TSTP Solution File: LCL011-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:48:46 EDT 2022
% Result : Unsatisfiable 13.30s 13.48s
% Output : CNFRefutation 13.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 3
% Syntax : Number of clauses : 117 ( 64 unt; 0 nHn; 37 RR)
% Number of literals : 183 ( 0 equ; 67 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 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 : 358 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(yqj,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))) ).
cnf(prove_yqf,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X_165,X_166))
| ~ is_a_theorem(equivalent(equivalent(X_165,X_166),equivalent(X_166,X_165)))
| is_a_theorem(equivalent(X_166,X_165)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_165,X_166))),bind(Y,$fot(equivalent(X_166,X_165)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(Z,X),equivalent(Y,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,X),equivalent(Y,Z))))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(equivalent(Z,X),equivalent(Y,Z))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))) )],[yqj,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(X_7,equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),X_7))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,X),equivalent(Y,Z)))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(equivalent(equivalent(X_7,equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),X_7))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))) )],[yqj,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_80,X_81),equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),equivalent(X_80,X_81)))),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(equivalent(X_80,X_81)))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(X_12,equivalent(X_14,equivalent(X_15,X_16))))
| ~ is_a_theorem(equivalent(equivalent(X_12,equivalent(X_14,equivalent(X_15,X_16))),equivalent(equivalent(equivalent(equivalent(X_13,X_15),equivalent(X_16,X_13)),X_14),X_12)))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_13,X_15),equivalent(X_16,X_13)),X_14),X_12)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_12,equivalent(X_14,equivalent(X_15,X_16))))),bind(Y,$fot(equivalent(equivalent(equivalent(equivalent(X_13,X_15),equivalent(X_16,X_13)),X_14),X_12)))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(X_8,X_9)),equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11)))
| is_a_theorem(equivalent(equivalent(Z,equivalent(X_11,equivalent(X_8,X_9))),equivalent(equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X_11,equivalent(X_8,X_9)))),bind(Y,$fot(equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11)))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(equivalent(equivalent(X_11,equivalent(X_8,X_9)),equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(X_11,equivalent(X_8,X_9))),equivalent(equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(X_8,X_9)),equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11))) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(equivalent(X_12,equivalent(X_14,equivalent(X_15,X_16))),equivalent(equivalent(equivalent(equivalent(X_13,X_15),equivalent(X_16,X_13)),X_14),X_12))),
inference(subst,[],[refute_0_9:[bind(Z,$fot(X_12)),bind(X_10,$fot(X_13)),bind(X_11,$fot(X_14)),bind(X_8,$fot(X_15)),bind(X_9,$fot(X_16))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(X_12,equivalent(X_14,equivalent(X_15,X_16))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_13,X_15),equivalent(X_16,X_13)),X_14),X_12)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_12,equivalent(X_14,equivalent(X_15,X_16))),equivalent(equivalent(equivalent(equivalent(X_13,X_15),equivalent(X_16,X_13)),X_14),X_12))) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_80,X_81),equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),equivalent(X_80,X_81))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_80),equivalent(X_81,X_78)),equivalent(equivalent(Z,X),equivalent(Y,Z))),equivalent(equivalent(X_80,X_81),equivalent(X,Y)))) ),
inference(subst,[],[refute_0_11:[bind(X_12,$fot(equivalent(equivalent(X_80,X_81),equivalent(X,Y)))),bind(X_13,$fot(X_78)),bind(X_14,$fot(equivalent(equivalent(Z,X),equivalent(Y,Z)))),bind(X_15,$fot(X_80)),bind(X_16,$fot(X_81))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_80),equivalent(X_81,X_78)),equivalent(equivalent(Z,X),equivalent(Y,Z))),equivalent(equivalent(X_80,X_81),equivalent(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_80,X_81),equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),equivalent(X_80,X_81)))) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_78),equivalent(X_78,X_78)),equivalent(equivalent(Z,X_78),equivalent(X_78,Z))),equivalent(equivalent(X_78,X_78),equivalent(X_78,X_78)))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_78)),bind(Y,$fot(X_78)),bind(X_80,$fot(X_78)),bind(X_81,$fot(X_78))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(equivalent(equivalent(X_127,X_126),X_127))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_127,X_126),X_127),X_126))
