TSTP Solution File: LCL014-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:48:47 EDT 2022
% Result : Unsatisfiable 2.94s 3.10s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 3
% Syntax : Number of clauses : 114 ( 65 unt; 0 nHn; 40 RR)
% Number of literals : 174 ( 0 equ; 61 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 387 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(wn,axiom,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y)))) ).
cnf(prove_xgf,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(X_587,equivalent(X_588,X_589)),X_589))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_587,equivalent(X_588,X_589)),X_589),equivalent(X_587,X_588)))
| is_a_theorem(equivalent(X_587,X_588)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_587,equivalent(X_588,X_589)),X_589))),bind(Y,$fot(equivalent(X_587,X_588)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X_34,equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,equivalent(X_36,X_34))),X_33)))
| ~ is_a_theorem(equivalent(equivalent(X_34,equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,equivalent(X_36,X_34))),X_33)),X_33))
| is_a_theorem(X_33) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_34,equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,equivalent(X_36,X_34))),X_33)))),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X,equivalent(Y,Z)))
| ~ is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y))))
| is_a_theorem(equivalent(Z,equivalent(X,Y))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,equivalent(Y,Z)))),bind(Y,$fot(equivalent(Z,equivalent(X,Y))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(X,equivalent(Y,Z)))
| is_a_theorem(equivalent(Z,equivalent(X,Y))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y)))) )],[wn,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10)))
| is_a_theorem(equivalent(X_10,equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_10))))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X_8,X_9))),bind(Y,$fot(equivalent(X_8,equivalent(X_9,X_10)))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,X_6)),equivalent(X_6,equivalent(X,Y)))),
inference(subst,[],[wn:[bind(Z,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(equivalent(X,equivalent(Y,X_6)),equivalent(X_6,equivalent(X,Y))))
| is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X,equivalent(Y,X_6)))),bind(Y,$fot(X_6)),bind(Z,$fot(equivalent(X,Y)))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,equivalent(Y,X_6)),equivalent(X_6,equivalent(X,Y)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10))),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(X_6,$fot(X_10))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(X_10,equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_10))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10))) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(X_15,equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_15))))),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_15))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(X_8,X_9))
| ~ is_a_theorem(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10)))
| is_a_theorem(equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_8,X_9))),bind(Y,$fot(equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(X_8,X_9))
| is_a_theorem(equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_8,equivalent(X_9,X_10)),X_10))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(equivalent(X_15,equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_15)))))
| is_a_theorem(equivalent(equivalent(X_15,equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_15))),X_14)),X_14)) ),
inference(subst,[],[refute_0_12:[bind(X_10,$fot(X_14)),bind(X_8,$fot(X_15)),bind(X_9,$fot(equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_15)))))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(X_15,equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_15))),X_14)),X_14)),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_15,equivalent(equivalent(X_8,X_9),equivalent(X_8,equivalent(X_9,X_15))))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(X_34,equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,equivalent(X_36,X_34))),X_33)),X_33)),
inference(subst,[],[refute_0_14:[bind(X_14,$fot(X_33)),bind(X_15,$fot(X_34)),bind(X_8,$fot(X_35)),bind(X_9,$fot(X_36))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(X_34,equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,equivalent(X_36,X_34))),X_33)))
| is_a_theorem(X_33) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_34,equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,equivalent(X_36,X_34))),X_33)),X_33)) )],[refute_0_15,refute_0_1]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(equivalent(X_582,equivalent(equivalent(equivalent(equivalent(X_583,X_584),equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))),equivalent(equivalent(X_583,X_584),equivalent(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584)),X_582))),equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))) ),
inference(subst,[],[refute_0_16:[bind(X_33,$fot(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584)))),bind(X_34,$fot(X_582)),bind(X_35,$fot(equivalent(X_583,X_584))),bind(X_36,$fot(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,equivalent(Y,Z))),equivalent(Y,Z)))
| is_a_theorem(equivalent(Z,equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,equivalent(Y,Z))),Y))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,equivalent(Y,Z)))))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)),X_31))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)),equivalent(X_31,X_10)),X_10)) ),
inference(subst,[],[refute_0_12:[bind(X_8,$fot(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)))),bind(X_9,$fot(X_31))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6)))
| is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(equivalent(X,equivalent(Y,X_6)),X_6),X_14)),X_14)) ),
inference(subst,[],[refute_0_12:[bind(X_10,$fot(X_14)),bind(X_8,$fot(equivalent(X,Y))),bind(X_9,$fot(equivalent(equivalent(X,equivalent(Y,X_6)),X_6)))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(equivalent(X,equivalent(Y,X_6)),X_6),X_14)),X_14)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6))) )],[refute_0_7,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)),X_31)),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(X_14,$fot(X_31)),bind(X_6,$fot(X_32))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)),equivalent(X_31,X_10)),X_10)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)),X_31)) )],[refute_0_22,refute_0_19]) ).
