TSTP Solution File: LCL096-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL096-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:49:28 EDT 2022
% Result : Unsatisfiable 51.78s 51.99s
% Output : CNFRefutation 51.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 5
% Syntax : Number of clauses : 132 ( 75 unt; 0 nHn; 40 RR)
% Number of literals : 203 ( 0 equ; 72 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 465 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(lg_2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) ).
cnf(lg_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)) ).
cnf(lg_4,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),U),equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),U)))) ).
cnf(prove_lg_1,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(X_34,X_35),equivalent(X_34,X_36)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_34,X_35),equivalent(X_34,X_36)),equivalent(X_35,X_36)))
| is_a_theorem(equivalent(X_35,X_36)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_34,X_35),equivalent(X_34,X_36)))),bind(Y,$fot(equivalent(X_35,X_36)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_5),X_5)),
inference(subst,[],[lg_2:[bind(U,$fot(X_5))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_5))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_5),X_5))
| is_a_theorem(X_5) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_5))),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_5))
| is_a_theorem(X_5) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_5),X_5)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32)),equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32))))
| is_a_theorem(equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_31)),bind(Z,$fot(X_32)),bind(X_5,$fot(equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32))))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_18)),equivalent(X_17,X_18)),equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_17,V),equivalent(X_17,X_18))))),
inference(subst,[],[lg_4:[bind(U,$fot(equivalent(X_17,X_18))),bind(X,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(equivalent(X_16,X_18)))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_18)),equivalent(X_17,X_18)),equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_17,V),equivalent(X_17,X_18)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_17,V),equivalent(X_17,X_18)))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18)),bind(X_5,$fot(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_17,V),equivalent(X_17,X_18)))))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_17,V),equivalent(X_17,X_18)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_18)),equivalent(X_17,X_18)),equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_17,V),equivalent(X_17,X_18))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_16,V),equivalent(X_16,X_18)))),
inference(subst,[],[refute_0_7:[bind(X_17,$fot(X_16))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equivalent(equivalent(X_21,X_20),equivalent(X_21,X_23)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_21,X_20),equivalent(X_21,X_23)),equivalent(equivalent(X_22,X_20),equivalent(X_22,X_23))))
| is_a_theorem(equivalent(equivalent(X_22,X_20),equivalent(X_22,X_23))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_21,X_20),equivalent(X_21,X_23)))),bind(Y,$fot(equivalent(equivalent(X_22,X_20),equivalent(X_22,X_23))))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_21,X_20),equivalent(X_21,X_23)),equivalent(equivalent(X_22,X_20),equivalent(X_22,X_23)))),
inference(subst,[],[refute_0_7:[bind(V,$fot(X_20)),bind(X_16,$fot(X_21)),bind(X_17,$fot(X_22)),bind(X_18,$fot(X_23))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(X_21,X_20),equivalent(X_21,X_23)))
| is_a_theorem(equivalent(equivalent(X_22,X_20),equivalent(X_22,X_23))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_21,X_20),equivalent(X_21,X_23)),equivalent(equivalent(X_22,X_20),equivalent(X_22,X_23)))) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_16,V),equivalent(X_16,X_18))))
| is_a_theorem(equivalent(equivalent(X_26,equivalent(X_16,X_18)),equivalent(X_26,equivalent(X_16,X_18)))) ),
inference(subst,[],[refute_0_11:[bind(X_20,$fot(equivalent(X_16,X_18))),bind(X_21,$fot(equivalent(X_16,V))),bind(X_22,$fot(X_26)),bind(X_23,$fot(equivalent(X_16,X_18)))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(X_26,equivalent(X_16,X_18)),equivalent(X_26,equivalent(X_16,X_18)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_16,V),equivalent(X_16,X_18)))) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32)),equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32)))),
inference(subst,[],[refute_0_13:[bind(X_16,$fot(X_31)),bind(X_18,$fot(X_32)),bind(X_26,$fot(equivalent(equivalent(X,X_31),equivalent(X,X_32))))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32)),equivalent(equivalent(equivalent(X,X_31),equivalent(X,X_32)),equivalent(X_31,X_32)))) )],[refute_0_14,refute_0_4]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_34,X_35),equivalent(X_34,X_36)),equivalent(X_35,X_36))),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_34)),bind(X_31,$fot(X_35)),bind(X_32,$fot(X_36))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(equivalent(equivalent(X_34,X_35),equivalent(X_34,X_36)))
| is_a_theorem(equivalent(X_35,X_36)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_34,X_35),equivalent(X_34,X_36)),equivalent(X_35,X_36))) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35),equivalent(equivalent(X_170,equivalent(X_171,X_171)),equivalent(X_170,equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35)))))
| is_a_theorem(equivalent(X_35,equivalent(X_170,equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35)))) ),
