TSTP Solution File: LCL370-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL370-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:51:47 EDT 2022
% Result : Unsatisfiable 62.17s 62.35s
% Output : CNFRefutation 62.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 5
% Syntax : Number of clauses : 157 ( 91 unt; 0 nHn; 39 RR)
% Number of literals : 237 ( 0 equ; 81 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 436 ( 102 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X),X),X)) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) ).
cnf(prove_cn_26,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(z,x),x))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(X_62,X_63),implies(X_61,X_63)),X_64))
| ~ is_a_theorem(implies(implies(implies(implies(X_62,X_63),implies(X_61,X_63)),X_64),implies(implies(X_61,X_62),X_64)))
| is_a_theorem(implies(implies(X_61,X_62),X_64)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_62,X_63),implies(X_61,X_63)),X_64))),bind(Y,$fot(implies(implies(X_61,X_62),X_64)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(X_62,X_63),implies(X_61,X_63)),X_64),implies(implies(X_61,X_62),X_64))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_61)),bind(Y,$fot(X_62)),bind(Z,$fot(X_63)),bind(X_21,$fot(X_64))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(X_62,X_63),implies(X_61,X_63)),X_64))
| is_a_theorem(implies(implies(X_61,X_62),X_64)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_62,X_63),implies(X_61,X_63)),X_64),implies(implies(X_61,X_62),X_64))) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(X_62,X_29651),implies(implies(X_29651,X_29652),X_29651)),implies(implies(X_62,X_29651),X_29651)))
| is_a_theorem(implies(implies(implies(X_29651,X_29652),X_62),implies(implies(X_62,X_29651),X_29651))) ),
inference(subst,[],[refute_0_6:[bind(X_61,$fot(implies(X_29651,X_29652))),bind(X_63,$fot(X_29651)),bind(X_64,$fot(implies(implies(X_62,X_29651),X_29651)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_21968,X_21969),X_21968),X_21968),implies(X_61,X_21968)),implies(X_61,X_21968)))
| is_a_theorem(implies(implies(X_61,implies(implies(X_21968,X_21969),X_21968)),implies(X_61,X_21968))) ),
inference(subst,[],[refute_0_6:[bind(X_62,$fot(implies(implies(X_21968,X_21969),X_21968))),bind(X_63,$fot(X_21968)),bind(X_64,$fot(implies(X_61,X_21968)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_1441)),X_1442),X_1441),X_1441))
| ~ is_a_theorem(implies(implies(not(not(X_1441)),X_1442),X_1441))
| is_a_theorem(X_1441) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_1441)),X_1442),X_1441))),bind(Y,$fot(X_1441))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(not(X_1437),X_1437),X_1437)),
inference(subst,[],[cn_2:[bind(X,$fot(X_1437))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(X_33,X_34),X_31))
| ~ is_a_theorem(implies(implies(implies(X_33,X_34),X_31),implies(implies(implies(not(X_33),X_32),X_34),X_31)))
| is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),X_31)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_33,X_34),X_31))),bind(Y,$fot(implies(implies(implies(not(X_33),X_32),X_34),X_31)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30)))
| is_a_theorem(implies(implies(implies(X_29,X_30),Z),implies(implies(implies(not(X_29),X_28),X_30),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(not(X_29),X_28),X_30))),bind(Y,$fot(implies(X_29,X_30)))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(X_19,implies(not(X_19),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(X_19,implies(not(X_19),Y)))
| is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_19)),bind(Y,$fot(implies(not(X_19),Y))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(X_19,implies(not(X_19),Y))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_28)),bind(X_19,$fot(X_29)),bind(X_21,$fot(X_30))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(X_29,X_30),Z),implies(implies(implies(not(X_29),X_28),X_30),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(implies(X_33,X_34),X_31),implies(implies(implies(not(X_33),X_32),X_34),X_31))),
inference(subst,[],[refute_0_17:[bind(Z,$fot(X_31)),bind(X_28,$fot(X_32)),bind(X_29,$fot(X_33)),bind(X_30,$fot(X_34))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(X_33,X_34),X_31))
| is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),X_31)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_33,X_34),X_31),implies(implies(implies(not(X_33),X_32),X_34),X_31))) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(not(X_1437),X_1437),X_1437))
| is_a_theorem(implies(implies(implies(not(not(X_1437)),X_1438),X_1437),X_1437)) ),
inference(subst,[],[refute_0_19:[bind(X_31,$fot(X_1437)),bind(X_32,$fot(X_1438)),bind(X_33,$fot(not(X_1437))),bind(X_34,$fot(X_1437))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(implies(not(not(X_1437)),X_1438),X_1437),X_1437)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_1437),X_1437),X_1437)) )],[refute_0_10,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(not(not(X_1441)),X_1442),X_1441),X_1441)),