cnf(refute_0_24,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,equivalent(Y,Z))),equivalent(Y,Z))),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(equivalent(Y,Z))),bind(X_29,$fot(X_78)),bind(X_30,$fot(X_79)),bind(X_31,$fot(X_80)),bind(X_32,$fot(X_81))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(equivalent(Z,equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,equivalent(Y,Z))),Y))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,equivalent(Y,Z))),equivalent(Y,Z))) )],[refute_0_24,refute_0_18]) ).
cnf(refute_0_26,plain,
is_a_theorem(equivalent(X_582,equivalent(equivalent(equivalent(equivalent(X_583,X_584),equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))),equivalent(equivalent(X_583,X_584),equivalent(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584)),X_582))),equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))))),
inference(subst,[],[refute_0_25:[bind(Y,$fot(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584)))),bind(Z,$fot(X_582)),bind(X_78,$fot(X_583)),bind(X_79,$fot(X_584)),bind(X_80,$fot(equivalent(X_583,X_584))),bind(X_81,$fot(X_586))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_582,equivalent(equivalent(equivalent(equivalent(X_583,X_584),equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))),equivalent(equivalent(X_583,X_584),equivalent(equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584)),X_582))),equivalent(equivalent(equivalent(X_583,equivalent(X_584,X_586)),X_586),equivalent(X_583,X_584))))) )],[refute_0_26,refute_0_17]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_587,equivalent(X_588,X_589)),X_589),equivalent(X_587,X_588))),
inference(subst,[],[refute_0_27:[bind(X_583,$fot(X_587)),bind(X_584,$fot(X_588)),bind(X_586,$fot(X_589))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(equivalent(equivalent(X_587,equivalent(X_588,X_589)),X_589))
| is_a_theorem(equivalent(X_587,X_588)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_587,equivalent(X_588,X_589)),X_589),equivalent(X_587,X_588))) )],[refute_0_28,refute_0_0]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(equivalent(equivalent(X_4895,equivalent(equivalent(equivalent(X_4894,equivalent(X_4895,X_4892)),equivalent(X_4892,X_4894)),X_4894)),X_4894))
| is_a_theorem(equivalent(X_4895,equivalent(equivalent(X_4894,equivalent(X_4895,X_4892)),equivalent(X_4892,X_4894)))) ),
inference(subst,[],[refute_0_29:[bind(X_587,$fot(X_4895)),bind(X_588,$fot(equivalent(equivalent(X_4894,equivalent(X_4895,X_4892)),equivalent(X_4892,X_4894)))),bind(X_589,$fot(X_4894))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(equivalent(X_654,X_655))
| ~ is_a_theorem(equivalent(equivalent(X_654,X_655),equivalent(X_655,X_654)))
| is_a_theorem(equivalent(X_655,X_654)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_654,X_655))),bind(Y,$fot(equivalent(X_655,X_654)))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(equivalent(equivalent(X_44,X_45),equivalent(X_44,equivalent(X_45,equivalent(equivalent(X_42,X_43),equivalent(equivalent(X_42,equivalent(X_43,X_46)),X_46))))))
| is_a_theorem(equivalent(equivalent(X_45,equivalent(equivalent(X_42,X_43),equivalent(equivalent(X_42,equivalent(X_43,X_46)),X_46))),equivalent(equivalent(X_44,X_45),X_44))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X_44,X_45))),bind(Y,$fot(X_44)),bind(Z,$fot(equivalent(X_45,equivalent(equivalent(X_42,X_43),equivalent(equivalent(X_42,equivalent(X_43,X_46)),X_46)))))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(X_11)
| ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,X_11)))))
| is_a_theorem(equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,X_11)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_11)),bind(Y,$fot(equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,X_11)))))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(equivalent(X_11,equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,X_11))))),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_11)),bind(X_8,$fot(X_12)),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(X_11)
| is_a_theorem(equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,X_11)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_11,equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,X_11))))) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6)))