inference(subst,[],[refute_0_17:[bind(X_34,$fot(equivalent(X_170,equivalent(X_171,X_171)))),bind(X_36,$fot(equivalent(X_170,equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35))))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_168,X_168),X_166),equivalent(equivalent(X_168,X_168),equivalent(equivalent(X_167,equivalent(X_168,X_168)),equivalent(X_167,X_166)))))
| is_a_theorem(equivalent(X_166,equivalent(equivalent(X_167,equivalent(X_168,X_168)),equivalent(X_167,X_166)))) ),
inference(subst,[],[refute_0_17:[bind(X_34,$fot(equivalent(X_168,X_168))),bind(X_35,$fot(X_166)),bind(X_36,$fot(equivalent(equivalent(X_167,equivalent(X_168,X_168)),equivalent(X_167,X_166))))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(X_105,X_107)),equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))))
| is_a_theorem(equivalent(equivalent(X_105,X_107),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))) ),
inference(subst,[],[refute_0_17:[bind(X_34,$fot(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))),bind(X_35,$fot(equivalent(X_105,X_107))),bind(X_36,$fot(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_62,X_62),equivalent(X_62,X_62)),equivalent(equivalent(X_62,X_62),equivalent(X_61,X_61))))
| is_a_theorem(equivalent(equivalent(X_22,equivalent(X_62,X_62)),equivalent(X_22,equivalent(X_61,X_61)))) ),
inference(subst,[],[refute_0_11:[bind(X_20,$fot(equivalent(X_62,X_62))),bind(X_21,$fot(equivalent(X_62,X_62))),bind(X_23,$fot(equivalent(X_61,X_61)))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(X_41)
| ~ is_a_theorem(equivalent(X_41,equivalent(equivalent(X_40,X_40),X_41)))
| is_a_theorem(equivalent(equivalent(X_40,X_40),X_41)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_41)),bind(Y,$fot(equivalent(equivalent(X_40,X_40),X_41)))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),X_38),equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(Y,Y),X_38)))),
inference(subst,[],[lg_4:[bind(U,$fot(X_38)),bind(V,$fot(Y))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),X_38),equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(Y,Y),X_38))))
| is_a_theorem(equivalent(X_38,equivalent(equivalent(Y,Y),X_38))) ),
inference(subst,[],[refute_0_17:[bind(X_34,$fot(equivalent(equivalent(X,Y),Z))),bind(X_35,$fot(X_38)),bind(X_36,$fot(equivalent(equivalent(Y,Y),X_38)))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(equivalent(X_38,equivalent(equivalent(Y,Y),X_38))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),X_38),equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(Y,Y),X_38)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(equivalent(X_41,equivalent(equivalent(X_40,X_40),X_41))),
inference(subst,[],[refute_0_25:[bind(Y,$fot(X_40)),bind(X_38,$fot(X_41))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(X_41)
| is_a_theorem(equivalent(equivalent(X_40,X_40),X_41)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_41,equivalent(equivalent(X_40,X_40),X_41))) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(equivalent(equivalent(X_48,X_48),equivalent(X_47,X_47)))
| is_a_theorem(equivalent(equivalent(X_40,X_40),equivalent(equivalent(X_48,X_48),equivalent(X_47,X_47)))) ),
inference(subst,[],[refute_0_27:[bind(X_41,$fot(equivalent(equivalent(X_48,X_48),equivalent(X_47,X_47))))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(equivalent(equivalent(X_42,X_43),equivalent(X_42,X_43)))
| is_a_theorem(equivalent(X_43,X_43)) ),
inference(subst,[],[refute_0_17:[bind(X_34,$fot(X_42)),bind(X_35,$fot(X_43)),bind(X_36,$fot(X_43))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_16,V),equivalent(X_16,X_18))))
| is_a_theorem(equivalent(equivalent(X_16,X_18),equivalent(X_16,X_18))) ),
inference(subst,[],[refute_0_17:[bind(X_34,$fot(equivalent(X_16,V))),bind(X_35,$fot(equivalent(X_16,X_18))),bind(X_36,$fot(equivalent(X_16,X_18)))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(equivalent(equivalent(X_16,X_18),equivalent(X_16,X_18))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_16,V),equivalent(X_16,X_18)),equivalent(equivalent(X_16,V),equivalent(X_16,X_18)))) )],[refute_0_8,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(equivalent(equivalent(X_42,X_43),equivalent(X_42,X_43))),
inference(subst,[],[refute_0_31:[bind(X_16,$fot(X_42)),bind(X_18,$fot(X_43))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(equivalent(X_43,X_43)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_42,X_43),equivalent(X_42,X_43))) )],[refute_0_32,refute_0_29]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(equivalent(X_43,X_43))
| is_a_theorem(equivalent(equivalent(X_45,X_45),equivalent(X_43,X_43))) ),
inference(subst,[],[refute_0_27:[bind(X_40,$fot(X_45)),bind(X_41,$fot(equivalent(X_43,X_43)))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(equivalent(equivalent(X_45,X_45),equivalent(X_43,X_43))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_43,X_43)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
is_a_theorem(equivalent(equivalent(X_48,X_48),equivalent(X_47,X_47))),
inference(subst,[],[refute_0_35:[bind(X_43,$fot(X_47)),bind(X_45,$fot(X_48))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(equivalent(equivalent(X_40,X_40),equivalent(equivalent(X_48,X_48),equivalent(X_47,X_47)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_48,X_48),equivalent(X_47,X_47))) )],[refute_0_36,refute_0_28]) ).
cnf(refute_0_38,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_62,X_62),equivalent(X_62,X_62)),equivalent(equivalent(X_62,X_62),equivalent(X_61,X_61)))),
inference(subst,[],[refute_0_37:[bind(X_40,$fot(equivalent(X_62,X_62))),bind(X_47,$fot(X_61)),bind(X_48,$fot(X_62))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(equivalent(equivalent(X_22,equivalent(X_62,X_62)),equivalent(X_22,equivalent(X_61,X_61)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_62,X_62),equivalent(X_62,X_62)),equivalent(equivalent(X_62,X_62),equivalent(X_61,X_61)))) )],[refute_0_38,refute_0_21]) ).
