TSTP Solution File: LCL257-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL257-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:51:12 EDT 2022
% Result : Unsatisfiable 1.22s 1.38s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 3
% Syntax : Number of clauses : 79 ( 45 unt; 0 nHn; 28 RR)
% Number of literals : 121 ( 0 equ; 43 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 : 219 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(yql,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
cnf(prove_xhn,negated_conjecture,
~ is_a_theorem(equivalent(x,equivalent(equivalent(y,z),equivalent(equivalent(z,x),y)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(X_219,X_219),X_218))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_219,X_219),X_218),X_218))
| is_a_theorem(X_218) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_219,X_219),X_218))),bind(Y,$fot(X_218))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11)))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))),bind(Y,$fot(equivalent(equivalent(X_8,X_9),X_11)))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z)))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))) )],[refute_0_6,refute_0_1]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(equivalent(X_31,X_31),equivalent(equivalent(X_31,X_30),equivalent(X_30,X_31))))
| is_a_theorem(equivalent(equivalent(X_30,X_30),equivalent(X_31,X_31))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(X_31)),bind(X_11,$fot(equivalent(X_31,X_31))),bind(X_8,$fot(X_30)),bind(X_9,$fot(X_30))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)),equivalent(equivalent(X_24,X_25),equivalent(X_8,X_24))))
| is_a_theorem(equivalent(equivalent(X_8,X_25),equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(X_24)),bind(X_11,$fot(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)))),bind(X_9,$fot(X_25))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_22)))
| is_a_theorem(equivalent(equivalent(Z,equivalent(X_21,X_22)),equivalent(equivalent(X_21,X_22),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X_21,X_22))),bind(Y,$fot(equivalent(X_21,X_22)))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17)))),
inference(subst,[],[yql:[bind(X,$fot(X_19)),bind(Y,$fot(X_20)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17))))
| is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(X_19,X_20))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(X_17)),bind(X_11,$fot(equivalent(X_19,X_20))),bind(X_8,$fot(X_19)),bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(X_19,X_20))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_22))),
inference(subst,[],[refute_0_13:[bind(X_19,$fot(X_21)),bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(X_21,X_22)),equivalent(equivalent(X_21,X_22),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_22))) )],[refute_0_14,refute_0_10]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)),equivalent(equivalent(X_24,X_25),equivalent(X_8,X_24)))),
inference(subst,[],[refute_0_15:[bind(Z,$fot(equivalent(X_8,X_24))),bind(X_21,$fot(X_24)),bind(X_22,$fot(X_25))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(X_8,X_25),equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)),equivalent(equivalent(X_24,X_25),equivalent(X_8,X_24)))) )],[refute_0_16,refute_0_9]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(X_31,X_31),equivalent(equivalent(X_31,X_30),equivalent(X_30,X_31)))),
inference(subst,[],[refute_0_17:[bind(X_24,$fot(X_30)),bind(X_25,$fot(X_31)),bind(X_8,$fot(X_31))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(equivalent(equivalent(X_30,X_30),equivalent(X_31,X_31))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_31,X_31),equivalent(equivalent(X_31,X_30),equivalent(X_30,X_31)))) )],[refute_0_18,refute_0_8]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(X_213,X_213),equivalent(X_31,X_31))),
inference(subst,[],[refute_0_19:[bind(X_30,$fot(X_213))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(equivalent(equivalent(X_35,X_37),X_36))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_35,X_37),X_36),equivalent(equivalent(X_36,X_35),X_37)))
