TSTP Solution File: LCL367-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL367-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:51:46 EDT 2022
% Result : Unsatisfiable 1.22s 1.42s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of clauses : 97 ( 54 unt; 0 nHn; 30 RR)
% Number of literals : 151 ( 0 equ; 55 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 268 ( 43 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_17,negated_conjecture,
~ is_a_theorem(implies(x,implies(implies(y,x),x))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_46),X_45),X_47),implies(X_46,X_47)))
| ~ is_a_theorem(implies(implies(not(X_46),X_45),X_47))
| is_a_theorem(implies(X_46,X_47)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_46),X_45),X_47))),bind(Y,$fot(implies(X_46,X_47)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_27,implies(not(X_27),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_27,implies(not(X_27),Y)))
| is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_27)),bind(Y,$fot(implies(not(X_27),Y))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(X_27,implies(not(X_27),Y))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(not(X_46),X_45),X_47),implies(X_46,X_47))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_45)),bind(X_27,$fot(X_46)),bind(X_29,$fot(X_47))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(not(X_46),X_45),X_47))
| is_a_theorem(implies(X_46,X_47)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_46),X_45),X_47),implies(X_46,X_47))) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(not(X_2371),X_2372),implies(implies(X_2372,X_2371),X_2371)))
| is_a_theorem(implies(X_2371,implies(implies(X_2372,X_2371),X_2371))) ),
inference(subst,[],[refute_0_7:[bind(X_45,$fot(X_2372)),bind(X_46,$fot(X_2371)),bind(X_47,$fot(implies(implies(X_2372,X_2371),X_2371)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(X_88,X_89),implies(X_87,X_89)),X_90))
| ~ is_a_theorem(implies(implies(implies(implies(X_88,X_89),implies(X_87,X_89)),X_90),implies(implies(X_87,X_88),X_90)))
| is_a_theorem(implies(implies(X_87,X_88),X_90)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_88,X_89),implies(X_87,X_89)),X_90))),bind(Y,$fot(implies(implies(X_87,X_88),X_90)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_10]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(implies(X_88,X_89),implies(X_87,X_89)),X_90),implies(implies(X_87,X_88),X_90))),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_87)),bind(Y,$fot(X_88)),bind(Z,$fot(X_89)),bind(X_29,$fot(X_90))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(X_88,X_89),implies(X_87,X_89)),X_90))
| is_a_theorem(implies(implies(X_87,X_88),X_90)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_88,X_89),implies(X_87,X_89)),X_90),implies(implies(X_87,X_88),X_90))) )],[refute_0_12,refute_0_9]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(implies(X_88,X_2348),implies(not(X_2348),X_2348)),implies(implies(X_88,X_2348),X_2348)))
| is_a_theorem(implies(implies(not(X_2348),X_88),implies(implies(X_88,X_2348),X_2348))) ),
inference(subst,[],[refute_0_13:[bind(X_87,$fot(not(X_2348))),bind(X_89,$fot(X_2348)),bind(X_90,$fot(implies(implies(X_88,X_2348),X_2348)))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(X_713,X_714),X_712),X_711))
| ~ is_a_theorem(implies(implies(implies(implies(X_713,X_714),X_712),X_711),implies(implies(implies(implies(not(X_713),X_713),X_714),X_712),X_711)))
| is_a_theorem(implies(implies(implies(implies(not(X_713),X_713),X_714),X_712),X_711)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_713,X_714),X_712),X_711))),bind(Y,$fot(implies(implies(implies(implies(not(X_713),X_713),X_714),X_712),X_711)))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_69),X_69),X_70),X_68),implies(implies(X_69,X_70),X_68)))
| is_a_theorem(implies(implies(implies(implies(X_69,X_70),X_68),Z),implies(implies(implies(implies(not(X_69),X_69),X_70),X_68),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(implies(not(X_69),X_69),X_70),X_68))),bind(Y,$fot(implies(implies(X_69,X_70),X_68)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31)))
| is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),Z),implies(implies(X_30,X_31),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X_30,X_31))),bind(Y,$fot(implies(implies(not(X_30),X_30),X_31)))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(not(X_28),X_28),X_28)),
inference(subst,[],[cn_2:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(not(X_28),X_28),X_28))
| is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(not(X_28),X_28))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_28),X_28),X_28)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))),
inference(subst,[],[refute_0_20:[bind(X_28,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),Z),implies(implies(X_30,X_31),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(implies(not(X_69),X_69),X_70),X_68),implies(implies(X_69,X_70),X_68))),
inference(subst,[],[refute_0_22:[bind(Z,$fot(X_68)),bind(X_30,$fot(X_69)),bind(X_31,$fot(X_70))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(implies(implies(X_69,X_70),X_68),Z),implies(implies(implies(implies(not(X_69),X_69),X_70),X_68),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_69),X_69),X_70),X_68),implies(implies(X_69,X_70),X_68))) )],[refute_0_23,refute_0_16]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(implies(implies(X_713,X_714),X_712),X_711),implies(implies(implies(implies(not(X_713),X_713),X_714),X_712),X_711))),
inference(subst,[],[refute_0_24:[bind(Z,$fot(X_711)),bind(X_68,$fot(X_712)),bind(X_69,$fot(X_713)),bind(X_70,$fot(X_714))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(X_713,X_714),X_712),X_711))