cnf(refute_0_40,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(equivalent(X_100,X_96),equivalent(X_100,X_96))),equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(X_61,X_61)))),
inference(subst,[],[refute_0_39:[bind(X_22,$fot(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)))),bind(X_62,$fot(equivalent(X_100,X_96)))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7),X_7)),
inference(subst,[],[lg_3:[bind(U,$fot(X_6)),bind(V,$fot(X_7)),bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7),X_7)) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(equivalent(X_100,X_96),equivalent(X_100,X_96))),equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(X_61,X_61))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(X_61,X_61))) ),
inference(subst,[],[refute_0_43:[bind(X_10,$fot(X_96)),bind(X_6,$fot(equivalent(X_100,X_96))),bind(X_7,$fot(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(X_61,X_61)))),bind(X_8,$fot(X_99)),bind(X_9,$fot(X_100))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(X_61,X_61))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(equivalent(X_100,X_96),equivalent(X_100,X_96))),equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),equivalent(X_100,X_96)),equivalent(X_61,X_61)))) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(X_105,X_107)),equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))),
inference(subst,[],[refute_0_45:[bind(X_100,$fot(X_105)),bind(X_61,$fot(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))),bind(X_96,$fot(X_107)),bind(X_99,$fot(X_108))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(equivalent(equivalent(X_105,X_107),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(X_105,X_107)),equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))) )],[refute_0_46,refute_0_20]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(equivalent(X_30,X_29))
| ~ is_a_theorem(equivalent(equivalent(X_30,X_29),equivalent(X_30,equivalent(equivalent(X_28,X_28),X_29))))
| is_a_theorem(equivalent(X_30,equivalent(equivalent(X_28,X_28),X_29))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_30,X_29))),bind(Y,$fot(equivalent(X_30,equivalent(equivalent(X_28,X_28),X_29))))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),X_24),equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(Y,Y),X_24)))),
inference(subst,[],[lg_4:[bind(U,$fot(X_24)),bind(V,$fot(Y))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),X_24),equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(Y,Y),X_24))))
| is_a_theorem(equivalent(equivalent(X_26,X_24),equivalent(X_26,equivalent(equivalent(Y,Y),X_24)))) ),
inference(subst,[],[refute_0_11:[bind(X_20,$fot(X_24)),bind(X_21,$fot(equivalent(equivalent(X,Y),Z))),bind(X_22,$fot(X_26)),bind(X_23,$fot(equivalent(equivalent(Y,Y),X_24)))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(equivalent(equivalent(X_26,X_24),equivalent(X_26,equivalent(equivalent(Y,Y),X_24)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),X_24),equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(Y,Y),X_24)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
is_a_theorem(equivalent(equivalent(X_30,X_29),equivalent(X_30,equivalent(equivalent(X_28,X_28),X_29)))),
inference(subst,[],[refute_0_51:[bind(Y,$fot(X_28)),bind(X_24,$fot(X_29)),bind(X_26,$fot(X_30))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(equivalent(X_30,X_29))
| is_a_theorem(equivalent(X_30,equivalent(equivalent(X_28,X_28),X_29))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_30,X_29),equivalent(X_30,equivalent(equivalent(X_28,X_28),X_29)))) )],[refute_0_52,refute_0_48]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(equivalent(equivalent(X_105,X_107),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))
| is_a_theorem(equivalent(equivalent(X_105,X_107),equivalent(equivalent(X_159,X_159),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))) ),
inference(subst,[],[refute_0_53:[bind(X_28,$fot(X_159)),bind(X_29,$fot(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))),bind(X_30,$fot(equivalent(X_105,X_107)))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(equivalent(equivalent(X_105,X_107),equivalent(equivalent(X_159,X_159),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_105,X_107),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))) )],[refute_0_47,refute_0_54]) ).
cnf(refute_0_56,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_168,X_168),X_166),equivalent(equivalent(X_168,X_168),equivalent(equivalent(X_167,equivalent(X_168,X_168)),equivalent(X_167,X_166))))),
inference(subst,[],[refute_0_55:[bind(X_105,$fot(equivalent(X_168,X_168))),bind(X_107,$fot(X_166)),bind(X_108,$fot(X_167)),bind(X_159,$fot(X_168))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(equivalent(X_166,equivalent(equivalent(X_167,equivalent(X_168,X_168)),equivalent(X_167,X_166)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_168,X_168),X_166),equivalent(equivalent(X_168,X_168),equivalent(equivalent(X_167,equivalent(X_168,X_168)),equivalent(X_167,X_166))))) )],[refute_0_56,refute_0_19]) ).
cnf(refute_0_58,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35),equivalent(equivalent(X_170,equivalent(X_171,X_171)),equivalent(X_170,equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35))))),
inference(subst,[],[refute_0_57:[bind(X_166,$fot(equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35))),bind(X_167,$fot(X_170)),bind(X_168,$fot(X_171))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(equivalent(X_35,equivalent(X_170,equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35),equivalent(equivalent(X_170,equivalent(X_171,X_171)),equivalent(X_170,equivalent(equivalent(X_170,equivalent(X_171,X_171)),X_35))))) )],[refute_0_58,refute_0_18]) ).
