TSTP Solution File: LCL104-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL104-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:49:30 EDT 2022
% Result : Unsatisfiable 0.78s 0.93s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of clauses : 57 ( 32 unt; 0 nHn; 20 RR)
% Number of literals : 89 ( 0 equ; 33 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 213 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(p_4,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))) ).
cnf(q_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),Z)),Z)) ).
cnf(prove_p_1,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_238,X_235),X_236),equivalent(X_235,X_237)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_238,X_235),X_236),equivalent(X_235,X_237)),equivalent(X_236,equivalent(X_238,X_237))))
| is_a_theorem(equivalent(X_236,equivalent(X_238,X_237))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_238,X_235),X_236),equivalent(X_235,X_237)))),bind(Y,$fot(equivalent(X_236,equivalent(X_238,X_237))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(equivalent(X_50,X_51),equivalent(X_50,X_49)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_50,X_51),equivalent(X_50,X_49)),equivalent(X_51,X_49)))
| is_a_theorem(equivalent(X_51,X_49)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_50,X_51),equivalent(X_50,X_49)))),bind(Y,$fot(equivalent(X_51,X_49)))]]) ).
cnf(refute_0_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U)))))),
inference(subst,[],[p_4:[bind(X,$fot(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U)))))]]) ).
cnf(refute_0_3,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_4)),X_4)),
inference(subst,[],[q_3:[bind(Z,$fot(X_4))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_4)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_4)),X_4))
| is_a_theorem(X_4) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_4)))),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_4)))
| is_a_theorem(X_4) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_4)),X_4)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))))))
| is_a_theorem(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(equivalent(Z,U))),bind(Y,$fot(equivalent(equivalent(Y,Z),equivalent(Y,U)))),bind(X_4,$fot(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U)))))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U)))))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(X_14,X_12))
| ~ is_a_theorem(equivalent(equivalent(X_14,X_12),equivalent(equivalent(X_13,X_14),equivalent(X_13,X_12))))
| is_a_theorem(equivalent(equivalent(X_13,X_14),equivalent(X_13,X_12))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_14,X_12))),bind(Y,$fot(equivalent(equivalent(X_13,X_14),equivalent(X_13,X_12))))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(equivalent(X_14,X_12),equivalent(equivalent(X_13,X_14),equivalent(X_13,X_12)))),
inference(subst,[],[refute_0_7:[bind(U,$fot(X_12)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(X_14,X_12))
| is_a_theorem(equivalent(equivalent(X_13,X_14),equivalent(X_13,X_12))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_14,X_12),equivalent(equivalent(X_13,X_14),equivalent(X_13,X_12)))) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))))
| is_a_theorem(equivalent(equivalent(X_17,equivalent(Z,U)),equivalent(X_17,equivalent(equivalent(Y,Z),equivalent(Y,U))))) ),
inference(subst,[],[refute_0_10:[bind(X_12,$fot(equivalent(equivalent(Y,Z),equivalent(Y,U)))),bind(X_13,$fot(X_17)),bind(X_14,$fot(equivalent(Z,U)))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(equivalent(equivalent(X_17,equivalent(Z,U)),equivalent(X_17,equivalent(equivalent(Y,Z),equivalent(Y,U))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U)))) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_45,X_46),equivalent(X_45,U)),equivalent(equivalent(X_45,X_46),equivalent(equivalent(X_46,X_45),equivalent(X_46,U))))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_46)),bind(Z,$fot(X_45)),bind(X_17,$fot(equivalent(X_45,X_46)))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(equivalent(X_35,equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),X_34))))
| ~ is_a_theorem(equivalent(equivalent(X_35,equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),X_34))),equivalent(X_35,X_34)))
| is_a_theorem(equivalent(X_35,X_34)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_35,equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),X_34))))),bind(Y,$fot(equivalent(X_35,X_34)))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_16)),X_16)),
inference(subst,[],[q_3:[bind(Z,$fot(X_16))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_16)),X_16))
| is_a_theorem(equivalent(equivalent(X_17,equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_16))),equivalent(X_17,X_16))) ),
inference(subst,[],[refute_0_10:[bind(X_12,$fot(X_16)),bind(X_13,$fot(X_17)),bind(X_14,$fot(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_16))))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(X_17,equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_16))),equivalent(X_17,X_16))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),X_16)),X_16)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(X_35,equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),X_34))),equivalent(X_35,X_34))),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_32)),bind(Y,$fot(X_33)),bind(X_16,$fot(X_34)),bind(X_17,$fot(X_35))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(X_35,equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),X_34))))