inference(subst,[],[refute_0_21:[bind(X_1437,$fot(X_1441)),bind(X_1438,$fot(X_1442))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(not(not(X_1441)),X_1442),X_1441))
| is_a_theorem(X_1441) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_1441)),X_1442),X_1441),X_1441)) )],[refute_0_22,refute_0_9]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477))),X_1442),implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477)))
| is_a_theorem(implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477)) ),
inference(subst,[],[refute_0_23:[bind(X_1441,$fot(implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(X_687,implies(not(X_688),X_688)))
| ~ is_a_theorem(implies(implies(X_687,implies(not(X_688),X_688)),implies(X_686,implies(X_687,X_688))))
| is_a_theorem(implies(X_686,implies(X_687,X_688))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_687,implies(not(X_688),X_688)))),bind(Y,$fot(implies(X_686,implies(X_687,X_688))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_52),X_52),X_53),X_51),implies(implies(X_52,X_53),X_51)))
| ~ is_a_theorem(implies(implies(implies(not(X_52),X_52),X_53),X_51))
| is_a_theorem(implies(implies(X_52,X_53),X_51)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_52),X_52),X_53),X_51))),bind(Y,$fot(implies(implies(X_52,X_53),X_51)))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23)))
| is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_23),Z),implies(implies(X_22,X_23),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_22,X_23))),bind(Y,$fot(implies(implies(not(X_22),X_22),X_23)))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(not(X_20),X_20),X_20)),
inference(subst,[],[cn_2:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(not(X_20),X_20),X_20))
| is_a_theorem(implies(implies(X_20,X_21),implies(implies(not(X_20),X_20),X_21))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_20),X_20))),bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(X_20,X_21),implies(implies(not(X_20),X_20),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_20),X_20),X_20)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))),
inference(subst,[],[refute_0_30:[bind(X_20,$fot(X_22)),bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_23),Z),implies(implies(X_22,X_23),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))) )],[refute_0_31,refute_0_27]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(implies(implies(not(X_52),X_52),X_53),X_51),implies(implies(X_52,X_53),X_51))),
inference(subst,[],[refute_0_32:[bind(Z,$fot(X_51)),bind(X_22,$fot(X_52)),bind(X_23,$fot(X_53))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_52),X_52),X_53),X_51))
| is_a_theorem(implies(implies(X_52,X_53),X_51)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_52),X_52),X_53),X_51),implies(implies(X_52,X_53),X_51))) )],[refute_0_33,refute_0_26]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_365),X_365),X_365)),implies(implies(not(X_365),X_365),X_365)),X_364),implies(X_367,X_364)))
| is_a_theorem(implies(implies(implies(implies(not(X_365),X_365),X_365),X_364),implies(X_367,X_364))) ),
inference(subst,[],[refute_0_34:[bind(X_51,$fot(implies(X_367,X_364))),bind(X_52,$fot(implies(implies(not(X_365),X_365),X_365))),bind(X_53,$fot(X_364))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(X_145,implies(not(implies(implies(not(X_143),X_143),X_143)),X_144)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_143),X_143),X_143)),X_144),Z),implies(X_145,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_145)),bind(Y,$fot(implies(not(implies(implies(not(X_143),X_143),X_143)),X_144)))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_39:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20)),
inference(subst,[],[refute_0_41:[bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20))
| is_a_theorem(implies(implies(X_20,X_21),implies(not(implies(implies(not(X),X),X)),X_21))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(X_20,X_21),implies(not(implies(implies(not(X),X),X)),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(not(X_123),X_122),implies(not(implies(implies(not(X),X),X)),X_122))),
inference(subst,[],[refute_0_44:[bind(X_20,$fot(not(X_123))),bind(X_21,$fot(X_122))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30)))
| ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_29),X_28),X_30))),bind(Y,$fot(implies(X_29,X_30)))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))) )],[refute_0_16,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(implies(not(X_123),X_122),implies(not(implies(implies(not(X),X),X)),X_122)))
| is_a_theorem(implies(X_123,implies(not(implies(implies(not(X),X),X)),X_122))) ),