cnf(refute_0_60,plain,
is_a_theorem(equivalent(X_971,equivalent(X_968,equivalent(equivalent(X_968,equivalent(X_171,X_171)),X_971)))),
inference(subst,[],[refute_0_59:[bind(X_170,$fot(X_968)),bind(X_35,$fot(X_971))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(equivalent(X_127,equivalent(X_124,X_126)))
| ~ is_a_theorem(equivalent(equivalent(X_127,equivalent(X_124,X_126)),equivalent(equivalent(equivalent(X_124,X_125),X_127),equivalent(X_125,X_126))))
| is_a_theorem(equivalent(equivalent(equivalent(X_124,X_125),X_127),equivalent(X_125,X_126))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_127,equivalent(X_124,X_126)))),bind(Y,$fot(equivalent(equivalent(equivalent(X_124,X_125),X_127),equivalent(X_125,X_126))))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),equivalent(equivalent(X_116,equivalent(X,Z)),equivalent(equivalent(equivalent(X,Y),X_116),equivalent(Y,Z)))))
| is_a_theorem(equivalent(equivalent(X_116,equivalent(X,Z)),equivalent(equivalent(equivalent(X,Y),X_116),equivalent(Y,Z)))) ),
inference(subst,[],[refute_0_3:[bind(X_5,$fot(equivalent(equivalent(X_116,equivalent(X,Z)),equivalent(equivalent(equivalent(X,Y),X_116),equivalent(Y,Z)))))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),equivalent(equivalent(X_8,X_9),X_102)),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102))),equivalent(equivalent(equivalent(X_8,X_10),X_102),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_8,X_10),X_102),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102)))) ),
inference(subst,[],[refute_0_43:[bind(X_6,$fot(equivalent(equivalent(X_8,X_9),X_102))),bind(X_7,$fot(equivalent(equivalent(equivalent(X_8,X_10),X_102),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102)))))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97)),equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97)))),
inference(subst,[],[refute_0_33:[bind(X_43,$fot(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97))))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97)),equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97))) ),
inference(subst,[],[refute_0_43:[bind(X_10,$fot(X_96)),bind(X_6,$fot(X_97)),bind(X_7,$fot(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97)))),bind(X_8,$fot(X_99)),bind(X_9,$fot(X_100))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97)),equivalent(equivalent(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_96)),X_97),equivalent(equivalent(X_100,X_96),X_97)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),equivalent(equivalent(X_8,X_9),X_102)),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102))),equivalent(equivalent(equivalent(X_8,X_10),X_102),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102))))),
inference(subst,[],[refute_0_66:[bind(X_100,$fot(equivalent(X_8,X_10))),bind(X_96,$fot(X_102)),bind(X_97,$fot(equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102)))),bind(X_99,$fot(equivalent(X_8,X_9)))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,X_10),X_102),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),equivalent(equivalent(X_8,X_9),X_102)),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102))),equivalent(equivalent(equivalent(X_8,X_10),X_102),equivalent(equivalent(X_9,X_10),equivalent(equivalent(X_8,X_9),X_102))))) )],[refute_0_67,refute_0_63]) ).
cnf(refute_0_69,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),equivalent(equivalent(X_116,equivalent(X,Z)),equivalent(equivalent(equivalent(X,Y),X_116),equivalent(Y,Z))))),
inference(subst,[],[refute_0_68:[bind(X_10,$fot(equivalent(X,Z))),bind(X_102,$fot(equivalent(Y,Z))),bind(X_8,$fot(equivalent(X,Y))),bind(X_9,$fot(X_116))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(equivalent(equivalent(X_116,equivalent(X,Z)),equivalent(equivalent(equivalent(X,Y),X_116),equivalent(Y,Z)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),equivalent(equivalent(X_116,equivalent(X,Z)),equivalent(equivalent(equivalent(X,Y),X_116),equivalent(Y,Z))))) )],[refute_0_69,refute_0_62]) ).
cnf(refute_0_71,plain,
is_a_theorem(equivalent(equivalent(X_127,equivalent(X_124,X_126)),equivalent(equivalent(equivalent(X_124,X_125),X_127),equivalent(X_125,X_126)))),
inference(subst,[],[refute_0_70:[bind(X,$fot(X_124)),bind(Y,$fot(X_125)),bind(Z,$fot(X_126)),bind(X_116,$fot(X_127))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(equivalent(X_127,equivalent(X_124,X_126)))
| is_a_theorem(equivalent(equivalent(equivalent(X_124,X_125),X_127),equivalent(X_125,X_126))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_127,equivalent(X_124,X_126)),equivalent(equivalent(equivalent(X_124,X_125),X_127),equivalent(X_125,X_126)))) )],[refute_0_71,refute_0_61]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(equivalent(X_971,equivalent(X_968,equivalent(equivalent(X_968,equivalent(X_171,X_171)),X_971))))
| is_a_theorem(equivalent(equivalent(equivalent(X_968,X_969),X_971),equivalent(X_969,equivalent(equivalent(X_968,equivalent(X_171,X_171)),X_971)))) ),
inference(subst,[],[refute_0_72:[bind(X_124,$fot(X_968)),bind(X_125,$fot(X_969)),bind(X_126,$fot(equivalent(equivalent(X_968,equivalent(X_171,X_171)),X_971))),bind(X_127,$fot(X_971))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_968,X_969),X_971),equivalent(X_969,equivalent(equivalent(X_968,equivalent(X_171,X_171)),X_971)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_971,equivalent(X_968,equivalent(equivalent(X_968,equivalent(X_171,X_171)),X_971)))) )],[refute_0_60,refute_0_73]) ).
