TSTP Solution File: LCL102-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL102-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 0.93s 1.13s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 55 ( 31 unt; 0 nHn; 21 RR)
% Number of literals : 86 ( 0 equ; 32 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 : 210 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(lg_2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) ).
cnf(q_1,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))) ).
cnf(q_2,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Z,Y)))) ).
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_290,X_291),X_292),X_293))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_290,X_291),X_292),X_293),equivalent(X_292,equivalent(equivalent(X_291,X_290),X_293))))
| is_a_theorem(equivalent(X_292,equivalent(equivalent(X_291,X_290),X_293))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_290,X_291),X_292),X_293))),bind(Y,$fot(equivalent(X_292,equivalent(equivalent(X_291,X_290),X_293))))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(equivalent(X_27,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27)))),
inference(subst,[],[q_1:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(Z,X),equivalent(Z,Y))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,X),equivalent(Z,Y))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(equivalent(Z,X),equivalent(Z,Y))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Z,Y)))) )],[q_2,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(X_27,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27))))
| is_a_theorem(equivalent(equivalent(X_29,X_27),equivalent(X_29,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27))))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_27)),bind(Y,$fot(equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27)))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(X_29,X_27),equivalent(X_29,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_27,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27)))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),X_238),X_27),equivalent(equivalent(equivalent(Y,Z),X_238),equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27))))),
inference(subst,[],[refute_0_5:[bind(X_29,$fot(equivalent(equivalent(Y,Z),X_238)))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))))
| ~ is_a_theorem(equivalent(equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))),equivalent(X_19,equivalent(X_21,X_22))))
| is_a_theorem(equivalent(X_19,equivalent(X_21,X_22))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))))),bind(Y,$fot(equivalent(X_19,equivalent(X_21,X_22))))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17)),equivalent(X_16,X_17)),equivalent(equivalent(Z,equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17))),equivalent(Z,equivalent(X_16,X_17))))),
inference(subst,[],[q_2:[bind(X,$fot(equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17)))),bind(Y,$fot(equivalent(X_16,X_17)))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_11),X_11)),
inference(subst,[],[lg_2:[bind(U,$fot(X_11))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_11))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_11),X_11))
| is_a_theorem(X_11) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_11))),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_11))
| is_a_theorem(X_11) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_11),X_11)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17)),equivalent(X_16,X_17)),equivalent(equivalent(Z,equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17))),equivalent(Z,equivalent(X_16,X_17)))))
| is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17))),equivalent(Z,equivalent(X_16,X_17)))) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_15)),bind(Y,$fot(X_16)),bind(Z,$fot(X_17)),bind(X_11,$fot(equivalent(equivalent(Z,equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17))),equivalent(Z,equivalent(X_16,X_17)))))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17))),equivalent(Z,equivalent(X_16,X_17)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17)),equivalent(X_16,X_17)),equivalent(equivalent(Z,equivalent(equivalent(X_15,X_16),equivalent(X_15,X_17))),equivalent(Z,equivalent(X_16,X_17))))) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))),equivalent(X_19,equivalent(X_21,X_22)))),
inference(subst,[],[refute_0_13:[bind(Z,$fot(X_19)),bind(X_15,$fot(X_20)),bind(X_16,$fot(X_21)),bind(X_17,$fot(X_22))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))))
| is_a_theorem(equivalent(X_19,equivalent(X_21,X_22))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))),equivalent(X_19,equivalent(X_21,X_22)))) )],[refute_0_14,refute_0_7]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),X_238),X_27),equivalent(equivalent(equivalent(Y,Z),X_238),equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),X_238),X_27),equivalent(X_238,equivalent(equivalent(Z,Y),X_27)))) ),
