%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL384+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:42:34 PM UTC 2026
% Result : Theorem 1.65s 1.90s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 5
% Syntax : Number of formulae : 117 ( 72 unt; 0 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 115 ( 58 ~; 55 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 281 ( 39 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ).
fof(cn_1,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
fof(cn_2,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)) ).
fof(cn_3,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))) ).
fof(prove_cn_45,conjecture,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))) ).
fof(subgoal_0,plain,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
inference(strip,[],[prove_cn_45]) ).
fof(negate_0_0,plain,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(canonicalize,[],[condensed_detachment]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(canonicalize,[],[cn_1]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(canonicalize,[],[cn_3]) ).
fof(normalize_0_6,plain,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
inference(canonicalize,[],[cn_2]) ).
fof(normalize_0_8,plain,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
inference(specialize,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(implies(X_39,X_40),implies(X_38,X_40)),X_41))
| ~ is_a_theorem(implies(implies(implies(implies(X_39,X_40),implies(X_38,X_40)),X_41),implies(implies(X_38,X_39),X_41)))
| is_a_theorem(implies(implies(X_38,X_39),X_41)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(implies(X_39,X_40),implies(X_38,X_40)),X_41))),bind(Y,$fot(implies(implies(X_38,X_39),X_41)))]]) ).
cnf(refute_0_3,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_4,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,[],[refute_0_1:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(implies(X_39,X_40),implies(X_38,X_40)),X_41),implies(implies(X_38,X_39),X_41))),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X_40)),bind(X_29,$fot(X_41))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(X_39,X_40),implies(X_38,X_40)),X_41))
| is_a_theorem(implies(implies(X_38,X_39),X_41)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_39,X_40),implies(X_38,X_40)),X_41),implies(implies(X_38,X_39),X_41))) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_2782,X_2781),X_2781),implies(X_38,X_2781)),implies(implies(not(X_2781),X_2782),implies(X_38,X_2781))))
| is_a_theorem(implies(implies(X_38,implies(X_2782,X_2781)),implies(implies(not(X_2781),X_2782),implies(X_38,X_2781)))) ),
inference(subst,[],[refute_0_9:[bind(X_39,$fot(implies(X_2782,X_2781))),bind(X_40,$fot(X_2781)),bind(X_41,$fot(implies(implies(not(X_2781),X_2782),implies(X_38,X_2781))))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(not(X_2358),X_2359),implies(implies(X_2359,X_2358),X_2358)))
| is_a_theorem(implies(implies(implies(implies(X_2359,X_2358),X_2358),Z),implies(implies(not(X_2358),X_2359),Z))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(not(X_2358),X_2359))),bind(Y,$fot(implies(implies(X_2359,X_2358),X_2358)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(X_39,X_2344),implies(not(X_2344),X_2344)),implies(implies(X_39,X_2344),X_2344)))
| is_a_theorem(implies(implies(not(X_2344),X_39),implies(implies(X_39,X_2344),X_2344))) ),
inference(subst,[],[refute_0_9:[bind(X_38,$fot(not(X_2344))),bind(X_40,$fot(X_2344)),bind(X_41,$fot(implies(implies(X_39,X_2344),X_2344)))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_31),X_30),X_32),implies(X_31,X_32)))
| ~ is_a_theorem(implies(implies(not(X_31),X_30),X_32))
| is_a_theorem(implies(X_31,X_32)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(not(X_31),X_30),X_32))),bind(Y,$fot(implies(X_31,X_32)))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(X,implies(not(X),Y))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(X_27,implies(not(X_27),Y))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(X_27,implies(not(X_27),Y)))
| is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_27)),bind(Y,$fot(implies(not(X_27),Y))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(X_27,implies(not(X_27),Y))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(implies(not(X_31),X_30),X_32),implies(X_31,X_32))),
inference(subst,[],[refute_0_17:[bind(Y,$fot(X_30)),bind(X_27,$fot(X_31)),bind(X_29,$fot(X_32))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(not(X_31),X_30),X_32))
| is_a_theorem(implies(X_31,X_32)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_31),X_30),X_32),implies(X_31,X_32))) )],[refute_0_18,refute_0_13]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561)),implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561)),X_1561))