| is_a_theorem(equivalent(equivalent(X_18,X_19),equivalent(X_18,equivalent(X_19,equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6)))))) ),
inference(subst,[],[refute_0_35:[bind(X_11,$fot(equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6)))),bind(X_12,$fot(X_18)),bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(equivalent(equivalent(X_18,X_19),equivalent(X_18,equivalent(X_19,equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,equivalent(Y,X_6)),X_6))) )],[refute_0_7,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(equivalent(equivalent(X_44,X_45),equivalent(X_44,equivalent(X_45,equivalent(equivalent(X_42,X_43),equivalent(equivalent(X_42,equivalent(X_43,X_46)),X_46)))))),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(X_18,$fot(X_44)),bind(X_19,$fot(X_45)),bind(X_6,$fot(X_46))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(equivalent(equivalent(X_45,equivalent(equivalent(X_42,X_43),equivalent(equivalent(X_42,equivalent(X_43,X_46)),X_46))),equivalent(equivalent(X_44,X_45),X_44))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_44,X_45),equivalent(X_44,equivalent(X_45,equivalent(equivalent(X_42,X_43),equivalent(equivalent(X_42,equivalent(X_43,X_46)),X_46)))))) )],[refute_0_38,refute_0_32]) ).
cnf(refute_0_40,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_43,X_46),equivalent(equivalent(X_46,X_43),equivalent(equivalent(X_46,equivalent(X_43,X_46)),X_46))),equivalent(equivalent(X_46,equivalent(X_43,X_46)),X_46))),
inference(subst,[],[refute_0_39:[bind(X_42,$fot(X_46)),bind(X_44,$fot(X_46)),bind(X_45,$fot(equivalent(X_43,X_46)))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_43,X_46),equivalent(equivalent(X_46,X_43),equivalent(equivalent(X_46,equivalent(X_43,X_46)),X_46))),equivalent(equivalent(X_46,equivalent(X_43,X_46)),X_46)))
| is_a_theorem(equivalent(equivalent(X_43,X_46),equivalent(X_46,X_43))) ),
inference(subst,[],[refute_0_29:[bind(X_587,$fot(equivalent(X_43,X_46))),bind(X_588,$fot(equivalent(X_46,X_43))),bind(X_589,$fot(equivalent(equivalent(X_46,equivalent(X_43,X_46)),X_46)))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(equivalent(equivalent(X_43,X_46),equivalent(X_46,X_43))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_43,X_46),equivalent(equivalent(X_46,X_43),equivalent(equivalent(X_46,equivalent(X_43,X_46)),X_46))),equivalent(equivalent(X_46,equivalent(X_43,X_46)),X_46))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
is_a_theorem(equivalent(equivalent(X_654,X_655),equivalent(X_655,X_654))),
inference(subst,[],[refute_0_42:[bind(X_43,$fot(X_654)),bind(X_46,$fot(X_655))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(equivalent(X_654,X_655))
| is_a_theorem(equivalent(X_655,X_654)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_654,X_655),equivalent(X_655,X_654))) )],[refute_0_43,refute_0_31]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(equivalent(X_4874,equivalent(X_4875,equivalent(equivalent(equivalent(X_4874,equivalent(X_4875,X_4872)),equivalent(X_4872,X_4873)),X_4873))))
| is_a_theorem(equivalent(equivalent(X_4875,equivalent(equivalent(equivalent(X_4874,equivalent(X_4875,X_4872)),equivalent(X_4872,X_4873)),X_4873)),X_4874)) ),
inference(subst,[],[refute_0_44:[bind(X_654,$fot(X_4874)),bind(X_655,$fot(equivalent(X_4875,equivalent(equivalent(equivalent(X_4874,equivalent(X_4875,X_4872)),equivalent(X_4872,X_4873)),X_4873))))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(equivalent(X_4863,equivalent(equivalent(equivalent(equivalent(X_4862,equivalent(X_4863,X_4860)),equivalent(X_4860,X_4861)),X_4861),X_4862)))
| is_a_theorem(equivalent(X_4862,equivalent(X_4863,equivalent(equivalent(equivalent(X_4862,equivalent(X_4863,X_4860)),equivalent(X_4860,X_4861)),X_4861)))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_4863)),bind(Y,$fot(equivalent(equivalent(equivalent(X_4862,equivalent(X_4863,X_4860)),equivalent(X_4860,X_4861)),X_4861))),bind(Z,$fot(X_4862))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_4858,equivalent(X_4859,X_4856)),equivalent(X_4856,X_4857)),X_4857),equivalent(X_4858,X_4859)))