| is_a_theorem(equivalent(equivalent(X_36,X_35),X_37)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_35,X_37),X_36))),bind(Y,$fot(equivalent(equivalent(X_36,X_35),X_37)))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(equivalent(X_27,X_26),X_27),equivalent(equivalent(X_26,X_29),equivalent(X_27,X_26)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_26,X_29),X_27),equivalent(equivalent(X_27,X_26),X_29))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(equivalent(X_27,X_26))),bind(X_11,$fot(equivalent(equivalent(X_27,X_26),X_29))),bind(X_8,$fot(equivalent(X_26,X_29))),bind(X_9,$fot(X_27))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_19,X_17),equivalent(equivalent(Z,X_20),equivalent(X_17,Z))),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17)))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_17)),bind(Y,$fot(X_20)),bind(X_7,$fot(equivalent(X_19,X_17)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_19,X_17),equivalent(equivalent(Z,X_20),equivalent(X_17,Z))),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17))))
| is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_19,X_17),equivalent(equivalent(Z,X_20),equivalent(X_17,Z))))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(X_17)),bind(X_11,$fot(equivalent(equivalent(X_19,X_17),equivalent(equivalent(Z,X_20),equivalent(X_17,Z))))),bind(X_8,$fot(X_19)),bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_19,X_17),equivalent(equivalent(Z,X_20),equivalent(X_17,Z))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_19,X_17),equivalent(equivalent(Z,X_20),equivalent(X_17,Z))),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(equivalent(X_27,X_26),X_27),equivalent(equivalent(X_26,X_29),equivalent(X_27,X_26))))),
inference(subst,[],[refute_0_25:[bind(Z,$fot(X_26)),bind(X_17,$fot(X_27)),bind(X_19,$fot(equivalent(X_27,X_26))),bind(X_20,$fot(X_29))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_26,X_29),X_27),equivalent(equivalent(X_27,X_26),X_29))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(equivalent(X_27,X_26),X_27),equivalent(equivalent(X_26,X_29),equivalent(X_27,X_26))))) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_35,X_37),X_36),equivalent(equivalent(X_36,X_35),X_37))),
inference(subst,[],[refute_0_27:[bind(X_26,$fot(X_35)),bind(X_27,$fot(X_36)),bind(X_29,$fot(X_37))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(equivalent(equivalent(X_35,X_37),X_36))
| is_a_theorem(equivalent(equivalent(X_36,X_35),X_37)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_35,X_37),X_36),equivalent(equivalent(X_36,X_35),X_37))) )],[refute_0_28,refute_0_21]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(equivalent(equivalent(X_213,X_213),equivalent(X_31,X_31)))
| is_a_theorem(equivalent(equivalent(equivalent(X_31,X_31),X_213),X_213)) ),
inference(subst,[],[refute_0_29:[bind(X_35,$fot(X_213)),bind(X_36,$fot(equivalent(X_31,X_31))),bind(X_37,$fot(X_213))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_31,X_31),X_213),X_213)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_213,X_213),equivalent(X_31,X_31))) )],[refute_0_20,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_219,X_219),X_218),X_218)),
inference(subst,[],[refute_0_31:[bind(X_213,$fot(X_218)),bind(X_31,$fot(X_219))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(equivalent(equivalent(X_219,X_219),X_218))
| is_a_theorem(X_218) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_219,X_219),X_218),X_218)) )],[refute_0_32,refute_0_0]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3098,X_3097),X_3099),equivalent(equivalent(X_3098,X_3097),X_3099)),equivalent(X_3097,equivalent(equivalent(X_3099,X_3098),equivalent(equivalent(X_3098,X_3097),X_3099)))))
| is_a_theorem(equivalent(X_3097,equivalent(equivalent(X_3099,X_3098),equivalent(equivalent(X_3098,X_3097),X_3099)))) ),