| is_a_theorem(X_126) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_127,X_126),X_127))),bind(Y,$fot(X_126))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(X_8,X_9)))
| ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(X_8,X_9)),equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11)))
| is_a_theorem(equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_11,equivalent(X_8,X_9)))),bind(Y,$fot(equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(X_8,X_9)))
| is_a_theorem(equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(X_8,X_9)),equivalent(equivalent(equivalent(X_10,X_8),equivalent(X_9,X_10)),X_11))) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)),equivalent(X_21,X_22)))
| is_a_theorem(equivalent(equivalent(equivalent(X_10,X_21),equivalent(X_22,X_10)),equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)))) ),
inference(subst,[],[refute_0_17:[bind(X_11,$fot(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)))),bind(X_8,$fot(X_21)),bind(X_9,$fot(X_22))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(X_17,equivalent(Z,X)),equivalent(equivalent(Y,Z),X_17)),equivalent(X,Y))) ),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(X_17)),bind(X_11,$fot(equivalent(X,Y))),bind(X_8,$fot(equivalent(Z,X))),bind(X_9,$fot(equivalent(Y,Z)))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_17,equivalent(Z,X)),equivalent(equivalent(Y,Z),X_17)),equivalent(X,Y))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))) )],[yqj,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)),equivalent(X_21,X_22))),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_21)),bind(Y,$fot(X_22)),bind(Z,$fot(X_23)),bind(X_17,$fot(X_24))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_10,X_21),equivalent(X_22,X_10)),equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)),equivalent(X_21,X_22))) )],[refute_0_21,refute_0_18]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21),equivalent(equivalent(X_23,X_21),equivalent(equivalent(X_23,X_21),X_23))),equivalent(equivalent(X_21,equivalent(X_23,X_21)),equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21)))),
inference(subst,[],[refute_0_22:[bind(X_10,$fot(equivalent(equivalent(X_23,X_21),X_23))),bind(X_22,$fot(equivalent(X_23,X_21))),bind(X_24,$fot(X_21))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)),equivalent(X_21,X_22)))
| is_a_theorem(equivalent(X_21,X_22)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)))),bind(Y,$fot(equivalent(X_21,X_22)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)))
| is_a_theorem(equivalent(X_21,X_22)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_24,equivalent(X_23,X_21)),equivalent(equivalent(X_22,X_23),X_24)),equivalent(X_21,X_22))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21),equivalent(equivalent(X_23,X_21),equivalent(equivalent(X_23,X_21),X_23))),equivalent(equivalent(X_21,equivalent(X_23,X_21)),equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21))))
| is_a_theorem(equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21)) ),
inference(subst,[],[refute_0_25:[bind(X_21,$fot(equivalent(equivalent(X_23,X_21),X_23))),bind(X_22,$fot(X_21)),bind(X_23,$fot(equivalent(X_23,X_21))),bind(X_24,$fot(equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21)))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21),equivalent(equivalent(X_23,X_21),equivalent(equivalent(X_23,X_21),X_23))),equivalent(equivalent(X_21,equivalent(X_23,X_21)),equivalent(equivalent(equivalent(X_23,X_21),X_23),X_21)))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_127,X_126),X_127),X_126)),
inference(subst,[],[refute_0_27:[bind(X_21,$fot(X_126)),bind(X_23,$fot(X_127))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(equivalent(equivalent(X_127,X_126),X_127))
| is_a_theorem(X_126) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_127,X_126),X_127),X_126)) )],[refute_0_28,refute_0_15]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_78),equivalent(X_78,X_78)),equivalent(equivalent(Z,X_78),equivalent(X_78,Z))),equivalent(equivalent(X_78,X_78),equivalent(X_78,X_78))))
| is_a_theorem(equivalent(equivalent(Z,X_78),equivalent(X_78,Z))) ),
inference(subst,[],[refute_0_29:[bind(X_126,$fot(equivalent(equivalent(Z,X_78),equivalent(X_78,Z)))),bind(X_127,$fot(equivalent(equivalent(X_78,X_78),equivalent(X_78,X_78))))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(equivalent(equivalent(Z,X_78),equivalent(X_78,Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_78),equivalent(X_78,X_78)),equivalent(equivalent(Z,X_78),equivalent(X_78,Z))),equivalent(equivalent(X_78,X_78),equivalent(X_78,X_78)))) )],[refute_0_14,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(equivalent(equivalent(X_165,X_166),equivalent(X_166,X_165))),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_165)),bind(X_78,$fot(X_166))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(equivalent(X_165,X_166))