inference(subst,[],[refute_0_47:[bind(X_28,$fot(X_122)),bind(X_29,$fot(X_123)),bind(X_30,$fot(implies(not(implies(implies(not(X),X),X)),X_122)))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(X_123,implies(not(implies(implies(not(X),X),X)),X_122))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_123),X_122),implies(not(implies(implies(not(X),X),X)),X_122))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(X_145,implies(not(implies(implies(not(X_143),X_143),X_143)),X_144))),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_143)),bind(X_122,$fot(X_144)),bind(X_123,$fot(X_145))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_143),X_143),X_143)),X_144),Z),implies(X_145,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_145,implies(not(implies(implies(not(X_143),X_143),X_143)),X_144))) )],[refute_0_50,refute_0_36]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_365),X_365),X_365)),implies(implies(not(X_365),X_365),X_365)),X_364),implies(X_367,X_364))),
inference(subst,[],[refute_0_51:[bind(Z,$fot(X_364)),bind(X_143,$fot(X_365)),bind(X_144,$fot(implies(implies(not(X_365),X_365),X_365))),bind(X_145,$fot(X_367))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(implies(not(X_365),X_365),X_365),X_364),implies(X_367,X_364))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_365),X_365),X_365)),implies(implies(not(X_365),X_365),X_365)),X_364),implies(X_367,X_364))) )],[refute_0_52,refute_0_35]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(implies(not(X_655),X_655),X_655),implies(X_653,X_655)),implies(X_367,implies(X_653,X_655)))),
inference(subst,[],[refute_0_53:[bind(X_364,$fot(implies(X_653,X_655))),bind(X_365,$fot(X_655))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_655),X_655),X_655),implies(X_653,X_655)),implies(X_367,implies(X_653,X_655))))
| is_a_theorem(implies(implies(X_653,implies(not(X_655),X_655)),implies(X_367,implies(X_653,X_655)))) ),
inference(subst,[],[refute_0_6:[bind(X_61,$fot(X_653)),bind(X_62,$fot(implies(not(X_655),X_655))),bind(X_63,$fot(X_655)),bind(X_64,$fot(implies(X_367,implies(X_653,X_655))))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(X_653,implies(not(X_655),X_655)),implies(X_367,implies(X_653,X_655)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_655),X_655),X_655),implies(X_653,X_655)),implies(X_367,implies(X_653,X_655)))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(X_687,implies(not(X_688),X_688)),implies(X_686,implies(X_687,X_688)))),
inference(subst,[],[refute_0_56:[bind(X_367,$fot(X_686)),bind(X_653,$fot(X_687)),bind(X_655,$fot(X_688))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(X_687,implies(not(X_688),X_688)))
| is_a_theorem(implies(X_686,implies(X_687,X_688))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_687,implies(not(X_688),X_688)),implies(X_686,implies(X_687,X_688)))) )],[refute_0_57,refute_0_25]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_21425,X_21426),X_21425),X_21425),X_21428),implies(not(X_21428),X_21428)))
| is_a_theorem(implies(X_686,implies(implies(implies(implies(implies(X_21425,X_21426),X_21425),X_21425),X_21428),X_21428))) ),
inference(subst,[],[refute_0_58:[bind(X_687,$fot(implies(implies(implies(implies(X_21425,X_21426),X_21425),X_21425),X_21428))),bind(X_688,$fot(X_21428))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(X_2397)
| ~ is_a_theorem(implies(X_2397,implies(X_2396,X_2397)))
| is_a_theorem(implies(X_2396,X_2397)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_2397)),bind(Y,$fot(implies(X_2396,X_2397)))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(X_2395,implies(X_2393,X_2395)))),X_1442),implies(X_2395,implies(X_2393,X_2395))))
| is_a_theorem(implies(X_2395,implies(X_2393,X_2395))) ),
inference(subst,[],[refute_0_23:[bind(X_1441,$fot(implies(X_2395,implies(X_2393,X_2395))))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(implies(not(X_1627),not(X_1625)),implies(X_1626,implies(X_1625,X_1627))))
| is_a_theorem(implies(X_1627,implies(X_1626,implies(X_1625,X_1627)))) ),
inference(subst,[],[refute_0_47:[bind(X_28,$fot(not(X_1625))),bind(X_29,$fot(X_1627)),bind(X_30,$fot(implies(X_1626,implies(X_1625,X_1627))))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1622),X_1624),implies(not(X_1624),X_1624)),implies(X_1623,implies(X_1622,X_1624))))
| is_a_theorem(implies(implies(not(X_1624),not(X_1622)),implies(X_1623,implies(X_1622,X_1624)))) ),
inference(subst,[],[refute_0_6:[bind(X_61,$fot(not(X_1624))),bind(X_62,$fot(not(X_1622))),bind(X_63,$fot(X_1624)),bind(X_64,$fot(implies(X_1623,implies(X_1622,X_1624))))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(X_1439,implies(not(X_655),X_655)),implies(X_367,implies(X_1439,X_655)))),
inference(subst,[],[refute_0_56:[bind(X_653,$fot(X_1439))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(X_1439,implies(not(X_655),X_655)),implies(X_367,implies(X_1439,X_655))))
| is_a_theorem(implies(implies(implies(not(X_1439),X_1438),implies(not(X_655),X_655)),implies(X_367,implies(X_1439,X_655)))) ),
inference(subst,[],[refute_0_19:[bind(X_31,$fot(implies(X_367,implies(X_1439,X_655)))),bind(X_32,$fot(X_1438)),bind(X_33,$fot(X_1439)),bind(X_34,$fot(implies(not(X_655),X_655)))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(not(X_1439),X_1438),implies(not(X_655),X_655)),implies(X_367,implies(X_1439,X_655)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1439,implies(not(X_655),X_655)),implies(X_367,implies(X_1439,X_655)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(implies(not(X_1622),X_1624),implies(not(X_1624),X_1624)),implies(X_1623,implies(X_1622,X_1624)))),
