TSTP Solution File: LCL055-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL055-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:49:06 EDT 2022
% Result : Unsatisfiable 5.85s 6.09s
% Output : CNFRefutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 5
% Syntax : Number of clauses : 165 ( 97 unt; 0 nHn; 44 RR)
% Number of literals : 247 ( 0 equ; 83 neg)
% Maximal clause size : 3 ( 1 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 : 463 ( 74 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_37,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(not(a),c))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(not(X_7369),implies(X_7369,X_7368)))
| is_a_theorem(implies(implies(implies(X_7369,X_7368),Z),implies(not(X_7369),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(X_7369))),bind(Y,$fot(implies(X_7369,X_7368)))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X_1940,implies(not(not(X_1942)),not(X_1942))))
| ~ is_a_theorem(implies(implies(X_1940,implies(not(not(X_1942)),not(X_1942))),implies(X_1942,implies(X_1940,X_1941))))
| is_a_theorem(implies(X_1942,implies(X_1940,X_1941))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1940,implies(not(not(X_1942)),not(X_1942))))),bind(Y,$fot(implies(X_1942,implies(X_1940,X_1941))))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_231,implies(implies(not(not(X_231)),not(X_231)),X_230)))
| is_a_theorem(implies(implies(implies(implies(not(not(X_231)),not(X_231)),X_230),Z),implies(X_231,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_231)),bind(Y,$fot(implies(implies(not(not(X_231)),not(X_231)),X_230)))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(not(X_28),X_28),X_28)),
inference(subst,[],[cn_2:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_6,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_1:[bind(X,$fot(implies(not(X_28),X_28))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_28),X_28),X_28)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(not(X_219),X_218),implies(implies(not(not(X_219)),not(X_219)),X_218))),
inference(subst,[],[refute_0_7:[bind(X_28,$fot(not(X_219))),bind(X_29,$fot(X_218))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34)))
| ~ is_a_theorem(implies(implies(not(X_33),X_32),X_34))
| is_a_theorem(implies(X_33,X_34)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_33),X_32),X_34))),bind(Y,$fot(implies(X_33,X_34)))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(X_27,implies(not(X_27),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(X_27,implies(not(X_27),Y)))
| is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_27)),bind(Y,$fot(implies(not(X_27),Y))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(X_27,implies(not(X_27),Y))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_32)),bind(X_27,$fot(X_33)),bind(X_29,$fot(X_34))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(not(X_33),X_32),X_34))
| is_a_theorem(implies(X_33,X_34)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34))) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(not(X_219),X_218),implies(implies(not(not(X_219)),not(X_219)),X_218)))
| is_a_theorem(implies(X_219,implies(implies(not(not(X_219)),not(X_219)),X_218))) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(X_218)),bind(X_33,$fot(X_219)),bind(X_34,$fot(implies(implies(not(not(X_219)),not(X_219)),X_218)))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_219,implies(implies(not(not(X_219)),not(X_219)),X_218))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_219),X_218),implies(implies(not(not(X_219)),not(X_219)),X_218))) )],[refute_0_8,refute_0_15]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(X_231,implies(implies(not(not(X_231)),not(X_231)),X_230))),
inference(subst,[],[refute_0_16:[bind(X_218,$fot(X_230)),bind(X_219,$fot(X_231))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_231)),not(X_231)),X_230),Z),implies(X_231,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_231,implies(implies(not(not(X_231)),not(X_231)),X_230))) )],[refute_0_17,refute_0_4]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_231)),not(X_231)),X_1772),implies(X_1770,X_1772)),implies(X_231,implies(X_1770,X_1772)))),
inference(subst,[],[refute_0_18:[bind(Z,$fot(implies(X_1770,X_1772))),bind(X_230,$fot(X_1772))]]) ).
cnf(refute_0_20,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,[],[condensed_detachment:[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_21,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_1:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_21]) ).
cnf(refute_0_23,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_22:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X_40)),bind(X_29,$fot(X_41))]]) ).