inference(subst,[],[refute_0_33:[bind(X_218,$fot(equivalent(X_3097,equivalent(equivalent(X_3099,X_3098),equivalent(equivalent(X_3098,X_3097),X_3099))))),bind(X_219,$fot(equivalent(equivalent(X_3098,X_3097),X_3099)))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(equivalent(equivalent(X_1772,equivalent(equivalent(X_1774,X_1773),X_9)),equivalent(equivalent(equivalent(X_1774,X_1773),X_9),equivalent(equivalent(equivalent(X_1773,X_1772),X_1774),equivalent(X_1774,X_1773)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1773,X_1772),X_1774),X_9),equivalent(X_1772,equivalent(equivalent(X_1774,X_1773),X_9)))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(equivalent(X_1774,X_1773))),bind(X_11,$fot(equivalent(X_1772,equivalent(equivalent(X_1774,X_1773),X_9)))),bind(X_8,$fot(equivalent(equivalent(X_1773,X_1772),X_1774)))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(equivalent(X_91,X_92))
| ~ is_a_theorem(equivalent(equivalent(X_91,X_92),equivalent(X_92,X_91)))
| is_a_theorem(equivalent(X_92,X_91)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_91,X_92))),bind(Y,$fot(equivalent(X_92,X_91)))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(equivalent(X_90,X_90))
| is_a_theorem(equivalent(equivalent(Z,X_90),equivalent(X_90,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_90)),bind(Y,$fot(X_90))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_67,X_68),X_68),equivalent(equivalent(equivalent(X_67,X_68),X_69),equivalent(equivalent(X_69,X_67),equivalent(X_67,X_68)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_69,X_67),X_69),equivalent(equivalent(X_67,X_68),X_68))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(equivalent(X_67,X_68))),bind(X_11,$fot(equivalent(equivalent(X_67,X_68),X_68))),bind(X_8,$fot(equivalent(X_69,X_67))),bind(X_9,$fot(X_69))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,X_50),equivalent(equivalent(X_50,X_48),equivalent(X_48,X_49))),equivalent(equivalent(X_50,X_49),equivalent(X_8,X_50))))
| is_a_theorem(equivalent(equivalent(X_8,X_49),equivalent(equivalent(X_8,X_50),equivalent(equivalent(X_50,X_48),equivalent(X_48,X_49))))) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(X_50)),bind(X_11,$fot(equivalent(equivalent(X_8,X_50),equivalent(equivalent(X_50,X_48),equivalent(X_48,X_49))))),bind(X_9,$fot(X_49))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(equivalent(equivalent(X_32,X_31),equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))))
| is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))),equivalent(equivalent(X_32,X_31),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X_32,X_31))),bind(Y,$fot(equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(equivalent(equivalent(X_32,X_31),equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31)))),
inference(subst,[],[refute_0_17:[bind(X_24,$fot(X_30)),bind(X_25,$fot(X_31)),bind(X_8,$fot(X_32))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))),equivalent(equivalent(X_32,X_31),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_32,X_31),equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31)))) )],[refute_0_41,refute_0_40]) ).
cnf(refute_0_43,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,X_50),equivalent(equivalent(X_50,X_48),equivalent(X_48,X_49))),equivalent(equivalent(X_50,X_49),equivalent(X_8,X_50)))),
inference(subst,[],[refute_0_42:[bind(Z,$fot(equivalent(X_8,X_50))),bind(X_30,$fot(X_48)),bind(X_31,$fot(X_49)),bind(X_32,$fot(X_50))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(equivalent(equivalent(X_8,X_49),equivalent(equivalent(X_8,X_50),equivalent(equivalent(X_50,X_48),equivalent(X_48,X_49))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_8,X_50),equivalent(equivalent(X_50,X_48),equivalent(X_48,X_49))),equivalent(equivalent(X_50,X_49),equivalent(X_8,X_50)))) )],[refute_0_43,refute_0_39]) ).
cnf(refute_0_45,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_67,X_68),X_68),equivalent(equivalent(equivalent(X_67,X_68),X_69),equivalent(equivalent(X_69,X_67),equivalent(X_67,X_68))))),
inference(subst,[],[refute_0_44:[bind(X_48,$fot(X_67)),bind(X_49,$fot(X_68)),bind(X_50,$fot(X_69)),bind(X_8,$fot(equivalent(X_67,X_68)))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_69,X_67),X_69),equivalent(equivalent(X_67,X_68),X_68))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_67,X_68),X_68),equivalent(equivalent(equivalent(X_67,X_68),X_69),equivalent(equivalent(X_69,X_67),equivalent(X_67,X_68))))) )],[refute_0_45,refute_0_38]) ).