| is_a_theorem(equivalent(X_166,X_165)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_165,X_166),equivalent(X_166,X_165))) )],[refute_0_32,refute_0_0]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_11892,X_11894),equivalent(X_11894,X_11893)),equivalent(X_11892,X_11893)))
| is_a_theorem(equivalent(equivalent(X_11892,X_11893),equivalent(equivalent(X_11892,X_11894),equivalent(X_11894,X_11893)))) ),
inference(subst,[],[refute_0_33:[bind(X_165,$fot(equivalent(equivalent(X_11892,X_11894),equivalent(X_11894,X_11893)))),bind(X_166,$fot(equivalent(X_11892,X_11893)))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(equivalent(X_157,equivalent(equivalent(X_159,X_158),X_159)))
| ~ is_a_theorem(equivalent(equivalent(X_157,equivalent(equivalent(X_159,X_158),X_159)),equivalent(X_158,X_157)))
| is_a_theorem(equivalent(X_158,X_157)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_157,equivalent(equivalent(X_159,X_158),X_159)))),bind(Y,$fot(equivalent(X_158,X_157)))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_127,X_126),X_127),X_126))
| is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_127,X_126),X_127)),equivalent(X_126,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(equivalent(X_127,X_126),X_127))),bind(Y,$fot(X_126))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_127,X_126),X_127)),equivalent(X_126,Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_127,X_126),X_127),X_126)) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(equivalent(equivalent(X_157,equivalent(equivalent(X_159,X_158),X_159)),equivalent(X_158,X_157))),
inference(subst,[],[refute_0_37:[bind(Z,$fot(X_157)),bind(X_126,$fot(X_158)),bind(X_127,$fot(X_159))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(equivalent(X_157,equivalent(equivalent(X_159,X_158),X_159)))
| is_a_theorem(equivalent(X_158,X_157)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_157,equivalent(equivalent(X_159,X_158),X_159)),equivalent(X_158,X_157))) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(equivalent(equivalent(X_3825,equivalent(equivalent(X_3825,X_3824),equivalent(X_3824,X_158))),equivalent(equivalent(X_3824,X_158),X_3824)))
| is_a_theorem(equivalent(X_158,equivalent(X_3825,equivalent(equivalent(X_3825,X_3824),equivalent(X_3824,X_158))))) ),
inference(subst,[],[refute_0_39:[bind(X_157,$fot(equivalent(X_3825,equivalent(equivalent(X_3825,X_3824),equivalent(X_3824,X_158))))),bind(X_159,$fot(X_3824))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(X_173)
| ~ is_a_theorem(equivalent(X_173,equivalent(equivalent(X_174,X_174),X_173)))
| is_a_theorem(equivalent(equivalent(X_174,X_174),X_173)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_173)),bind(Y,$fot(equivalent(equivalent(X_174,X_174),X_173)))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(X_124)
| ~ is_a_theorem(equivalent(X_124,equivalent(X_125,equivalent(X_124,X_125))))
| is_a_theorem(equivalent(X_125,equivalent(X_124,X_125))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_124)),bind(Y,$fot(equivalent(X_125,equivalent(X_124,X_125))))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_83,X_84),equivalent(X_85,X_83)),equivalent(X_85,X_82)),equivalent(X_82,X_84)))
| is_a_theorem(equivalent(equivalent(equivalent(X_10,X_82),equivalent(X_84,X_10)),equivalent(equivalent(equivalent(X_83,X_84),equivalent(X_85,X_83)),equivalent(X_85,X_82)))) ),
inference(subst,[],[refute_0_17:[bind(X_11,$fot(equivalent(equivalent(equivalent(X_83,X_84),equivalent(X_85,X_83)),equivalent(X_85,X_82)))),bind(X_8,$fot(X_82)),bind(X_9,$fot(X_84))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(equivalent(equivalent(X,X_80),equivalent(equivalent(X_81,X),equivalent(X_80,X_81)))),
inference(subst,[],[yqj:[bind(Y,$fot(X_80)),bind(Z,$fot(X_81))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(equivalent(equivalent(X,X_80),equivalent(equivalent(X_81,X),equivalent(X_80,X_81))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_80),equivalent(X_81,X_78)),equivalent(X_81,X)),equivalent(X,X_80))) ),
inference(subst,[],[refute_0_11:[bind(X_12,$fot(equivalent(X,X_80))),bind(X_13,$fot(X_78)),bind(X_14,$fot(equivalent(X_81,X))),bind(X_15,$fot(X_80)),bind(X_16,$fot(X_81))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_80),equivalent(X_81,X_78)),equivalent(X_81,X)),equivalent(X,X_80))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,X_80),equivalent(equivalent(X_81,X),equivalent(X_80,X_81)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_83,X_84),equivalent(X_85,X_83)),equivalent(X_85,X_82)),equivalent(X_82,X_84))),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_82)),bind(X_78,$fot(X_83)),bind(X_80,$fot(X_84)),bind(X_81,$fot(X_85))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_10,X_82),equivalent(X_84,X_10)),equivalent(equivalent(equivalent(X_83,X_84),equivalent(X_85,X_83)),equivalent(X_85,X_82)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_83,X_84),equivalent(X_85,X_83)),equivalent(X_85,X_82)),equivalent(X_82,X_84))) )],[refute_0_47,refute_0_43]) ).