cnf(refute_0_24,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,[$cnf( is_a_theorem(implies(implies(implies(implies(X_39,X_40),implies(X_38,X_40)),X_41),implies(implies(X_38,X_39),X_41))) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_231)),not(X_231)),X_1772),implies(X_1770,X_1772)),implies(X_231,implies(X_1770,X_1772))))
| is_a_theorem(implies(implies(X_1770,implies(not(not(X_231)),not(X_231))),implies(X_231,implies(X_1770,X_1772)))) ),
inference(subst,[],[refute_0_24:[bind(X_38,$fot(X_1770)),bind(X_39,$fot(implies(not(not(X_231)),not(X_231)))),bind(X_40,$fot(X_1772)),bind(X_41,$fot(implies(X_231,implies(X_1770,X_1772))))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(X_1770,implies(not(not(X_231)),not(X_231))),implies(X_231,implies(X_1770,X_1772)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_231)),not(X_231)),X_1772),implies(X_1770,X_1772)),implies(X_231,implies(X_1770,X_1772)))) )],[refute_0_19,refute_0_25]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(X_1940,implies(not(not(X_1942)),not(X_1942))),implies(X_1942,implies(X_1940,X_1941)))),
inference(subst,[],[refute_0_26:[bind(X_1770,$fot(X_1940)),bind(X_1772,$fot(X_1941)),bind(X_231,$fot(X_1942))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(X_1940,implies(not(not(X_1942)),not(X_1942))))
| is_a_theorem(implies(X_1942,implies(X_1940,X_1941))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1940,implies(not(not(X_1942)),not(X_1942))),implies(X_1942,implies(X_1940,X_1941)))) )],[refute_0_27,refute_0_3]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(X_7366,implies(not(not(not(X_7366))),not(not(X_7366)))))
| is_a_theorem(implies(not(X_7366),implies(X_7366,X_1941))) ),
inference(subst,[],[refute_0_28:[bind(X_1940,$fot(X_7366)),bind(X_1942,$fot(not(X_7366)))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(X_1776,not(X_1778)))
| ~ is_a_theorem(implies(implies(X_1776,not(X_1778)),implies(X_1778,implies(X_1776,X_1777))))
| is_a_theorem(implies(X_1778,implies(X_1776,X_1777))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1776,not(X_1778)))),bind(Y,$fot(implies(X_1778,implies(X_1776,X_1777))))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(not(X_27),X_1772),implies(X_1770,X_1772)),implies(X_27,implies(X_1770,X_1772)))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_1772)),bind(X_29,$fot(implies(X_1770,X_1772)))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_27),X_1772),implies(X_1770,X_1772)),implies(X_27,implies(X_1770,X_1772))))
| is_a_theorem(implies(implies(X_1770,not(X_27)),implies(X_27,implies(X_1770,X_1772)))) ),
inference(subst,[],[refute_0_24:[bind(X_38,$fot(X_1770)),bind(X_39,$fot(not(X_27))),bind(X_40,$fot(X_1772)),bind(X_41,$fot(implies(X_27,implies(X_1770,X_1772))))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(X_1770,not(X_27)),implies(X_27,implies(X_1770,X_1772)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_27),X_1772),implies(X_1770,X_1772)),implies(X_27,implies(X_1770,X_1772)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(X_1776,not(X_1778)),implies(X_1778,implies(X_1776,X_1777)))),
inference(subst,[],[refute_0_33:[bind(X_1770,$fot(X_1776)),bind(X_1772,$fot(X_1777)),bind(X_27,$fot(X_1778))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(X_1776,not(X_1778)))
| is_a_theorem(implies(X_1778,implies(X_1776,X_1777))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1776,not(X_1778)),implies(X_1778,implies(X_1776,X_1777)))) )],[refute_0_34,refute_0_30]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(not(not(not(X_1778))),not(X_1778)))
| is_a_theorem(implies(X_1778,implies(not(not(not(X_1778))),X_1777))) ),
inference(subst,[],[refute_0_35:[bind(X_1776,$fot(not(not(not(X_1778)))))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_1167)),X_1168),X_1167),X_1167))
| ~ is_a_theorem(implies(implies(not(not(X_1167)),X_1168),X_1167))
| is_a_theorem(X_1167) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_1167)),X_1168),X_1167))),bind(Y,$fot(X_1167))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)),implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)))
| is_a_theorem(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)) ),
inference(subst,[],[refute_0_40:[bind(X_7,$fot(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34)))
| is_a_theorem(implies(implies(implies(X_33,X_34),Z),implies(implies(implies(not(X_33),X_32),X_34),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(not(X_33),X_32),X_34))),bind(Y,$fot(implies(X_33,X_34)))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(implies(X_33,X_34),Z),implies(implies(implies(not(X_33),X_32),X_34),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34))) )],[refute_0_13,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(implies(not(X_697),X_697),X_698),implies(implies(implies(not(not(X_697)),X_32),X_697),X_698))),
inference(subst,[],[refute_0_43:[bind(Z,$fot(X_698)),bind(X_33,$fot(not(X_697))),bind(X_34,$fot(X_697))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_62),X_62),X_63),X_61),implies(implies(X_62,X_63),X_61)))
| ~ is_a_theorem(implies(implies(implies(not(X_62),X_62),X_63),X_61))
| is_a_theorem(implies(implies(X_62,X_63),X_61)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_62),X_62),X_63),X_61))),bind(Y,$fot(implies(implies(X_62,X_63),X_61)))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31)))