inference(subst,[],[refute_0_15:[bind(X_19,$fot(equivalent(equivalent(equivalent(Y,Z),X_238),X_27))),bind(X_20,$fot(equivalent(Y,Z))),bind(X_21,$fot(X_238)),bind(X_22,$fot(equivalent(equivalent(Z,Y),X_27)))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),X_238),X_27),equivalent(X_238,equivalent(equivalent(Z,Y),X_27)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),X_238),X_27),equivalent(equivalent(equivalent(Y,Z),X_238),equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_27))))) )],[refute_0_6,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_290,X_291),X_292),X_293),equivalent(X_292,equivalent(equivalent(X_291,X_290),X_293)))),
inference(subst,[],[refute_0_17:[bind(Y,$fot(X_290)),bind(Z,$fot(X_291)),bind(X_238,$fot(X_292)),bind(X_27,$fot(X_293))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_290,X_291),X_292),X_293))
| is_a_theorem(equivalent(X_292,equivalent(equivalent(X_291,X_290),X_293))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_290,X_291),X_292),X_293),equivalent(X_292,equivalent(equivalent(X_291,X_290),X_293)))) )],[refute_0_18,refute_0_0]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_1786,X_1787),equivalent(equivalent(X_1785,X_1786),X_1788)),equivalent(equivalent(X_1785,X_1787),X_1788)))
| is_a_theorem(equivalent(equivalent(equivalent(X_1785,X_1786),X_1788),equivalent(equivalent(X_1787,X_1786),equivalent(equivalent(X_1785,X_1787),X_1788)))) ),
inference(subst,[],[refute_0_19:[bind(X_290,$fot(X_1786)),bind(X_291,$fot(X_1787)),bind(X_292,$fot(equivalent(equivalent(X_1785,X_1786),X_1788))),bind(X_293,$fot(equivalent(equivalent(X_1785,X_1787),X_1788)))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_1782,X_1783),equivalent(equivalent(X_1781,X_1782),X_22)),equivalent(equivalent(equivalent(X_1781,X_1782),equivalent(X_1781,X_1783)),equivalent(equivalent(X_1781,X_1782),X_22))))
| is_a_theorem(equivalent(equivalent(equivalent(X_1782,X_1783),equivalent(equivalent(X_1781,X_1782),X_22)),equivalent(equivalent(X_1781,X_1783),X_22))) ),
inference(subst,[],[refute_0_15:[bind(X_19,$fot(equivalent(equivalent(X_1782,X_1783),equivalent(equivalent(X_1781,X_1782),X_22)))),bind(X_20,$fot(equivalent(X_1781,X_1782))),bind(X_21,$fot(equivalent(X_1781,X_1783)))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_363),X_363)),
inference(subst,[],[lg_2:[bind(U,$fot(X_363))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_363),X_363))
| is_a_theorem(equivalent(X_363,equivalent(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))),X_363))) ),
inference(subst,[],[refute_0_19:[bind(X_290,$fot(equivalent(equivalent(X,Y),equivalent(X,Z)))),bind(X_291,$fot(equivalent(Y,Z))),bind(X_292,$fot(X_363)),bind(X_293,$fot(X_363))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(equivalent(X_363,equivalent(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))),X_363))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),X_363),X_363)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
is_a_theorem(equivalent(X_941,equivalent(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))),X_941))),
inference(subst,[],[refute_0_24:[bind(X_363,$fot(X_941))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(equivalent(X_33,equivalent(X_30,X_31)))
| ~ is_a_theorem(equivalent(equivalent(X_33,equivalent(X_30,X_31)),equivalent(X_33,equivalent(equivalent(X_32,X_30),equivalent(X_32,X_31)))))
| is_a_theorem(equivalent(X_33,equivalent(equivalent(X_32,X_30),equivalent(X_32,X_31)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_33,equivalent(X_30,X_31)))),bind(Y,$fot(equivalent(X_33,equivalent(equivalent(X_32,X_30),equivalent(X_32,X_31)))))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(X_29,equivalent(X,Y)),equivalent(X_29,equivalent(equivalent(Z,X),equivalent(Z,Y))))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,X),equivalent(Z,Y)))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(X_29,equivalent(X,Y)),equivalent(X_29,equivalent(equivalent(Z,X),equivalent(Z,Y))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Z,Y)))) )],[q_2,refute_0_27]) ).
cnf(refute_0_29,plain,
is_a_theorem(equivalent(equivalent(X_33,equivalent(X_30,X_31)),equivalent(X_33,equivalent(equivalent(X_32,X_30),equivalent(X_32,X_31))))),
inference(subst,[],[refute_0_28:[bind(X,$fot(X_30)),bind(Y,$fot(X_31)),bind(Z,$fot(X_32)),bind(X_29,$fot(X_33))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(equivalent(X_33,equivalent(X_30,X_31)))
| is_a_theorem(equivalent(X_33,equivalent(equivalent(X_32,X_30),equivalent(X_32,X_31)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_33,equivalent(X_30,X_31)),equivalent(X_33,equivalent(equivalent(X_32,X_30),equivalent(X_32,X_31))))) )],[refute_0_29,refute_0_26]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(equivalent(X_941,equivalent(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))),X_941)))
| is_a_theorem(equivalent(X_941,equivalent(equivalent(X_942,equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z)))),equivalent(X_942,X_941)))) ),
inference(subst,[],[refute_0_30:[bind(X_30,$fot(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))))),bind(X_31,$fot(X_941)),bind(X_32,$fot(X_942)),bind(X_33,$fot(X_941))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(equivalent(X_941,equivalent(equivalent(X_942,equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z)))),equivalent(X_942,X_941)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_941,equivalent(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))),X_941))) )],[refute_0_25,refute_0_31]) ).
