TSTP Solution File: LCL118-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL118-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:49:43 EDT 2022
% Result : Unsatisfiable 0.47s 0.63s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of clauses : 58 ( 32 unt; 0 nHn; 20 RR)
% Number of literals : 91 ( 0 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 196 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(wo,axiom,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(Y,X)))) ).
cnf(prove_yqm,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X,equivalent(Y,Z)))
| ~ is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(Y,X))))
| is_a_theorem(equivalent(Z,equivalent(Y,X))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,equivalent(Y,Z)))),bind(Y,$fot(equivalent(Z,equivalent(Y,X))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X,equivalent(Y,Z)))
| is_a_theorem(equivalent(Z,equivalent(Y,X))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(Y,X)))) )],[wo,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(equivalent(X_589,X_588),equivalent(equivalent(X_589,X_587),equivalent(X_588,X_587))))
| is_a_theorem(equivalent(equivalent(X_588,X_587),equivalent(equivalent(X_589,X_587),equivalent(X_589,X_588)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X_589,X_588))),bind(Y,$fot(equivalent(X_589,X_587))),bind(Z,$fot(equivalent(X_588,X_587)))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))),equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104)))))
| is_a_theorem(equivalent(equivalent(X_105,equivalent(X_106,X_104)),equivalent(X_104,equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107)))))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))))),bind(Y,$fot(X_104)),bind(Z,$fot(equivalent(X_105,equivalent(X_106,X_104))))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,X_6)),equivalent(X_6,equivalent(Y,X)))),
inference(subst,[],[wo:[bind(Z,$fot(X_6))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(equivalent(equivalent(X,equivalent(Y,X_6)),equivalent(X_6,equivalent(Y,X))))
| is_a_theorem(equivalent(equivalent(Y,X),equivalent(X_6,equivalent(X,equivalent(Y,X_6))))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X,equivalent(Y,X_6)))),bind(Y,$fot(X_6)),bind(Z,$fot(equivalent(Y,X)))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(equivalent(equivalent(Y,X),equivalent(X_6,equivalent(X,equivalent(Y,X_6))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,equivalent(Y,X_6)),equivalent(X_6,equivalent(Y,X)))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(equivalent(X_97,X_96),equivalent(X_6,equivalent(X_96,equivalent(X_97,X_6))))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_96)),bind(Y,$fot(X_97))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(equivalent(X_23,X_22),X_24))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_23,X_22),X_24),equivalent(equivalent(X_25,equivalent(X_22,equivalent(X_23,X_25))),X_24)))
| is_a_theorem(equivalent(equivalent(X_25,equivalent(X_22,equivalent(X_23,X_25))),X_24)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_23,X_22),X_24))),bind(Y,$fot(equivalent(equivalent(X_25,equivalent(X_22,equivalent(X_23,X_25))),X_24)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equivalent(X_20,equivalent(equivalent(X_21,equivalent(X_18,equivalent(X_19,X_21))),equivalent(equivalent(X_19,X_18),X_20))))
| is_a_theorem(equivalent(equivalent(equivalent(X_19,X_18),X_20),equivalent(equivalent(X_21,equivalent(X_18,equivalent(X_19,X_21))),X_20))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_20)),bind(Y,$fot(equivalent(X_21,equivalent(X_18,equivalent(X_19,X_21))))),bind(Z,$fot(equivalent(equivalent(X_19,X_18),X_20)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(X_9,X_8))
| ~ is_a_theorem(equivalent(equivalent(X_9,X_8),equivalent(X_10,equivalent(X_8,equivalent(X_9,X_10)))))
| is_a_theorem(equivalent(X_10,equivalent(X_8,equivalent(X_9,X_10)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_9,X_8))),bind(Y,$fot(equivalent(X_10,equivalent(X_8,equivalent(X_9,X_10)))))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(equivalent(equivalent(X_9,X_8),equivalent(X_10,equivalent(X_8,equivalent(X_9,X_10))))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(X_6,$fot(X_10))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(X_9,X_8))
| is_a_theorem(equivalent(X_10,equivalent(X_8,equivalent(X_9,X_10)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_9,X_8),equivalent(X_10,equivalent(X_8,equivalent(X_9,X_10))))) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(equivalent(equivalent(Y,X),equivalent(X_6,equivalent(X,equivalent(Y,X_6)))))
| is_a_theorem(equivalent(X_11,equivalent(equivalent(X_6,equivalent(X,equivalent(Y,X_6))),equivalent(equivalent(Y,X),X_11)))) ),