cnf(refute_0_47,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_69,X_69),X_69),equivalent(equivalent(X_69,X_69),X_69))),
inference(subst,[],[refute_0_46:[bind(X_67,$fot(X_69)),bind(X_68,$fot(X_69))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(equivalent(X_33,X_33))
| ~ is_a_theorem(equivalent(equivalent(X_33,X_33),equivalent(X_34,X_34)))
| is_a_theorem(equivalent(X_34,X_34)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_33,X_33))),bind(Y,$fot(equivalent(X_34,X_34)))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(equivalent(equivalent(X_33,X_33),equivalent(X_34,X_34))),
inference(subst,[],[refute_0_19:[bind(X_30,$fot(X_33)),bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(equivalent(X_33,X_33))
| is_a_theorem(equivalent(X_34,X_34)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_33,X_33),equivalent(X_34,X_34))) )],[refute_0_49,refute_0_48]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_69,X_69),X_69),equivalent(equivalent(X_69,X_69),X_69)))
| is_a_theorem(equivalent(X_89,X_89)) ),
inference(subst,[],[refute_0_50:[bind(X_33,$fot(equivalent(equivalent(X_69,X_69),X_69))),bind(X_34,$fot(X_89))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(equivalent(X_89,X_89)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_69,X_69),X_69),equivalent(equivalent(X_69,X_69),X_69))) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(equivalent(X_90,X_90)),
inference(subst,[],[refute_0_52:[bind(X_89,$fot(X_90))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(equivalent(equivalent(Z,X_90),equivalent(X_90,Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_90,X_90)) )],[refute_0_53,refute_0_37]) ).
cnf(refute_0_55,plain,
is_a_theorem(equivalent(equivalent(X_91,X_92),equivalent(X_92,X_91))),
inference(subst,[],[refute_0_54:[bind(Z,$fot(X_91)),bind(X_90,$fot(X_92))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(equivalent(X_91,X_92))
| is_a_theorem(equivalent(X_92,X_91)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_91,X_92),equivalent(X_92,X_91))) )],[refute_0_55,refute_0_36]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_248,X_247),X_249),equivalent(X_249,X_248)),X_247))
| is_a_theorem(equivalent(X_247,equivalent(equivalent(equivalent(X_248,X_247),X_249),equivalent(X_249,X_248)))) ),
inference(subst,[],[refute_0_56:[bind(X_91,$fot(equivalent(equivalent(equivalent(X_248,X_247),X_249),equivalent(X_249,X_248)))),bind(X_92,$fot(X_247))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_26,X_29),X_27),equivalent(equivalent(X_27,X_26),X_29)))
| is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(X_26,X_29),X_27))) ),
inference(subst,[],[refute_0_56:[bind(X_91,$fot(equivalent(equivalent(X_26,X_29),X_27))),bind(X_92,$fot(equivalent(equivalent(X_27,X_26),X_29)))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(X_26,X_29),X_27))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_26,X_29),X_27),equivalent(equivalent(X_27,X_26),X_29))) )],[refute_0_27,refute_0_58]) ).
cnf(refute_0_60,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_213),equivalent(equivalent(X_26,X_213),X_27))),
inference(subst,[],[refute_0_59:[bind(X_29,$fot(X_213))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_213),equivalent(equivalent(X_26,X_213),X_27)))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_26,X_213),X_27),equivalent(X_27,X_26)),X_213)) ),
inference(subst,[],[refute_0_29:[bind(X_35,$fot(equivalent(X_27,X_26))),bind(X_36,$fot(equivalent(equivalent(X_26,X_213),X_27))),bind(X_37,$fot(X_213))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_26,X_213),X_27),equivalent(X_27,X_26)),X_213)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_213),equivalent(equivalent(X_26,X_213),X_27))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_248,X_247),X_249),equivalent(X_249,X_248)),X_247)),
inference(subst,[],[refute_0_62:[bind(X_213,$fot(X_247)),bind(X_26,$fot(X_248)),bind(X_27,$fot(X_249))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(equivalent(X_247,equivalent(equivalent(equivalent(X_248,X_247),X_249),equivalent(X_249,X_248)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_248,X_247),X_249),equivalent(X_249,X_248)),X_247)) )],[refute_0_63,refute_0_57]) ).