| is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),Z),implies(implies(X_30,X_31),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X_30,X_31))),bind(Y,$fot(implies(implies(not(X_30),X_30),X_31)))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))),
inference(subst,[],[refute_0_7:[bind(X_28,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),Z),implies(implies(X_30,X_31),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) )],[refute_0_47,refute_0_46]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(implies(not(X_62),X_62),X_63),X_61),implies(implies(X_62,X_63),X_61))),
inference(subst,[],[refute_0_48:[bind(Z,$fot(X_61)),bind(X_30,$fot(X_62)),bind(X_31,$fot(X_63))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_62),X_62),X_63),X_61))
| is_a_theorem(implies(implies(X_62,X_63),X_61)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_62),X_62),X_63),X_61),implies(implies(X_62,X_63),X_61))) )],[refute_0_49,refute_0_45]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_697),X_697),X_698),implies(implies(implies(not(not(X_697)),X_32),X_697),X_698)))
| is_a_theorem(implies(implies(X_697,X_698),implies(implies(implies(not(not(X_697)),X_32),X_697),X_698))) ),
inference(subst,[],[refute_0_50:[bind(X_61,$fot(implies(implies(implies(not(not(X_697)),X_32),X_697),X_698))),bind(X_62,$fot(X_697)),bind(X_63,$fot(X_698))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(X_697,X_698),implies(implies(implies(not(not(X_697)),X_32),X_697),X_698))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_697),X_697),X_698),implies(implies(implies(not(not(X_697)),X_32),X_697),X_698))) )],[refute_0_44,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(X_1044,X_1044),implies(implies(implies(not(not(X_1044)),X_32),X_1044),X_1044))),
inference(subst,[],[refute_0_52:[bind(X_697,$fot(X_1044)),bind(X_698,$fot(X_1044))]]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(implies(X_702,X_702),X_704))
| ~ is_a_theorem(implies(implies(implies(X_702,X_702),X_704),implies(X_703,X_704)))
| is_a_theorem(implies(X_703,X_704)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_702,X_702),X_704))),bind(Y,$fot(implies(X_703,X_704)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(X_271,implies(not(implies(X_270,X_270)),X_269)))
| is_a_theorem(implies(implies(implies(not(implies(X_270,X_270)),X_269),Z),implies(X_271,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_271)),bind(Y,$fot(implies(not(implies(X_270,X_270)),X_269)))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(not(X_33),X_266),implies(not(implies(X_268,X_268)),X_266)))
| is_a_theorem(implies(X_33,implies(not(implies(X_268,X_268)),X_266))) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(X_266)),bind(X_34,$fot(implies(not(implies(X_268,X_268)),X_266)))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(not(implies(X_223,X_223)),X_222))
| is_a_theorem(implies(implies(X_222,Z),implies(not(implies(X_223,X_223)),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(implies(X_223,X_223)))),bind(Y,$fot(X_222))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(X_221,X_221))
| is_a_theorem(implies(not(implies(X_221,X_221)),Y)) ),
inference(subst,[],[refute_0_60:[bind(X_6,$fot(implies(X_221,X_221)))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(not(X_220),X_220),X_220)),
inference(subst,[],[cn_2:[bind(X,$fot(X_220))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(not(X_220),X_220),X_220))
| is_a_theorem(implies(X_220,X_220)) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(X_220)),bind(X_33,$fot(X_220)),bind(X_34,$fot(X_220))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(X_220,X_220)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_220),X_220),X_220)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(X_221,X_221)),
inference(subst,[],[refute_0_64:[bind(X_220,$fot(X_221))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(not(implies(X_221,X_221)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_221,X_221)) )],[refute_0_65,refute_0_61]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(not(implies(X_223,X_223)),X_222)),
inference(subst,[],[refute_0_66:[bind(Y,$fot(X_222)),bind(X_221,$fot(X_223))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(X_222,Z),implies(not(implies(X_223,X_223)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_223,X_223)),X_222)) )],[refute_0_67,refute_0_57]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(not(X_33),X_266),implies(not(implies(X_268,X_268)),X_266))),
inference(subst,[],[refute_0_68:[bind(Z,$fot(X_266)),bind(X_222,$fot(not(X_33))),bind(X_223,$fot(X_268))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(X_33,implies(not(implies(X_268,X_268)),X_266))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_33),X_266),implies(not(implies(X_268,X_268)),X_266))) )],[refute_0_69,refute_0_56]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(X_271,implies(not(implies(X_270,X_270)),X_269))),
inference(subst,[],[refute_0_70:[bind(X_266,$fot(X_269)),bind(X_268,$fot(X_270)),bind(X_33,$fot(X_271))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(implies(not(implies(X_270,X_270)),X_269),Z),implies(X_271,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_271,implies(not(implies(X_270,X_270)),X_269))) )],[refute_0_71,refute_0_55]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(implies(not(implies(X_270,X_270)),implies(X_270,X_270)),X_698),implies(X_271,X_698))),
