%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL363-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %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 12:42:30 PM UTC 2026
% Result : Unsatisfiable 0.65s 0.97s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 51 ( 30 unt; 0 nHn; 14 RR)
% Number of literals : 78 ( 0 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 118 ( 24 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(cn_2,axiom,
is_a_theorem(implies(implies(not(X),X),X)) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) ).
cnf(prove_cn_12,negated_conjecture,
~ is_a_theorem(implies(x,implies(implies(not(y),y),y))) ).
cnf(refute_0_0,plain,
is_a_theorem(implies(implies(not(X_24),X_24),X_24)),
inference(subst,[],[cn_2:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(not(X_24),X_24),X_24))
| is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_24),X_24))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_24),X_24),X_24)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(X_1034,X_1034),implies(implies(not(X_1034),X_1034),X_1034))),
inference(subst,[],[refute_0_4:[bind(X_24,$fot(X_1034)),bind(X_25,$fot(X_1034))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(X_827,X_827),X_829))
| ~ is_a_theorem(implies(implies(implies(X_827,X_827),X_829),implies(X_828,X_829)))
| is_a_theorem(implies(X_828,X_829)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_827,X_827),X_829))),bind(Y,$fot(implies(X_828,X_829)))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(X_192,implies(not(implies(X_191,X_191)),X_190)))
| is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),X_190),Z),implies(X_192,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_192)),bind(Y,$fot(implies(not(implies(X_191,X_191)),X_190)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_27),X_26),X_28),implies(X_27,X_28)))
| ~ is_a_theorem(implies(implies(not(X_27),X_26),X_28))
| is_a_theorem(implies(X_27,X_28)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_27),X_26),X_28))),bind(Y,$fot(implies(X_27,X_28)))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(X_23,implies(not(X_23),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(X_23,implies(not(X_23),Y)))
| is_a_theorem(implies(implies(implies(not(X_23),Y),X_25),implies(X_23,X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_23)),bind(Y,$fot(implies(not(X_23),Y))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(not(X_23),Y),X_25),implies(X_23,X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(X_23,implies(not(X_23),Y))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(not(X_27),X_26),X_28),implies(X_27,X_28))),
inference(subst,[],[refute_0_11:[bind(Y,$fot(X_26)),bind(X_23,$fot(X_27)),bind(X_25,$fot(X_28))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(not(X_27),X_26),X_28))
| is_a_theorem(implies(X_27,X_28)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_27),X_26),X_28),implies(X_27,X_28))) )],[refute_0_12,refute_0_8]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(not(X_27),X_187),implies(not(implies(X_189,X_189)),X_187)))
| is_a_theorem(implies(X_27,implies(not(implies(X_189,X_189)),X_187))) ),
inference(subst,[],[refute_0_13:[bind(X_26,$fot(X_187)),bind(X_28,$fot(implies(not(implies(X_189,X_189)),X_187)))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(not(implies(X_170,X_170)),X_169))
| is_a_theorem(implies(implies(X_169,Z),implies(not(implies(X_170,X_170)),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(X_170,X_170)))),bind(Y,$fot(X_169))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(X_168,X_168))
| is_a_theorem(implies(not(implies(X_168,X_168)),Y)) ),
inference(subst,[],[refute_0_18:[bind(X_6,$fot(implies(X_168,X_168)))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(not(X_167),X_167),X_167)),
inference(subst,[],[cn_2:[bind(X,$fot(X_167))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(not(X_167),X_167),X_167))
| is_a_theorem(implies(X_167,X_167)) ),
inference(subst,[],[refute_0_13:[bind(X_26,$fot(X_167)),bind(X_27,$fot(X_167)),bind(X_28,$fot(X_167))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(X_167,X_167)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_167),X_167),X_167)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(X_168,X_168)),
inference(subst,[],[refute_0_22:[bind(X_167,$fot(X_168))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(not(implies(X_168,X_168)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_168,X_168)) )],[refute_0_23,refute_0_19]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(not(implies(X_170,X_170)),X_169)),
inference(subst,[],[refute_0_24:[bind(Y,$fot(X_169)),bind(X_168,$fot(X_170))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(X_169,Z),implies(not(implies(X_170,X_170)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_170,X_170)),X_169)) )],[refute_0_25,refute_0_15]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(not(X_27),X_187),implies(not(implies(X_189,X_189)),X_187))),