| is_a_theorem(equivalent(X_4859,equivalent(equivalent(equivalent(equivalent(X_4858,equivalent(X_4859,X_4856)),equivalent(X_4856,X_4857)),X_4857),X_4858))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(equivalent(equivalent(X_4858,equivalent(X_4859,X_4856)),equivalent(X_4856,X_4857)),X_4857))),bind(Y,$fot(X_4858)),bind(Z,$fot(X_4859))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)),X_31))
| is_a_theorem(X_31) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)))),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)))
| is_a_theorem(X_31) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_32)),X_32),X_31)),X_31)) )],[refute_0_22,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),X_1518),equivalent(equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),equivalent(X_1518,X_1520)),X_1520),equivalent(X_29,X_30)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),equivalent(X_1518,X_1520)),X_1520),equivalent(X_29,X_30))) ),
inference(subst,[],[refute_0_49:[bind(X_31,$fot(equivalent(equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),equivalent(X_1518,X_1520)),X_1520),equivalent(X_29,X_30)))),bind(X_32,$fot(X_1518))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(equivalent(equivalent(X_660,X_660),X_661))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_660,X_660),X_661),X_661))
| is_a_theorem(X_661) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_660,X_660),X_661))),bind(Y,$fot(X_661))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(equivalent(equivalent(X_281,equivalent(X_282,X_282)),equivalent(equivalent(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281)),X_281),equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281)))))
| is_a_theorem(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))) ),
inference(subst,[],[refute_0_49:[bind(X_29,$fot(X_281)),bind(X_30,$fot(equivalent(X_282,X_282))),bind(X_31,$fot(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281)))),bind(X_32,$fot(X_281))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(equivalent(equivalent(X_234,X_235),equivalent(X_234,equivalent(X_235,equivalent(X_236,X_236)))))
| is_a_theorem(equivalent(equivalent(X_235,equivalent(X_236,X_236)),equivalent(equivalent(X_234,X_235),X_234))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X_234,X_235))),bind(Y,$fot(X_234)),bind(Z,$fot(equivalent(X_235,equivalent(X_236,X_236))))]]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(equivalent(X_227,X_227))
| is_a_theorem(equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,equivalent(X_227,X_227))))) ),
inference(subst,[],[refute_0_35:[bind(X_11,$fot(equivalent(X_227,X_227)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224))),equivalent(X_225,X_225)))
| is_a_theorem(equivalent(X_225,X_225)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224))))),bind(Y,$fot(equivalent(X_225,X_225)))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(equivalent(X_221,equivalent(X_221,equivalent(equivalent(X_219,equivalent(X_220,X_222)),equivalent(X_222,equivalent(X_219,X_220))))))
| is_a_theorem(equivalent(equivalent(equivalent(X_219,equivalent(X_220,X_222)),equivalent(X_222,equivalent(X_219,X_220))),equivalent(X_221,X_221))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_221)),bind(Y,$fot(X_221)),bind(Z,$fot(equivalent(equivalent(X_219,equivalent(X_220,X_222)),equivalent(X_222,equivalent(X_219,X_220)))))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(equivalent(X_213,equivalent(equivalent(equivalent(X_211,equivalent(X_212,X_214)),equivalent(X_214,equivalent(X_211,X_212))),X_213)))
| is_a_theorem(equivalent(X_213,equivalent(X_213,equivalent(equivalent(X_211,equivalent(X_212,X_214)),equivalent(X_214,equivalent(X_211,X_212)))))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_213)),bind(Y,$fot(equivalent(equivalent(X_211,equivalent(X_212,X_214)),equivalent(X_214,equivalent(X_211,X_212))))),bind(Z,$fot(X_213))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(equivalent(equivalent(X_23,X_24),equivalent(X_23,equivalent(X_24,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21)))))))