inference(subst,[],[refute_0_72:[bind(Z,$fot(X_698)),bind(X_269,$fot(implies(X_270,X_270)))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_270,X_270)),implies(X_270,X_270)),X_698),implies(X_271,X_698)))
| is_a_theorem(implies(implies(implies(X_270,X_270),X_698),implies(X_271,X_698))) ),
inference(subst,[],[refute_0_50:[bind(X_61,$fot(implies(X_271,X_698))),bind(X_62,$fot(implies(X_270,X_270))),bind(X_63,$fot(X_698))]]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(implies(X_270,X_270),X_698),implies(X_271,X_698))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_270,X_270)),implies(X_270,X_270)),X_698),implies(X_271,X_698))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(implies(X_702,X_702),X_704),implies(X_703,X_704))),
inference(subst,[],[refute_0_75:[bind(X_270,$fot(X_702)),bind(X_271,$fot(X_703)),bind(X_698,$fot(X_704))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(X_702,X_702),X_704))
| is_a_theorem(implies(X_703,X_704)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_702,X_702),X_704),implies(X_703,X_704))) )],[refute_0_76,refute_0_54]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(X_1044,X_1044),implies(implies(implies(not(not(X_1044)),X_32),X_1044),X_1044)))
| is_a_theorem(implies(X_1045,implies(implies(implies(not(not(X_1044)),X_32),X_1044),X_1044))) ),
inference(subst,[],[refute_0_77:[bind(X_702,$fot(X_1044)),bind(X_703,$fot(X_1045)),bind(X_704,$fot(implies(implies(implies(not(not(X_1044)),X_32),X_1044),X_1044)))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(X_1045,implies(implies(implies(not(not(X_1044)),X_32),X_1044),X_1044))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1044,X_1044),implies(implies(implies(not(not(X_1044)),X_32),X_1044),X_1044))) )],[refute_0_53,refute_0_78]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(not(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)),implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164))),
inference(subst,[],[refute_0_79:[bind(X_1044,$fot(X_1164)),bind(X_1045,$fot(not(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)))),bind(X_32,$fot(X_1166))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)),implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164))) )],[refute_0_80,refute_0_41]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(implies(not(not(X_1167)),X_1168),X_1167),X_1167)),
inference(subst,[],[refute_0_81:[bind(X_1164,$fot(X_1167)),bind(X_1166,$fot(X_1168))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(implies(not(not(X_1167)),X_1168),X_1167))
| is_a_theorem(X_1167) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_1167)),X_1168),X_1167),X_1167)) )],[refute_0_82,refute_0_37]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(not(not(X_7354)),X_7354))),X_1168),implies(not(not(X_7354)),X_7354)))
| is_a_theorem(implies(not(not(X_7354)),X_7354)) ),
inference(subst,[],[refute_0_83:[bind(X_1167,$fot(implies(not(not(X_7354)),X_7354)))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(implies(not(X_7033),X_7033),implies(implies(X_7033,X_7034),X_7034)))
| is_a_theorem(implies(X_7033,implies(implies(X_7033,X_7034),X_7034))) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(X_7033)),bind(X_33,$fot(X_7033)),bind(X_34,$fot(implies(implies(X_7033,X_7034),X_7034)))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(implies(X_1111,X_1111),X_1110))
| ~ is_a_theorem(implies(implies(implies(X_1111,X_1111),X_1110),X_1110))
| is_a_theorem(X_1110) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1111,X_1111),X_1110))),bind(Y,$fot(X_1110))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)),implies(implies(implies(X_1109,X_1109),X_1107),X_1107)))
| is_a_theorem(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)) ),
inference(subst,[],[refute_0_40:[bind(X_7,$fot(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_715),X_715),X_712),implies(implies(implies(X_713,X_713),X_715),X_712)))
| is_a_theorem(implies(implies(X_715,X_712),implies(implies(implies(X_713,X_713),X_715),X_712))) ),
inference(subst,[],[refute_0_50:[bind(X_61,$fot(implies(implies(implies(X_713,X_713),X_715),X_712))),bind(X_62,$fot(X_715)),bind(X_63,$fot(X_712))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(implies(implies(implies(X_702,X_702),X_704),implies(X_703,X_704)))
| is_a_theorem(implies(implies(implies(X_703,X_704),Z),implies(implies(implies(X_702,X_702),X_704),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(X_702,X_702),X_704))),bind(Y,$fot(implies(X_703,X_704)))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(implies(X_703,X_704),Z),implies(implies(implies(X_702,X_702),X_704),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_702,X_702),X_704),implies(X_703,X_704))) )],[refute_0_76,refute_0_89]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(implies(not(X_715),X_715),X_712),implies(implies(implies(X_713,X_713),X_715),X_712))),
inference(subst,[],[refute_0_90:[bind(Z,$fot(X_712)),bind(X_702,$fot(X_713)),bind(X_703,$fot(not(X_715))),bind(X_704,$fot(X_715))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(X_715,X_712),implies(implies(implies(X_713,X_713),X_715),X_712))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_715),X_715),X_712),implies(implies(implies(X_713,X_713),X_715),X_712))) )],[refute_0_91,refute_0_88]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(X_1044,X_1044),implies(implies(implies(X_713,X_713),X_1044),X_1044))),
inference(subst,[],[refute_0_92:[bind(X_712,$fot(X_1044)),bind(X_715,$fot(X_1044))]]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(implies(implies(X_1044,X_1044),implies(implies(implies(X_713,X_713),X_1044),X_1044)))