cnf(refute_0_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(Y,Z),X_1779),equivalent(equivalent(X_1776,equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z)))),equivalent(X_1776,equivalent(equivalent(Y,Z),X_1779))))),
inference(subst,[],[refute_0_32:[bind(X_941,$fot(equivalent(equivalent(Y,Z),X_1779))),bind(X_942,$fot(X_1776))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(equivalent(X_57,equivalent(equivalent(X_53,equivalent(X_54,X_55)),equivalent(X_53,equivalent(X_54,X_56)))))
| ~ is_a_theorem(equivalent(equivalent(X_57,equivalent(equivalent(X_53,equivalent(X_54,X_55)),equivalent(X_53,equivalent(X_54,X_56)))),equivalent(X_57,equivalent(X_55,X_56))))
| is_a_theorem(equivalent(X_57,equivalent(X_55,X_56))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_57,equivalent(equivalent(X_53,equivalent(X_54,X_55)),equivalent(X_53,equivalent(X_54,X_56)))))),bind(Y,$fot(equivalent(X_57,equivalent(X_55,X_56))))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))),equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22))))
| is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22))) ),
inference(subst,[],[refute_0_11:[bind(Y,$fot(equivalent(X_20,X_21))),bind(Z,$fot(equivalent(X_20,X_22))),bind(X_11,$fot(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22))))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))),equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22)))),
inference(subst,[],[refute_0_13:[bind(Z,$fot(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))))),bind(X_15,$fot(X_20)),bind(X_16,$fot(X_21)),bind(X_17,$fot(X_22))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(equivalent(X_20,X_21),equivalent(X_20,X_22))),equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22)))) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22)))
| is_a_theorem(equivalent(equivalent(X_29,equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22)))),equivalent(X_29,equivalent(X_21,X_22)))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))))),bind(Y,$fot(equivalent(X_21,X_22))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(equivalent(equivalent(X_29,equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22)))),equivalent(X_29,equivalent(X_21,X_22)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(X_20,X_21)),equivalent(X,equivalent(X_20,X_22))),equivalent(X_21,X_22))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(equivalent(equivalent(X_57,equivalent(equivalent(X_53,equivalent(X_54,X_55)),equivalent(X_53,equivalent(X_54,X_56)))),equivalent(X_57,equivalent(X_55,X_56)))),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_53)),bind(X_20,$fot(X_54)),bind(X_21,$fot(X_55)),bind(X_22,$fot(X_56)),bind(X_29,$fot(X_57))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(equivalent(X_57,equivalent(equivalent(X_53,equivalent(X_54,X_55)),equivalent(X_53,equivalent(X_54,X_56)))))
| is_a_theorem(equivalent(X_57,equivalent(X_55,X_56))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_57,equivalent(equivalent(X_53,equivalent(X_54,X_55)),equivalent(X_53,equivalent(X_54,X_56)))),equivalent(X_57,equivalent(X_55,X_56)))) )],[refute_0_40,refute_0_34]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(Y,Z),X_1779),equivalent(equivalent(X_1776,equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z)))),equivalent(X_1776,equivalent(equivalent(Y,Z),X_1779)))))
| is_a_theorem(equivalent(equivalent(equivalent(Y,Z),X_1779),equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),X_1779))) ),
inference(subst,[],[refute_0_41:[bind(X_53,$fot(X_1776)),bind(X_54,$fot(equivalent(Y,Z))),bind(X_55,$fot(equivalent(equivalent(X,Y),equivalent(X,Z)))),bind(X_56,$fot(X_1779)),bind(X_57,$fot(equivalent(equivalent(Y,Z),X_1779)))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(equivalent(equivalent(equivalent(Y,Z),X_1779),equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),X_1779))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(Y,Z),X_1779),equivalent(equivalent(X_1776,equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z)))),equivalent(X_1776,equivalent(equivalent(Y,Z),X_1779))))) )],[refute_0_33,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_1782,X_1783),equivalent(equivalent(X_1781,X_1782),X_22)),equivalent(equivalent(equivalent(X_1781,X_1782),equivalent(X_1781,X_1783)),equivalent(equivalent(X_1781,X_1782),X_22)))),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_1781)),bind(Y,$fot(X_1782)),bind(Z,$fot(X_1783)),bind(X_1779,$fot(equivalent(equivalent(X_1781,X_1782),X_22)))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_1782,X_1783),equivalent(equivalent(X_1781,X_1782),X_22)),equivalent(equivalent(X_1781,X_1783),X_22))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_1782,X_1783),equivalent(equivalent(X_1781,X_1782),X_22)),equivalent(equivalent(equivalent(X_1781,X_1782),equivalent(X_1781,X_1783)),equivalent(equivalent(X_1781,X_1782),X_22)))) )],[refute_0_44,refute_0_21]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_1786,X_1787),equivalent(equivalent(X_1785,X_1786),X_1788)),equivalent(equivalent(X_1785,X_1787),X_1788))),
inference(subst,[],[refute_0_45:[bind(X_1781,$fot(X_1785)),bind(X_1782,$fot(X_1786)),bind(X_1783,$fot(X_1787)),bind(X_22,$fot(X_1788))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_1785,X_1786),X_1788),equivalent(equivalent(X_1787,X_1786),equivalent(equivalent(X_1785,X_1787),X_1788)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_1786,X_1787),equivalent(equivalent(X_1785,X_1786),X_1788)),equivalent(equivalent(X_1785,X_1787),X_1788))) )],[refute_0_46,refute_0_20]) ).
cnf(refute_0_48,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(subst,[],[refute_0_47:[bind(X_1785,$fot(a)),bind(X_1786,$fot(b)),bind(X_1787,$fot(e)),bind(X_1788,$fot(c))]]) ).
cnf(refute_0_49,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_48,prove_p_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL102-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 14:16:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.93/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/1.13
% 0.93/1.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.93/1.13
%------------------------------------------------------------------------------