| is_a_theorem(implies(implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561),X_1561)) ),
inference(subst,[],[refute_0_19:[bind(X_30,$fot(implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561))),bind(X_31,$fot(implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561))),bind(X_32,$fot(X_1561))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_97,X_98)),implies(X_97,X_98)),implies(implies(not(X_97),X_97),X_98)))
| ~ is_a_theorem(implies(not(implies(X_97,X_98)),implies(X_97,X_98)))
| is_a_theorem(implies(implies(not(X_97),X_97),X_98)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(not(implies(X_97,X_98)),implies(X_97,X_98)))),bind(Y,$fot(implies(implies(not(X_97),X_97),X_98)))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(not(X),X),X)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(not(X_28),X_28),X_28)),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(not(X_28),X_28),X_28))
| is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(not(X_28),X_28))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_28),X_28),X_28)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(X_33,X_34))
| ~ is_a_theorem(implies(implies(X_33,X_34),implies(implies(not(X_33),X_33),X_34)))
| is_a_theorem(implies(implies(not(X_33),X_33),X_34)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X_33,X_34))),bind(Y,$fot(implies(implies(not(X_33),X_33),X_34)))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(X_33,X_34),implies(implies(not(X_33),X_33),X_34))),
inference(subst,[],[refute_0_25:[bind(X_28,$fot(X_33)),bind(X_29,$fot(X_34))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(X_33,X_34))
| is_a_theorem(implies(implies(not(X_33),X_33),X_34)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_33,X_34),implies(implies(not(X_33),X_33),X_34))) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29)))
| is_a_theorem(implies(implies(not(implies(X_28,X_29)),implies(X_28,X_29)),implies(implies(not(X_28),X_28),X_29))) ),
inference(subst,[],[refute_0_28:[bind(X_33,$fot(implies(X_28,X_29))),bind(X_34,$fot(implies(implies(not(X_28),X_28),X_29)))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(not(implies(X_28,X_29)),implies(X_28,X_29)),implies(implies(not(X_28),X_28),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(not(implies(X_97,X_98)),implies(X_97,X_98)),implies(implies(not(X_97),X_97),X_98))),
inference(subst,[],[refute_0_30:[bind(X_28,$fot(X_97)),bind(X_29,$fot(X_98))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(not(implies(X_97,X_98)),implies(X_97,X_98)))
| is_a_theorem(implies(implies(not(X_97),X_97),X_98)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(X_97,X_98)),implies(X_97,X_98)),implies(implies(not(X_97),X_97),X_98))) )],[refute_0_31,refute_0_21]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541),X_1541)),implies(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541),X_1541)))
| is_a_theorem(implies(implies(not(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541)),implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541)),X_1541)) ),
inference(subst,[],[refute_0_32:[bind(X_97,$fot(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541))),bind(X_98,$fot(X_1541))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_36),X_36),X_37),X_35),implies(implies(X_36,X_37),X_35)))
| ~ is_a_theorem(implies(implies(implies(not(X_36),X_36),X_37),X_35))
| is_a_theorem(implies(implies(X_36,X_37),X_35)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(implies(not(X_36),X_36),X_37),X_35))),bind(Y,$fot(implies(implies(X_36,X_37),X_35)))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(X_33,X_34),implies(implies(not(X_33),X_33),X_34)))
| is_a_theorem(implies(implies(implies(implies(not(X_33),X_33),X_34),Z),implies(implies(X_33,X_34),Z))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_33,X_34))),bind(Y,$fot(implies(implies(not(X_33),X_33),X_34)))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(implies(implies(not(X_33),X_33),X_34),Z),implies(implies(X_33,X_34),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_33,X_34),implies(implies(not(X_33),X_33),X_34))) )],[refute_0_27,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(implies(implies(not(X_36),X_36),X_37),X_35),implies(implies(X_36,X_37),X_35))),
inference(subst,[],[refute_0_36:[bind(Z,$fot(X_35)),bind(X_33,$fot(X_36)),bind(X_34,$fot(X_37))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_36),X_36),X_37),X_35))
| is_a_theorem(implies(implies(X_36,X_37),X_35)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_36),X_36),X_37),X_35),implies(implies(X_36,X_37),X_35))) )],[refute_0_37,refute_0_34]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_873),X_873),X_870),implies(implies(implies(implies(not(X_871),X_871),X_871),X_873),X_870)))
| is_a_theorem(implies(implies(X_873,X_870),implies(implies(implies(implies(not(X_871),X_871),X_871),X_873),X_870))) ),