| is_a_theorem(implies(X_1045,implies(implies(implies(X_713,X_713),X_1044),X_1044))) ),
inference(subst,[],[refute_0_77:[bind(X_702,$fot(X_1044)),bind(X_703,$fot(X_1045)),bind(X_704,$fot(implies(implies(implies(X_713,X_713),X_1044),X_1044)))]]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(X_1045,implies(implies(implies(X_713,X_713),X_1044),X_1044))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1044,X_1044),implies(implies(implies(X_713,X_713),X_1044),X_1044))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(not(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)),implies(implies(implies(X_1109,X_1109),X_1107),X_1107))),
inference(subst,[],[refute_0_95:[bind(X_1044,$fot(X_1107)),bind(X_1045,$fot(not(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)))),bind(X_713,$fot(X_1109))]]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)),implies(implies(implies(X_1109,X_1109),X_1107),X_1107))) )],[refute_0_96,refute_0_87]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(implies(X_1111,X_1111),X_1110),X_1110)),
inference(subst,[],[refute_0_97:[bind(X_1107,$fot(X_1110)),bind(X_1109,$fot(X_1111))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(implies(X_1111,X_1111),X_1110))
| is_a_theorem(X_1110) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1111,X_1111),X_1110),X_1110)) )],[refute_0_98,refute_0_86]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(implies(X_7030,X_7030),implies(implies(not(X_7030),X_7030),implies(implies(X_7030,X_7032),X_7032))))
| is_a_theorem(implies(implies(not(X_7030),X_7030),implies(implies(X_7030,X_7032),X_7032))) ),
inference(subst,[],[refute_0_99:[bind(X_1110,$fot(implies(implies(not(X_7030),X_7030),implies(implies(X_7030,X_7032),X_7032)))),bind(X_1111,$fot(X_7030))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_6950),X_6950),X_6949),implies(implies(not(X_6950),X_6950),implies(implies(X_6949,X_6951),X_6951))))
| is_a_theorem(implies(implies(X_6950,X_6949),implies(implies(not(X_6950),X_6950),implies(implies(X_6949,X_6951),X_6951)))) ),
inference(subst,[],[refute_0_50:[bind(X_61,$fot(implies(implies(not(X_6950),X_6950),implies(implies(X_6949,X_6951),X_6951)))),bind(X_62,$fot(X_6950)),bind(X_63,$fot(X_6949))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(implies(implies(X_39,X_6812),implies(implies(X_6813,X_6811),X_6812)),implies(implies(X_6813,X_6811),implies(implies(X_39,X_6812),X_6812))))
| is_a_theorem(implies(implies(implies(X_6813,X_6811),X_39),implies(implies(X_6813,X_6811),implies(implies(X_39,X_6812),X_6812)))) ),
inference(subst,[],[refute_0_24:[bind(X_38,$fot(implies(X_6813,X_6811))),bind(X_40,$fot(X_6812)),bind(X_41,$fot(implies(implies(X_6813,X_6811),implies(implies(X_39,X_6812),X_6812))))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_6758,X_6756),X_6757),X_6757),implies(X_38,X_6757)),implies(implies(X_6758,X_6756),implies(X_38,X_6757))))
| is_a_theorem(implies(implies(X_38,implies(implies(X_6758,X_6756),X_6757)),implies(implies(X_6758,X_6756),implies(X_38,X_6757)))) ),
inference(subst,[],[refute_0_24:[bind(X_39,$fot(implies(implies(X_6758,X_6756),X_6757))),bind(X_40,$fot(X_6757)),bind(X_41,$fot(implies(implies(X_6758,X_6756),implies(X_38,X_6757))))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(implies(implies(X_2198,X_2198),implies(X_38,X_2198)),implies(X_2197,implies(implies(implies(X_38,X_2198),X_2199),X_2199))))
| is_a_theorem(implies(implies(X_38,X_2198),implies(X_2197,implies(implies(implies(X_38,X_2198),X_2199),X_2199)))) ),
inference(subst,[],[refute_0_24:[bind(X_39,$fot(X_2198)),bind(X_40,$fot(X_2198)),bind(X_41,$fot(implies(X_2197,implies(implies(implies(X_38,X_2198),X_2199),X_2199))))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(implies(implies(X_39,X_2196),implies(implies(X_2194,X_2194),X_2196)),implies(X_2193,implies(implies(X_39,X_2196),X_2196))))
| is_a_theorem(implies(implies(implies(X_2194,X_2194),X_39),implies(X_2193,implies(implies(X_39,X_2196),X_2196)))) ),
inference(subst,[],[refute_0_24:[bind(X_38,$fot(implies(X_2194,X_2194))),bind(X_40,$fot(X_2196)),bind(X_41,$fot(implies(X_2193,implies(implies(X_39,X_2196),X_2196))))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(X_1108,implies(implies(implies(X_1109,X_1109),X_1107),X_1107)))
| is_a_theorem(implies(implies(implies(implies(implies(X_1109,X_1109),X_1107),X_1107),Z),implies(X_1108,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_1108)),bind(Y,$fot(implies(implies(implies(X_1109,X_1109),X_1107),X_1107)))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(X_1108,implies(implies(implies(X_1109,X_1109),X_1107),X_1107))),
inference(subst,[],[refute_0_95:[bind(X_1044,$fot(X_1107)),bind(X_1045,$fot(X_1108)),bind(X_713,$fot(X_1109))]]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_1109,X_1109),X_1107),X_1107),Z),implies(X_1108,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1108,implies(implies(implies(X_1109,X_1109),X_1107),X_1107))) )],[refute_0_107,refute_0_106]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_1109,X_1109),X_1772),X_1772),implies(X_1770,X_1772)),implies(X_1108,implies(X_1770,X_1772)))),
inference(subst,[],[refute_0_108:[bind(Z,$fot(implies(X_1770,X_1772))),bind(X_1107,$fot(X_1772))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_1109,X_1109),X_1772),X_1772),implies(X_1770,X_1772)),implies(X_1108,implies(X_1770,X_1772))))