cnf(refute_0_49,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_120,X_82),equivalent(equivalent(X_120,X_83),X_120)),equivalent(equivalent(equivalent(X_83,equivalent(X_120,X_83)),equivalent(X_120,X_83)),equivalent(X_120,X_82)))),
inference(subst,[],[refute_0_48:[bind(X_10,$fot(X_120)),bind(X_84,$fot(equivalent(X_120,X_83))),bind(X_85,$fot(X_120))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_120,X_82),equivalent(equivalent(X_120,X_83),X_120)),equivalent(equivalent(equivalent(X_83,equivalent(X_120,X_83)),equivalent(X_120,X_83)),equivalent(X_120,X_82))))
| is_a_theorem(equivalent(X_120,equivalent(X_83,equivalent(X_120,X_83)))) ),
inference(subst,[],[refute_0_25:[bind(X_21,$fot(X_120)),bind(X_22,$fot(equivalent(X_83,equivalent(X_120,X_83)))),bind(X_23,$fot(equivalent(X_120,X_83))),bind(X_24,$fot(equivalent(X_120,X_82)))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(equivalent(X_120,equivalent(X_83,equivalent(X_120,X_83)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_120,X_82),equivalent(equivalent(X_120,X_83),X_120)),equivalent(equivalent(equivalent(X_83,equivalent(X_120,X_83)),equivalent(X_120,X_83)),equivalent(X_120,X_82)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
is_a_theorem(equivalent(X_124,equivalent(X_125,equivalent(X_124,X_125)))),
inference(subst,[],[refute_0_51:[bind(X_120,$fot(X_124)),bind(X_83,$fot(X_125))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(X_124)
| is_a_theorem(equivalent(X_125,equivalent(X_124,X_125))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_124,equivalent(X_125,equivalent(X_124,X_125)))) )],[refute_0_52,refute_0_42]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(equivalent(X_167,X_167))
| is_a_theorem(equivalent(X_125,equivalent(equivalent(X_167,X_167),X_125))) ),
inference(subst,[],[refute_0_53:[bind(X_124,$fot(equivalent(X_167,X_167)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(equivalent(equivalent(X_165,equivalent(X_21,X_21)),equivalent(equivalent(X_21,X_21),X_165)))
| is_a_theorem(equivalent(X_21,X_21)) ),
inference(subst,[],[refute_0_25:[bind(X_22,$fot(X_21)),bind(X_23,$fot(X_21)),bind(X_24,$fot(X_165))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(equivalent(equivalent(X_165,equivalent(X_21,X_21)),equivalent(equivalent(X_21,X_21),X_165))),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_165)),bind(X_78,$fot(equivalent(X_21,X_21)))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(equivalent(X_21,X_21)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_165,equivalent(X_21,X_21)),equivalent(equivalent(X_21,X_21),X_165))) )],[refute_0_56,refute_0_55]) ).
cnf(refute_0_58,plain,
is_a_theorem(equivalent(X_167,X_167)),
inference(subst,[],[refute_0_57:[bind(X_21,$fot(X_167))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(equivalent(X_125,equivalent(equivalent(X_167,X_167),X_125))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_167,X_167)) )],[refute_0_58,refute_0_54]) ).