| is_a_theorem(equivalent(equivalent(X_24,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21)))),equivalent(equivalent(X_23,X_24),X_23))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X_23,X_24))),bind(Y,$fot(X_23)),bind(Z,$fot(equivalent(X_24,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))))))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y))))
| is_a_theorem(equivalent(equivalent(X_18,X_19),equivalent(X_18,equivalent(X_19,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y))))))) ),
inference(subst,[],[refute_0_35:[bind(X_11,$fot(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y))))),bind(X_12,$fot(X_18)),bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(equivalent(equivalent(X_18,X_19),equivalent(X_18,equivalent(X_19,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y))))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y)))) )],[wn,refute_0_59]) ).
cnf(refute_0_61,plain,
is_a_theorem(equivalent(equivalent(X_23,X_24),equivalent(X_23,equivalent(X_24,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))))))),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22)),bind(X_18,$fot(X_23)),bind(X_19,$fot(X_24))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(equivalent(equivalent(X_24,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21)))),equivalent(equivalent(X_23,X_24),X_23))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_23,X_24),equivalent(X_23,equivalent(X_24,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))))))) )],[refute_0_61,refute_0_58]) ).
cnf(refute_0_63,plain,
is_a_theorem(equivalent(equivalent(X_210,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21)))),equivalent(equivalent(equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210)),X_210),equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210))))),
inference(subst,[],[refute_0_62:[bind(X_23,$fot(equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210)))),bind(X_24,$fot(X_210))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(equivalent(equivalent(X_210,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21)))),equivalent(equivalent(equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210)),X_210),equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210)))))
| is_a_theorem(equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210))) ),
inference(subst,[],[refute_0_49:[bind(X_29,$fot(X_210)),bind(X_30,$fot(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))))),bind(X_31,$fot(equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210)))),bind(X_32,$fot(X_210))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_210,equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21)))),equivalent(equivalent(equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210)),X_210),equivalent(X_210,equivalent(equivalent(equivalent(X_20,equivalent(X_21,X_22)),equivalent(X_22,equivalent(X_20,X_21))),X_210))))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(equivalent(X_213,equivalent(equivalent(equivalent(X_211,equivalent(X_212,X_214)),equivalent(X_214,equivalent(X_211,X_212))),X_213))),
inference(subst,[],[refute_0_65:[bind(X_20,$fot(X_211)),bind(X_21,$fot(X_212)),bind(X_210,$fot(X_213)),bind(X_22,$fot(X_214))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(equivalent(X_213,equivalent(X_213,equivalent(equivalent(X_211,equivalent(X_212,X_214)),equivalent(X_214,equivalent(X_211,X_212)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_213,equivalent(equivalent(equivalent(X_211,equivalent(X_212,X_214)),equivalent(X_214,equivalent(X_211,X_212))),X_213))) )],[refute_0_66,refute_0_57]) ).
cnf(refute_0_68,plain,
is_a_theorem(equivalent(X_221,equivalent(X_221,equivalent(equivalent(X_219,equivalent(X_220,X_222)),equivalent(X_222,equivalent(X_219,X_220)))))),
inference(subst,[],[refute_0_67:[bind(X_211,$fot(X_219)),bind(X_212,$fot(X_220)),bind(X_213,$fot(X_221)),bind(X_214,$fot(X_222))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_219,equivalent(X_220,X_222)),equivalent(X_222,equivalent(X_219,X_220))),equivalent(X_221,X_221))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_221,equivalent(X_221,equivalent(equivalent(X_219,equivalent(X_220,X_222)),equivalent(X_222,equivalent(X_219,X_220)))))) )],[refute_0_68,refute_0_56]) ).