| is_a_theorem(implies(implies(X_1770,implies(implies(X_1109,X_1109),X_1772)),implies(X_1108,implies(X_1770,X_1772)))) ),
inference(subst,[],[refute_0_24:[bind(X_38,$fot(X_1770)),bind(X_39,$fot(implies(implies(X_1109,X_1109),X_1772))),bind(X_40,$fot(X_1772)),bind(X_41,$fot(implies(X_1108,implies(X_1770,X_1772))))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(X_1770,implies(implies(X_1109,X_1109),X_1772)),implies(X_1108,implies(X_1770,X_1772)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_1109,X_1109),X_1772),X_1772),implies(X_1770,X_1772)),implies(X_1108,implies(X_1770,X_1772)))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(implies(X_39,X_2196),implies(implies(X_2194,X_2194),X_2196)),implies(X_2193,implies(implies(X_39,X_2196),X_2196)))),
inference(subst,[],[refute_0_111:[bind(X_1108,$fot(X_2193)),bind(X_1109,$fot(X_2194)),bind(X_1770,$fot(implies(X_39,X_2196))),bind(X_1772,$fot(X_2196))]]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(implies(X_2194,X_2194),X_39),implies(X_2193,implies(implies(X_39,X_2196),X_2196)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_39,X_2196),implies(implies(X_2194,X_2194),X_2196)),implies(X_2193,implies(implies(X_39,X_2196),X_2196)))) )],[refute_0_112,refute_0_105]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(implies(X_2198,X_2198),implies(X_38,X_2198)),implies(X_2197,implies(implies(implies(X_38,X_2198),X_2199),X_2199)))),
inference(subst,[],[refute_0_113:[bind(X_2193,$fot(X_2197)),bind(X_2194,$fot(X_2198)),bind(X_2196,$fot(X_2199)),bind(X_39,$fot(implies(X_38,X_2198)))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(X_38,X_2198),implies(X_2197,implies(implies(implies(X_38,X_2198),X_2199),X_2199)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_2198,X_2198),implies(X_38,X_2198)),implies(X_2197,implies(implies(implies(X_38,X_2198),X_2199),X_2199)))) )],[refute_0_114,refute_0_104]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(X_38,X_2198),implies(implies(X_6726,X_6726),implies(implies(implies(X_38,X_2198),X_2199),X_2199)))),
inference(subst,[],[refute_0_115:[bind(X_2197,$fot(implies(X_6726,X_6726)))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(X_1812,implies(implies(X_1814,X_1814),X_1815)))
| ~ is_a_theorem(implies(implies(X_1812,implies(implies(X_1814,X_1814),X_1815)),implies(implies(X_1815,X_1813),implies(X_1812,X_1813))))
| is_a_theorem(implies(implies(X_1815,X_1813),implies(X_1812,X_1813))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1812,implies(implies(X_1814,X_1814),X_1815)))),bind(Y,$fot(implies(implies(X_1815,X_1813),implies(X_1812,X_1813))))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(implies(X_718,X_716),implies(implies(implies(X_717,X_717),X_718),X_716)))
| is_a_theorem(implies(implies(implies(implies(implies(X_717,X_717),X_718),X_716),Z),implies(implies(X_718,X_716),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X_718,X_716))),bind(Y,$fot(implies(implies(implies(X_717,X_717),X_718),X_716)))]]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(X_718,X_716),implies(implies(implies(X_717,X_717),X_718),X_716))),
inference(subst,[],[refute_0_92:[bind(X_712,$fot(X_716)),bind(X_713,$fot(X_717)),bind(X_715,$fot(X_718))]]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_717,X_717),X_718),X_716),Z),implies(implies(X_718,X_716),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_718,X_716),implies(implies(implies(X_717,X_717),X_718),X_716))) )],[refute_0_119,refute_0_118]) ).
cnf(refute_0_121,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_717,X_717),X_718),X_1772),implies(X_1770,X_1772)),implies(implies(X_718,X_1772),implies(X_1770,X_1772)))),
inference(subst,[],[refute_0_120:[bind(Z,$fot(implies(X_1770,X_1772))),bind(X_716,$fot(X_1772))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_717,X_717),X_718),X_1772),implies(X_1770,X_1772)),implies(implies(X_718,X_1772),implies(X_1770,X_1772))))
| is_a_theorem(implies(implies(X_1770,implies(implies(X_717,X_717),X_718)),implies(implies(X_718,X_1772),implies(X_1770,X_1772)))) ),
inference(subst,[],[refute_0_24:[bind(X_38,$fot(X_1770)),bind(X_39,$fot(implies(implies(X_717,X_717),X_718))),bind(X_40,$fot(X_1772)),bind(X_41,$fot(implies(implies(X_718,X_1772),implies(X_1770,X_1772))))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(X_1770,implies(implies(X_717,X_717),X_718)),implies(implies(X_718,X_1772),implies(X_1770,X_1772)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_717,X_717),X_718),X_1772),implies(X_1770,X_1772)),implies(implies(X_718,X_1772),implies(X_1770,X_1772)))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(X_1812,implies(implies(X_1814,X_1814),X_1815)),implies(implies(X_1815,X_1813),implies(X_1812,X_1813)))),
inference(subst,[],[refute_0_123:[bind(X_1770,$fot(X_1812)),bind(X_1772,$fot(X_1813)),bind(X_717,$fot(X_1814)),bind(X_718,$fot(X_1815))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(X_1812,implies(implies(X_1814,X_1814),X_1815)))
| is_a_theorem(implies(implies(X_1815,X_1813),implies(X_1812,X_1813))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1812,implies(implies(X_1814,X_1814),X_1815)),implies(implies(X_1815,X_1813),implies(X_1812,X_1813)))) )],[refute_0_124,refute_0_117]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(implies(implies(X_38,X_2198),implies(implies(X_6726,X_6726),implies(implies(implies(X_38,X_2198),X_2199),X_2199))))
