TSTP Solution File: LCL052-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL052-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:49:04 EDT 2022
% Result : Unsatisfiable 10.73s 10.92s
% Output : CNFRefutation 10.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 5
% Syntax : Number of clauses : 170 ( 101 unt; 0 nHn; 46 RR)
% Number of literals : 252 ( 0 equ; 83 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 3 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 : 427 ( 73 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_24,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(X_2128),X_2129),implies(implies(X_2129,X_2128),X_2128)))
| ~ is_a_theorem(implies(not(X_2128),X_2129))
| is_a_theorem(implies(implies(X_2129,X_2128),X_2128)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_2128),X_2129))),bind(Y,$fot(implies(implies(X_2129,X_2128),X_2128)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37))
| ~ is_a_theorem(implies(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37),implies(implies(X_34,X_35),X_37)))
| is_a_theorem(implies(implies(X_34,X_35),X_37)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37))),bind(Y,$fot(implies(implies(X_34,X_35),X_37)))]]) ).
cnf(refute_0_2,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_3,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37),implies(implies(X_34,X_35),X_37))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_34)),bind(Y,$fot(X_35)),bind(Z,$fot(X_36)),bind(X_21,$fot(X_37))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37))
| is_a_theorem(implies(implies(X_34,X_35),X_37)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37),implies(implies(X_34,X_35),X_37))) )],[refute_0_6,refute_0_1]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(X_35,X_2127),implies(not(X_2127),X_2127)),implies(implies(X_35,X_2127),X_2127)))
| is_a_theorem(implies(implies(not(X_2127),X_35),implies(implies(X_35,X_2127),X_2127))) ),
inference(subst,[],[refute_0_7:[bind(X_34,$fot(not(X_2127))),bind(X_36,$fot(X_2127)),bind(X_37,$fot(implies(implies(X_35,X_2127),X_2127)))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554)),implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554)))
| is_a_theorem(implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554)) ),
inference(subst,[],[refute_0_11:[bind(X_7,$fot(implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554)))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_46),X_46),X_47),X_45),implies(implies(X_46,X_47),X_45)))
| ~ is_a_theorem(implies(implies(implies(not(X_46),X_46),X_47),X_45))
| is_a_theorem(implies(implies(X_46,X_47),X_45)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_46),X_46),X_47),X_45))),bind(Y,$fot(implies(implies(X_46,X_47),X_45)))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23)))
| is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_23),Z),implies(implies(X_22,X_23),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X_22,X_23))),bind(Y,$fot(implies(implies(not(X_22),X_22),X_23)))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(not(X_20),X_20),X_20)),
inference(subst,[],[cn_2:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(not(X_20),X_20),X_20))
| is_a_theorem(implies(implies(X_20,X_21),implies(implies(not(X_20),X_20),X_21))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(not(X_20),X_20))),bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(X_20,X_21),implies(implies(not(X_20),X_20),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_20),X_20),X_20)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))),
inference(subst,[],[refute_0_17:[bind(X_20,$fot(X_22)),bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_23),Z),implies(implies(X_22,X_23),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(implies(implies(not(X_46),X_46),X_47),X_45),implies(implies(X_46,X_47),X_45))),
inference(subst,[],[refute_0_19:[bind(Z,$fot(X_45)),bind(X_22,$fot(X_46)),bind(X_23,$fot(X_47))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_46),X_46),X_47),X_45))
| is_a_theorem(implies(implies(X_46,X_47),X_45)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_46),X_46),X_47),X_45),implies(implies(X_46,X_47),X_45))) )],[refute_0_20,refute_0_13]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1137),X_1137),X_1136),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1137),X_1136)))
| is_a_theorem(implies(implies(X_1137,X_1136),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1137),X_1136))) ),
inference(subst,[],[refute_0_21:[bind(X_45,$fot(implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1137),X_1136))),bind(X_46,$fot(X_1137)),bind(X_47,$fot(X_1136))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1099),X_1099),X_1099),X_1098),implies(X_1100,X_1098)))
| is_a_theorem(implies(implies(implies(X_1100,X_1098),Z),implies(implies(implies(implies(not(X_1099),X_1099),X_1099),X_1098),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(implies(not(X_1099),X_1099),X_1099),X_1098))),bind(Y,$fot(implies(X_1100,X_1098)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(X_254,implies(not(implies(implies(not(X_252),X_252),X_252)),X_253)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_252),X_252),X_252)),X_253),Z),implies(X_254,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_254)),bind(Y,$fot(implies(not(implies(implies(not(X_252),X_252),X_252)),X_253)))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_26,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_27,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_28]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20)),