inference(subst,[],[refute_0_66:[bind(X_1438,$fot(X_1624)),bind(X_1439,$fot(X_1622)),bind(X_367,$fot(X_1623)),bind(X_655,$fot(X_1624))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(not(X_1624),not(X_1622)),implies(X_1623,implies(X_1622,X_1624)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1622),X_1624),implies(not(X_1624),X_1624)),implies(X_1623,implies(X_1622,X_1624)))) )],[refute_0_67,refute_0_63]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(not(X_1627),not(X_1625)),implies(X_1626,implies(X_1625,X_1627)))),
inference(subst,[],[refute_0_68:[bind(X_1622,$fot(X_1625)),bind(X_1623,$fot(X_1626)),bind(X_1624,$fot(X_1627))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(X_1627,implies(X_1626,implies(X_1625,X_1627)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_1627),not(X_1625)),implies(X_1626,implies(X_1625,X_1627)))) )],[refute_0_69,refute_0_62]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(X_2391,implies(not(implies(X_1625,X_2391)),implies(X_1625,X_2391)))),
inference(subst,[],[refute_0_70:[bind(X_1626,$fot(not(implies(X_1625,X_2391)))),bind(X_1627,$fot(X_2391))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(X_2391,implies(not(implies(X_1625,X_2391)),implies(X_1625,X_2391))))
| is_a_theorem(implies(X_2390,implies(X_2391,implies(X_1625,X_2391)))) ),
inference(subst,[],[refute_0_58:[bind(X_686,$fot(X_2390)),bind(X_687,$fot(X_2391)),bind(X_688,$fot(implies(X_1625,X_2391)))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(X_2390,implies(X_2391,implies(X_1625,X_2391)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2391,implies(not(implies(X_1625,X_2391)),implies(X_1625,X_2391)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(not(not(implies(X_2395,implies(X_2393,X_2395)))),X_1442),implies(X_2395,implies(X_2393,X_2395)))),
inference(subst,[],[refute_0_73:[bind(X_1625,$fot(X_2393)),bind(X_2390,$fot(implies(not(not(implies(X_2395,implies(X_2393,X_2395)))),X_1442))),bind(X_2391,$fot(X_2395))]]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(X_2395,implies(X_2393,X_2395))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(X_2395,implies(X_2393,X_2395)))),X_1442),implies(X_2395,implies(X_2393,X_2395)))) )],[refute_0_74,refute_0_61]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(X_2397,implies(X_2396,X_2397))),
inference(subst,[],[refute_0_75:[bind(X_2393,$fot(X_2396)),bind(X_2395,$fot(X_2397))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(X_2397)
| is_a_theorem(implies(X_2396,X_2397)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_2397,implies(X_2396,X_2397))) )],[refute_0_76,refute_0_60]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(X_11053,implies(implies(implies(X_11051,X_11052),X_11051),X_11051)))
| is_a_theorem(implies(X_2396,implies(X_11053,implies(implies(implies(X_11051,X_11052),X_11051),X_11051)))) ),
inference(subst,[],[refute_0_77:[bind(X_2397,$fot(implies(X_11053,implies(implies(implies(X_11051,X_11052),X_11051),X_11051))))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(implies(implies(X_11044,X_11046),X_11044),implies(not(X_11044),X_11044)))
| is_a_theorem(implies(X_686,implies(implies(implies(X_11044,X_11046),X_11044),X_11044))) ),
inference(subst,[],[refute_0_58:[bind(X_687,$fot(implies(implies(X_11044,X_11046),X_11044))),bind(X_688,$fot(X_11044))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(not(X_2521),implies(X_2521,X_2522)))
| is_a_theorem(implies(X_2396,implies(not(X_2521),implies(X_2521,X_2522)))) ),
inference(subst,[],[refute_0_77:[bind(X_2397,$fot(implies(not(X_2521),implies(X_2521,X_2522))))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(not(not(X_2519)),not(X_2519)),implies(X_2519,X_2520)))
| is_a_theorem(implies(not(X_2519),implies(X_2519,X_2520))) ),
inference(subst,[],[refute_0_47:[bind(X_28,$fot(not(X_2519))),bind(X_29,$fot(not(X_2519))),bind(X_30,$fot(implies(X_2519,X_2520)))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(X_703,implies(not(not(X_702)),not(X_702))))
| ~ is_a_theorem(implies(implies(X_703,implies(not(not(X_702)),not(X_702))),implies(X_702,implies(X_703,X_704))))
| is_a_theorem(implies(X_702,implies(X_703,X_704))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_703,implies(not(not(X_702)),not(X_702))))),bind(Y,$fot(implies(X_702,implies(X_703,X_704))))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(X_129,implies(implies(not(not(X_129)),not(X_129)),X_128)))
| is_a_theorem(implies(implies(implies(implies(not(not(X_129)),not(X_129)),X_128),Z),implies(X_129,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_129)),bind(Y,$fot(implies(implies(not(not(X_129)),not(X_129)),X_128)))]]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(implies(not(X_123),X_122),implies(implies(not(not(X_123)),not(X_123)),X_122))),
inference(subst,[],[refute_0_30:[bind(X_20,$fot(not(X_123))),bind(X_21,$fot(X_122))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(implies(not(X_123),X_122),implies(implies(not(not(X_123)),not(X_123)),X_122)))
| is_a_theorem(implies(X_123,implies(implies(not(not(X_123)),not(X_123)),X_122))) ),