| is_a_theorem(implies(implies(implies(implies(implies(X_38,X_2198),X_2199),X_2199),X_6725),implies(implies(X_38,X_2198),X_6725))) ),
inference(subst,[],[refute_0_125:[bind(X_1812,$fot(implies(X_38,X_2198))),bind(X_1813,$fot(X_6725)),bind(X_1814,$fot(X_6726)),bind(X_1815,$fot(implies(implies(implies(X_38,X_2198),X_2199),X_2199)))]]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_38,X_2198),X_2199),X_2199),X_6725),implies(implies(X_38,X_2198),X_6725))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_38,X_2198),implies(implies(X_6726,X_6726),implies(implies(implies(X_38,X_2198),X_2199),X_2199)))) )],[refute_0_116,refute_0_126]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_6758,X_6756),X_6757),X_6757),implies(X_38,X_6757)),implies(implies(X_6758,X_6756),implies(X_38,X_6757)))),
inference(subst,[],[refute_0_127:[bind(X_2198,$fot(X_6756)),bind(X_2199,$fot(X_6757)),bind(X_38,$fot(X_6758)),bind(X_6725,$fot(implies(X_38,X_6757)))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_38,implies(implies(X_6758,X_6756),X_6757)),implies(implies(X_6758,X_6756),implies(X_38,X_6757)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_6758,X_6756),X_6757),X_6757),implies(X_38,X_6757)),implies(implies(X_6758,X_6756),implies(X_38,X_6757)))) )],[refute_0_128,refute_0_103]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(implies(X_39,X_6812),implies(implies(X_6813,X_6811),X_6812)),implies(implies(X_6813,X_6811),implies(implies(X_39,X_6812),X_6812)))),
inference(subst,[],[refute_0_129:[bind(X_38,$fot(implies(X_39,X_6812))),bind(X_6756,$fot(X_6811)),bind(X_6757,$fot(X_6812)),bind(X_6758,$fot(X_6813))]]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(implies(X_6813,X_6811),X_39),implies(implies(X_6813,X_6811),implies(implies(X_39,X_6812),X_6812)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_39,X_6812),implies(implies(X_6813,X_6811),X_6812)),implies(implies(X_6813,X_6811),implies(implies(X_39,X_6812),X_6812)))) )],[refute_0_130,refute_0_102]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(implies(not(X_6950),X_6950),X_6949),implies(implies(not(X_6950),X_6950),implies(implies(X_6949,X_6951),X_6951)))),
inference(subst,[],[refute_0_131:[bind(X_39,$fot(X_6949)),bind(X_6811,$fot(X_6950)),bind(X_6812,$fot(X_6951)),bind(X_6813,$fot(not(X_6950)))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(X_6950,X_6949),implies(implies(not(X_6950),X_6950),implies(implies(X_6949,X_6951),X_6951)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_6950),X_6950),X_6949),implies(implies(not(X_6950),X_6950),implies(implies(X_6949,X_6951),X_6951)))) )],[refute_0_132,refute_0_101]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(X_7030,X_7030),implies(implies(not(X_7030),X_7030),implies(implies(X_7030,X_7032),X_7032)))),
inference(subst,[],[refute_0_133:[bind(X_6949,$fot(X_7030)),bind(X_6950,$fot(X_7030)),bind(X_6951,$fot(X_7032))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(not(X_7030),X_7030),implies(implies(X_7030,X_7032),X_7032))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_7030,X_7030),implies(implies(not(X_7030),X_7030),implies(implies(X_7030,X_7032),X_7032)))) )],[refute_0_134,refute_0_100]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(implies(not(X_7033),X_7033),implies(implies(X_7033,X_7034),X_7034))),
inference(subst,[],[refute_0_135:[bind(X_7030,$fot(X_7033)),bind(X_7032,$fot(X_7034))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(X_7033,implies(implies(X_7033,X_7034),X_7034))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7033),X_7033),implies(implies(X_7033,X_7034),X_7034))) )],[refute_0_136,refute_0_85]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(not(not(X_7349)),implies(implies(not(not(X_7349)),X_7349),X_7349))),
inference(subst,[],[refute_0_137:[bind(X_7033,$fot(not(not(X_7349)))),bind(X_7034,$fot(X_7349))]]) ).
cnf(refute_0_139,plain,
( ~ is_a_theorem(implies(X_2804,implies(implies(not(not(X_2805)),X_2803),X_2805)))
| ~ is_a_theorem(implies(implies(X_2804,implies(implies(not(not(X_2805)),X_2803),X_2805)),implies(X_2802,implies(X_2804,X_2805))))
| is_a_theorem(implies(X_2802,implies(X_2804,X_2805))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_2804,implies(implies(not(not(X_2805)),X_2803),X_2805)))),bind(Y,$fot(implies(X_2802,implies(X_2804,X_2805))))]]) ).
cnf(refute_0_140,plain,
( ~ is_a_theorem(implies(X_1165,implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)))
| is_a_theorem(implies(implies(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164),Z),implies(X_1165,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_1165)),bind(Y,$fot(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164)))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(X_1165,implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164))),
inference(subst,[],[refute_0_79:[bind(X_1044,$fot(X_1164)),bind(X_1045,$fot(X_1165)),bind(X_32,$fot(X_1166))]]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(implies(implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164),Z),implies(X_1165,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1165,implies(implies(implies(not(not(X_1164)),X_1166),X_1164),X_1164))) )],[refute_0_141,refute_0_140]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(implies(implies(implies(implies(not(not(X_1772)),X_1166),X_1772),X_1772),implies(X_1770,X_1772)),implies(X_1165,implies(X_1770,X_1772)))),
inference(subst,[],[refute_0_142:[bind(Z,$fot(implies(X_1770,X_1772))),bind(X_1164,$fot(X_1772))]]) ).