inference(subst,[],[refute_0_29:[bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20))
| is_a_theorem(implies(implies(X_20,X_21),implies(not(implies(implies(not(X),X),X)),X_21))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(X_20,X_21),implies(not(implies(implies(not(X),X),X)),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(not(X_227),X_226),implies(not(implies(implies(not(X),X),X)),X_226))),
inference(subst,[],[refute_0_32:[bind(X_20,$fot(not(X_227))),bind(X_21,$fot(X_226))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26)))
| ~ is_a_theorem(implies(implies(not(X_25),X_24),X_26))
| is_a_theorem(implies(X_25,X_26)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_25),X_24),X_26))),bind(Y,$fot(implies(X_25,X_26)))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(X_19,implies(not(X_19),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(X_19,implies(not(X_19),Y)))
| is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_19)),bind(Y,$fot(implies(not(X_19),Y))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(X_19,implies(not(X_19),Y))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26))),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_24)),bind(X_19,$fot(X_25)),bind(X_21,$fot(X_26))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(not(X_25),X_24),X_26))
| is_a_theorem(implies(X_25,X_26)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26))) )],[refute_0_38,refute_0_34]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(not(X_227),X_226),implies(not(implies(implies(not(X),X),X)),X_226)))
| is_a_theorem(implies(X_227,implies(not(implies(implies(not(X),X),X)),X_226))) ),
inference(subst,[],[refute_0_39:[bind(X_24,$fot(X_226)),bind(X_25,$fot(X_227)),bind(X_26,$fot(implies(not(implies(implies(not(X),X),X)),X_226)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(X_227,implies(not(implies(implies(not(X),X),X)),X_226))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_227),X_226),implies(not(implies(implies(not(X),X),X)),X_226))) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(X_254,implies(not(implies(implies(not(X_252),X_252),X_252)),X_253))),
inference(subst,[],[refute_0_41:[bind(X,$fot(X_252)),bind(X_226,$fot(X_253)),bind(X_227,$fot(X_254))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_252),X_252),X_252)),X_253),Z),implies(X_254,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_254,implies(not(implies(implies(not(X_252),X_252),X_252)),X_253))) )],[refute_0_42,refute_0_24]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_252),X_252),X_252)),implies(implies(not(X_252),X_252),X_252)),X_1094),implies(X_254,X_1094))),
inference(subst,[],[refute_0_43:[bind(Z,$fot(X_1094)),bind(X_253,$fot(implies(implies(not(X_252),X_252),X_252)))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_252),X_252),X_252)),implies(implies(not(X_252),X_252),X_252)),X_1094),implies(X_254,X_1094)))
| is_a_theorem(implies(implies(implies(implies(not(X_252),X_252),X_252),X_1094),implies(X_254,X_1094))) ),
inference(subst,[],[refute_0_21:[bind(X_45,$fot(implies(X_254,X_1094))),bind(X_46,$fot(implies(implies(not(X_252),X_252),X_252))),bind(X_47,$fot(X_1094))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(implies(implies(not(X_252),X_252),X_252),X_1094),implies(X_254,X_1094))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_252),X_252),X_252)),implies(implies(not(X_252),X_252),X_252)),X_1094),implies(X_254,X_1094))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1099),X_1099),X_1099),X_1098),implies(X_1100,X_1098))),
inference(subst,[],[refute_0_46:[bind(X_1094,$fot(X_1098)),bind(X_252,$fot(X_1099)),bind(X_254,$fot(X_1100))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(implies(X_1100,X_1098),Z),implies(implies(implies(implies(not(X_1099),X_1099),X_1099),X_1098),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1099),X_1099),X_1099),X_1098),implies(X_1100,X_1098))) )],[refute_0_47,refute_0_23]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(not(X_1137),X_1137),X_1136),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1137),X_1136))),
inference(subst,[],[refute_0_48:[bind(Z,$fot(X_1136)),bind(X_1098,$fot(X_1137)),bind(X_1099,$fot(X_1138)),bind(X_1100,$fot(not(X_1137)))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(X_1137,X_1136),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1137),X_1136))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1137),X_1137),X_1136),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1137),X_1136))) )],[refute_0_49,refute_0_22]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(X_1431,X_1431),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1431),X_1431))),
inference(subst,[],[refute_0_50:[bind(X_1136,$fot(X_1431)),bind(X_1137,$fot(X_1431))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(X_1096,X_1096),X_1095))
| ~ is_a_theorem(implies(implies(implies(X_1096,X_1096),X_1095),implies(X_1097,X_1095)))
| is_a_theorem(implies(X_1097,X_1095)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1096,X_1096),X_1095))),bind(Y,$fot(implies(X_1097,X_1095)))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(X_288,implies(not(implies(X_287,X_287)),X_286)))
| is_a_theorem(implies(implies(implies(not(implies(X_287,X_287)),X_286),Z),implies(X_288,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_288)),bind(Y,$fot(implies(not(implies(X_287,X_287)),X_286)))]]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(implies(not(X_25),X_237),implies(not(implies(X_239,X_239)),X_237)))