cnf(refute_0_60,plain,
is_a_theorem(equivalent(X_173,equivalent(equivalent(X_174,X_174),X_173))),
inference(subst,[],[refute_0_59:[bind(X_125,$fot(X_173)),bind(X_167,$fot(X_174))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(X_173)
| is_a_theorem(equivalent(equivalent(X_174,X_174),X_173)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_173,equivalent(equivalent(X_174,X_174),X_173))) )],[refute_0_60,refute_0_41]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(equivalent(equivalent(X_399,X_397),equivalent(X_397,equivalent(X_398,equivalent(X_399,X_398)))))
| is_a_theorem(equivalent(equivalent(X_174,X_174),equivalent(equivalent(X_399,X_397),equivalent(X_397,equivalent(X_398,equivalent(X_399,X_398)))))) ),
inference(subst,[],[refute_0_61:[bind(X_173,$fot(equivalent(equivalent(X_399,X_397),equivalent(X_397,equivalent(X_398,equivalent(X_399,X_398))))))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(equivalent(equivalent(X_394,equivalent(X_395,equivalent(X_396,X_395))),equivalent(X_396,X_394)))
| is_a_theorem(equivalent(equivalent(X_396,X_394),equivalent(X_394,equivalent(X_395,equivalent(X_396,X_395))))) ),
inference(subst,[],[refute_0_33:[bind(X_165,$fot(equivalent(X_394,equivalent(X_395,equivalent(X_396,X_395))))),bind(X_166,$fot(equivalent(X_396,X_394)))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(equivalent(equivalent(X_195,equivalent(X_196,X_195)),X_196))
| is_a_theorem(equivalent(equivalent(Z,equivalent(X_195,equivalent(X_196,X_195))),equivalent(X_196,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X_195,equivalent(X_196,X_195)))),bind(Y,$fot(X_196))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_121),equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78)),equivalent(equivalent(Z,equivalent(X_78,X_121)),equivalent(equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78),Z))),equivalent(equivalent(X_121,equivalent(Z,equivalent(X_78,X_121))),equivalent(equivalent(X_78,X_121),equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78))))),
inference(subst,[],[refute_0_13:[bind(X,$fot(equivalent(X_78,X_121))),bind(Y,$fot(equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78))),bind(X_80,$fot(X_121)),bind(X_81,$fot(equivalent(Z,equivalent(X_78,X_121))))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_121),equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78)),equivalent(equivalent(Z,equivalent(X_78,X_121)),equivalent(equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78),Z))),equivalent(equivalent(X_121,equivalent(Z,equivalent(X_78,X_121))),equivalent(equivalent(X_78,X_121),equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78),Z),X_121)) ),
inference(subst,[],[refute_0_25:[bind(X_21,$fot(equivalent(equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78),Z))),bind(X_22,$fot(X_121)),bind(X_23,$fot(equivalent(Z,equivalent(X_78,X_121)))),bind(X_24,$fot(equivalent(equivalent(X_78,X_121),equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78))))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78),Z),X_121)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_78,X_121),equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78)),equivalent(equivalent(Z,equivalent(X_78,X_121)),equivalent(equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78),Z))),equivalent(equivalent(X_121,equivalent(Z,equivalent(X_78,X_121))),equivalent(equivalent(X_78,X_121),equivalent(equivalent(Z,equivalent(X_78,X_121)),X_78))))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_194,equivalent(X_78,X_194)),X_78),X_194),X_194)),
inference(subst,[],[refute_0_67:[bind(Z,$fot(X_194)),bind(X_121,$fot(X_194))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(equivalent(equivalent(X_168,X_169),X_169))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_168,X_169),X_169),X_168))
| is_a_theorem(X_168) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_168,X_169),X_169))),bind(Y,$fot(X_168))]]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(equivalent(X_124,equivalent(X_125,equivalent(X_124,X_125))))
| is_a_theorem(equivalent(equivalent(equivalent(X_10,X_125),equivalent(equivalent(X_124,X_125),X_10)),X_124)) ),
inference(subst,[],[refute_0_17:[bind(X_11,$fot(X_124)),bind(X_8,$fot(X_125)),bind(X_9,$fot(equivalent(X_124,X_125)))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_10,X_125),equivalent(equivalent(X_124,X_125),X_10)),X_124)),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_124,equivalent(X_125,equivalent(X_124,X_125)))) )],[refute_0_52,refute_0_70]) ).
cnf(refute_0_72,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_10,X_125),equivalent(equivalent(equivalent(X_10,X_125),X_125),X_10)),equivalent(X_10,X_125))),
inference(subst,[],[refute_0_71:[bind(X_124,$fot(equivalent(X_10,X_125)))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_10,X_125),equivalent(equivalent(equivalent(X_10,X_125),X_125),X_10)),equivalent(X_10,X_125)))
| is_a_theorem(equivalent(equivalent(equivalent(X_10,X_125),X_125),X_10)) ),
inference(subst,[],[refute_0_29:[bind(X_126,$fot(equivalent(equivalent(equivalent(X_10,X_125),X_125),X_10))),bind(X_127,$fot(equivalent(X_10,X_125)))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_10,X_125),X_125),X_10)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_10,X_125),equivalent(equivalent(equivalent(X_10,X_125),X_125),X_10)),equivalent(X_10,X_125))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_168,X_169),X_169),X_168)),
inference(subst,[],[refute_0_74:[bind(X_10,$fot(X_168)),bind(X_125,$fot(X_169))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(equivalent(equivalent(X_168,X_169),X_169))
| is_a_theorem(X_168) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_168,X_169),X_169),X_168)) )],[refute_0_75,refute_0_69]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_194,equivalent(X_78,X_194)),X_78),X_194),X_194))
| is_a_theorem(equivalent(equivalent(X_194,equivalent(X_78,X_194)),X_78)) ),
inference(subst,[],[refute_0_76:[bind(X_168,$fot(equivalent(equivalent(X_194,equivalent(X_78,X_194)),X_78))),bind(X_169,$fot(X_194))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(equivalent(equivalent(X_194,equivalent(X_78,X_194)),X_78)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_194,equivalent(X_78,X_194)),X_78),X_194),X_194)) )],[refute_0_68,refute_0_77]) ).