inference(subst,[],[refute_0_47:[bind(X_28,$fot(X_122)),bind(X_29,$fot(X_123)),bind(X_30,$fot(implies(implies(not(not(X_123)),not(X_123)),X_122)))]]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(X_123,implies(implies(not(not(X_123)),not(X_123)),X_122))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_123),X_122),implies(implies(not(not(X_123)),not(X_123)),X_122))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(X_129,implies(implies(not(not(X_129)),not(X_129)),X_128))),
inference(subst,[],[refute_0_86:[bind(X_122,$fot(X_128)),bind(X_123,$fot(X_129))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_129)),not(X_129)),X_128),Z),implies(X_129,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_129,implies(implies(not(not(X_129)),not(X_129)),X_128))) )],[refute_0_87,refute_0_83]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_129)),not(X_129)),X_655),implies(X_653,X_655)),implies(X_129,implies(X_653,X_655)))),
inference(subst,[],[refute_0_88:[bind(Z,$fot(implies(X_653,X_655))),bind(X_128,$fot(X_655))]]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_129)),not(X_129)),X_655),implies(X_653,X_655)),implies(X_129,implies(X_653,X_655))))
| is_a_theorem(implies(implies(X_653,implies(not(not(X_129)),not(X_129))),implies(X_129,implies(X_653,X_655)))) ),
inference(subst,[],[refute_0_6:[bind(X_61,$fot(X_653)),bind(X_62,$fot(implies(not(not(X_129)),not(X_129)))),bind(X_63,$fot(X_655)),bind(X_64,$fot(implies(X_129,implies(X_653,X_655))))]]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(X_653,implies(not(not(X_129)),not(X_129))),implies(X_129,implies(X_653,X_655)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_129)),not(X_129)),X_655),implies(X_653,X_655)),implies(X_129,implies(X_653,X_655)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(X_703,implies(not(not(X_702)),not(X_702))),implies(X_702,implies(X_703,X_704)))),
inference(subst,[],[refute_0_91:[bind(X_129,$fot(X_702)),bind(X_653,$fot(X_703)),bind(X_655,$fot(X_704))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(X_703,implies(not(not(X_702)),not(X_702))))
| is_a_theorem(implies(X_702,implies(X_703,X_704))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_703,implies(not(not(X_702)),not(X_702))),implies(X_702,implies(X_703,X_704)))) )],[refute_0_92,refute_0_82]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(implies(X_2517,implies(not(not(implies(not(not(X_2517)),not(X_2517)))),not(implies(not(not(X_2517)),not(X_2517))))))
| is_a_theorem(implies(implies(not(not(X_2517)),not(X_2517)),implies(X_2517,X_704))) ),
inference(subst,[],[refute_0_93:[bind(X_702,$fot(implies(not(not(X_2517)),not(X_2517)))),bind(X_703,$fot(X_2517))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(not(not(implies(not(not(X_702)),not(X_702)))),implies(not(not(X_702)),not(X_702))))
| is_a_theorem(implies(X_702,implies(not(not(implies(not(not(X_702)),not(X_702)))),X_704))) ),
inference(subst,[],[refute_0_93:[bind(X_703,$fot(not(not(implies(not(not(X_702)),not(X_702))))))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501)))),X_1442),implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501))))
| is_a_theorem(implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501))) ),
inference(subst,[],[refute_0_23:[bind(X_1441,$fot(implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501))))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(implies(not(not(X_2273)),not(X_2274)),implies(X_2273,implies(X_2274,X_2275))))
| is_a_theorem(implies(not(X_2273),implies(X_2273,implies(X_2274,X_2275)))) ),
inference(subst,[],[refute_0_47:[bind(X_28,$fot(not(X_2274))),bind(X_29,$fot(not(X_2273))),bind(X_30,$fot(implies(X_2273,implies(X_2274,X_2275))))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_2271),not(X_2269)),implies(not(not(X_2269)),not(X_2269))),implies(X_2269,implies(X_2271,X_2272))))
| is_a_theorem(implies(implies(not(not(X_2269)),not(X_2271)),implies(X_2269,implies(X_2271,X_2272)))) ),
inference(subst,[],[refute_0_6:[bind(X_61,$fot(not(not(X_2269)))),bind(X_62,$fot(not(X_2271))),bind(X_63,$fot(not(X_2269))),bind(X_64,$fot(implies(X_2269,implies(X_2271,X_2272))))]]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(X_1439,implies(not(not(X_129)),not(X_129))),implies(X_129,implies(X_1439,X_655)))),
inference(subst,[],[refute_0_91:[bind(X_653,$fot(X_1439))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(implies(X_1439,implies(not(not(X_129)),not(X_129))),implies(X_129,implies(X_1439,X_655))))
| is_a_theorem(implies(implies(implies(not(X_1439),X_1438),implies(not(not(X_129)),not(X_129))),implies(X_129,implies(X_1439,X_655)))) ),
inference(subst,[],[refute_0_19:[bind(X_31,$fot(implies(X_129,implies(X_1439,X_655)))),bind(X_32,$fot(X_1438)),bind(X_33,$fot(X_1439)),bind(X_34,$fot(implies(not(not(X_129)),not(X_129))))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(implies(not(X_1439),X_1438),implies(not(not(X_129)),not(X_129))),implies(X_129,implies(X_1439,X_655)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1439,implies(not(not(X_129)),not(X_129))),implies(X_129,implies(X_1439,X_655)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(implies(implies(not(X_2271),not(X_2269)),implies(not(not(X_2269)),not(X_2269))),implies(X_2269,implies(X_2271,X_2272)))),