inference(subst,[],[refute_0_12:[bind(X_10,$fot(X_11)),bind(X_8,$fot(equivalent(X_6,equivalent(X,equivalent(Y,X_6))))),bind(X_9,$fot(equivalent(Y,X)))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(X_11,equivalent(equivalent(X_6,equivalent(X,equivalent(Y,X_6))),equivalent(equivalent(Y,X),X_11)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(Y,X),equivalent(X_6,equivalent(X,equivalent(Y,X_6))))) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(X_20,equivalent(equivalent(X_21,equivalent(X_18,equivalent(X_19,X_21))),equivalent(equivalent(X_19,X_18),X_20)))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(X_11,$fot(X_20)),bind(X_6,$fot(X_21))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_19,X_18),X_20),equivalent(equivalent(X_21,equivalent(X_18,equivalent(X_19,X_21))),X_20))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_20,equivalent(equivalent(X_21,equivalent(X_18,equivalent(X_19,X_21))),equivalent(equivalent(X_19,X_18),X_20)))) )],[refute_0_15,refute_0_9]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_23,X_22),X_24),equivalent(equivalent(X_25,equivalent(X_22,equivalent(X_23,X_25))),X_24))),
inference(subst,[],[refute_0_16:[bind(X_18,$fot(X_22)),bind(X_19,$fot(X_23)),bind(X_20,$fot(X_24)),bind(X_21,$fot(X_25))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(equivalent(equivalent(X_23,X_22),X_24))
| is_a_theorem(equivalent(equivalent(X_25,equivalent(X_22,equivalent(X_23,X_25))),X_24)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_23,X_22),X_24),equivalent(equivalent(X_25,equivalent(X_22,equivalent(X_23,X_25))),X_24))) )],[refute_0_17,refute_0_8]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(equivalent(X_97,X_96),equivalent(X_6,equivalent(X_96,equivalent(X_97,X_6)))))
| is_a_theorem(equivalent(equivalent(X_99,equivalent(X_96,equivalent(X_97,X_99))),equivalent(X_6,equivalent(X_96,equivalent(X_97,X_6))))) ),
inference(subst,[],[refute_0_18:[bind(X_22,$fot(X_96)),bind(X_23,$fot(X_97)),bind(X_24,$fot(equivalent(X_6,equivalent(X_96,equivalent(X_97,X_6))))),bind(X_25,$fot(X_99))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(X_99,equivalent(X_96,equivalent(X_97,X_99))),equivalent(X_6,equivalent(X_96,equivalent(X_97,X_6))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_97,X_96),equivalent(X_6,equivalent(X_96,equivalent(X_97,X_6))))) )],[refute_0_7,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))),equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104))))),
inference(subst,[],[refute_0_20:[bind(X_6,$fot(X_104)),bind(X_96,$fot(X_105)),bind(X_97,$fot(X_106)),bind(X_99,$fot(X_107))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(X_105,equivalent(X_106,X_104)),equivalent(X_104,equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))),equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104))))) )],[refute_0_21,refute_0_3]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(X_116,equivalent(X_117,X_118)),equivalent(X_118,equivalent(X_107,equivalent(X_116,equivalent(X_117,X_107)))))),
inference(subst,[],[refute_0_22:[bind(X_104,$fot(X_118)),bind(X_105,$fot(X_116)),bind(X_106,$fot(X_117))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(equivalent(X_26,equivalent(X_27,X_28)),X_29))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_26,equivalent(X_27,X_28)),X_29),equivalent(equivalent(X_28,equivalent(X_27,X_26)),X_29)))
| is_a_theorem(equivalent(equivalent(X_28,equivalent(X_27,X_26)),X_29)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_26,equivalent(X_27,X_28)),X_29))),bind(Y,$fot(equivalent(equivalent(X_28,equivalent(X_27,X_26)),X_29)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(equivalent(X_17,equivalent(equivalent(X_16,equivalent(X_15,X_14)),equivalent(equivalent(X_14,equivalent(X_15,X_16)),X_17))))
| is_a_theorem(equivalent(equivalent(equivalent(X_14,equivalent(X_15,X_16)),X_17),equivalent(equivalent(X_16,equivalent(X_15,X_14)),X_17))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_17)),bind(Y,$fot(equivalent(X_16,equivalent(X_15,X_14)))),bind(Z,$fot(equivalent(equivalent(X_14,equivalent(X_15,X_16)),X_17)))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(Y,X))))
| is_a_theorem(equivalent(X_11,equivalent(equivalent(Z,equivalent(Y,X)),equivalent(equivalent(X,equivalent(Y,Z)),X_11)))) ),
inference(subst,[],[refute_0_12:[bind(X_10,$fot(X_11)),bind(X_8,$fot(equivalent(Z,equivalent(Y,X)))),bind(X_9,$fot(equivalent(X,equivalent(Y,Z))))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(X_11,equivalent(equivalent(Z,equivalent(Y,X)),equivalent(equivalent(X,equivalent(Y,Z)),X_11)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(Y,X)))) )],[wo,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(X_17,equivalent(equivalent(X_16,equivalent(X_15,X_14)),equivalent(equivalent(X_14,equivalent(X_15,X_16)),X_17)))),
inference(subst,[],[refute_0_27:[bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(X_16)),bind(X_11,$fot(X_17))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_14,equivalent(X_15,X_16)),X_17),equivalent(equivalent(X_16,equivalent(X_15,X_14)),X_17))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_17,equivalent(equivalent(X_16,equivalent(X_15,X_14)),equivalent(equivalent(X_14,equivalent(X_15,X_16)),X_17)))) )],[refute_0_28,refute_0_25]) ).