| is_a_theorem(implies(X_25,implies(not(implies(X_239,X_239)),X_237))) ),
inference(subst,[],[refute_0_39:[bind(X_24,$fot(X_237)),bind(X_26,$fot(implies(not(implies(X_239,X_239)),X_237)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(not(implies(X_231,X_231)),X_230))
| is_a_theorem(implies(implies(X_230,Z),implies(not(implies(X_231,X_231)),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(X_231,X_231)))),bind(Y,$fot(X_230))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(X_229,X_229))
| is_a_theorem(implies(not(implies(X_229,X_229)),Y)) ),
inference(subst,[],[refute_0_27:[bind(X_6,$fot(implies(X_229,X_229)))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(not(X_228),X_228),X_228)),
inference(subst,[],[cn_2:[bind(X,$fot(X_228))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(not(X_228),X_228),X_228))
| is_a_theorem(implies(X_228,X_228)) ),
inference(subst,[],[refute_0_39:[bind(X_24,$fot(X_228)),bind(X_25,$fot(X_228)),bind(X_26,$fot(X_228))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(X_228,X_228)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_228),X_228),X_228)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(X_229,X_229)),
inference(subst,[],[refute_0_59:[bind(X_228,$fot(X_229))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(not(implies(X_229,X_229)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_229,X_229)) )],[refute_0_60,refute_0_56]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(not(implies(X_231,X_231)),X_230)),
inference(subst,[],[refute_0_61:[bind(Y,$fot(X_230)),bind(X_229,$fot(X_231))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(X_230,Z),implies(not(implies(X_231,X_231)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_231,X_231)),X_230)) )],[refute_0_62,refute_0_55]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(not(X_25),X_237),implies(not(implies(X_239,X_239)),X_237))),
inference(subst,[],[refute_0_63:[bind(Z,$fot(X_237)),bind(X_230,$fot(not(X_25))),bind(X_231,$fot(X_239))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(X_25,implies(not(implies(X_239,X_239)),X_237))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_25),X_237),implies(not(implies(X_239,X_239)),X_237))) )],[refute_0_64,refute_0_54]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(X_288,implies(not(implies(X_287,X_287)),X_286))),
inference(subst,[],[refute_0_65:[bind(X_237,$fot(X_286)),bind(X_239,$fot(X_287)),bind(X_25,$fot(X_288))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(implies(not(implies(X_287,X_287)),X_286),Z),implies(X_288,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_288,implies(not(implies(X_287,X_287)),X_286))) )],[refute_0_66,refute_0_53]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(implies(not(implies(X_287,X_287)),implies(X_287,X_287)),X_1094),implies(X_288,X_1094))),
inference(subst,[],[refute_0_67:[bind(Z,$fot(X_1094)),bind(X_286,$fot(implies(X_287,X_287)))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_287,X_287)),implies(X_287,X_287)),X_1094),implies(X_288,X_1094)))
| is_a_theorem(implies(implies(implies(X_287,X_287),X_1094),implies(X_288,X_1094))) ),
inference(subst,[],[refute_0_21:[bind(X_45,$fot(implies(X_288,X_1094))),bind(X_46,$fot(implies(X_287,X_287))),bind(X_47,$fot(X_1094))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(X_287,X_287),X_1094),implies(X_288,X_1094))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_287,X_287)),implies(X_287,X_287)),X_1094),implies(X_288,X_1094))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(implies(X_1096,X_1096),X_1095),implies(X_1097,X_1095))),
inference(subst,[],[refute_0_70:[bind(X_1094,$fot(X_1095)),bind(X_287,$fot(X_1096)),bind(X_288,$fot(X_1097))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(X_1096,X_1096),X_1095))
| is_a_theorem(implies(X_1097,X_1095)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1096,X_1096),X_1095),implies(X_1097,X_1095))) )],[refute_0_71,refute_0_52]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(implies(X_1431,X_1431),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1431),X_1431)))
| is_a_theorem(implies(X_1432,implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1431),X_1431))) ),
inference(subst,[],[refute_0_72:[bind(X_1095,$fot(implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1431),X_1431))),bind(X_1096,$fot(X_1431)),bind(X_1097,$fot(X_1432))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(X_1432,implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1431),X_1431))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1431,X_1431),implies(implies(implies(implies(not(X_1138),X_1138),X_1138),X_1431),X_1431))) )],[refute_0_51,refute_0_73]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554)),implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554))),
inference(subst,[],[refute_0_74:[bind(X_1138,$fot(X_1553)),bind(X_1431,$fot(X_1554)),bind(X_1432,$fot(not(implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554))))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554)),implies(implies(implies(implies(not(X_1553),X_1553),X_1553),X_1554),X_1554))) )],[refute_0_75,refute_0_12]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(implies(implies(not(X_2118),X_2118),X_2118),implies(X_2116,X_2118)),implies(X_2116,X_2118))),
inference(subst,[],[refute_0_76:[bind(X_1553,$fot(X_2118)),bind(X_1554,$fot(implies(X_2116,X_2118)))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_2118),X_2118),X_2118),implies(X_2116,X_2118)),implies(X_2116,X_2118)))
