TSTP Solution File: LCL024-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL024-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:48:51 EDT 2022
% Result : Unsatisfiable 5.25s 5.49s
% Output : CNFRefutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of clauses : 57 ( 33 unt; 0 nHn; 23 RR)
% Number of literals : 87 ( 0 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 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 : 239 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(xgk,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y)))) ).
cnf(prove_pyo,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X_45,equivalent(X_46,equivalent(X_47,X_47))))
| ~ is_a_theorem(equivalent(equivalent(X_45,equivalent(X_46,equivalent(X_47,X_47))),equivalent(X_46,X_45)))
| is_a_theorem(equivalent(X_46,X_45)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_45,equivalent(X_46,equivalent(X_47,X_47))))),bind(Y,$fot(equivalent(X_46,X_45)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(equivalent(X_3,equivalent(equivalent(Y,equivalent(Z,X_3)),equivalent(Z,Y)))),
inference(subst,[],[xgk:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(X_3)
| ~ is_a_theorem(equivalent(X_3,equivalent(equivalent(Y,equivalent(Z,X_3)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(Y,equivalent(Z,X_3)),equivalent(Z,Y))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_3)),bind(Y,$fot(equivalent(equivalent(Y,equivalent(Z,X_3)),equivalent(Z,Y))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X_3)
| is_a_theorem(equivalent(equivalent(Y,equivalent(Z,X_3)),equivalent(Z,Y))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_3,equivalent(equivalent(Y,equivalent(Z,X_3)),equivalent(Z,Y)))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(X_40,X_40))
| is_a_theorem(equivalent(equivalent(Y,equivalent(Z,equivalent(X_40,X_40))),equivalent(Z,Y))) ),
inference(subst,[],[refute_0_3:[bind(X_3,$fot(equivalent(X_40,X_40)))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(X_14,equivalent(equivalent(equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)),equivalent(X_16,X_14)),equivalent(X_16,equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)))))),
inference(subst,[],[xgk:[bind(X,$fot(X_14)),bind(Y,$fot(equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)))),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))))
| ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11)))
| is_a_theorem(equivalent(X_12,X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))))),bind(Y,$fot(equivalent(X_12,X_11)))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(X_5,equivalent(X_6,equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y))))),equivalent(X_6,X_5))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_5)),bind(Z,$fot(X_6)),bind(X_3,$fot(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y)))))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(equivalent(equivalent(X_5,equivalent(X_6,equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y))))),equivalent(X_6,X_5))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y)))) )],[xgk,refute_0_7]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11))),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10)),bind(X_5,$fot(X_11)),bind(X_6,$fot(X_12))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))))
| is_a_theorem(equivalent(X_12,X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11))) )],[refute_0_9,refute_0_6]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(X_14,equivalent(equivalent(equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)),equivalent(X_16,X_14)),equivalent(X_16,equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)),equivalent(X_16,X_14)),X_14)) ),
inference(subst,[],[refute_0_10:[bind(X_10,$fot(X_13)),bind(X_11,$fot(X_14)),bind(X_12,$fot(equivalent(equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)),equivalent(X_16,X_14)))),bind(X_8,$fot(X_16)),bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)),equivalent(X_16,X_14)),X_14)),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_14,equivalent(equivalent(equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)),equivalent(X_16,X_14)),equivalent(X_16,equivalent(equivalent(X_17,equivalent(X_13,X_16)),equivalent(X_13,X_17)))))) )],[refute_0_5,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_38,equivalent(X_36,X_36)),equivalent(X_36,X_38)),equivalent(X_36,equivalent(X_38,equivalent(X_36,X_36)))),equivalent(X_38,equivalent(X_36,X_36)))),