inference(subst,[],[refute_0_38:[bind(X_35,$fot(implies(implies(implies(implies(not(X_871),X_871),X_871),X_873),X_870))),bind(X_36,$fot(X_873)),bind(X_37,$fot(X_870))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_835),X_835),X_835),X_837),implies(X_836,X_837)))
| is_a_theorem(implies(implies(implies(X_836,X_837),Z),implies(implies(implies(implies(not(X_835),X_835),X_835),X_837),Z))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(implies(implies(not(X_835),X_835),X_835),X_837))),bind(Y,$fot(implies(X_836,X_837)))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(X_180,implies(not(implies(implies(not(X_178),X_178),X_178)),X_179)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_178),X_178),X_178)),X_179),Z),implies(X_180,Z))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_180)),bind(Y,$fot(implies(not(implies(implies(not(X_178),X_178),X_178)),X_179)))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_44:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[refute_0_22,refute_0_45]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_28)),
inference(subst,[],[refute_0_46:[bind(X_9,$fot(X_28))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_28))
| is_a_theorem(implies(implies(X_28,X_29),implies(not(implies(implies(not(X),X),X)),X_29))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(not(implies(implies(not(X),X),X)),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_28)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(not(X_162),X_161),implies(not(implies(implies(not(X),X),X)),X_161))),
inference(subst,[],[refute_0_49:[bind(X_28,$fot(not(X_162))),bind(X_29,$fot(X_161))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(not(X_162),X_161),implies(not(implies(implies(not(X),X),X)),X_161)))
| is_a_theorem(implies(X_162,implies(not(implies(implies(not(X),X),X)),X_161))) ),
inference(subst,[],[refute_0_19:[bind(X_30,$fot(X_161)),bind(X_31,$fot(X_162)),bind(X_32,$fot(implies(not(implies(implies(not(X),X),X)),X_161)))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(X_162,implies(not(implies(implies(not(X),X),X)),X_161))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_162),X_161),implies(not(implies(implies(not(X),X),X)),X_161))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_180,implies(not(implies(implies(not(X_178),X_178),X_178)),X_179))),
inference(subst,[],[refute_0_52:[bind(X,$fot(X_178)),bind(X_161,$fot(X_179)),bind(X_162,$fot(X_180))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_178),X_178),X_178)),X_179),Z),implies(X_180,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_180,implies(not(implies(implies(not(X_178),X_178),X_178)),X_179))) )],[refute_0_53,refute_0_41]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_178),X_178),X_178)),implies(implies(not(X_178),X_178),X_178)),X_817),implies(X_180,X_817))),
inference(subst,[],[refute_0_54:[bind(Z,$fot(X_817)),bind(X_179,$fot(implies(implies(not(X_178),X_178),X_178)))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_178),X_178),X_178)),implies(implies(not(X_178),X_178),X_178)),X_817),implies(X_180,X_817)))
| is_a_theorem(implies(implies(implies(implies(not(X_178),X_178),X_178),X_817),implies(X_180,X_817))) ),
inference(subst,[],[refute_0_38:[bind(X_35,$fot(implies(X_180,X_817))),bind(X_36,$fot(implies(implies(not(X_178),X_178),X_178))),bind(X_37,$fot(X_817))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(implies(implies(not(X_178),X_178),X_178),X_817),implies(X_180,X_817))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_178),X_178),X_178)),implies(implies(not(X_178),X_178),X_178)),X_817),implies(X_180,X_817))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(implies(not(X_835),X_835),X_835),X_837),implies(X_836,X_837))),
inference(subst,[],[refute_0_57:[bind(X_178,$fot(X_835)),bind(X_180,$fot(X_836)),bind(X_817,$fot(X_837))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(implies(implies(X_836,X_837),Z),implies(implies(implies(implies(not(X_835),X_835),X_835),X_837),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_835),X_835),X_835),X_837),implies(X_836,X_837))) )],[refute_0_58,refute_0_40]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(not(X_873),X_873),X_870),implies(implies(implies(implies(not(X_871),X_871),X_871),X_873),X_870))),
inference(subst,[],[refute_0_59:[bind(Z,$fot(X_870)),bind(X_835,$fot(X_871)),bind(X_836,$fot(not(X_873))),bind(X_837,$fot(X_873))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(X_873,X_870),implies(implies(implies(implies(not(X_871),X_871),X_871),X_873),X_870))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_873),X_873),X_870),implies(implies(implies(implies(not(X_871),X_871),X_871),X_873),X_870))) )],[refute_0_60,refute_0_39]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(X_1457,X_1457),implies(implies(implies(implies(not(X_871),X_871),X_871),X_1457),X_1457))),