cnf(refute_0_75,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_25408,equivalent(equivalent(X_171,X_171),X_25408)),X_25409),equivalent(equivalent(equivalent(X_171,X_171),X_25408),equivalent(equivalent(X_25408,equivalent(X_171,X_171)),X_25409)))),
inference(subst,[],[refute_0_74:[bind(X_968,$fot(X_25408)),bind(X_969,$fot(equivalent(equivalent(X_171,X_171),X_25408))),bind(X_971,$fot(X_25409))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(equivalent(X_3864,equivalent(equivalent(X_3865,X_3866),equivalent(equivalent(X_3866,X_3865),X_3867))))
| ~ is_a_theorem(equivalent(equivalent(X_3864,equivalent(equivalent(X_3865,X_3866),equivalent(equivalent(X_3866,X_3865),X_3867))),equivalent(X_3864,X_3867)))
| is_a_theorem(equivalent(X_3864,X_3867)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_3864,equivalent(equivalent(X_3865,X_3866),equivalent(equivalent(X_3866,X_3865),X_3867))))),bind(Y,$fot(equivalent(X_3864,X_3867)))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(equivalent(X_121,X_122))
| ~ is_a_theorem(equivalent(equivalent(X_121,X_122),equivalent(equivalent(X_123,X_121),equivalent(X_123,X_122))))
| is_a_theorem(equivalent(equivalent(X_123,X_121),equivalent(X_123,X_122))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_121,X_122))),bind(Y,$fot(equivalent(equivalent(X_123,X_121),equivalent(X_123,X_122))))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(equivalent(equivalent(X_121,X_122),equivalent(equivalent(X_123,X_121),equivalent(X_123,X_122)))),
inference(subst,[],[refute_0_47:[bind(X_105,$fot(X_121)),bind(X_107,$fot(X_122)),bind(X_108,$fot(X_123))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(equivalent(X_121,X_122))
| is_a_theorem(equivalent(equivalent(X_123,X_121),equivalent(X_123,X_122))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_121,X_122),equivalent(equivalent(X_123,X_121),equivalent(X_123,X_122)))) )],[refute_0_78,refute_0_77]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_3857,X_3858),equivalent(equivalent(X_3858,X_3857),X_3859)),X_3859))
| is_a_theorem(equivalent(equivalent(X_123,equivalent(equivalent(X_3857,X_3858),equivalent(equivalent(X_3858,X_3857),X_3859))),equivalent(X_123,X_3859))) ),
inference(subst,[],[refute_0_79:[bind(X_121,$fot(equivalent(equivalent(X_3857,X_3858),equivalent(equivalent(X_3858,X_3857),X_3859)))),bind(X_122,$fot(X_3859))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646)),equivalent(equivalent(X_647,X_647),X_646)),equivalent(equivalent(X_644,equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(X_644,X_646))))
| is_a_theorem(equivalent(equivalent(X_644,equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(X_644,X_646))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(equivalent(X_647,X_647))),bind(Z,$fot(X_646)),bind(X_5,$fot(equivalent(equivalent(X_644,equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(X_644,X_646))))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(equivalent(X_120,equivalent(X_117,X_118)))
| ~ is_a_theorem(equivalent(equivalent(X_120,equivalent(X_117,X_118)),equivalent(X_120,equivalent(equivalent(X_119,X_117),equivalent(X_119,X_118)))))
| is_a_theorem(equivalent(X_120,equivalent(equivalent(X_119,X_117),equivalent(X_119,X_118)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_120,equivalent(X_117,X_118)))),bind(Y,$fot(equivalent(X_120,equivalent(equivalent(X_119,X_117),equivalent(X_119,X_118)))))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(X_105,X_107)),equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))))
| is_a_theorem(equivalent(equivalent(X_22,equivalent(X_105,X_107)),equivalent(X_22,equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))) ),
inference(subst,[],[refute_0_11:[bind(X_20,$fot(equivalent(X_105,X_107))),bind(X_21,$fot(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)))),bind(X_23,$fot(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))]]) ).
cnf(refute_0_84,plain,
is_a_theorem(equivalent(equivalent(X_22,equivalent(X_105,X_107)),equivalent(X_22,equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(X_105,X_107)),equivalent(equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107)),equivalent(equivalent(X_108,X_105),equivalent(X_108,X_107))))) )],[refute_0_46,refute_0_83]) ).