| is_a_theorem(implies(implies(X_2116,implies(not(X_2118),X_2118)),implies(X_2116,X_2118))) ),
inference(subst,[],[refute_0_7:[bind(X_34,$fot(X_2116)),bind(X_35,$fot(implies(not(X_2118),X_2118))),bind(X_36,$fot(X_2118)),bind(X_37,$fot(implies(X_2116,X_2118)))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(X_2116,implies(not(X_2118),X_2118)),implies(X_2116,X_2118))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_2118),X_2118),X_2118),implies(X_2116,X_2118)),implies(X_2116,X_2118))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(implies(implies(X_35,X_2127),implies(not(X_2127),X_2127)),implies(implies(X_35,X_2127),X_2127))),
inference(subst,[],[refute_0_79:[bind(X_2116,$fot(implies(X_35,X_2127))),bind(X_2118,$fot(X_2127))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(not(X_2127),X_35),implies(implies(X_35,X_2127),X_2127))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_35,X_2127),implies(not(X_2127),X_2127)),implies(implies(X_35,X_2127),X_2127))) )],[refute_0_80,refute_0_8]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(not(X_2128),X_2129),implies(implies(X_2129,X_2128),X_2128))),
inference(subst,[],[refute_0_81:[bind(X_2127,$fot(X_2128)),bind(X_35,$fot(X_2129))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(not(X_2128),X_2129))
| is_a_theorem(implies(implies(X_2129,X_2128),X_2128)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_2128),X_2129),implies(implies(X_2129,X_2128),X_2128))) )],[refute_0_82,refute_0_0]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(not(X_13881),implies(X_13881,X_13882)))
| is_a_theorem(implies(implies(implies(X_13881,X_13882),X_13881),X_13881)) ),
inference(subst,[],[refute_0_83:[bind(X_2128,$fot(X_13881)),bind(X_2129,$fot(implies(X_13881,X_13882)))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(not(X_281),X_280)),X_279),X_278),implies(X_281,X_278)))
| ~ is_a_theorem(implies(implies(not(implies(not(X_281),X_280)),X_279),X_278))
| is_a_theorem(implies(X_281,X_278)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(not(X_281),X_280)),X_279),X_278))),bind(Y,$fot(implies(X_281,X_278)))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(X_236,implies(not(implies(not(X_236),X_235)),X_234)))
| is_a_theorem(implies(implies(implies(not(implies(not(X_236),X_235)),X_234),Z),implies(X_236,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_236)),bind(Y,$fot(implies(not(implies(not(X_236),X_235)),X_234)))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(implies(not(X_227),X_226),implies(not(implies(not(X_227),X_226)),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(implies(not(X_227),X_226)))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(not(X_227),X_226),implies(not(implies(not(X_227),X_226)),Y)))
| is_a_theorem(implies(X_227,implies(not(implies(not(X_227),X_226)),Y))) ),
inference(subst,[],[refute_0_39:[bind(X_24,$fot(X_226)),bind(X_25,$fot(X_227)),bind(X_26,$fot(implies(not(implies(not(X_227),X_226)),Y)))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(X_227,implies(not(implies(not(X_227),X_226)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_227),X_226),implies(not(implies(not(X_227),X_226)),Y))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(X_236,implies(not(implies(not(X_236),X_235)),X_234))),
inference(subst,[],[refute_0_89:[bind(Y,$fot(X_234)),bind(X_226,$fot(X_235)),bind(X_227,$fot(X_236))]]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(implies(not(implies(not(X_236),X_235)),X_234),Z),implies(X_236,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_236,implies(not(implies(not(X_236),X_235)),X_234))) )],[refute_0_90,refute_0_86]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(implies(not(implies(not(X_281),X_280)),X_279),X_278),implies(X_281,X_278))),
inference(subst,[],[refute_0_91:[bind(Z,$fot(X_278)),bind(X_234,$fot(X_279)),bind(X_235,$fot(X_280)),bind(X_236,$fot(X_281))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(X_281),X_280)),X_279),X_278))
| is_a_theorem(implies(X_281,X_278)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(not(X_281),X_280)),X_279),X_278),implies(X_281,X_278))) )],[refute_0_92,refute_0_85]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(not(X_13879)),not(X_13879))),X_13880),implies(X_13879,X_13880)))
| is_a_theorem(implies(not(X_13879),implies(X_13879,X_13880))) ),
inference(subst,[],[refute_0_93:[bind(X_278,$fot(implies(X_13879,X_13880))),bind(X_279,$fot(X_13880)),bind(X_280,$fot(not(X_13879))),bind(X_281,$fot(not(X_13879)))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(X_2268,implies(not(X_2270),X_2270)))
| ~ is_a_theorem(implies(implies(X_2268,implies(not(X_2270),X_2270)),implies(implies(X_2270,X_2269),implies(X_2268,X_2269))))
| is_a_theorem(implies(implies(X_2270,X_2269),implies(X_2268,X_2269))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_2268,implies(not(X_2270),X_2270)))),bind(Y,$fot(implies(implies(X_2270,X_2269),implies(X_2268,X_2269))))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_2118),implies(X_2116,X_2118)),implies(implies(X_22,X_2118),implies(X_2116,X_2118)))),
inference(subst,[],[refute_0_19:[bind(Z,$fot(implies(X_2116,X_2118))),bind(X_23,$fot(X_2118))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_2118),implies(X_2116,X_2118)),implies(implies(X_22,X_2118),implies(X_2116,X_2118))))
| is_a_theorem(implies(implies(X_2116,implies(not(X_22),X_22)),implies(implies(X_22,X_2118),implies(X_2116,X_2118)))) ),