inference(subst,[],[refute_0_12:[bind(X_13,$fot(X_36)),bind(X_14,$fot(equivalent(X_38,equivalent(X_36,X_36)))),bind(X_16,$fot(X_36)),bind(X_17,$fot(X_38))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,X_19)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,X_19)),X_19))
| is_a_theorem(X_19) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,X_19)))),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,X_19)),X_19)),
inference(subst,[],[refute_0_12:[bind(X_13,$fot(X_18)),bind(X_14,$fot(X_19)),bind(X_16,$fot(X_20)),bind(X_17,$fot(X_21))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,X_19)))
| is_a_theorem(X_19) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,X_19)),X_19)) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_38,equivalent(X_36,X_36)),equivalent(X_36,X_38)),equivalent(X_36,equivalent(X_38,equivalent(X_36,X_36)))),equivalent(X_38,equivalent(X_36,X_36))))
| is_a_theorem(equivalent(X_36,X_36)) ),
inference(subst,[],[refute_0_16:[bind(X_18,$fot(X_36)),bind(X_19,$fot(equivalent(X_36,X_36))),bind(X_20,$fot(X_38)),bind(X_21,$fot(equivalent(X_38,equivalent(X_36,X_36))))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(X_36,X_36)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_38,equivalent(X_36,X_36)),equivalent(X_36,X_38)),equivalent(X_36,equivalent(X_38,equivalent(X_36,X_36)))),equivalent(X_38,equivalent(X_36,X_36)))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(equivalent(X_40,X_40)),
inference(subst,[],[refute_0_18:[bind(X_36,$fot(X_40))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(Y,equivalent(Z,equivalent(X_40,X_40))),equivalent(Z,Y))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_40,X_40)) )],[refute_0_19,refute_0_4]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(X_45,equivalent(X_46,equivalent(X_47,X_47))),equivalent(X_46,X_45))),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_45)),bind(Z,$fot(X_46)),bind(X_40,$fot(X_47))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(equivalent(X_45,equivalent(X_46,equivalent(X_47,X_47))))
| is_a_theorem(equivalent(X_46,X_45)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_45,equivalent(X_46,equivalent(X_47,X_47))),equivalent(X_46,X_45))) )],[refute_0_21,refute_0_0]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(equivalent(equivalent(X_5166,X_5168),equivalent(equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),X_5167),equivalent(equivalent(X_5167,equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),equivalent(X_5166,X_5168))),equivalent(X_5167,equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),equivalent(X_5166,X_5168)))))))
| is_a_theorem(equivalent(equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),X_5167),equivalent(X_5166,X_5168))) ),
inference(subst,[],[refute_0_22:[bind(X_45,$fot(equivalent(X_5166,X_5168))),bind(X_46,$fot(equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),X_5167))),bind(X_47,$fot(equivalent(X_5167,equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),equivalent(X_5166,X_5168)))))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_10,X_9),equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_3580,equivalent(equivalent(X_3581,equivalent(X_3577,X_3580)),equivalent(X_3577,X_3581))))),equivalent(X_3576,equivalent(X_3576,equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_10,X_9))))))
| is_a_theorem(equivalent(X_3576,equivalent(equivalent(X_10,X_9),equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_3580,equivalent(equivalent(X_3581,equivalent(X_3577,X_3580)),equivalent(X_3577,X_3581))))))) ),
inference(subst,[],[refute_0_10:[bind(X_11,$fot(equivalent(equivalent(X_10,X_9),equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_3580,equivalent(equivalent(X_3581,equivalent(X_3577,X_3580)),equivalent(X_3577,X_3581))))))),bind(X_12,$fot(X_3576)),bind(X_8,$fot(X_3576))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(equivalent(equivalent(X_499,equivalent(X_499,X_498)),equivalent(equivalent(X_500,equivalent(X_500,X_498)),equivalent(X_500,X_500))))
| is_a_theorem(equivalent(equivalent(X_500,equivalent(X_500,X_498)),equivalent(X_499,equivalent(X_499,X_498)))) ),
inference(subst,[],[refute_0_22:[bind(X_45,$fot(equivalent(X_499,equivalent(X_499,X_498)))),bind(X_46,$fot(equivalent(X_500,equivalent(X_500,X_498)))),bind(X_47,$fot(X_500))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_246,equivalent(X_242,X_244)),equivalent(X_242,X_246)),equivalent(equivalent(X_245,equivalent(X_245,X_244)),equivalent(X_245,X_245))))
| is_a_theorem(equivalent(equivalent(X_245,equivalent(X_245,X_244)),equivalent(equivalent(X_246,equivalent(X_242,X_244)),equivalent(X_242,X_246)))) ),