cnf(refute_0_79,plain,
is_a_theorem(equivalent(equivalent(X_195,equivalent(X_196,X_195)),X_196)),
inference(subst,[],[refute_0_78:[bind(X_194,$fot(X_195)),bind(X_78,$fot(X_196))]]) ).
cnf(refute_0_80,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(X_195,equivalent(X_196,X_195))),equivalent(X_196,Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_195,equivalent(X_196,X_195)),X_196)) )],[refute_0_79,refute_0_64]) ).
cnf(refute_0_81,plain,
is_a_theorem(equivalent(equivalent(X_394,equivalent(X_395,equivalent(X_396,X_395))),equivalent(X_396,X_394))),
inference(subst,[],[refute_0_80:[bind(Z,$fot(X_394)),bind(X_195,$fot(X_395)),bind(X_196,$fot(X_396))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(equivalent(equivalent(X_396,X_394),equivalent(X_394,equivalent(X_395,equivalent(X_396,X_395))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_394,equivalent(X_395,equivalent(X_396,X_395))),equivalent(X_396,X_394))) )],[refute_0_81,refute_0_63]) ).
cnf(refute_0_83,plain,
is_a_theorem(equivalent(equivalent(X_399,X_397),equivalent(X_397,equivalent(X_398,equivalent(X_399,X_398))))),
inference(subst,[],[refute_0_82:[bind(X_394,$fot(X_397)),bind(X_395,$fot(X_398)),bind(X_396,$fot(X_399))]]) ).
cnf(refute_0_84,plain,
is_a_theorem(equivalent(equivalent(X_174,X_174),equivalent(equivalent(X_399,X_397),equivalent(X_397,equivalent(X_398,equivalent(X_399,X_398)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_399,X_397),equivalent(X_397,equivalent(X_398,equivalent(X_399,X_398))))) )],[refute_0_83,refute_0_62]) ).
cnf(refute_0_85,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629))),equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629)))),equivalent(equivalent(X_399,equivalent(equivalent(X_399,X_3629),X_3628)),equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629)))))),
inference(subst,[],[refute_0_84:[bind(X_174,$fot(equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629))))),bind(X_397,$fot(equivalent(equivalent(X_399,X_3629),X_3628))),bind(X_398,$fot(X_3629))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(equivalent(equivalent(X_28,equivalent(equivalent(X_27,X_25),equivalent(X_26,X_27))),equivalent(X_29,X_28)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_28,equivalent(equivalent(X_27,X_25),equivalent(X_26,X_27))),equivalent(X_29,X_28)),equivalent(X_29,equivalent(X_25,X_26))))
| is_a_theorem(equivalent(X_29,equivalent(X_25,X_26))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_28,equivalent(equivalent(X_27,X_25),equivalent(X_26,X_27))),equivalent(X_29,X_28)))),bind(Y,$fot(equivalent(X_29,equivalent(X_25,X_26))))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(equivalent(equivalent(X_20,equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),X_20))),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(X_20))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(equivalent(equivalent(X_20,equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),X_20)))
| is_a_theorem(equivalent(equivalent(equivalent(X_17,equivalent(equivalent(Z,X),equivalent(Y,Z))),equivalent(X_20,X_17)),equivalent(X_20,equivalent(X,Y)))) ),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(X_17)),bind(X_11,$fot(equivalent(X_20,equivalent(X,Y)))),bind(X_8,$fot(equivalent(equivalent(Z,X),equivalent(Y,Z)))),bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_17,equivalent(equivalent(Z,X),equivalent(Y,Z))),equivalent(X_20,X_17)),equivalent(X_20,equivalent(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_20,equivalent(X,Y)),equivalent(equivalent(equivalent(Z,X),equivalent(Y,Z)),X_20))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_28,equivalent(equivalent(X_27,X_25),equivalent(X_26,X_27))),equivalent(X_29,X_28)),equivalent(X_29,equivalent(X_25,X_26)))),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_25)),bind(Y,$fot(X_26)),bind(Z,$fot(X_27)),bind(X_17,$fot(X_28)),bind(X_20,$fot(X_29))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(equivalent(equivalent(X_28,equivalent(equivalent(X_27,X_25),equivalent(X_26,X_27))),equivalent(X_29,X_28)))
| is_a_theorem(equivalent(X_29,equivalent(X_25,X_26))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_28,equivalent(equivalent(X_27,X_25),equivalent(X_26,X_27))),equivalent(X_29,X_28)),equivalent(X_29,equivalent(X_25,X_26)))) )],[refute_0_90,refute_0_86]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629))),equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629)))),equivalent(equivalent(X_399,equivalent(equivalent(X_399,X_3629),X_3628)),equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629))))))
| is_a_theorem(equivalent(equivalent(X_399,equivalent(equivalent(X_399,X_3629),X_3628)),equivalent(X_3628,X_3629))) ),
inference(subst,[],[refute_0_91:[bind(X_25,$fot(X_3628)),bind(X_26,$fot(X_3629)),bind(X_27,$fot(equivalent(X_399,X_3629))),bind(X_28,$fot(equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629))))),bind(X_29,$fot(equivalent(X_399,equivalent(equivalent(X_399,X_3629),X_3628))))]]) ).