cnf(refute_0_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_26,equivalent(X_27,X_28)),X_29),equivalent(equivalent(X_28,equivalent(X_27,X_26)),X_29))),
inference(subst,[],[refute_0_29:[bind(X_14,$fot(X_26)),bind(X_15,$fot(X_27)),bind(X_16,$fot(X_28)),bind(X_17,$fot(X_29))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(equivalent(equivalent(X_26,equivalent(X_27,X_28)),X_29))
| is_a_theorem(equivalent(equivalent(X_28,equivalent(X_27,X_26)),X_29)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_26,equivalent(X_27,X_28)),X_29),equivalent(equivalent(X_28,equivalent(X_27,X_26)),X_29))) )],[refute_0_30,refute_0_24]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(equivalent(equivalent(X_116,equivalent(X_117,X_118)),equivalent(X_118,equivalent(X_107,equivalent(X_116,equivalent(X_117,X_107))))))
| is_a_theorem(equivalent(equivalent(X_118,equivalent(X_117,X_116)),equivalent(X_118,equivalent(X_107,equivalent(X_116,equivalent(X_117,X_107)))))) ),
inference(subst,[],[refute_0_31:[bind(X_26,$fot(X_116)),bind(X_27,$fot(X_117)),bind(X_28,$fot(X_118)),bind(X_29,$fot(equivalent(X_118,equivalent(X_107,equivalent(X_116,equivalent(X_117,X_107))))))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(equivalent(equivalent(X_118,equivalent(X_117,X_116)),equivalent(X_118,equivalent(X_107,equivalent(X_116,equivalent(X_117,X_107)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_116,equivalent(X_117,X_118)),equivalent(X_118,equivalent(X_107,equivalent(X_116,equivalent(X_117,X_107)))))) )],[refute_0_23,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(equivalent(equivalent(X_189,equivalent(X_117,X_189)),equivalent(X_189,equivalent(X_189,equivalent(X_189,equivalent(X_117,X_189)))))),
inference(subst,[],[refute_0_33:[bind(X_107,$fot(X_189)),bind(X_116,$fot(X_189)),bind(X_118,$fot(X_189))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))))
| ~ is_a_theorem(equivalent(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))),equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104)))))
| is_a_theorem(equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))))),bind(Y,$fot(equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104)))))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))))
| is_a_theorem(equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_107,equivalent(X_105,equivalent(X_106,X_107))),equivalent(X_104,equivalent(X_105,equivalent(X_106,X_104))))) )],[refute_0_21,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(equivalent(equivalent(X_189,equivalent(X_117,X_189)),equivalent(X_189,equivalent(X_189,equivalent(X_189,equivalent(X_117,X_189))))))
| is_a_theorem(equivalent(X_188,equivalent(X_189,equivalent(X_189,X_188)))) ),
inference(subst,[],[refute_0_36:[bind(X_104,$fot(X_188)),bind(X_105,$fot(X_189)),bind(X_106,$fot(X_189)),bind(X_107,$fot(equivalent(X_189,equivalent(X_117,X_189))))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(equivalent(X_188,equivalent(X_189,equivalent(X_189,X_188)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_189,equivalent(X_117,X_189)),equivalent(X_189,equivalent(X_189,equivalent(X_189,equivalent(X_117,X_189)))))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
is_a_theorem(equivalent(X_584,equivalent(X_586,equivalent(X_586,X_584)))),
inference(subst,[],[refute_0_38:[bind(X_188,$fot(X_584)),bind(X_189,$fot(X_586))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(equivalent(X_296,equivalent(X_298,X_297)))
| ~ is_a_theorem(equivalent(equivalent(X_296,equivalent(X_298,X_297)),equivalent(X_297,equivalent(equivalent(X_298,X_295),equivalent(X_296,X_295)))))
| is_a_theorem(equivalent(X_297,equivalent(equivalent(X_298,X_295),equivalent(X_296,X_295)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_296,equivalent(X_298,X_297)))),bind(Y,$fot(equivalent(X_297,equivalent(equivalent(X_298,X_295),equivalent(X_296,X_295)))))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_130,X_127),equivalent(X_128,X_127)),equivalent(X_129,equivalent(X_128,equivalent(X_130,X_129)))))