inference(subst,[],[refute_0_22:[bind(X_45,$fot(equivalent(equivalent(X_246,equivalent(X_242,X_244)),equivalent(X_242,X_246)))),bind(X_46,$fot(equivalent(X_245,equivalent(X_245,X_244)))),bind(X_47,$fot(X_245))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_208,equivalent(X_206,X_207)),equivalent(X_206,X_208)),equivalent(equivalent(equivalent(X_210,equivalent(X_205,X_207)),equivalent(X_205,X_210)),equivalent(X_207,X_207))))
| is_a_theorem(equivalent(equivalent(equivalent(X_210,equivalent(X_205,X_207)),equivalent(X_205,X_210)),equivalent(equivalent(X_208,equivalent(X_206,X_207)),equivalent(X_206,X_208)))) ),
inference(subst,[],[refute_0_22:[bind(X_45,$fot(equivalent(equivalent(X_208,equivalent(X_206,X_207)),equivalent(X_206,X_208)))),bind(X_46,$fot(equivalent(equivalent(X_210,equivalent(X_205,X_207)),equivalent(X_205,X_210)))),bind(X_47,$fot(X_207))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)),equivalent(equivalent(equivalent(X_202,equivalent(X_200,X_201)),equivalent(X_200,X_202)),equivalent(X_201,equivalent(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)),equivalent(X_203,equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204))))))))
| is_a_theorem(equivalent(equivalent(equivalent(X_202,equivalent(X_200,X_201)),equivalent(X_200,X_202)),equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)))) ),
inference(subst,[],[refute_0_10:[bind(X_10,$fot(X_203)),bind(X_11,$fot(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)))),bind(X_12,$fot(equivalent(equivalent(X_202,equivalent(X_200,X_201)),equivalent(X_200,X_202)))),bind(X_8,$fot(X_201)),bind(X_9,$fot(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204))))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))),equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))))
| is_a_theorem(equivalent(X_12,equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))))) ),
inference(subst,[],[refute_0_10:[bind(X_11,$fot(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))))))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))),equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))),
inference(subst,[],[refute_0_12:[bind(X_13,$fot(X_18)),bind(X_14,$fot(equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))),bind(X_16,$fot(X_20)),bind(X_17,$fot(X_21))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(equivalent(X_12,equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_21,equivalent(X_18,X_20)),equivalent(X_18,X_21)),equivalent(X_20,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))),equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9)))))) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)),equivalent(equivalent(equivalent(X_202,equivalent(X_200,X_201)),equivalent(X_200,X_202)),equivalent(X_201,equivalent(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)),equivalent(X_203,equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)))))))),
inference(subst,[],[refute_0_31:[bind(X_10,$fot(X_198)),bind(X_12,$fot(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)))),bind(X_18,$fot(X_200)),bind(X_20,$fot(X_201)),bind(X_21,$fot(X_202)),bind(X_8,$fot(X_203)),bind(X_9,$fot(X_204))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_202,equivalent(X_200,X_201)),equivalent(X_200,X_202)),equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)),equivalent(equivalent(equivalent(X_202,equivalent(X_200,X_201)),equivalent(X_200,X_202)),equivalent(X_201,equivalent(equivalent(equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)),equivalent(X_203,X_201)),equivalent(X_203,equivalent(equivalent(X_204,equivalent(X_198,X_203)),equivalent(X_198,X_204)))))))) )],[refute_0_32,refute_0_28]) ).
cnf(refute_0_34,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_208,equivalent(X_206,X_207)),equivalent(X_206,X_208)),equivalent(equivalent(equivalent(X_210,equivalent(X_205,X_207)),equivalent(X_205,X_210)),equivalent(X_207,X_207)))),
inference(subst,[],[refute_0_33:[bind(X_198,$fot(X_205)),bind(X_200,$fot(X_206)),bind(X_201,$fot(X_207)),bind(X_202,$fot(X_208)),bind(X_203,$fot(X_207)),bind(X_204,$fot(X_210))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_210,equivalent(X_205,X_207)),equivalent(X_205,X_210)),equivalent(equivalent(X_208,equivalent(X_206,X_207)),equivalent(X_206,X_208)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_208,equivalent(X_206,X_207)),equivalent(X_206,X_208)),equivalent(equivalent(equivalent(X_210,equivalent(X_205,X_207)),equivalent(X_205,X_210)),equivalent(X_207,X_207)))) )],[refute_0_34,refute_0_27]) ).