cnf(refute_0_93,plain,
is_a_theorem(equivalent(equivalent(X_399,equivalent(equivalent(X_399,X_3629),X_3628)),equivalent(X_3628,X_3629))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629))),equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629)))),equivalent(equivalent(X_399,equivalent(equivalent(X_399,X_3629),X_3628)),equivalent(equivalent(equivalent(X_399,X_3629),X_3628),equivalent(X_3629,equivalent(X_399,X_3629)))))) )],[refute_0_85,refute_0_92]) ).
cnf(refute_0_94,plain,
is_a_theorem(equivalent(equivalent(X_3825,equivalent(equivalent(X_3825,X_3824),equivalent(X_3824,X_158))),equivalent(equivalent(X_3824,X_158),X_3824))),
inference(subst,[],[refute_0_93:[bind(X_3628,$fot(equivalent(X_3824,X_158))),bind(X_3629,$fot(X_3824)),bind(X_399,$fot(X_3825))]]) ).
cnf(refute_0_95,plain,
is_a_theorem(equivalent(X_158,equivalent(X_3825,equivalent(equivalent(X_3825,X_3824),equivalent(X_3824,X_158))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_3825,equivalent(equivalent(X_3825,X_3824),equivalent(X_3824,X_158))),equivalent(equivalent(X_3824,X_158),X_3824))) )],[refute_0_94,refute_0_40]) ).
cnf(refute_0_96,plain,
is_a_theorem(equivalent(X_11858,equivalent(X_11857,equivalent(equivalent(X_11857,X_3824),equivalent(X_3824,X_11858))))),
inference(subst,[],[refute_0_95:[bind(X_158,$fot(X_11858)),bind(X_3825,$fot(X_11857))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(equivalent(X_3831,equivalent(X_3830,X_3829)))
| ~ is_a_theorem(equivalent(equivalent(X_3831,equivalent(X_3830,X_3829)),equivalent(X_3829,equivalent(X_3830,X_3831))))
| is_a_theorem(equivalent(X_3829,equivalent(X_3830,X_3831))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_3831,equivalent(X_3830,X_3829)))),bind(Y,$fot(equivalent(X_3829,equivalent(X_3830,X_3831))))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(equivalent(equivalent(X_653,X_652),equivalent(X_652,equivalent(equivalent(X_654,X_653),X_654))))
| is_a_theorem(equivalent(equivalent(X_174,X_174),equivalent(equivalent(X_653,X_652),equivalent(X_652,equivalent(equivalent(X_654,X_653),X_654))))) ),
inference(subst,[],[refute_0_61:[bind(X_173,$fot(equivalent(equivalent(X_653,X_652),equivalent(X_652,equivalent(equivalent(X_654,X_653),X_654)))))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_127,X_126),X_127)),equivalent(X_126,Z)))
| is_a_theorem(equivalent(equivalent(X_126,Z),equivalent(Z,equivalent(equivalent(X_127,X_126),X_127)))) ),
inference(subst,[],[refute_0_33:[bind(X_165,$fot(equivalent(Z,equivalent(equivalent(X_127,X_126),X_127)))),bind(X_166,$fot(equivalent(X_126,Z)))]]) ).
cnf(refute_0_100,plain,
is_a_theorem(equivalent(equivalent(X_126,Z),equivalent(Z,equivalent(equivalent(X_127,X_126),X_127)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_127,X_126),X_127)),equivalent(X_126,Z))) )],[refute_0_37,refute_0_99]) ).