cnf(refute_0_144,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(not(not(X_1772)),X_1166),X_1772),X_1772),implies(X_1770,X_1772)),implies(X_1165,implies(X_1770,X_1772))))
| is_a_theorem(implies(implies(X_1770,implies(implies(not(not(X_1772)),X_1166),X_1772)),implies(X_1165,implies(X_1770,X_1772)))) ),
inference(subst,[],[refute_0_24:[bind(X_38,$fot(X_1770)),bind(X_39,$fot(implies(implies(not(not(X_1772)),X_1166),X_1772))),bind(X_40,$fot(X_1772)),bind(X_41,$fot(implies(X_1165,implies(X_1770,X_1772))))]]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(implies(X_1770,implies(implies(not(not(X_1772)),X_1166),X_1772)),implies(X_1165,implies(X_1770,X_1772)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(not(not(X_1772)),X_1166),X_1772),X_1772),implies(X_1770,X_1772)),implies(X_1165,implies(X_1770,X_1772)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(X_2804,implies(implies(not(not(X_2805)),X_2803),X_2805)),implies(X_2802,implies(X_2804,X_2805)))),
inference(subst,[],[refute_0_145:[bind(X_1165,$fot(X_2802)),bind(X_1166,$fot(X_2803)),bind(X_1770,$fot(X_2804)),bind(X_1772,$fot(X_2805))]]) ).
cnf(refute_0_147,plain,
( ~ is_a_theorem(implies(X_2804,implies(implies(not(not(X_2805)),X_2803),X_2805)))
| is_a_theorem(implies(X_2802,implies(X_2804,X_2805))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2804,implies(implies(not(not(X_2805)),X_2803),X_2805)),implies(X_2802,implies(X_2804,X_2805)))) )],[refute_0_146,refute_0_139]) ).
cnf(refute_0_148,plain,
( ~ is_a_theorem(implies(not(not(X_7349)),implies(implies(not(not(X_7349)),X_7349),X_7349)))
| is_a_theorem(implies(X_7346,implies(not(not(X_7349)),X_7349))) ),
inference(subst,[],[refute_0_147:[bind(X_2802,$fot(X_7346)),bind(X_2803,$fot(X_7349)),bind(X_2804,$fot(not(not(X_7349)))),bind(X_2805,$fot(X_7349))]]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(X_7346,implies(not(not(X_7349)),X_7349))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_7349)),implies(implies(not(not(X_7349)),X_7349),X_7349))) )],[refute_0_138,refute_0_148]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(implies(not(not(implies(not(not(X_7354)),X_7354))),X_1168),implies(not(not(X_7354)),X_7354))),
inference(subst,[],[refute_0_149:[bind(X_7346,$fot(implies(not(not(implies(not(not(X_7354)),X_7354))),X_1168))),bind(X_7349,$fot(X_7354))]]) ).
cnf(refute_0_151,plain,
is_a_theorem(implies(not(not(X_7354)),X_7354)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(not(not(X_7354)),X_7354))),X_1168),implies(not(not(X_7354)),X_7354))) )],[refute_0_150,refute_0_84]) ).
cnf(refute_0_152,plain,
is_a_theorem(implies(not(not(not(X_1778))),not(X_1778))),
inference(subst,[],[refute_0_151:[bind(X_7354,$fot(not(X_1778)))]]) ).
cnf(refute_0_153,plain,
is_a_theorem(implies(X_1778,implies(not(not(not(X_1778))),X_1777))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(X_1778))),not(X_1778))) )],[refute_0_152,refute_0_36]) ).
cnf(refute_0_154,plain,
is_a_theorem(implies(X_7366,implies(not(not(not(X_7366))),not(not(X_7366))))),
inference(subst,[],[refute_0_153:[bind(X_1777,$fot(not(not(X_7366)))),bind(X_1778,$fot(X_7366))]]) ).
cnf(refute_0_155,plain,
is_a_theorem(implies(not(X_7366),implies(X_7366,X_1941))),
inference(resolve,[$cnf( is_a_theorem(implies(X_7366,implies(not(not(not(X_7366))),not(not(X_7366))))) )],[refute_0_154,refute_0_29]) ).
cnf(refute_0_156,plain,
is_a_theorem(implies(not(X_7369),implies(X_7369,X_7368))),
inference(subst,[],[refute_0_155:[bind(X_1941,$fot(X_7368)),bind(X_7366,$fot(X_7369))]]) ).
cnf(refute_0_157,plain,
is_a_theorem(implies(implies(implies(X_7369,X_7368),Z),implies(not(X_7369),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_7369),implies(X_7369,X_7368))) )],[refute_0_156,refute_0_2]) ).
cnf(refute_0_158,plain,
is_a_theorem(implies(implies(implies(a,b),c),implies(not(a),c))),
inference(subst,[],[refute_0_157:[bind(Z,$fot(c)),bind(X_7368,$fot(b)),bind(X_7369,$fot(a))]]) ).
cnf(refute_0_159,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(a,b),c),implies(not(a),c))) )],[refute_0_158,prove_cn_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL055-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 3 13:18:10 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.85/6.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.85/6.09
% 5.85/6.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.94/6.10
%------------------------------------------------------------------------------