cnf(refute_0_85,plain,
is_a_theorem(equivalent(equivalent(X_120,equivalent(X_117,X_118)),equivalent(X_120,equivalent(equivalent(X_119,X_117),equivalent(X_119,X_118))))),
inference(subst,[],[refute_0_84:[bind(X_105,$fot(X_117)),bind(X_107,$fot(X_118)),bind(X_108,$fot(X_119)),bind(X_22,$fot(X_120))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(equivalent(X_120,equivalent(X_117,X_118)))
| is_a_theorem(equivalent(X_120,equivalent(equivalent(X_119,X_117),equivalent(X_119,X_118)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_120,equivalent(X_117,X_118)),equivalent(X_120,equivalent(equivalent(X_119,X_117),equivalent(X_119,X_118))))) )],[refute_0_85,refute_0_82]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(equivalent(equivalent(X_623,equivalent(equivalent(X_625,X_625),X_624)),equivalent(X_623,X_624)))
| is_a_theorem(equivalent(equivalent(X_623,equivalent(equivalent(X_625,X_625),X_624)),equivalent(equivalent(X_119,X_623),equivalent(X_119,X_624)))) ),
inference(subst,[],[refute_0_86:[bind(X_117,$fot(X_623)),bind(X_118,$fot(X_624)),bind(X_120,$fot(equivalent(X_623,equivalent(equivalent(X_625,X_625),X_624))))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_618,X_620),equivalent(equivalent(X_618,X_618),X_617)),equivalent(equivalent(X_618,X_620),X_617)))
| is_a_theorem(equivalent(equivalent(X_22,equivalent(equivalent(X_618,X_618),X_617)),equivalent(X_22,X_617))) ),
inference(subst,[],[refute_0_11:[bind(X_20,$fot(equivalent(equivalent(X_618,X_618),X_617))),bind(X_21,$fot(equivalent(X_618,X_620))),bind(X_23,$fot(X_617))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_612,X_613),equivalent(X_612,X_614)),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z)),equivalent(equivalent(equivalent(X_613,X_614),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z))))
| is_a_theorem(equivalent(equivalent(equivalent(X_613,X_614),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X_612,X_613))),bind(Y,$fot(equivalent(X_612,X_614))),bind(X_5,$fot(equivalent(equivalent(equivalent(X_613,X_614),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z))))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_133),X_133)),
inference(subst,[],[lg_2:[bind(U,$fot(X_133))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_13,X_14),X_15),X_11))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_13,X_14),X_15),X_11),equivalent(equivalent(equivalent(X_13,X_12),X_15),equivalent(equivalent(X_14,X_12),X_11))))
| is_a_theorem(equivalent(equivalent(equivalent(X_13,X_12),X_15),equivalent(equivalent(X_14,X_12),X_11))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_13,X_14),X_15),X_11))),bind(Y,$fot(equivalent(equivalent(equivalent(X_13,X_12),X_15),equivalent(equivalent(X_14,X_12),X_11))))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_13,X_14),X_15),X_11),equivalent(equivalent(equivalent(X_13,X_12),X_15),equivalent(equivalent(X_14,X_12),X_11)))),
inference(subst,[],[lg_4:[bind(U,$fot(X_11)),bind(V,$fot(X_12)),bind(X,$fot(X_13)),bind(Y,$fot(X_14)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_13,X_14),X_15),X_11))
| is_a_theorem(equivalent(equivalent(equivalent(X_13,X_12),X_15),equivalent(equivalent(X_14,X_12),X_11))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_13,X_14),X_15),X_11),equivalent(equivalent(equivalent(X_13,X_12),X_15),equivalent(equivalent(X_14,X_12),X_11)))) )],[refute_0_92,refute_0_91]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_133),X_133))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),X_134),X_133),equivalent(equivalent(equivalent(Y,Z),X_134),X_133))) ),
inference(subst,[],[refute_0_93:[bind(X_11,$fot(X_133)),bind(X_12,$fot(X_134)),bind(X_13,$fot(equivalent(equivalent(X,Y),equivalent(X,Z)))),bind(X_14,$fot(equivalent(Y,Z))),bind(X_15,$fot(X_133))]]) ).
cnf(refute_0_95,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),X_134),X_133),equivalent(equivalent(equivalent(Y,Z),X_134),X_133))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_133),X_133)) )],[refute_0_90,refute_0_94]) ).
cnf(refute_0_96,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_612,X_613),equivalent(X_612,X_614)),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z)),equivalent(equivalent(equivalent(X_613,X_614),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z)))),
inference(subst,[],[refute_0_95:[bind(X,$fot(X_612)),bind(Y,$fot(X_613)),bind(Z,$fot(X_614)),bind(X_133,$fot(equivalent(equivalent(X_612,X_614),Z))),bind(X_134,$fot(equivalent(equivalent(X_612,X_613),Z)))]]) ).
cnf(refute_0_97,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_613,X_614),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_612,X_613),equivalent(X_612,X_614)),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z)),equivalent(equivalent(equivalent(X_613,X_614),equivalent(equivalent(X_612,X_613),Z)),equivalent(equivalent(X_612,X_614),Z)))) )],[refute_0_96,refute_0_89]) ).
cnf(refute_0_98,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_618,X_620),equivalent(equivalent(X_618,X_618),X_617)),equivalent(equivalent(X_618,X_620),X_617))),
inference(subst,[],[refute_0_97:[bind(Z,$fot(X_617)),bind(X_612,$fot(X_618)),bind(X_613,$fot(X_618)),bind(X_614,$fot(X_620))]]) ).
cnf(refute_0_99,plain,
is_a_theorem(equivalent(equivalent(X_22,equivalent(equivalent(X_618,X_618),X_617)),equivalent(X_22,X_617))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_618,X_620),equivalent(equivalent(X_618,X_618),X_617)),equivalent(equivalent(X_618,X_620),X_617))) )],[refute_0_98,refute_0_88]) ).