inference(subst,[],[refute_0_61:[bind(X_870,$fot(X_1457)),bind(X_873,$fot(X_1457))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(X_818,X_818),X_820))
| ~ is_a_theorem(implies(implies(implies(X_818,X_818),X_820),implies(X_819,X_820)))
| is_a_theorem(implies(X_819,X_820)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(X_818,X_818),X_820))),bind(Y,$fot(implies(X_819,X_820)))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(X_192,implies(not(implies(X_191,X_191)),X_190)))
| is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),X_190),Z),implies(X_192,Z))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_192)),bind(Y,$fot(implies(not(implies(X_191,X_191)),X_190)))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(not(X_31),X_169),implies(not(implies(X_171,X_171)),X_169)))
| is_a_theorem(implies(X_31,implies(not(implies(X_171,X_171)),X_169))) ),
inference(subst,[],[refute_0_19:[bind(X_30,$fot(X_169)),bind(X_32,$fot(implies(not(implies(X_171,X_171)),X_169)))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(not(implies(X_166,X_166)),X_165))
| is_a_theorem(implies(implies(X_165,Z),implies(not(implies(X_166,X_166)),Z))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(not(implies(X_166,X_166)))),bind(Y,$fot(X_165))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(X_164,X_164))
| is_a_theorem(implies(not(implies(X_164,X_164)),Y)) ),
inference(subst,[],[refute_0_44:[bind(X_6,$fot(implies(X_164,X_164)))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(not(X_163),X_163),X_163)),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_163))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(implies(not(X_163),X_163),X_163))
| is_a_theorem(implies(X_163,X_163)) ),
inference(subst,[],[refute_0_19:[bind(X_30,$fot(X_163)),bind(X_31,$fot(X_163)),bind(X_32,$fot(X_163))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(X_163,X_163)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_163),X_163),X_163)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(X_164,X_164)),
inference(subst,[],[refute_0_70:[bind(X_163,$fot(X_164))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(not(implies(X_164,X_164)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_164,X_164)) )],[refute_0_71,refute_0_67]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(not(implies(X_166,X_166)),X_165)),
inference(subst,[],[refute_0_72:[bind(Y,$fot(X_165)),bind(X_164,$fot(X_166))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(X_165,Z),implies(not(implies(X_166,X_166)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_166,X_166)),X_165)) )],[refute_0_73,refute_0_66]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(not(X_31),X_169),implies(not(implies(X_171,X_171)),X_169))),
inference(subst,[],[refute_0_74:[bind(Z,$fot(X_169)),bind(X_165,$fot(not(X_31))),bind(X_166,$fot(X_171))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(X_31,implies(not(implies(X_171,X_171)),X_169))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_31),X_169),implies(not(implies(X_171,X_171)),X_169))) )],[refute_0_75,refute_0_65]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(X_192,implies(not(implies(X_191,X_191)),X_190))),
inference(subst,[],[refute_0_76:[bind(X_169,$fot(X_190)),bind(X_171,$fot(X_191)),bind(X_31,$fot(X_192))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),X_190),Z),implies(X_192,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_192,implies(not(implies(X_191,X_191)),X_190))) )],[refute_0_77,refute_0_64]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),implies(X_191,X_191)),X_817),implies(X_192,X_817))),
inference(subst,[],[refute_0_78:[bind(Z,$fot(X_817)),bind(X_190,$fot(implies(X_191,X_191)))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),implies(X_191,X_191)),X_817),implies(X_192,X_817)))
| is_a_theorem(implies(implies(implies(X_191,X_191),X_817),implies(X_192,X_817))) ),
inference(subst,[],[refute_0_38:[bind(X_35,$fot(implies(X_192,X_817))),bind(X_36,$fot(implies(X_191,X_191))),bind(X_37,$fot(X_817))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(implies(X_191,X_191),X_817),implies(X_192,X_817))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_191,X_191)),implies(X_191,X_191)),X_817),implies(X_192,X_817))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(implies(X_818,X_818),X_820),implies(X_819,X_820))),
inference(subst,[],[refute_0_81:[bind(X_191,$fot(X_818)),bind(X_192,$fot(X_819)),bind(X_817,$fot(X_820))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(implies(X_818,X_818),X_820))
| is_a_theorem(implies(X_819,X_820)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_818,X_818),X_820),implies(X_819,X_820))) )],[refute_0_82,refute_0_63]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(X_1457,X_1457),implies(implies(implies(implies(not(X_871),X_871),X_871),X_1457),X_1457)))