inference(subst,[],[refute_0_101:[bind(X_129,$fot(X_2269)),bind(X_1438,$fot(not(X_2269))),bind(X_1439,$fot(X_2271)),bind(X_655,$fot(X_2272))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(not(not(X_2269)),not(X_2271)),implies(X_2269,implies(X_2271,X_2272)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_2271),not(X_2269)),implies(not(not(X_2269)),not(X_2269))),implies(X_2269,implies(X_2271,X_2272)))) )],[refute_0_102,refute_0_98]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(implies(not(not(X_2273)),not(X_2274)),implies(X_2273,implies(X_2274,X_2275)))),
inference(subst,[],[refute_0_103:[bind(X_2269,$fot(X_2273)),bind(X_2271,$fot(X_2274)),bind(X_2272,$fot(X_2275))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(not(X_2273),implies(X_2273,implies(X_2274,X_2275)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_2273)),not(X_2274)),implies(X_2273,implies(X_2274,X_2275)))) )],[refute_0_104,refute_0_97]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(not(not(implies(X_2274,X_2275))),implies(not(implies(X_2274,X_2275)),implies(X_2274,X_2275)))),
inference(subst,[],[refute_0_105:[bind(X_2273,$fot(not(implies(X_2274,X_2275))))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(not(not(implies(X_2274,X_2275))),implies(not(implies(X_2274,X_2275)),implies(X_2274,X_2275))))
| is_a_theorem(implies(X_2390,implies(not(not(implies(X_2274,X_2275))),implies(X_2274,X_2275)))) ),
inference(subst,[],[refute_0_58:[bind(X_686,$fot(X_2390)),bind(X_687,$fot(not(not(implies(X_2274,X_2275))))),bind(X_688,$fot(implies(X_2274,X_2275)))]]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(X_2390,implies(not(not(implies(X_2274,X_2275))),implies(X_2274,X_2275)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(X_2274,X_2275))),implies(not(implies(X_2274,X_2275)),implies(X_2274,X_2275)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(implies(not(not(implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501)))),X_1442),implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501)))),
inference(subst,[],[refute_0_108:[bind(X_2274,$fot(X_2500)),bind(X_2275,$fot(X_2501)),bind(X_2390,$fot(implies(not(not(implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501)))),X_1442)))]]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501)))),X_1442),implies(not(not(implies(X_2500,X_2501))),implies(X_2500,X_2501)))) )],[refute_0_109,refute_0_96]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(not(not(implies(not(not(X_702)),not(X_702)))),implies(not(not(X_702)),not(X_702)))),
inference(subst,[],[refute_0_110:[bind(X_2500,$fot(not(not(X_702)))),bind(X_2501,$fot(not(X_702)))]]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(X_702,implies(not(not(implies(not(not(X_702)),not(X_702)))),X_704))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(not(X_702)),not(X_702)))),implies(not(not(X_702)),not(X_702)))) )],[refute_0_111,refute_0_95]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(X_2517,implies(not(not(implies(not(not(X_2517)),not(X_2517)))),not(implies(not(not(X_2517)),not(X_2517)))))),
inference(subst,[],[refute_0_112:[bind(X_702,$fot(X_2517)),bind(X_704,$fot(not(implies(not(not(X_2517)),not(X_2517)))))]]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(not(not(X_2517)),not(X_2517)),implies(X_2517,X_704))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2517,implies(not(not(implies(not(not(X_2517)),not(X_2517)))),not(implies(not(not(X_2517)),not(X_2517)))))) )],[refute_0_113,refute_0_94]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(not(not(X_2519)),not(X_2519)),implies(X_2519,X_2520))),
inference(subst,[],[refute_0_114:[bind(X_2517,$fot(X_2519)),bind(X_704,$fot(X_2520))]]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(not(X_2519),implies(X_2519,X_2520))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_2519)),not(X_2519)),implies(X_2519,X_2520))) )],[refute_0_115,refute_0_81]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(not(X_2521),implies(X_2521,X_2522))),
inference(subst,[],[refute_0_116:[bind(X_2519,$fot(X_2521)),bind(X_2520,$fot(X_2522))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(X_2396,implies(not(X_2521),implies(X_2521,X_2522)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_2521),implies(X_2521,X_2522))) )],[refute_0_117,refute_0_80]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(not(implies(not(X_2521),implies(X_2521,X_2522))),implies(not(X_2521),implies(X_2521,X_2522)))),
inference(subst,[],[refute_0_118:[bind(X_2396,$fot(not(implies(not(X_2521),implies(X_2521,X_2522)))))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_236,X_237)),implies(X_236,X_237)),implies(implies(X_237,X_238),implies(X_236,X_238))))
| ~ is_a_theorem(implies(not(implies(X_236,X_237)),implies(X_236,X_237)))
| is_a_theorem(implies(implies(X_237,X_238),implies(X_236,X_238))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(implies(X_236,X_237)),implies(X_236,X_237)))),bind(Y,$fot(implies(implies(X_237,X_238),implies(X_236,X_238))))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(X_22,X_23))