| is_a_theorem(equivalent(X_35,X_34)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_35,equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),X_34))),equivalent(X_35,X_34))) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_45,X_46),equivalent(X_45,U)),equivalent(equivalent(X_45,X_46),equivalent(equivalent(X_46,X_45),equivalent(X_46,U)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_45,X_46),equivalent(X_45,U)),equivalent(X_46,U))) ),
inference(subst,[],[refute_0_19:[bind(X_32,$fot(X_45)),bind(X_33,$fot(X_46)),bind(X_34,$fot(equivalent(X_46,U))),bind(X_35,$fot(equivalent(equivalent(X_45,X_46),equivalent(X_45,U))))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_45,X_46),equivalent(X_45,U)),equivalent(X_46,U))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_45,X_46),equivalent(X_45,U)),equivalent(equivalent(X_45,X_46),equivalent(equivalent(X_46,X_45),equivalent(X_46,U))))) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_50,X_51),equivalent(X_50,X_49)),equivalent(X_51,X_49))),
inference(subst,[],[refute_0_21:[bind(U,$fot(X_49)),bind(X_45,$fot(X_50)),bind(X_46,$fot(X_51))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(equivalent(equivalent(X_50,X_51),equivalent(X_50,X_49)))
| is_a_theorem(equivalent(X_51,X_49)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_50,X_51),equivalent(X_50,X_49)),equivalent(X_51,X_49))) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_230,equivalent(X_234,X_229)),equivalent(equivalent(equivalent(X_234,X_229),X_230),equivalent(X_229,X_233))),equivalent(equivalent(X_230,equivalent(X_234,X_229)),equivalent(X_230,equivalent(X_234,X_233)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_234,X_229),X_230),equivalent(X_229,X_233)),equivalent(X_230,equivalent(X_234,X_233)))) ),
inference(subst,[],[refute_0_23:[bind(X_49,$fot(equivalent(X_230,equivalent(X_234,X_233)))),bind(X_50,$fot(equivalent(X_230,equivalent(X_234,X_229)))),bind(X_51,$fot(equivalent(equivalent(equivalent(X_234,X_229),X_230),equivalent(X_229,X_233))))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98))))))
| is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98)))) ),
inference(subst,[],[refute_0_19:[bind(X_34,$fot(equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98)))),bind(X_35,$fot(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98)))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(equivalent(equivalent(X_39,equivalent(X_38,X_36)),equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36)))))
| is_a_theorem(equivalent(equivalent(X_13,equivalent(X_39,equivalent(X_38,X_36))),equivalent(X_13,equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36)))))) ),
inference(subst,[],[refute_0_10:[bind(X_12,$fot(equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36))))),bind(X_14,$fot(equivalent(X_39,equivalent(X_38,X_36))))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(equivalent(X_39,equivalent(X_38,X_36)),equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36))))),
inference(subst,[],[refute_0_12:[bind(U,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38)),bind(X_17,$fot(X_39))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(X_13,equivalent(X_39,equivalent(X_38,X_36))),equivalent(X_13,equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_39,equivalent(X_38,X_36)),equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36))))) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98)))))),
inference(subst,[],[refute_0_28:[bind(X_13,$fot(equivalent(X_32,X_33))),bind(X_36,$fot(X_98)),bind(X_37,$fot(X_99)),bind(X_38,$fot(X_100)),bind(X_39,$fot(equivalent(X_33,X_32)))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98)))))) )],[refute_0_29,refute_0_25]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(equivalent(X_39,equivalent(X_38,X_36)))
| ~ is_a_theorem(equivalent(equivalent(X_39,equivalent(X_38,X_36)),equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36)))))
| is_a_theorem(equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_39,equivalent(X_38,X_36)))),bind(Y,$fot(equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36)))))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(equivalent(X_39,equivalent(X_38,X_36)))
| is_a_theorem(equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_39,equivalent(X_38,X_36)),equivalent(X_39,equivalent(equivalent(X_37,X_38),equivalent(X_37,X_36))))) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98))))
| is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_213,equivalent(X_99,X_100)),equivalent(X_213,equivalent(X_99,X_98))))) ),
inference(subst,[],[refute_0_32:[bind(X_36,$fot(equivalent(X_99,X_98))),bind(X_37,$fot(X_213)),bind(X_38,$fot(equivalent(X_99,X_100))),bind(X_39,$fot(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98)))))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_213,equivalent(X_99,X_100)),equivalent(X_213,equivalent(X_99,X_98))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_32,X_33),equivalent(equivalent(X_33,X_32),equivalent(X_100,X_98))),equivalent(equivalent(X_99,X_100),equivalent(X_99,X_98)))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_230,equivalent(X_234,X_229)),equivalent(equivalent(equivalent(X_234,X_229),X_230),equivalent(X_229,X_233))),equivalent(equivalent(X_230,equivalent(X_234,X_229)),equivalent(X_230,equivalent(X_234,X_233))))),
inference(subst,[],[refute_0_34:[bind(X_100,$fot(X_229)),bind(X_213,$fot(X_230)),bind(X_32,$fot(X_230)),bind(X_33,$fot(equivalent(X_234,X_229))),bind(X_98,$fot(X_233)),bind(X_99,$fot(X_234))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_234,X_229),X_230),equivalent(X_229,X_233)),equivalent(X_230,equivalent(X_234,X_233)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_230,equivalent(X_234,X_229)),equivalent(equivalent(equivalent(X_234,X_229),X_230),equivalent(X_229,X_233))),equivalent(equivalent(X_230,equivalent(X_234,X_229)),equivalent(X_230,equivalent(X_234,X_233))))) )],[refute_0_35,refute_0_24]) ).