inference(subst,[],[refute_0_7:[bind(X_34,$fot(X_2116)),bind(X_35,$fot(implies(not(X_22),X_22))),bind(X_36,$fot(X_2118)),bind(X_37,$fot(implies(implies(X_22,X_2118),implies(X_2116,X_2118))))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(X_2116,implies(not(X_22),X_22)),implies(implies(X_22,X_2118),implies(X_2116,X_2118)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_2118),implies(X_2116,X_2118)),implies(implies(X_22,X_2118),implies(X_2116,X_2118)))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(X_2268,implies(not(X_2270),X_2270)),implies(implies(X_2270,X_2269),implies(X_2268,X_2269)))),
inference(subst,[],[refute_0_98:[bind(X_2116,$fot(X_2268)),bind(X_2118,$fot(X_2269)),bind(X_22,$fot(X_2270))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(X_2268,implies(not(X_2270),X_2270)))
| is_a_theorem(implies(implies(X_2270,X_2269),implies(X_2268,X_2269))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2268,implies(not(X_2270),X_2270)),implies(implies(X_2270,X_2269),implies(X_2268,X_2269)))) )],[refute_0_99,refute_0_95]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(X_13878,implies(not(not(implies(not(not(X_13878)),not(X_13878)))),not(implies(not(not(X_13878)),not(X_13878))))))
| is_a_theorem(implies(implies(not(implies(not(not(X_13878)),not(X_13878))),X_2269),implies(X_13878,X_2269))) ),
inference(subst,[],[refute_0_100:[bind(X_2268,$fot(X_13878)),bind(X_2270,$fot(not(implies(not(not(X_13878)),not(X_13878)))))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(implies(not(X_25),X_13512),implies(not(not(implies(not(not(X_25)),not(X_25)))),X_13512)))
| is_a_theorem(implies(X_25,implies(not(not(implies(not(not(X_25)),not(X_25)))),X_13512))) ),
inference(subst,[],[refute_0_39:[bind(X_24,$fot(X_13512)),bind(X_26,$fot(implies(not(not(implies(not(not(X_25)),not(X_25)))),X_13512)))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(not(not(implies(not(X_13459),X_13459))),X_13459))
| is_a_theorem(implies(implies(X_13459,Z),implies(not(not(implies(not(X_13459),X_13459))),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(not(implies(not(X_13459),X_13459))))),bind(Y,$fot(X_13459))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(implies(not(not(not(implies(not(X_13458),X_13458)))),not(not(X_13458))),X_13458))
| is_a_theorem(implies(not(not(implies(not(X_13458),X_13458))),X_13458)) ),
inference(subst,[],[refute_0_39:[bind(X_24,$fot(not(not(X_13458)))),bind(X_25,$fot(not(not(implies(not(X_13458),X_13458))))),bind(X_26,$fot(X_13458))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_13456)),not(not(implies(not(X_13456),X_13456)))),implies(not(not(not(implies(not(X_13456),X_13456)))),not(not(implies(not(X_13456),X_13456))))),X_13456))
| is_a_theorem(implies(implies(not(not(not(implies(not(X_13456),X_13456)))),not(not(X_13456))),X_13456)) ),
inference(subst,[],[refute_0_7:[bind(X_34,$fot(not(not(not(implies(not(X_13456),X_13456)))))),bind(X_35,$fot(not(not(X_13456)))),bind(X_36,$fot(not(not(implies(not(X_13456),X_13456))))),bind(X_37,$fot(X_13456))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(implies(X_1449,X_1449),X_1450))
| ~ is_a_theorem(implies(implies(implies(X_1449,X_1449),X_1450),X_1450))
| is_a_theorem(X_1450) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1449,X_1449),X_1450))),bind(Y,$fot(X_1450))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(X_1446,X_1446),X_1447),X_1447)),implies(implies(implies(X_1446,X_1446),X_1447),X_1447)))
| is_a_theorem(implies(implies(implies(X_1446,X_1446),X_1447),X_1447)) ),
inference(subst,[],[refute_0_11:[bind(X_7,$fot(implies(implies(implies(X_1446,X_1446),X_1447),X_1447)))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1380),X_1380),X_1379),implies(implies(implies(X_1381,X_1381),X_1380),X_1379)))
| is_a_theorem(implies(implies(X_1380,X_1379),implies(implies(implies(X_1381,X_1381),X_1380),X_1379))) ),
inference(subst,[],[refute_0_21:[bind(X_45,$fot(implies(implies(implies(X_1381,X_1381),X_1380),X_1379))),bind(X_46,$fot(X_1380)),bind(X_47,$fot(X_1379))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(implies(implies(X_1096,X_1096),X_1095),implies(X_1097,X_1095)))
| is_a_theorem(implies(implies(implies(X_1097,X_1095),Z),implies(implies(implies(X_1096,X_1096),X_1095),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(X_1096,X_1096),X_1095))),bind(Y,$fot(implies(X_1097,X_1095)))]]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(implies(implies(X_1097,X_1095),Z),implies(implies(implies(X_1096,X_1096),X_1095),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1096,X_1096),X_1095),implies(X_1097,X_1095))) )],[refute_0_71,refute_0_109]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(implies(not(X_1380),X_1380),X_1379),implies(implies(implies(X_1381,X_1381),X_1380),X_1379))),
inference(subst,[],[refute_0_110:[bind(Z,$fot(X_1379)),bind(X_1095,$fot(X_1380)),bind(X_1096,$fot(X_1381)),bind(X_1097,$fot(not(X_1380)))]]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(X_1380,X_1379),implies(implies(implies(X_1381,X_1381),X_1380),X_1379))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1380),X_1380),X_1379),implies(implies(implies(X_1381,X_1381),X_1380),X_1379))) )],[refute_0_111,refute_0_108]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(X_1431,X_1431),implies(implies(implies(X_1381,X_1381),X_1431),X_1431))),
inference(subst,[],[refute_0_112:[bind(X_1379,$fot(X_1431)),bind(X_1380,$fot(X_1431))]]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(implies(X_1431,X_1431),implies(implies(implies(X_1381,X_1381),X_1431),X_1431)))