cnf(refute_0_100,plain,
is_a_theorem(equivalent(equivalent(X_623,equivalent(equivalent(X_625,X_625),X_624)),equivalent(X_623,X_624))),
inference(subst,[],[refute_0_99:[bind(X_22,$fot(X_623)),bind(X_617,$fot(X_624)),bind(X_618,$fot(X_625))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(equivalent(equivalent(X_623,equivalent(equivalent(X_625,X_625),X_624)),equivalent(equivalent(X_119,X_623),equivalent(X_119,X_624)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_623,equivalent(equivalent(X_625,X_625),X_624)),equivalent(X_623,X_624))) )],[refute_0_100,refute_0_87]) ).
cnf(refute_0_102,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646)),equivalent(equivalent(X_647,X_647),X_646)),equivalent(equivalent(X_644,equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(X_644,X_646)))),
inference(subst,[],[refute_0_101:[bind(X_119,$fot(X_644)),bind(X_623,$fot(equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646)))),bind(X_624,$fot(X_646)),bind(X_625,$fot(X_647))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(equivalent(equivalent(X_644,equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(X_644,X_646))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646)),equivalent(equivalent(X_647,X_647),X_646)),equivalent(equivalent(X_644,equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(X_644,X_646)))) )],[refute_0_102,refute_0_81]) ).
cnf(refute_0_104,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),X_646))),
inference(subst,[],[refute_0_103:[bind(X_644,$fot(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374)))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_104,X_101),equivalent(X_104,X_102)),X_103))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_104,X_101),equivalent(X_104,X_102)),X_103),equivalent(equivalent(X_101,X_102),X_103)))
| is_a_theorem(equivalent(equivalent(X_101,X_102),X_103)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_104,X_101),equivalent(X_104,X_102)),X_103))),bind(Y,$fot(equivalent(equivalent(X_101,X_102),X_103)))]]) ).
cnf(refute_0_106,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_104,X_101),equivalent(X_104,X_102)),X_103),equivalent(equivalent(X_101,X_102),X_103))),
inference(subst,[],[refute_0_66:[bind(X_100,$fot(X_101)),bind(X_96,$fot(X_102)),bind(X_97,$fot(X_103)),bind(X_99,$fot(X_104))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_104,X_101),equivalent(X_104,X_102)),X_103))
| is_a_theorem(equivalent(equivalent(X_101,X_102),X_103)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_104,X_101),equivalent(X_104,X_102)),X_103),equivalent(equivalent(X_101,X_102),X_103))) )],[refute_0_106,refute_0_105]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),X_646)))
| is_a_theorem(equivalent(equivalent(X_2374,equivalent(X,X_646)),equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),X_646))) ),
inference(subst,[],[refute_0_107:[bind(X_101,$fot(X_2374)),bind(X_102,$fot(equivalent(X,X_646))),bind(X_103,$fot(equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),X_646))),bind(X_104,$fot(equivalent(X,equivalent(X_647,X_647))))]]) ).
cnf(refute_0_109,plain,
is_a_theorem(equivalent(equivalent(X_2374,equivalent(X,X_646)),equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),X_646))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),equivalent(equivalent(X,equivalent(X_647,X_647)),equivalent(X,X_646))),equivalent(equivalent(equivalent(X,equivalent(X_647,X_647)),X_2374),X_646))) )],[refute_0_104,refute_0_108]) ).
cnf(refute_0_110,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_3853,X_3854),equivalent(equivalent(X_3854,X_3853),X_3856)),equivalent(equivalent(equivalent(equivalent(X_3854,X_3853),equivalent(X_3854,X_3854)),equivalent(X_3853,X_3854)),X_3856))),
inference(subst,[],[refute_0_109:[bind(X,$fot(equivalent(X_3854,X_3853))),bind(X_2374,$fot(equivalent(X_3853,X_3854))),bind(X_646,$fot(X_3856)),bind(X_647,$fot(X_3854))]]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(equivalent(X_85,equivalent(equivalent(equivalent(equivalent(X_82,X_83),equivalent(X_82,X_84)),equivalent(X_83,X_84)),X_86)))
| ~ is_a_theorem(equivalent(equivalent(X_85,equivalent(equivalent(equivalent(equivalent(X_82,X_83),equivalent(X_82,X_84)),equivalent(X_83,X_84)),X_86)),equivalent(X_85,X_86)))
| is_a_theorem(equivalent(X_85,X_86)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_85,equivalent(equivalent(equivalent(equivalent(X_82,X_83),equivalent(X_82,X_84)),equivalent(X_83,X_84)),X_86)))),bind(Y,$fot(equivalent(X_85,X_86)))]]) ).
cnf(refute_0_112,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27)),equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27))),
inference(subst,[],[lg_2:[bind(U,$fot(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27)))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27)),equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27)))
| is_a_theorem(equivalent(equivalent(X_26,equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27)),equivalent(X_26,X_27))) ),
inference(subst,[],[refute_0_11:[bind(X_20,$fot(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27))),bind(X_21,$fot(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)))),bind(X_22,$fot(X_26)),bind(X_23,$fot(X_27))]]) ).