cnf(refute_0_101,plain,
is_a_theorem(equivalent(equivalent(X_653,X_652),equivalent(X_652,equivalent(equivalent(X_654,X_653),X_654)))),
inference(subst,[],[refute_0_100:[bind(Z,$fot(X_652)),bind(X_126,$fot(X_653)),bind(X_127,$fot(X_654))]]) ).
cnf(refute_0_102,plain,
is_a_theorem(equivalent(equivalent(X_174,X_174),equivalent(equivalent(X_653,X_652),equivalent(X_652,equivalent(equivalent(X_654,X_653),X_654))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_653,X_652),equivalent(X_652,equivalent(equivalent(X_654,X_653),X_654)))) )],[refute_0_101,refute_0_98]) ).
cnf(refute_0_103,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630)),equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630))),equivalent(equivalent(X_653,equivalent(X_3630,X_3628)),equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630))))),
inference(subst,[],[refute_0_102:[bind(X_174,$fot(equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630)))),bind(X_652,$fot(equivalent(X_3630,X_3628))),bind(X_654,$fot(X_3630))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630)),equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630))),equivalent(equivalent(X_653,equivalent(X_3630,X_3628)),equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630)))))
| is_a_theorem(equivalent(equivalent(X_653,equivalent(X_3630,X_3628)),equivalent(X_3628,equivalent(X_3630,X_653)))) ),
inference(subst,[],[refute_0_91:[bind(X_25,$fot(X_3628)),bind(X_26,$fot(equivalent(X_3630,X_653))),bind(X_27,$fot(X_3630)),bind(X_28,$fot(equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630)))),bind(X_29,$fot(equivalent(X_653,equivalent(X_3630,X_3628))))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(equivalent(equivalent(X_653,equivalent(X_3630,X_3628)),equivalent(X_3628,equivalent(X_3630,X_653)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630)),equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630))),equivalent(equivalent(X_653,equivalent(X_3630,X_3628)),equivalent(equivalent(X_3630,X_3628),equivalent(equivalent(X_3630,X_653),X_3630))))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
is_a_theorem(equivalent(equivalent(X_3831,equivalent(X_3830,X_3829)),equivalent(X_3829,equivalent(X_3830,X_3831)))),
inference(subst,[],[refute_0_105:[bind(X_3628,$fot(X_3829)),bind(X_3630,$fot(X_3830)),bind(X_653,$fot(X_3831))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(equivalent(X_3831,equivalent(X_3830,X_3829)))
| is_a_theorem(equivalent(X_3829,equivalent(X_3830,X_3831))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_3831,equivalent(X_3830,X_3829)),equivalent(X_3829,equivalent(X_3830,X_3831)))) )],[refute_0_106,refute_0_97]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(equivalent(X_11858,equivalent(X_11857,equivalent(equivalent(X_11857,X_3824),equivalent(X_3824,X_11858)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_11857,X_3824),equivalent(X_3824,X_11858)),equivalent(X_11857,X_11858))) ),
inference(subst,[],[refute_0_107:[bind(X_3829,$fot(equivalent(equivalent(X_11857,X_3824),equivalent(X_3824,X_11858)))),bind(X_3830,$fot(X_11857)),bind(X_3831,$fot(X_11858))]]) ).
cnf(refute_0_109,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_11857,X_3824),equivalent(X_3824,X_11858)),equivalent(X_11857,X_11858))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_11858,equivalent(X_11857,equivalent(equivalent(X_11857,X_3824),equivalent(X_3824,X_11858))))) )],[refute_0_96,refute_0_108]) ).
cnf(refute_0_110,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_11892,X_11894),equivalent(X_11894,X_11893)),equivalent(X_11892,X_11893))),
inference(subst,[],[refute_0_109:[bind(X_11857,$fot(X_11892)),bind(X_11858,$fot(X_11893)),bind(X_3824,$fot(X_11894))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(equivalent(equivalent(X_11892,X_11893),equivalent(equivalent(X_11892,X_11894),equivalent(X_11894,X_11893)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_11892,X_11894),equivalent(X_11894,X_11893)),equivalent(X_11892,X_11893))) )],[refute_0_110,refute_0_34]) ).
cnf(refute_0_112,plain,
is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))),
inference(subst,[],[refute_0_111:[bind(X_11892,$fot(a)),bind(X_11893,$fot(b)),bind(X_11894,$fot(c))]]) ).
cnf(refute_0_113,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))) )],[refute_0_112,prove_yqf]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n008.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 22:12:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.30/13.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.30/13.48
% 13.30/13.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.30/13.50
%------------------------------------------------------------------------------