| is_a_theorem(implies(X_1432,implies(implies(implies(X_1381,X_1381),X_1431),X_1431))) ),
inference(subst,[],[refute_0_72:[bind(X_1095,$fot(implies(implies(implies(X_1381,X_1381),X_1431),X_1431))),bind(X_1096,$fot(X_1431)),bind(X_1097,$fot(X_1432))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(X_1432,implies(implies(implies(X_1381,X_1381),X_1431),X_1431))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1431,X_1431),implies(implies(implies(X_1381,X_1381),X_1431),X_1431))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(not(implies(implies(implies(X_1446,X_1446),X_1447),X_1447)),implies(implies(implies(X_1446,X_1446),X_1447),X_1447))),
inference(subst,[],[refute_0_115:[bind(X_1381,$fot(X_1446)),bind(X_1431,$fot(X_1447)),bind(X_1432,$fot(not(implies(implies(implies(X_1446,X_1446),X_1447),X_1447))))]]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(implies(X_1446,X_1446),X_1447),X_1447)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(X_1446,X_1446),X_1447),X_1447)),implies(implies(implies(X_1446,X_1446),X_1447),X_1447))) )],[refute_0_116,refute_0_107]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(implies(X_1449,X_1449),X_1450),X_1450)),
inference(subst,[],[refute_0_117:[bind(X_1446,$fot(X_1449)),bind(X_1447,$fot(X_1450))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(implies(X_1449,X_1449),X_1450))
| is_a_theorem(X_1450) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1449,X_1449),X_1450),X_1450)) )],[refute_0_118,refute_0_106]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(X_1839,X_1839),implies(implies(implies(implies(not(not(not(implies(not(X_1839),X_1839)))),not(not(implies(not(X_1839),X_1839)))),X_1840),implies(not(X_1839),X_1839)),X_1839)))
| is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(X_1839),X_1839)))),not(not(implies(not(X_1839),X_1839)))),X_1840),implies(not(X_1839),X_1839)),X_1839)) ),
inference(subst,[],[refute_0_119:[bind(X_1449,$fot(X_1839)),bind(X_1450,$fot(implies(implies(implies(implies(not(not(not(implies(not(X_1839),X_1839)))),not(not(implies(not(X_1839),X_1839)))),X_1840),implies(not(X_1839),X_1839)),X_1839)))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_46),X_46),X_1159),implies(implies(implies(implies(not(not(not(implies(not(X_46),X_46)))),not(not(implies(not(X_46),X_46)))),X_1160),implies(not(X_46),X_46)),X_1159)))
| is_a_theorem(implies(implies(X_46,X_1159),implies(implies(implies(implies(not(not(not(implies(not(X_46),X_46)))),not(not(implies(not(X_46),X_46)))),X_1160),implies(not(X_46),X_46)),X_1159))) ),
inference(subst,[],[refute_0_21:[bind(X_45,$fot(implies(implies(implies(implies(not(not(not(implies(not(X_46),X_46)))),not(not(implies(not(X_46),X_46)))),X_1160),implies(not(X_46),X_46)),X_1159))),bind(X_47,$fot(X_1159))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_299)),not(X_299)),X_298),X_297),implies(X_299,X_297)))
| is_a_theorem(implies(implies(implies(X_299,X_297),Z),implies(implies(implies(implies(not(not(X_299)),not(X_299)),X_298),X_297),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(implies(not(not(X_299)),not(X_299)),X_298),X_297))),bind(Y,$fot(implies(X_299,X_297)))]]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(X_233,implies(implies(not(not(X_233)),not(X_233)),X_232)))
| is_a_theorem(implies(implies(implies(implies(not(not(X_233)),not(X_233)),X_232),Z),implies(X_233,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_233)),bind(Y,$fot(implies(implies(not(not(X_233)),not(X_233)),X_232)))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(not(X_227),X_226),implies(implies(not(not(X_227)),not(X_227)),X_226))),
inference(subst,[],[refute_0_17:[bind(X_20,$fot(not(X_227))),bind(X_21,$fot(X_226))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(implies(not(X_227),X_226),implies(implies(not(not(X_227)),not(X_227)),X_226)))
| is_a_theorem(implies(X_227,implies(implies(not(not(X_227)),not(X_227)),X_226))) ),
inference(subst,[],[refute_0_39:[bind(X_24,$fot(X_226)),bind(X_25,$fot(X_227)),bind(X_26,$fot(implies(implies(not(not(X_227)),not(X_227)),X_226)))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(X_227,implies(implies(not(not(X_227)),not(X_227)),X_226))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_227),X_226),implies(implies(not(not(X_227)),not(X_227)),X_226))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(X_233,implies(implies(not(not(X_233)),not(X_233)),X_232))),
inference(subst,[],[refute_0_126:[bind(X_226,$fot(X_232)),bind(X_227,$fot(X_233))]]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_233)),not(X_233)),X_232),Z),implies(X_233,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_233,implies(implies(not(not(X_233)),not(X_233)),X_232))) )],[refute_0_127,refute_0_123]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_299)),not(X_299)),X_298),X_297),implies(X_299,X_297))),
inference(subst,[],[refute_0_128:[bind(Z,$fot(X_297)),bind(X_232,$fot(X_298)),bind(X_233,$fot(X_299))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(implies(X_299,X_297),Z),implies(implies(implies(implies(not(not(X_299)),not(X_299)),X_298),X_297),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_299)),not(X_299)),X_298),X_297),implies(X_299,X_297))) )],[refute_0_129,refute_0_122]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(implies(not(X_1093),X_1093),X_1094),implies(implies(implies(implies(not(not(not(X_1093))),not(not(X_1093))),X_298),X_1093),X_1094))),
inference(subst,[],[refute_0_130:[bind(Z,$fot(X_1094)),bind(X_297,$fot(X_1093)),bind(X_299,$fot(not(X_1093)))]]) ).