cnf(refute_0_70,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224))),equivalent(X_225,X_225))),
inference(subst,[],[refute_0_69:[bind(X_219,$fot(X_223)),bind(X_220,$fot(X_224)),bind(X_221,$fot(X_225)),bind(X_222,$fot(X_226))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224))))
| is_a_theorem(equivalent(X_225,X_225)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224))),equivalent(X_225,X_225))) )],[refute_0_70,refute_0_55]) ).
cnf(refute_0_72,plain,
is_a_theorem(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224)))),
inference(subst,[],[wn:[bind(X,$fot(X_223)),bind(Y,$fot(X_224)),bind(Z,$fot(X_226))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(equivalent(X_225,X_225)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_223,equivalent(X_224,X_226)),equivalent(X_226,equivalent(X_223,X_224)))) )],[refute_0_72,refute_0_71]) ).
cnf(refute_0_74,plain,
is_a_theorem(equivalent(X_227,X_227)),
inference(subst,[],[refute_0_73:[bind(X_225,$fot(X_227))]]) ).
cnf(refute_0_75,plain,
is_a_theorem(equivalent(equivalent(X_12,X_13),equivalent(X_12,equivalent(X_13,equivalent(X_227,X_227))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_227,X_227)) )],[refute_0_74,refute_0_54]) ).
cnf(refute_0_76,plain,
is_a_theorem(equivalent(equivalent(X_234,X_235),equivalent(X_234,equivalent(X_235,equivalent(X_236,X_236))))),
inference(subst,[],[refute_0_75:[bind(X_12,$fot(X_234)),bind(X_13,$fot(X_235)),bind(X_227,$fot(X_236))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(equivalent(equivalent(X_235,equivalent(X_236,X_236)),equivalent(equivalent(X_234,X_235),X_234))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_234,X_235),equivalent(X_234,equivalent(X_235,equivalent(X_236,X_236))))) )],[refute_0_76,refute_0_53]) ).
cnf(refute_0_78,plain,
is_a_theorem(equivalent(equivalent(X_281,equivalent(X_282,X_282)),equivalent(equivalent(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281)),X_281),equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))))),
inference(subst,[],[refute_0_77:[bind(X_234,$fot(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281)))),bind(X_235,$fot(X_281)),bind(X_236,$fot(X_282))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_281,equivalent(X_282,X_282)),equivalent(equivalent(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281)),X_281),equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))))) )],[refute_0_78,refute_0_52]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(X_229)
| ~ is_a_theorem(equivalent(X_229,equivalent(equivalent(X_228,X_229),X_228)))
| is_a_theorem(equivalent(equivalent(X_228,X_229),X_228)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_229)),bind(Y,$fot(equivalent(equivalent(X_228,X_229),X_228)))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(equivalent(equivalent(Y,Z),equivalent(Y,Z)))
| is_a_theorem(equivalent(Z,equivalent(equivalent(Y,Z),Y))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(Y,Z)))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(equivalent(equivalent(Y,Z),equivalent(Y,Z))),
inference(subst,[],[refute_0_73:[bind(X_225,$fot(equivalent(Y,Z)))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(equivalent(Z,equivalent(equivalent(Y,Z),Y))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(Y,Z),equivalent(Y,Z))) )],[refute_0_82,refute_0_81]) ).
cnf(refute_0_84,plain,
is_a_theorem(equivalent(X_229,equivalent(equivalent(X_228,X_229),X_228))),
inference(subst,[],[refute_0_83:[bind(Y,$fot(X_228)),bind(Z,$fot(X_229))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(X_229)
| is_a_theorem(equivalent(equivalent(X_228,X_229),X_228)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_229,equivalent(equivalent(X_228,X_229),X_228))) )],[refute_0_84,refute_0_80]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281)))
| is_a_theorem(equivalent(equivalent(X_329,equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))),X_329)) ),
inference(subst,[],[refute_0_85:[bind(X_228,$fot(X_329)),bind(X_229,$fot(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(equivalent(equivalent(X_329,equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))),X_329)),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_281,equivalent(equivalent(X_282,X_282),X_281))) )],[refute_0_79,refute_0_86]) ).