| is_a_theorem(implies(X_1458,implies(implies(implies(implies(not(X_871),X_871),X_871),X_1457),X_1457))) ),
inference(subst,[],[refute_0_83:[bind(X_818,$fot(X_1457)),bind(X_819,$fot(X_1458)),bind(X_820,$fot(implies(implies(implies(implies(not(X_871),X_871),X_871),X_1457),X_1457)))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(X_1458,implies(implies(implies(implies(not(X_871),X_871),X_871),X_1457),X_1457))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1457,X_1457),implies(implies(implies(implies(not(X_871),X_871),X_871),X_1457),X_1457))) )],[refute_0_62,refute_0_84]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541),X_1541)),implies(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541),X_1541))),
inference(subst,[],[refute_0_85:[bind(X_1457,$fot(X_1541)),bind(X_1458,$fot(not(implies(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541),X_1541)))),bind(X_871,$fot(X_1543))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(implies(not(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541)),implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541)),X_1541)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541),X_1541)),implies(implies(implies(implies(not(X_1543),X_1543),X_1543),X_1541),X_1541))) )],[refute_0_86,refute_0_33]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(implies(not(implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561)),implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561)),X_1561)),
inference(subst,[],[refute_0_87:[bind(X_1541,$fot(X_1561)),bind(X_1543,$fot(X_1562))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561),X_1561)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561)),implies(implies(implies(not(X_1562),X_1562),X_1562),X_1561)),X_1561)) )],[refute_0_88,refute_0_20]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(implies(implies(not(X_2340),X_2340),X_2340),implies(X_2338,X_2340)),implies(X_2338,X_2340))),
inference(subst,[],[refute_0_89:[bind(X_1561,$fot(implies(X_2338,X_2340))),bind(X_1562,$fot(X_2340))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_2340),X_2340),X_2340),implies(X_2338,X_2340)),implies(X_2338,X_2340)))
| is_a_theorem(implies(implies(X_2338,implies(not(X_2340),X_2340)),implies(X_2338,X_2340))) ),
inference(subst,[],[refute_0_9:[bind(X_38,$fot(X_2338)),bind(X_39,$fot(implies(not(X_2340),X_2340))),bind(X_40,$fot(X_2340)),bind(X_41,$fot(implies(X_2338,X_2340)))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(X_2338,implies(not(X_2340),X_2340)),implies(X_2338,X_2340))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_2340),X_2340),X_2340),implies(X_2338,X_2340)),implies(X_2338,X_2340))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(implies(X_39,X_2344),implies(not(X_2344),X_2344)),implies(implies(X_39,X_2344),X_2344))),
inference(subst,[],[refute_0_92:[bind(X_2338,$fot(implies(X_39,X_2344))),bind(X_2340,$fot(X_2344))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(not(X_2344),X_39),implies(implies(X_39,X_2344),X_2344))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_39,X_2344),implies(not(X_2344),X_2344)),implies(implies(X_39,X_2344),X_2344))) )],[refute_0_93,refute_0_12]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(implies(not(X_2358),X_2359),implies(implies(X_2359,X_2358),X_2358))),
inference(subst,[],[refute_0_94:[bind(X_2344,$fot(X_2358)),bind(X_39,$fot(X_2359))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(implies(implies(implies(X_2359,X_2358),X_2358),Z),implies(implies(not(X_2358),X_2359),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_2358),X_2359),implies(implies(X_2359,X_2358),X_2358))) )],[refute_0_95,refute_0_11]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(implies(implies(X_2782,X_2781),X_2781),implies(X_38,X_2781)),implies(implies(not(X_2781),X_2782),implies(X_38,X_2781)))),
inference(subst,[],[refute_0_96:[bind(Z,$fot(implies(X_38,X_2781))),bind(X_2358,$fot(X_2781)),bind(X_2359,$fot(X_2782))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(X_38,implies(X_2782,X_2781)),implies(implies(not(X_2781),X_2782),implies(X_38,X_2781)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_2782,X_2781),X_2781),implies(X_38,X_2781)),implies(implies(not(X_2781),X_2782),implies(X_38,X_2781)))) )],[refute_0_97,refute_0_10]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
inference(subst,[],[refute_0_98:[bind(X_2781,$fot(z)),bind(X_2782,$fot(y)),bind(X_38,$fot(x))]]) ).
cnf(refute_0_100,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))) )],[refute_0_99,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL384+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 5 00:05:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.65/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.90
% 1.65/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.65/1.92
%------------------------------------------------------------------------------