cnf(refute_0_132,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1093),X_1093),X_1094),implies(implies(implies(implies(not(not(not(X_1093))),not(not(X_1093))),X_298),X_1093),X_1094)))
| is_a_theorem(implies(implies(X_1093,X_1094),implies(implies(implies(implies(not(not(not(X_1093))),not(not(X_1093))),X_298),X_1093),X_1094))) ),
inference(subst,[],[refute_0_21:[bind(X_45,$fot(implies(implies(implies(implies(not(not(not(X_1093))),not(not(X_1093))),X_298),X_1093),X_1094))),bind(X_46,$fot(X_1093)),bind(X_47,$fot(X_1094))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(X_1093,X_1094),implies(implies(implies(implies(not(not(not(X_1093))),not(not(X_1093))),X_298),X_1093),X_1094))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1093),X_1093),X_1094),implies(implies(implies(implies(not(not(not(X_1093))),not(not(X_1093))),X_298),X_1093),X_1094))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(implies(not(X_46),X_46),X_1159),implies(implies(implies(implies(not(not(not(implies(not(X_46),X_46)))),not(not(implies(not(X_46),X_46)))),X_1160),implies(not(X_46),X_46)),X_1159))),
inference(subst,[],[refute_0_133:[bind(X_1093,$fot(implies(not(X_46),X_46))),bind(X_1094,$fot(X_1159)),bind(X_298,$fot(X_1160))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(X_46,X_1159),implies(implies(implies(implies(not(not(not(implies(not(X_46),X_46)))),not(not(implies(not(X_46),X_46)))),X_1160),implies(not(X_46),X_46)),X_1159))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_46),X_46),X_1159),implies(implies(implies(implies(not(not(not(implies(not(X_46),X_46)))),not(not(implies(not(X_46),X_46)))),X_1160),implies(not(X_46),X_46)),X_1159))) )],[refute_0_134,refute_0_121]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(implies(X_1839,X_1839),implies(implies(implies(implies(not(not(not(implies(not(X_1839),X_1839)))),not(not(implies(not(X_1839),X_1839)))),X_1840),implies(not(X_1839),X_1839)),X_1839))),
inference(subst,[],[refute_0_135:[bind(X_1159,$fot(X_1839)),bind(X_1160,$fot(X_1840)),bind(X_46,$fot(X_1839))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(X_1839),X_1839)))),not(not(implies(not(X_1839),X_1839)))),X_1840),implies(not(X_1839),X_1839)),X_1839)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1839,X_1839),implies(implies(implies(implies(not(not(not(implies(not(X_1839),X_1839)))),not(not(implies(not(X_1839),X_1839)))),X_1840),implies(not(X_1839),X_1839)),X_1839))) )],[refute_0_136,refute_0_120]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(X_2119),X_2119)))),not(not(implies(not(X_2119),X_2119)))),X_2119),implies(not(X_2119),X_2119)),X_2119)),
inference(subst,[],[refute_0_137:[bind(X_1839,$fot(X_2119)),bind(X_1840,$fot(X_2119))]]) ).
cnf(refute_0_139,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(X_2119),X_2119)))),not(not(implies(not(X_2119),X_2119)))),X_2119),implies(not(X_2119),X_2119)),X_2119))
| is_a_theorem(implies(implies(not(X_2119),implies(not(not(not(implies(not(X_2119),X_2119)))),not(not(implies(not(X_2119),X_2119))))),X_2119)) ),
inference(subst,[],[refute_0_7:[bind(X_34,$fot(not(X_2119))),bind(X_35,$fot(implies(not(not(not(implies(not(X_2119),X_2119)))),not(not(implies(not(X_2119),X_2119)))))),bind(X_36,$fot(X_2119)),bind(X_37,$fot(X_2119))]]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(implies(not(X_2119),implies(not(not(not(implies(not(X_2119),X_2119)))),not(not(implies(not(X_2119),X_2119))))),X_2119)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(X_2119),X_2119)))),not(not(implies(not(X_2119),X_2119)))),X_2119),implies(not(X_2119),X_2119)),X_2119)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(implies(not(X_12254),implies(not(not(not(implies(not(X_12254),X_12254)))),not(not(implies(not(X_12254),X_12254))))),X_12254)),
inference(subst,[],[refute_0_140:[bind(X_2119,$fot(X_12254))]]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(implies(implies(X_137,X_138),X_135))
| ~ is_a_theorem(implies(implies(implies(X_137,X_138),X_135),implies(implies(implies(not(X_137),X_136),X_138),X_135)))
| is_a_theorem(implies(implies(implies(not(X_137),X_136),X_138),X_135)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_137,X_138),X_135))),bind(Y,$fot(implies(implies(implies(not(X_137),X_136),X_138),X_135)))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26)))
| is_a_theorem(implies(implies(implies(X_25,X_26),Z),implies(implies(implies(not(X_25),X_24),X_26),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(X_25),X_24),X_26))),bind(Y,$fot(implies(X_25,X_26)))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(implies(implies(X_25,X_26),Z),implies(implies(implies(not(X_25),X_24),X_26),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26))) )],[refute_0_38,refute_0_143]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(implies(implies(X_137,X_138),X_135),implies(implies(implies(not(X_137),X_136),X_138),X_135))),
inference(subst,[],[refute_0_144:[bind(Z,$fot(X_135)),bind(X_24,$fot(X_136)),bind(X_25,$fot(X_137)),bind(X_26,$fot(X_138))]]) ).
cnf(refute_0_146,plain,
( ~ is_a_theorem(implies(implies(X_137,X_138),X_135))
| is_a_theorem(implies(implies(implies(not(X_137),X_136),X_138),X_135)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_137,X_138),X_135),implies(implies(implies(not(X_137),X_136),X_138),X_135))) )],[refute_0_145,refute_0_142]) ).