cnf(refute_0_37,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_238,X_235),X_236),equivalent(X_235,X_237)),equivalent(X_236,equivalent(X_238,X_237)))),
inference(subst,[],[refute_0_36:[bind(X_229,$fot(X_235)),bind(X_230,$fot(X_236)),bind(X_233,$fot(X_237)),bind(X_234,$fot(X_238))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_238,X_235),X_236),equivalent(X_235,X_237)))
| is_a_theorem(equivalent(X_236,equivalent(X_238,X_237))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_238,X_235),X_236),equivalent(X_235,X_237)),equivalent(X_236,equivalent(X_238,X_237)))) )],[refute_0_37,refute_0_0]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1348,X_1346),equivalent(equivalent(X_1347,X_1348),equivalent(X_1347,X_1346))),equivalent(equivalent(X_1347,X_1346),X_1349)),equivalent(equivalent(equivalent(X_1347,X_1348),equivalent(X_1347,X_1346)),equivalent(equivalent(X_1347,X_1348),X_1349))))
| is_a_theorem(equivalent(equivalent(equivalent(X_1347,X_1346),X_1349),equivalent(equivalent(X_1348,X_1346),equivalent(equivalent(X_1347,X_1348),X_1349)))) ),
inference(subst,[],[refute_0_38:[bind(X_235,$fot(equivalent(equivalent(X_1347,X_1348),equivalent(X_1347,X_1346)))),bind(X_236,$fot(equivalent(equivalent(X_1347,X_1346),X_1349))),bind(X_237,$fot(equivalent(equivalent(X_1347,X_1348),X_1349))),bind(X_238,$fot(equivalent(X_1348,X_1346)))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(equivalent(X_18,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_18))),
inference(subst,[],[p_4:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(equivalent(X_18,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_18)))
| is_a_theorem(equivalent(equivalent(X_17,X_18),equivalent(X_17,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_18)))) ),
inference(subst,[],[refute_0_10:[bind(X_12,$fot(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_18))),bind(X_13,$fot(X_17)),bind(X_14,$fot(X_18))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(equivalent(equivalent(X_17,X_18),equivalent(X_17,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_18)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_18,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_18))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),X_47),equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_47)))),
inference(subst,[],[refute_0_42:[bind(X_17,$fot(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))))),bind(X_18,$fot(X_47))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),X_47),equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_47))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),X_47),X_47)) ),
inference(subst,[],[refute_0_19:[bind(X_32,$fot(equivalent(Z,U))),bind(X_33,$fot(equivalent(equivalent(Y,Z),equivalent(Y,U)))),bind(X_34,$fot(X_47)),bind(X_35,$fot(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),X_47)))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),X_47),X_47)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),X_47),equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X_47)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(X_214,X_212)),equivalent(X_214,X_212))),
inference(subst,[],[refute_0_45:[bind(X_47,$fot(equivalent(X_214,X_212)))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(X_214,X_212)),equivalent(X_214,X_212)))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(X_214,X_212)),equivalent(equivalent(X_213,X_214),equivalent(X_213,X_212)))) ),
inference(subst,[],[refute_0_32:[bind(X_36,$fot(X_212)),bind(X_37,$fot(X_213)),bind(X_38,$fot(X_214)),bind(X_39,$fot(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(X_214,X_212))))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(X_214,X_212)),equivalent(equivalent(X_213,X_214),equivalent(X_213,X_212)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(equivalent(Y,Z),equivalent(Y,U))),equivalent(X_214,X_212)),equivalent(X_214,X_212))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1348,X_1346),equivalent(equivalent(X_1347,X_1348),equivalent(X_1347,X_1346))),equivalent(equivalent(X_1347,X_1346),X_1349)),equivalent(equivalent(equivalent(X_1347,X_1348),equivalent(X_1347,X_1346)),equivalent(equivalent(X_1347,X_1348),X_1349)))),
inference(subst,[],[refute_0_48:[bind(U,$fot(X_1346)),bind(Y,$fot(X_1347)),bind(Z,$fot(X_1348)),bind(X_212,$fot(X_1349)),bind(X_213,$fot(equivalent(X_1347,X_1348))),bind(X_214,$fot(equivalent(X_1347,X_1346)))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_1347,X_1346),X_1349),equivalent(equivalent(X_1348,X_1346),equivalent(equivalent(X_1347,X_1348),X_1349)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1348,X_1346),equivalent(equivalent(X_1347,X_1348),equivalent(X_1347,X_1346))),equivalent(equivalent(X_1347,X_1346),X_1349)),equivalent(equivalent(equivalent(X_1347,X_1348),equivalent(X_1347,X_1346)),equivalent(equivalent(X_1347,X_1348),X_1349)))) )],[refute_0_49,refute_0_39]) ).
cnf(refute_0_51,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(subst,[],[refute_0_50:[bind(X_1346,$fot(b)),bind(X_1347,$fot(a)),bind(X_1348,$fot(e)),bind(X_1349,$fot(c))]]) ).
cnf(refute_0_52,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) )],[refute_0_51,prove_p_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL104-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 4 03:58:44 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.78/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.93
% 0.78/0.93 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.78/0.94
%------------------------------------------------------------------------------