cnf(refute_0_65,plain,
is_a_theorem(equivalent(X_1294,equivalent(equivalent(equivalent(X_248,X_1294),X_249),equivalent(X_249,X_248)))),
inference(subst,[],[refute_0_64:[bind(X_247,$fot(X_1294))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(equivalent(X_32,X_31))
| ~ is_a_theorem(equivalent(equivalent(X_32,X_31),equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))))
| is_a_theorem(equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_32,X_31))),bind(Y,$fot(equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(equivalent(X_32,X_31))
| is_a_theorem(equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_32,X_31),equivalent(equivalent(X_32,X_30),equivalent(X_30,X_31)))) )],[refute_0_41,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(equivalent(X_1294,equivalent(equivalent(equivalent(X_248,X_1294),X_249),equivalent(X_249,X_248))))
| is_a_theorem(equivalent(equivalent(X_1294,X_1292),equivalent(X_1292,equivalent(equivalent(equivalent(X_248,X_1294),X_249),equivalent(X_249,X_248))))) ),
inference(subst,[],[refute_0_67:[bind(X_30,$fot(X_1292)),bind(X_31,$fot(equivalent(equivalent(equivalent(X_248,X_1294),X_249),equivalent(X_249,X_248)))),bind(X_32,$fot(X_1294))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(equivalent(equivalent(X_1294,X_1292),equivalent(X_1292,equivalent(equivalent(equivalent(X_248,X_1294),X_249),equivalent(X_249,X_248))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_1294,equivalent(equivalent(equivalent(X_248,X_1294),X_249),equivalent(X_249,X_248)))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(equivalent(equivalent(X_1772,equivalent(equivalent(X_1774,X_1773),X_9)),equivalent(equivalent(equivalent(X_1774,X_1773),X_9),equivalent(equivalent(equivalent(X_1773,X_1772),X_1774),equivalent(X_1774,X_1773))))),
inference(subst,[],[refute_0_69:[bind(X_1292,$fot(equivalent(equivalent(X_1774,X_1773),X_9))),bind(X_1294,$fot(X_1772)),bind(X_248,$fot(X_1773)),bind(X_249,$fot(X_1774))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1773,X_1772),X_1774),X_9),equivalent(X_1772,equivalent(equivalent(X_1774,X_1773),X_9)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_1772,equivalent(equivalent(X_1774,X_1773),X_9)),equivalent(equivalent(equivalent(X_1774,X_1773),X_9),equivalent(equivalent(equivalent(X_1773,X_1772),X_1774),equivalent(X_1774,X_1773))))) )],[refute_0_70,refute_0_35]) ).
cnf(refute_0_72,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3098,X_3097),X_3099),equivalent(equivalent(X_3098,X_3097),X_3099)),equivalent(X_3097,equivalent(equivalent(X_3099,X_3098),equivalent(equivalent(X_3098,X_3097),X_3099))))),
inference(subst,[],[refute_0_71:[bind(X_1772,$fot(X_3097)),bind(X_1773,$fot(X_3098)),bind(X_1774,$fot(X_3099)),bind(X_9,$fot(equivalent(equivalent(X_3098,X_3097),X_3099)))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(equivalent(X_3097,equivalent(equivalent(X_3099,X_3098),equivalent(equivalent(X_3098,X_3097),X_3099)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3098,X_3097),X_3099),equivalent(equivalent(X_3098,X_3097),X_3099)),equivalent(X_3097,equivalent(equivalent(X_3099,X_3098),equivalent(equivalent(X_3098,X_3097),X_3099))))) )],[refute_0_72,refute_0_34]) ).
cnf(refute_0_74,plain,
is_a_theorem(equivalent(x,equivalent(equivalent(y,z),equivalent(equivalent(z,x),y)))),
inference(subst,[],[refute_0_73:[bind(X_3097,$fot(x)),bind(X_3098,$fot(z)),bind(X_3099,$fot(y))]]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(x,equivalent(equivalent(y,z),equivalent(equivalent(z,x),y)))) )],[refute_0_74,prove_xhn]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL257-1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 16:40:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.22/1.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.22/1.38
% 1.22/1.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.22/1.39
%------------------------------------------------------------------------------