inference(subst,[],[refute_0_26:[bind(Z,$fot(X_187)),bind(X_169,$fot(not(X_27))),bind(X_170,$fot(X_189))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(X_27,implies(not(implies(X_189,X_189)),X_187))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_27),X_187),implies(not(implies(X_189,X_189)),X_187))) )],[refute_0_27,refute_0_14]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(X_192,implies(not(implies(X_191,X_191)),X_190))),
inference(subst,[],[refute_0_28:[bind(X_187,$fot(X_190)),bind(X_189,$fot(X_191)),bind(X_27,$fot(X_192))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),X_190),Z),implies(X_192,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_192,implies(not(implies(X_191,X_191)),X_190))) )],[refute_0_29,refute_0_7]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),implies(X_191,X_191)),X_826),implies(X_192,X_826))),
inference(subst,[],[refute_0_30:[bind(Z,$fot(X_826)),bind(X_190,$fot(implies(X_191,X_191)))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53)))
| ~ is_a_theorem(implies(implies(implies(not(X_54),X_54),X_55),X_53))
| is_a_theorem(implies(implies(X_54,X_55),X_53)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_54),X_54),X_55),X_53))),bind(Y,$fot(implies(implies(X_54,X_55),X_53)))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(X_29,X_30),implies(implies(not(X_29),X_29),X_30)))
| is_a_theorem(implies(implies(implies(implies(not(X_29),X_29),X_30),Z),implies(implies(X_29,X_30),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_29,X_30))),bind(Y,$fot(implies(implies(not(X_29),X_29),X_30)))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(X_29,X_30),implies(implies(not(X_29),X_29),X_30))),
inference(subst,[],[refute_0_4:[bind(X_24,$fot(X_29)),bind(X_25,$fot(X_30))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(implies(implies(implies(not(X_29),X_29),X_30),Z),implies(implies(X_29,X_30),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_29,X_30),implies(implies(not(X_29),X_29),X_30))) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53))),
inference(subst,[],[refute_0_35:[bind(Z,$fot(X_53)),bind(X_29,$fot(X_54)),bind(X_30,$fot(X_55))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_54),X_54),X_55),X_53))
| is_a_theorem(implies(implies(X_54,X_55),X_53)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53))) )],[refute_0_36,refute_0_32]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),implies(X_191,X_191)),X_826),implies(X_192,X_826)))
| is_a_theorem(implies(implies(implies(X_191,X_191),X_826),implies(X_192,X_826))) ),
inference(subst,[],[refute_0_37:[bind(X_53,$fot(implies(X_192,X_826))),bind(X_54,$fot(implies(X_191,X_191))),bind(X_55,$fot(X_826))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(X_191,X_191),X_826),implies(X_192,X_826))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),implies(X_191,X_191)),X_826),implies(X_192,X_826))) )],[refute_0_31,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(X_827,X_827),X_829),implies(X_828,X_829))),
inference(subst,[],[refute_0_39:[bind(X_191,$fot(X_827)),bind(X_192,$fot(X_828)),bind(X_826,$fot(X_829))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(X_827,X_827),X_829))
| is_a_theorem(implies(X_828,X_829)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_827,X_827),X_829),implies(X_828,X_829))) )],[refute_0_40,refute_0_6]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(X_1034,X_1034),implies(implies(not(X_1034),X_1034),X_1034)))
| is_a_theorem(implies(X_1035,implies(implies(not(X_1034),X_1034),X_1034))) ),
inference(subst,[],[refute_0_41:[bind(X_827,$fot(X_1034)),bind(X_828,$fot(X_1035)),bind(X_829,$fot(implies(implies(not(X_1034),X_1034),X_1034)))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(X_1035,implies(implies(not(X_1034),X_1034),X_1034))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1034,X_1034),implies(implies(not(X_1034),X_1034),X_1034))) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(x,implies(implies(not(y),y),y))),
inference(subst,[],[refute_0_43:[bind(X_1034,$fot(y)),bind(X_1035,$fot(x))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(x,implies(implies(not(y),y),y))) )],[refute_0_44,prove_cn_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL363-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n005.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 01:10:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.65/0.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.65/0.97
% 0.65/0.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.65/0.99
%------------------------------------------------------------------------------