cnf(refute_0_88,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_282,X_282),X_652),equivalent(X_652,equivalent(equivalent(X_282,X_282),X_652))),equivalent(equivalent(X_282,X_282),X_652))),
inference(subst,[],[refute_0_87:[bind(X_281,$fot(X_652)),bind(X_329,$fot(equivalent(equivalent(X_282,X_282),X_652)))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_282,X_282),X_652),equivalent(X_652,equivalent(equivalent(X_282,X_282),X_652))),equivalent(equivalent(X_282,X_282),X_652)))
| is_a_theorem(equivalent(equivalent(equivalent(X_282,X_282),X_652),X_652)) ),
inference(subst,[],[refute_0_29:[bind(X_587,$fot(equivalent(equivalent(X_282,X_282),X_652))),bind(X_588,$fot(X_652)),bind(X_589,$fot(equivalent(equivalent(X_282,X_282),X_652)))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_282,X_282),X_652),X_652)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_282,X_282),X_652),equivalent(X_652,equivalent(equivalent(X_282,X_282),X_652))),equivalent(equivalent(X_282,X_282),X_652))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_660,X_660),X_661),X_661)),
inference(subst,[],[refute_0_90:[bind(X_282,$fot(X_660)),bind(X_652,$fot(X_661))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(equivalent(equivalent(X_660,X_660),X_661))
| is_a_theorem(X_661) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_660,X_660),X_661),X_661)) )],[refute_0_91,refute_0_51]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))),equivalent(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490))))),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))))
| is_a_theorem(equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))) ),
inference(subst,[],[refute_0_92:[bind(X_660,$fot(equivalent(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))))),bind(X_661,$fot(equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))))]]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,X_77)),X_77))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,X_77)),equivalent(X_77,X_10)),X_10)) ),
inference(subst,[],[refute_0_12:[bind(X_8,$fot(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,X_77)))),bind(X_9,$fot(X_77))]]) ).
cnf(refute_0_95,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,X_77)),X_77)),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(X_77)),bind(X_29,$fot(X_78)),bind(X_30,$fot(X_79)),bind(X_31,$fot(X_80)),bind(X_32,$fot(X_81))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,X_77)),equivalent(X_77,X_10)),X_10)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_79),equivalent(equivalent(equivalent(X_78,equivalent(X_79,X_81)),X_81),X_80)),equivalent(X_80,X_77)),X_77)) )],[refute_0_95,refute_0_94]) ).
cnf(refute_0_97,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))),equivalent(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490))))),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490))))),
inference(subst,[],[refute_0_96:[bind(X_10,$fot(equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490))))),bind(X_77,$fot(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))),bind(X_78,$fot(X_1488)),bind(X_79,$fot(X_1489)),bind(X_80,$fot(X_1490)),bind(X_81,$fot(X_1491))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)))),equivalent(equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490)),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490))))),equivalent(X_1490,equivalent(equivalent(X_1488,X_1489),equivalent(equivalent(equivalent(X_1488,equivalent(X_1489,X_1491)),X_1491),X_1490))))) )],[refute_0_97,refute_0_93]) ).
cnf(refute_0_99,plain,
is_a_theorem(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),X_1518),equivalent(equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),equivalent(X_1518,X_1520)),X_1520),equivalent(X_29,X_30))))),
inference(subst,[],[refute_0_98:[bind(X_1488,$fot(equivalent(X_29,equivalent(X_30,X_1518)))),bind(X_1489,$fot(X_1518)),bind(X_1490,$fot(equivalent(X_29,X_30))),bind(X_1491,$fot(X_1520))]]) ).
cnf(refute_0_100,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),equivalent(X_1518,X_1520)),X_1520),equivalent(X_29,X_30))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_29,X_30),equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),X_1518),equivalent(equivalent(equivalent(equivalent(X_29,equivalent(X_30,X_1518)),equivalent(X_1518,X_1520)),X_1520),equivalent(X_29,X_30))))) )],[refute_0_99,refute_0_50]) ).