| is_a_theorem(equivalent(equivalent(X_128,equivalent(X_130,X_129)),equivalent(X_129,equivalent(equivalent(X_130,X_127),equivalent(X_128,X_127))))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(equivalent(X_130,X_127),equivalent(X_128,X_127)))),bind(Y,$fot(X_129)),bind(Z,$fot(equivalent(X_128,equivalent(X_130,X_129))))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(equivalent(equivalent(X_116,equivalent(X_117,equivalent(X_97,X_116))),equivalent(X_6,equivalent(X_117,equivalent(X_97,X_6))))),
inference(subst,[],[refute_0_20:[bind(X_96,$fot(X_117)),bind(X_99,$fot(X_116))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(equivalent(equivalent(X_116,equivalent(X_117,equivalent(X_97,X_116))),equivalent(X_6,equivalent(X_117,equivalent(X_97,X_6)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_97,X_116),equivalent(X_117,X_116)),equivalent(X_6,equivalent(X_117,equivalent(X_97,X_6))))) ),
inference(subst,[],[refute_0_31:[bind(X_26,$fot(X_116)),bind(X_27,$fot(X_117)),bind(X_28,$fot(equivalent(X_97,X_116))),bind(X_29,$fot(equivalent(X_6,equivalent(X_117,equivalent(X_97,X_6)))))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_97,X_116),equivalent(X_117,X_116)),equivalent(X_6,equivalent(X_117,equivalent(X_97,X_6))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_116,equivalent(X_117,equivalent(X_97,X_116))),equivalent(X_6,equivalent(X_117,equivalent(X_97,X_6))))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_130,X_127),equivalent(X_128,X_127)),equivalent(X_129,equivalent(X_128,equivalent(X_130,X_129))))),
inference(subst,[],[refute_0_44:[bind(X_116,$fot(X_127)),bind(X_117,$fot(X_128)),bind(X_6,$fot(X_129)),bind(X_97,$fot(X_130))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(X_128,equivalent(X_130,X_129)),equivalent(X_129,equivalent(equivalent(X_130,X_127),equivalent(X_128,X_127))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_130,X_127),equivalent(X_128,X_127)),equivalent(X_129,equivalent(X_128,equivalent(X_130,X_129))))) )],[refute_0_45,refute_0_41]) ).
cnf(refute_0_47,plain,
is_a_theorem(equivalent(equivalent(X_296,equivalent(X_298,X_297)),equivalent(X_297,equivalent(equivalent(X_298,X_295),equivalent(X_296,X_295))))),
inference(subst,[],[refute_0_46:[bind(X_127,$fot(X_295)),bind(X_128,$fot(X_296)),bind(X_129,$fot(X_297)),bind(X_130,$fot(X_298))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(equivalent(X_296,equivalent(X_298,X_297)))
| is_a_theorem(equivalent(X_297,equivalent(equivalent(X_298,X_295),equivalent(X_296,X_295)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_296,equivalent(X_298,X_297)),equivalent(X_297,equivalent(equivalent(X_298,X_295),equivalent(X_296,X_295))))) )],[refute_0_47,refute_0_40]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(equivalent(X_584,equivalent(X_586,equivalent(X_586,X_584))))
| is_a_theorem(equivalent(equivalent(X_586,X_584),equivalent(equivalent(X_586,X_583),equivalent(X_584,X_583)))) ),
inference(subst,[],[refute_0_48:[bind(X_295,$fot(X_583)),bind(X_296,$fot(X_584)),bind(X_297,$fot(equivalent(X_586,X_584))),bind(X_298,$fot(X_586))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(equivalent(equivalent(X_586,X_584),equivalent(equivalent(X_586,X_583),equivalent(X_584,X_583)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_584,equivalent(X_586,equivalent(X_586,X_584)))) )],[refute_0_39,refute_0_49]) ).
cnf(refute_0_51,plain,
is_a_theorem(equivalent(equivalent(X_589,X_588),equivalent(equivalent(X_589,X_587),equivalent(X_588,X_587)))),
inference(subst,[],[refute_0_50:[bind(X_583,$fot(X_587)),bind(X_584,$fot(X_588)),bind(X_586,$fot(X_589))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(equivalent(equivalent(X_588,X_587),equivalent(equivalent(X_589,X_587),equivalent(X_589,X_588)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_589,X_588),equivalent(equivalent(X_589,X_587),equivalent(X_588,X_587)))) )],[refute_0_51,refute_0_2]) ).
cnf(refute_0_53,plain,
is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
inference(subst,[],[refute_0_52:[bind(X_587,$fot(b)),bind(X_588,$fot(a)),bind(X_589,$fot(c))]]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))) )],[refute_0_53,prove_yqm]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL118-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 06:04:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.63
% 0.47/0.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.64
%------------------------------------------------------------------------------