 0 equ; 12 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) ).
cnf(cn_21,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))) ).
cnf(cn_54,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))) ).
cnf(prove_cn_30,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))) ).
cnf(refute_0_0,plain,
is_a_theorem(implies(X_86,implies(not(X_86),X_88))),
inference(subst,[],[cn_3:[bind(X,$fot(X_86)),bind(Y,$fot(X_88))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| ~ is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z))))
| is_a_theorem(implies(Y,implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,implies(Y,Z)))),bind(Y,$fot(implies(Y,implies(X,Z))))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| is_a_theorem(implies(Y,implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))) )],[cn_21,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X_86,implies(not(X_86),X_88)))
| is_a_theorem(implies(not(X_86),implies(X_86,X_88))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_86)),bind(Y,$fot(not(X_86))),bind(Z,$fot(X_88))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(not(X_86),implies(X_86,X_88))),
inference(resolve,[$cnf( is_a_theorem(implies(X_86,implies(not(X_86),X_88))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(not(X_562),implies(X_562,X_88))),
inference(subst,[],[refute_0_4:[bind(X_86,$fot(X_562))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(not(X_96),X_97),implies(implies(X_96,X_97),X_97)))
| ~ is_a_theorem(implies(not(X_96),X_97))
| is_a_theorem(implies(implies(X_96,X_97),X_97)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_96),X_97))),bind(Y,$fot(implies(implies(X_96,X_97),X_97)))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(X,X_88),implies(implies(not(X),X_88),X_88))),
inference(subst,[],[cn_54:[bind(Y,$fot(X_88))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(X,X_88),implies(implies(not(X),X_88),X_88)))
| is_a_theorem(implies(implies(not(X),X_88),implies(implies(X,X_88),X_88))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,X_88))),bind(Y,$fot(implies(not(X),X_88))),bind(Z,$fot(X_88))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(not(X),X_88),implies(implies(X,X_88),X_88))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X_88),implies(implies(not(X),X_88),X_88))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(not(X_96),X_97),implies(implies(X_96,X_97),X_97))),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_96)),bind(X_88,$fot(X_97))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(not(X_96),X_97))
| is_a_theorem(implies(implies(X_96,X_97),X_97)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_96),X_97),implies(implies(X_96,X_97),X_97))) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(not(X_562),implies(X_562,X_88)))
| is_a_theorem(implies(implies(X_562,implies(X_562,X_88)),implies(X_562,X_88))) ),
inference(subst,[],[refute_0_11:[bind(X_96,$fot(X_562)),bind(X_97,$fot(implies(X_562,X_88)))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(X_562,implies(X_562,X_88)),implies(X_562,X_88))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_562),implies(X_562,X_88))) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))),
inference(subst,[],[refute_0_13:[bind(X_562,$fot(a)),bind(X_88,$fot(b))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))) )],[refute_0_14,prove_cn_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 08:35:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.73
% 0.47/0.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.73
%------------------------------------------------------------------------------