cnf(refute_0_101,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_4858,equivalent(X_4859,X_4856)),equivalent(X_4856,X_4857)),X_4857),equivalent(X_4858,X_4859))),
inference(subst,[],[refute_0_100:[bind(X_1518,$fot(X_4856)),bind(X_1520,$fot(X_4857)),bind(X_29,$fot(X_4858)),bind(X_30,$fot(X_4859))]]) ).
cnf(refute_0_102,plain,
is_a_theorem(equivalent(X_4859,equivalent(equivalent(equivalent(equivalent(X_4858,equivalent(X_4859,X_4856)),equivalent(X_4856,X_4857)),X_4857),X_4858))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_4858,equivalent(X_4859,X_4856)),equivalent(X_4856,X_4857)),X_4857),equivalent(X_4858,X_4859))) )],[refute_0_101,refute_0_47]) ).
cnf(refute_0_103,plain,
is_a_theorem(equivalent(X_4863,equivalent(equivalent(equivalent(equivalent(X_4862,equivalent(X_4863,X_4860)),equivalent(X_4860,X_4861)),X_4861),X_4862))),
inference(subst,[],[refute_0_102:[bind(X_4856,$fot(X_4860)),bind(X_4857,$fot(X_4861)),bind(X_4858,$fot(X_4862)),bind(X_4859,$fot(X_4863))]]) ).
cnf(refute_0_104,plain,
is_a_theorem(equivalent(X_4862,equivalent(X_4863,equivalent(equivalent(equivalent(X_4862,equivalent(X_4863,X_4860)),equivalent(X_4860,X_4861)),X_4861)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_4863,equivalent(equivalent(equivalent(equivalent(X_4862,equivalent(X_4863,X_4860)),equivalent(X_4860,X_4861)),X_4861),X_4862))) )],[refute_0_103,refute_0_46]) ).
cnf(refute_0_105,plain,
is_a_theorem(equivalent(X_4874,equivalent(X_4875,equivalent(equivalent(equivalent(X_4874,equivalent(X_4875,X_4872)),equivalent(X_4872,X_4873)),X_4873)))),
inference(subst,[],[refute_0_104:[bind(X_4860,$fot(X_4872)),bind(X_4861,$fot(X_4873)),bind(X_4862,$fot(X_4874)),bind(X_4863,$fot(X_4875))]]) ).
cnf(refute_0_106,plain,
is_a_theorem(equivalent(equivalent(X_4875,equivalent(equivalent(equivalent(X_4874,equivalent(X_4875,X_4872)),equivalent(X_4872,X_4873)),X_4873)),X_4874)),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_4874,equivalent(X_4875,equivalent(equivalent(equivalent(X_4874,equivalent(X_4875,X_4872)),equivalent(X_4872,X_4873)),X_4873)))) )],[refute_0_105,refute_0_45]) ).
cnf(refute_0_107,plain,
is_a_theorem(equivalent(equivalent(X_4895,equivalent(equivalent(equivalent(X_4894,equivalent(X_4895,X_4892)),equivalent(X_4892,X_4894)),X_4894)),X_4894)),
inference(subst,[],[refute_0_106:[bind(X_4872,$fot(X_4892)),bind(X_4873,$fot(X_4894)),bind(X_4874,$fot(X_4894)),bind(X_4875,$fot(X_4895))]]) ).
cnf(refute_0_108,plain,
is_a_theorem(equivalent(X_4895,equivalent(equivalent(X_4894,equivalent(X_4895,X_4892)),equivalent(X_4892,X_4894)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_4895,equivalent(equivalent(equivalent(X_4894,equivalent(X_4895,X_4892)),equivalent(X_4892,X_4894)),X_4894)),X_4894)) )],[refute_0_107,refute_0_30]) ).
cnf(refute_0_109,plain,
is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
inference(subst,[],[refute_0_108:[bind(X_4892,$fot(c)),bind(X_4894,$fot(b)),bind(X_4895,$fot(a))]]) ).
cnf(refute_0_110,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))) )],[refute_0_109,prove_xgf]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 05:22:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.94/3.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.94/3.10
% 2.94/3.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.94/3.12
%------------------------------------------------------------------------------