cnf(refute_0_114,plain,
is_a_theorem(equivalent(equivalent(X_26,equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27)),equivalent(X_26,X_27))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27)),equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_27))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
is_a_theorem(equivalent(equivalent(X_85,equivalent(equivalent(equivalent(equivalent(X_82,X_83),equivalent(X_82,X_84)),equivalent(X_83,X_84)),X_86)),equivalent(X_85,X_86))),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(X_84)),bind(X_26,$fot(X_85)),bind(X_27,$fot(X_86))]]) ).
cnf(refute_0_116,plain,
( ~ is_a_theorem(equivalent(X_85,equivalent(equivalent(equivalent(equivalent(X_82,X_83),equivalent(X_82,X_84)),equivalent(X_83,X_84)),X_86)))
| is_a_theorem(equivalent(X_85,X_86)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_85,equivalent(equivalent(equivalent(equivalent(X_82,X_83),equivalent(X_82,X_84)),equivalent(X_83,X_84)),X_86)),equivalent(X_85,X_86))) )],[refute_0_115,refute_0_111]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_3853,X_3854),equivalent(equivalent(X_3854,X_3853),X_3856)),equivalent(equivalent(equivalent(equivalent(X_3854,X_3853),equivalent(X_3854,X_3854)),equivalent(X_3853,X_3854)),X_3856)))
| is_a_theorem(equivalent(equivalent(equivalent(X_3853,X_3854),equivalent(equivalent(X_3854,X_3853),X_3856)),X_3856)) ),
inference(subst,[],[refute_0_116:[bind(X_82,$fot(X_3854)),bind(X_83,$fot(X_3853)),bind(X_84,$fot(X_3854)),bind(X_85,$fot(equivalent(equivalent(X_3853,X_3854),equivalent(equivalent(X_3854,X_3853),X_3856)))),bind(X_86,$fot(X_3856))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_3853,X_3854),equivalent(equivalent(X_3854,X_3853),X_3856)),X_3856)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_3853,X_3854),equivalent(equivalent(X_3854,X_3853),X_3856)),equivalent(equivalent(equivalent(equivalent(X_3854,X_3853),equivalent(X_3854,X_3854)),equivalent(X_3853,X_3854)),X_3856))) )],[refute_0_110,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_3857,X_3858),equivalent(equivalent(X_3858,X_3857),X_3859)),X_3859)),
inference(subst,[],[refute_0_118:[bind(X_3853,$fot(X_3857)),bind(X_3854,$fot(X_3858)),bind(X_3856,$fot(X_3859))]]) ).
cnf(refute_0_120,plain,
is_a_theorem(equivalent(equivalent(X_123,equivalent(equivalent(X_3857,X_3858),equivalent(equivalent(X_3858,X_3857),X_3859))),equivalent(X_123,X_3859))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_3857,X_3858),equivalent(equivalent(X_3858,X_3857),X_3859)),X_3859)) )],[refute_0_119,refute_0_80]) ).
cnf(refute_0_121,plain,
is_a_theorem(equivalent(equivalent(X_3864,equivalent(equivalent(X_3865,X_3866),equivalent(equivalent(X_3866,X_3865),X_3867))),equivalent(X_3864,X_3867))),
inference(subst,[],[refute_0_120:[bind(X_123,$fot(X_3864)),bind(X_3857,$fot(X_3865)),bind(X_3858,$fot(X_3866)),bind(X_3859,$fot(X_3867))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(equivalent(X_3864,equivalent(equivalent(X_3865,X_3866),equivalent(equivalent(X_3866,X_3865),X_3867))))
| is_a_theorem(equivalent(X_3864,X_3867)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_3864,equivalent(equivalent(X_3865,X_3866),equivalent(equivalent(X_3866,X_3865),X_3867))),equivalent(X_3864,X_3867))) )],[refute_0_121,refute_0_76]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_25408,equivalent(equivalent(X_171,X_171),X_25408)),X_25409),equivalent(equivalent(equivalent(X_171,X_171),X_25408),equivalent(equivalent(X_25408,equivalent(X_171,X_171)),X_25409))))
| is_a_theorem(equivalent(equivalent(equivalent(X_25408,equivalent(equivalent(X_171,X_171),X_25408)),X_25409),X_25409)) ),
inference(subst,[],[refute_0_122:[bind(X_3864,$fot(equivalent(equivalent(X_25408,equivalent(equivalent(X_171,X_171),X_25408)),X_25409))),bind(X_3865,$fot(equivalent(X_171,X_171))),bind(X_3866,$fot(X_25408)),bind(X_3867,$fot(X_25409))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_25408,equivalent(equivalent(X_171,X_171),X_25408)),X_25409),X_25409)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_25408,equivalent(equivalent(X_171,X_171),X_25408)),X_25409),equivalent(equivalent(equivalent(X_171,X_171),X_25408),equivalent(equivalent(X_25408,equivalent(X_171,X_171)),X_25409)))) )],[refute_0_75,refute_0_123]) ).
cnf(refute_0_125,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
inference(subst,[],[refute_0_124:[bind(X_171,$fot(b)),bind(X_25408,$fot(a)),bind(X_25409,$fot(c))]]) ).
cnf(refute_0_126,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) )],[refute_0_125,prove_lg_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL096-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 3 04:22:14 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 51.78/51.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.78/51.99
% 51.78/51.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 51.78/52.01
%------------------------------------------------------------------------------