| ~ is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23)))
| is_a_theorem(implies(implies(not(X_22),X_22),X_23)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_22,X_23))),bind(Y,$fot(implies(implies(not(X_22),X_22),X_23)))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(X_22,X_23))
| is_a_theorem(implies(implies(not(X_22),X_22),X_23)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))) )],[refute_0_31,refute_0_121]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(not(implies(X,Y)),implies(X,Y)),implies(implies(Y,Z),implies(X,Z)))) ),
inference(subst,[],[refute_0_122:[bind(X_22,$fot(implies(X,Y))),bind(X_23,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(not(implies(X,Y)),implies(X,Y)),implies(implies(Y,Z),implies(X,Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_123]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(implies(not(implies(X_236,X_237)),implies(X_236,X_237)),implies(implies(X_237,X_238),implies(X_236,X_238)))),
inference(subst,[],[refute_0_124:[bind(X,$fot(X_236)),bind(Y,$fot(X_237)),bind(Z,$fot(X_238))]]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(implies(not(implies(X_236,X_237)),implies(X_236,X_237)))
| is_a_theorem(implies(implies(X_237,X_238),implies(X_236,X_238))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(X_236,X_237)),implies(X_236,X_237)),implies(implies(X_237,X_238),implies(X_236,X_238)))) )],[refute_0_125,refute_0_120]) ).
cnf(refute_0_127,plain,
( ~ is_a_theorem(implies(not(implies(not(X_2521),implies(X_2521,X_2522))),implies(not(X_2521),implies(X_2521,X_2522))))
| is_a_theorem(implies(implies(implies(X_2521,X_2522),X_11006),implies(not(X_2521),X_11006))) ),
inference(subst,[],[refute_0_126:[bind(X_236,$fot(not(X_2521))),bind(X_237,$fot(implies(X_2521,X_2522))),bind(X_238,$fot(X_11006))]]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(implies(X_2521,X_2522),X_11006),implies(not(X_2521),X_11006))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(not(X_2521),implies(X_2521,X_2522))),implies(not(X_2521),implies(X_2521,X_2522)))) )],[refute_0_119,refute_0_127]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(implies(X_11044,X_11046),X_11044),implies(not(X_11044),X_11044))),
inference(subst,[],[refute_0_128:[bind(X_11006,$fot(X_11044)),bind(X_2521,$fot(X_11044)),bind(X_2522,$fot(X_11046))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(X_686,implies(implies(implies(X_11044,X_11046),X_11044),X_11044))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_11044,X_11046),X_11044),implies(not(X_11044),X_11044))) )],[refute_0_129,refute_0_79]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(X_11053,implies(implies(implies(X_11051,X_11052),X_11051),X_11051))),
inference(subst,[],[refute_0_130:[bind(X_11044,$fot(X_11051)),bind(X_11046,$fot(X_11052)),bind(X_686,$fot(X_11053))]]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(X_2396,implies(X_11053,implies(implies(implies(X_11051,X_11052),X_11051),X_11051)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_11053,implies(implies(implies(X_11051,X_11052),X_11051),X_11051))) )],[refute_0_131,refute_0_78]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(X_21417,implies(not(implies(implies(implies(X_11051,X_11052),X_11051),X_11051)),implies(implies(implies(X_11051,X_11052),X_11051),X_11051)))),
inference(subst,[],[refute_0_132:[bind(X_11053,$fot(not(implies(implies(implies(X_11051,X_11052),X_11051),X_11051)))),bind(X_2396,$fot(X_21417))]]) ).
cnf(refute_0_134,plain,
( ~ is_a_theorem(implies(X_690,implies(not(X_689),X_689)))
| ~ is_a_theorem(implies(implies(X_690,implies(not(X_689),X_689)),implies(implies(X_689,X_691),implies(X_690,X_691))))
| is_a_theorem(implies(implies(X_689,X_691),implies(X_690,X_691))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_690,implies(not(X_689),X_689)))),bind(Y,$fot(implies(implies(X_689,X_691),implies(X_690,X_691))))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_655),implies(X_653,X_655)),implies(implies(X_22,X_655),implies(X_653,X_655)))),
inference(subst,[],[refute_0_32:[bind(Z,$fot(implies(X_653,X_655))),bind(X_23,$fot(X_655))]]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_655),implies(X_653,X_655)),implies(implies(X_22,X_655),implies(X_653,X_655))))
| is_a_theorem(implies(implies(X_653,implies(not(X_22),X_22)),implies(implies(X_22,X_655),implies(X_653,X_655)))) ),
inference(subst,[],[refute_0_6:[bind(X_61,$fot(X_653)),bind(X_62,$fot(implies(not(X_22),X_22))),bind(X_63,$fot(X_655)),bind(X_64,$fot(implies(implies(X_22,X_655),implies(X_653,X_655))))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(implies(X_653,implies(not(X_22),X_22)),implies(implies(X_22,X_655),implies(X_653,X_655)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_655),implies(X_653,X_655)),implies(implies(X_22,X_655),implies(X_653,X_655)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(implies(X_690,implies(not(X_689),X_689)),implies(implies(X_689,X_691),implies(X_690,X_691)))),
inference(subst,[],[refute_0_137:[bind(X_22,$fot(X_689)),bind(X_653,$fot(X_690)),bind(X_655,$fot(X_691))]]) ).