cnf(refute_0_36,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_246,equivalent(X_242,X_244)),equivalent(X_242,X_246)),equivalent(equivalent(X_245,equivalent(X_245,X_244)),equivalent(X_245,X_245)))),
inference(subst,[],[refute_0_35:[bind(X_205,$fot(X_242)),bind(X_206,$fot(X_245)),bind(X_207,$fot(X_244)),bind(X_208,$fot(X_245)),bind(X_210,$fot(X_246))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(equivalent(equivalent(X_245,equivalent(X_245,X_244)),equivalent(equivalent(X_246,equivalent(X_242,X_244)),equivalent(X_242,X_246)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_246,equivalent(X_242,X_244)),equivalent(X_242,X_246)),equivalent(equivalent(X_245,equivalent(X_245,X_244)),equivalent(X_245,X_245)))) )],[refute_0_36,refute_0_26]) ).
cnf(refute_0_38,plain,
is_a_theorem(equivalent(equivalent(X_499,equivalent(X_499,X_498)),equivalent(equivalent(X_500,equivalent(X_500,X_498)),equivalent(X_500,X_500)))),
inference(subst,[],[refute_0_37:[bind(X_242,$fot(X_500)),bind(X_244,$fot(X_498)),bind(X_245,$fot(X_499)),bind(X_246,$fot(X_500))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(equivalent(equivalent(X_500,equivalent(X_500,X_498)),equivalent(X_499,equivalent(X_499,X_498)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_499,equivalent(X_499,X_498)),equivalent(equivalent(X_500,equivalent(X_500,X_498)),equivalent(X_500,X_500)))) )],[refute_0_38,refute_0_25]) ).
cnf(refute_0_40,plain,
is_a_theorem(equivalent(equivalent(X_500,equivalent(X_500,equivalent(X_923,X_922))),equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(X_923,X_922))))),
inference(subst,[],[refute_0_39:[bind(X_498,$fot(equivalent(X_923,X_922))),bind(X_499,$fot(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925)))))))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(equivalent(X_22,equivalent(X_23,equivalent(equivalent(X_25,equivalent(X_26,equivalent(X_27,equivalent(equivalent(X_28,equivalent(X_24,X_27)),equivalent(X_24,X_28))))),equivalent(X_26,X_25)))))
| ~ is_a_theorem(equivalent(equivalent(X_22,equivalent(X_23,equivalent(equivalent(X_25,equivalent(X_26,equivalent(X_27,equivalent(equivalent(X_28,equivalent(X_24,X_27)),equivalent(X_24,X_28))))),equivalent(X_26,X_25)))),equivalent(X_23,X_22)))
| is_a_theorem(equivalent(X_23,X_22)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_22,equivalent(X_23,equivalent(equivalent(X_25,equivalent(X_26,equivalent(X_27,equivalent(equivalent(X_28,equivalent(X_24,X_27)),equivalent(X_24,X_28))))),equivalent(X_26,X_25)))))),bind(Y,$fot(equivalent(X_23,X_22)))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11)))
| is_a_theorem(equivalent(equivalent(Y,equivalent(Z,equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11)))),equivalent(Z,Y))) ),
inference(subst,[],[refute_0_3:[bind(X_3,$fot(equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11))))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(equivalent(equivalent(Y,equivalent(Z,equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11)))),equivalent(Z,Y))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(X_12,equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_10,X_8)),equivalent(X_10,X_9))))),equivalent(X_12,X_11))) )],[refute_0_9,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(equivalent(equivalent(X_22,equivalent(X_23,equivalent(equivalent(X_25,equivalent(X_26,equivalent(X_27,equivalent(equivalent(X_28,equivalent(X_24,X_27)),equivalent(X_24,X_28))))),equivalent(X_26,X_25)))),equivalent(X_23,X_22))),
inference(subst,[],[refute_0_43:[bind(Y,$fot(X_22)),bind(Z,$fot(X_23)),bind(X_10,$fot(X_24)),bind(X_11,$fot(X_25)),bind(X_12,$fot(X_26)),bind(X_8,$fot(X_27)),bind(X_9,$fot(X_28))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(equivalent(X_22,equivalent(X_23,equivalent(equivalent(X_25,equivalent(X_26,equivalent(X_27,equivalent(equivalent(X_28,equivalent(X_24,X_27)),equivalent(X_24,X_28))))),equivalent(X_26,X_25)))))