cnf(refute_0_147,plain,
( ~ is_a_theorem(implies(implies(not(X_12254),implies(not(not(not(implies(not(X_12254),X_12254)))),not(not(implies(not(X_12254),X_12254))))),X_12254))
| is_a_theorem(implies(implies(implies(not(not(X_12254)),X_12255),implies(not(not(not(implies(not(X_12254),X_12254)))),not(not(implies(not(X_12254),X_12254))))),X_12254)) ),
inference(subst,[],[refute_0_146:[bind(X_135,$fot(X_12254)),bind(X_136,$fot(X_12255)),bind(X_137,$fot(not(X_12254))),bind(X_138,$fot(implies(not(not(not(implies(not(X_12254),X_12254)))),not(not(implies(not(X_12254),X_12254))))))]]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(implies(not(not(X_12254)),X_12255),implies(not(not(not(implies(not(X_12254),X_12254)))),not(not(implies(not(X_12254),X_12254))))),X_12254)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_12254),implies(not(not(not(implies(not(X_12254),X_12254)))),not(not(implies(not(X_12254),X_12254))))),X_12254)) )],[refute_0_141,refute_0_147]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(implies(implies(not(not(X_13456)),not(not(implies(not(X_13456),X_13456)))),implies(not(not(not(implies(not(X_13456),X_13456)))),not(not(implies(not(X_13456),X_13456))))),X_13456)),
inference(subst,[],[refute_0_148:[bind(X_12254,$fot(X_13456)),bind(X_12255,$fot(not(not(implies(not(X_13456),X_13456)))))]]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(implies(not(not(not(implies(not(X_13456),X_13456)))),not(not(X_13456))),X_13456)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_13456)),not(not(implies(not(X_13456),X_13456)))),implies(not(not(not(implies(not(X_13456),X_13456)))),not(not(implies(not(X_13456),X_13456))))),X_13456)) )],[refute_0_149,refute_0_105]) ).
cnf(refute_0_151,plain,
is_a_theorem(implies(implies(not(not(not(implies(not(X_13458),X_13458)))),not(not(X_13458))),X_13458)),
inference(subst,[],[refute_0_150:[bind(X_13456,$fot(X_13458))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(implies(not(not(implies(not(X_13458),X_13458))),X_13458)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(implies(not(X_13458),X_13458)))),not(not(X_13458))),X_13458)) )],[refute_0_151,refute_0_104]) ).
cnf(refute_0_153,plain,
is_a_theorem(implies(not(not(implies(not(X_13459),X_13459))),X_13459)),
inference(subst,[],[refute_0_152:[bind(X_13458,$fot(X_13459))]]) ).
cnf(refute_0_154,plain,
is_a_theorem(implies(implies(X_13459,Z),implies(not(not(implies(not(X_13459),X_13459))),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(X_13459),X_13459))),X_13459)) )],[refute_0_153,refute_0_103]) ).
cnf(refute_0_155,plain,
is_a_theorem(implies(implies(not(X_25),X_13512),implies(not(not(implies(not(not(X_25)),not(X_25)))),X_13512))),
inference(subst,[],[refute_0_154:[bind(Z,$fot(X_13512)),bind(X_13459,$fot(not(X_25)))]]) ).
cnf(refute_0_156,plain,
is_a_theorem(implies(X_25,implies(not(not(implies(not(not(X_25)),not(X_25)))),X_13512))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_25),X_13512),implies(not(not(implies(not(not(X_25)),not(X_25)))),X_13512))) )],[refute_0_155,refute_0_102]) ).
cnf(refute_0_157,plain,
is_a_theorem(implies(X_13878,implies(not(not(implies(not(not(X_13878)),not(X_13878)))),not(implies(not(not(X_13878)),not(X_13878)))))),
inference(subst,[],[refute_0_156:[bind(X_13512,$fot(not(implies(not(not(X_13878)),not(X_13878))))),bind(X_25,$fot(X_13878))]]) ).
cnf(refute_0_158,plain,
is_a_theorem(implies(implies(not(implies(not(not(X_13878)),not(X_13878))),X_2269),implies(X_13878,X_2269))),
inference(resolve,[$cnf( is_a_theorem(implies(X_13878,implies(not(not(implies(not(not(X_13878)),not(X_13878)))),not(implies(not(not(X_13878)),not(X_13878)))))) )],[refute_0_157,refute_0_101]) ).
cnf(refute_0_159,plain,
is_a_theorem(implies(implies(not(implies(not(not(X_13879)),not(X_13879))),X_13880),implies(X_13879,X_13880))),
inference(subst,[],[refute_0_158:[bind(X_13878,$fot(X_13879)),bind(X_2269,$fot(X_13880))]]) ).
cnf(refute_0_160,plain,
is_a_theorem(implies(not(X_13879),implies(X_13879,X_13880))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(not(not(X_13879)),not(X_13879))),X_13880),implies(X_13879,X_13880))) )],[refute_0_159,refute_0_94]) ).
cnf(refute_0_161,plain,
is_a_theorem(implies(not(X_13881),implies(X_13881,X_13882))),
inference(subst,[],[refute_0_160:[bind(X_13879,$fot(X_13881)),bind(X_13880,$fot(X_13882))]]) ).
cnf(refute_0_162,plain,
is_a_theorem(implies(implies(implies(X_13881,X_13882),X_13881),X_13881)),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_13881),implies(X_13881,X_13882))) )],[refute_0_161,refute_0_84]) ).
cnf(refute_0_163,plain,
is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(subst,[],[refute_0_162:[bind(X_13881,$fot(a)),bind(X_13882,$fot(b))]]) ).
cnf(refute_0_164,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(a,b),a),a)) )],[refute_0_163,prove_cn_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL052-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.29 % Computer : n018.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jul 4 15:50:06 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10.73/10.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.73/10.92
% 10.73/10.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.73/10.94
%------------------------------------------------------------------------------