cnf(refute_0_139,plain,
( ~ is_a_theorem(implies(X_690,implies(not(X_689),X_689)))
| is_a_theorem(implies(implies(X_689,X_691),implies(X_690,X_691))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_690,implies(not(X_689),X_689)),implies(implies(X_689,X_691),implies(X_690,X_691)))) )],[refute_0_138,refute_0_134]) ).
cnf(refute_0_140,plain,
( ~ is_a_theorem(implies(X_21417,implies(not(implies(implies(implies(X_11051,X_11052),X_11051),X_11051)),implies(implies(implies(X_11051,X_11052),X_11051),X_11051))))
| is_a_theorem(implies(implies(implies(implies(implies(X_11051,X_11052),X_11051),X_11051),X_21418),implies(X_21417,X_21418))) ),
inference(subst,[],[refute_0_139:[bind(X_689,$fot(implies(implies(implies(X_11051,X_11052),X_11051),X_11051))),bind(X_690,$fot(X_21417)),bind(X_691,$fot(X_21418))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_11051,X_11052),X_11051),X_11051),X_21418),implies(X_21417,X_21418))),
inference(resolve,[$cnf( is_a_theorem(implies(X_21417,implies(not(implies(implies(implies(X_11051,X_11052),X_11051),X_11051)),implies(implies(implies(X_11051,X_11052),X_11051),X_11051)))) )],[refute_0_133,refute_0_140]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_21425,X_21426),X_21425),X_21425),X_21428),implies(not(X_21428),X_21428))),
inference(subst,[],[refute_0_141:[bind(X_11051,$fot(X_21425)),bind(X_11052,$fot(X_21426)),bind(X_21417,$fot(not(X_21428))),bind(X_21418,$fot(X_21428))]]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(X_686,implies(implies(implies(implies(implies(X_21425,X_21426),X_21425),X_21425),X_21428),X_21428))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_21425,X_21426),X_21425),X_21425),X_21428),implies(not(X_21428),X_21428))) )],[refute_0_142,refute_0_59]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477))),X_1442),implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477))),
inference(subst,[],[refute_0_143:[bind(X_21425,$fot(X_21475)),bind(X_21426,$fot(X_21476)),bind(X_21428,$fot(X_21477)),bind(X_686,$fot(implies(not(not(implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477))),X_1442)))]]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477))),X_1442),implies(implies(implies(implies(implies(X_21475,X_21476),X_21475),X_21475),X_21477),X_21477))) )],[refute_0_144,refute_0_24]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_21968,X_21969),X_21968),X_21968),implies(X_61,X_21968)),implies(X_61,X_21968))),
inference(subst,[],[refute_0_145:[bind(X_21475,$fot(X_21968)),bind(X_21476,$fot(X_21969)),bind(X_21477,$fot(implies(X_61,X_21968)))]]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(X_61,implies(implies(X_21968,X_21969),X_21968)),implies(X_61,X_21968))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_21968,X_21969),X_21968),X_21968),implies(X_61,X_21968)),implies(X_61,X_21968))) )],[refute_0_146,refute_0_8]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(implies(X_62,X_29651),implies(implies(X_29651,X_29652),X_29651)),implies(implies(X_62,X_29651),X_29651))),
inference(subst,[],[refute_0_147:[bind(X_21968,$fot(X_29651)),bind(X_21969,$fot(X_29652)),bind(X_61,$fot(implies(X_62,X_29651)))]]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(implies(implies(X_29651,X_29652),X_62),implies(implies(X_62,X_29651),X_29651))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_62,X_29651),implies(implies(X_29651,X_29652),X_29651)),implies(implies(X_62,X_29651),X_29651))) )],[refute_0_148,refute_0_7]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(implies(implies(x,y),z),implies(implies(z,x),x))),
inference(subst,[],[refute_0_149:[bind(X_29651,$fot(x)),bind(X_29652,$fot(y)),bind(X_62,$fot(z))]]) ).
cnf(refute_0_151,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(x,y),z),implies(implies(z,x),x))) )],[refute_0_150,prove_cn_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL370-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 12:44:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 62.17/62.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.17/62.35
% 62.17/62.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 62.17/62.37
%------------------------------------------------------------------------------