| is_a_theorem(equivalent(X_23,X_22)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_22,equivalent(X_23,equivalent(equivalent(X_25,equivalent(X_26,equivalent(X_27,equivalent(equivalent(X_28,equivalent(X_24,X_27)),equivalent(X_24,X_28))))),equivalent(X_26,X_25)))),equivalent(X_23,X_22))) )],[refute_0_44,refute_0_41]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(equivalent(equivalent(X_500,equivalent(X_500,equivalent(X_923,X_922))),equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(X_923,X_922)))))
| is_a_theorem(equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(X_500,equivalent(X_500,equivalent(X_923,X_922))))) ),
inference(subst,[],[refute_0_45:[bind(X_22,$fot(equivalent(X_500,equivalent(X_500,equivalent(X_923,X_922))))),bind(X_23,$fot(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))))),bind(X_24,$fot(X_921)),bind(X_25,$fot(X_922)),bind(X_26,$fot(X_923)),bind(X_27,$fot(X_924)),bind(X_28,$fot(X_925))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(X_500,equivalent(X_500,equivalent(X_923,X_922))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_500,equivalent(X_500,equivalent(X_923,X_922))),equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(equivalent(X_922,equivalent(X_923,equivalent(X_924,equivalent(equivalent(X_925,equivalent(X_921,X_924)),equivalent(X_921,X_925))))),equivalent(X_923,X_922))))) )],[refute_0_40,refute_0_46]) ).
cnf(refute_0_48,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_10,X_9),equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_3580,equivalent(equivalent(X_3581,equivalent(X_3577,X_3580)),equivalent(X_3577,X_3581))))),equivalent(X_3576,equivalent(X_3576,equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_10,X_9)))))),
inference(subst,[],[refute_0_47:[bind(X_500,$fot(X_3576)),bind(X_921,$fot(X_3577)),bind(X_922,$fot(equivalent(X_10,X_9))),bind(X_923,$fot(equivalent(X_9,equivalent(X_10,X_3576)))),bind(X_924,$fot(X_3580)),bind(X_925,$fot(X_3581))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(equivalent(X_3576,equivalent(equivalent(X_10,X_9),equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_3580,equivalent(equivalent(X_3581,equivalent(X_3577,X_3580)),equivalent(X_3577,X_3581))))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_10,X_9),equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_3580,equivalent(equivalent(X_3581,equivalent(X_3577,X_3580)),equivalent(X_3577,X_3581))))),equivalent(X_3576,equivalent(X_3576,equivalent(equivalent(X_9,equivalent(X_10,X_3576)),equivalent(X_10,X_9)))))) )],[refute_0_48,refute_0_24]) ).
cnf(refute_0_50,plain,
is_a_theorem(equivalent(equivalent(X_5166,X_5168),equivalent(equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),X_5167),equivalent(equivalent(X_5167,equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),equivalent(X_5166,X_5168))),equivalent(X_5167,equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),equivalent(X_5166,X_5168))))))),
inference(subst,[],[refute_0_49:[bind(X_10,$fot(equivalent(X_5168,equivalent(X_5166,X_5167)))),bind(X_3576,$fot(equivalent(X_5166,X_5168))),bind(X_3577,$fot(X_5166)),bind(X_3580,$fot(X_5167)),bind(X_3581,$fot(X_5168)),bind(X_9,$fot(X_5167))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),X_5167),equivalent(X_5166,X_5168))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_5166,X_5168),equivalent(equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),X_5167),equivalent(equivalent(X_5167,equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),equivalent(X_5166,X_5168))),equivalent(X_5167,equivalent(equivalent(X_5168,equivalent(X_5166,X_5167)),equivalent(X_5166,X_5168))))))) )],[refute_0_50,refute_0_23]) ).
cnf(refute_0_52,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))),
inference(subst,[],[refute_0_51:[bind(X_5166,$fot(b)),bind(X_5167,$fot(c)),bind(X_5168,$fot(a))]]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))) )],[refute_0_52,prove_pyo]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL024-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 4 12:43:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.25/5.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.25/5.49
% 5.25/5.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.25/5.50
%------------------------------------------------------------------------------