| is_a_theorem(implies(implies(implies(implies(not(X_713),X_713),X_714),X_712),X_711)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_713,X_714),X_712),X_711),implies(implies(implies(implies(not(X_713),X_713),X_714),X_712),X_711))) )],[refute_0_25,refute_0_15]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(X_1426,X_1426),X_1425),X_1425))
| is_a_theorem(implies(implies(implies(implies(not(X_1426),X_1426),X_1426),X_1425),X_1425)) ),
inference(subst,[],[refute_0_26:[bind(X_711,$fot(X_1425)),bind(X_712,$fot(X_1425)),bind(X_713,$fot(X_1426)),bind(X_714,$fot(X_1426))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_69),X_69),X_70),X_68),implies(implies(X_69,X_70),X_68)))
| ~ is_a_theorem(implies(implies(implies(not(X_69),X_69),X_70),X_68))
| is_a_theorem(implies(implies(X_69,X_70),X_68)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_69),X_69),X_70),X_68))),bind(Y,$fot(implies(implies(X_69,X_70),X_68)))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_69),X_69),X_70),X_68))
| is_a_theorem(implies(implies(X_69,X_70),X_68)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_69),X_69),X_70),X_68),implies(implies(X_69,X_70),X_68))) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_1424,X_1424)),implies(X_1424,X_1424)),X_1422),X_1422))
| is_a_theorem(implies(implies(implies(X_1424,X_1424),X_1422),X_1422)) ),
inference(subst,[],[refute_0_29:[bind(X_68,$fot(X_1422)),bind(X_69,$fot(implies(X_1424,X_1424))),bind(X_70,$fot(X_1422))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_313)),X_314),X_313),X_313))
| ~ is_a_theorem(implies(implies(not(not(X_313)),X_314),X_313))
| is_a_theorem(X_313) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_313)),X_314),X_313))),bind(Y,$fot(X_313))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(not(X_309),X_309),X_309)),
inference(subst,[],[cn_2:[bind(X,$fot(X_309))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(X_54,X_55),X_52))
| ~ is_a_theorem(implies(implies(implies(X_54,X_55),X_52),implies(implies(implies(not(X_54),X_53),X_55),X_52)))
| is_a_theorem(implies(implies(implies(not(X_54),X_53),X_55),X_52)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_54,X_55),X_52))),bind(Y,$fot(implies(implies(implies(not(X_54),X_53),X_55),X_52)))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_46),X_45),X_47),implies(X_46,X_47)))
| is_a_theorem(implies(implies(implies(X_46,X_47),Z),implies(implies(implies(not(X_46),X_45),X_47),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(X_46),X_45),X_47))),bind(Y,$fot(implies(X_46,X_47)))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(implies(implies(X_46,X_47),Z),implies(implies(implies(not(X_46),X_45),X_47),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_46),X_45),X_47),implies(X_46,X_47))) )],[refute_0_6,refute_0_34]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(implies(X_54,X_55),X_52),implies(implies(implies(not(X_54),X_53),X_55),X_52))),
inference(subst,[],[refute_0_35:[bind(Z,$fot(X_52)),bind(X_45,$fot(X_53)),bind(X_46,$fot(X_54)),bind(X_47,$fot(X_55))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(X_54,X_55),X_52))
| is_a_theorem(implies(implies(implies(not(X_54),X_53),X_55),X_52)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_54,X_55),X_52),implies(implies(implies(not(X_54),X_53),X_55),X_52))) )],[refute_0_36,refute_0_33]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(not(X_309),X_309),X_309))
| is_a_theorem(implies(implies(implies(not(not(X_309)),X_310),X_309),X_309)) ),
inference(subst,[],[refute_0_37:[bind(X_52,$fot(X_309)),bind(X_53,$fot(X_310)),bind(X_54,$fot(not(X_309))),bind(X_55,$fot(X_309))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(not(not(X_309)),X_310),X_309),X_309)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_309),X_309),X_309)) )],[refute_0_32,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(not(not(X_313)),X_314),X_313),X_313)),
inference(subst,[],[refute_0_39:[bind(X_309,$fot(X_313)),bind(X_310,$fot(X_314))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(not(not(X_313)),X_314),X_313))
| is_a_theorem(X_313) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_313)),X_314),X_313),X_313)) )],[refute_0_40,refute_0_31]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418))),X_314),implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418)))
| is_a_theorem(implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418)) ),
inference(subst,[],[refute_0_41:[bind(X_313,$fot(implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418)))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_204,X_204)),X_203),X_202),implies(X_205,X_202)))
| ~ is_a_theorem(implies(implies(not(implies(X_204,X_204)),X_203),X_202))
| is_a_theorem(implies(X_205,X_202)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(X_204,X_204)),X_203),X_202))),bind(Y,$fot(implies(X_205,X_202)))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(X_164,implies(not(implies(X_163,X_163)),X_162)))
| is_a_theorem(implies(implies(implies(not(implies(X_163,X_163)),X_162),Z),implies(X_164,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_164)),bind(Y,$fot(implies(not(implies(X_163,X_163)),X_162)))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(not(X_46),X_159),implies(not(implies(X_161,X_161)),X_159)))
| is_a_theorem(implies(X_46,implies(not(implies(X_161,X_161)),X_159))) ),
inference(subst,[],[refute_0_7:[bind(X_45,$fot(X_159)),bind(X_47,$fot(implies(not(implies(X_161,X_161)),X_159)))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(not(implies(X_139,X_139)),X_138))
| is_a_theorem(implies(implies(X_138,Z),implies(not(implies(X_139,X_139)),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(X_139,X_139)))),bind(Y,$fot(X_138))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(X_137,X_137))
| is_a_theorem(implies(not(implies(X_137,X_137)),Y)) ),
inference(subst,[],[refute_0_49:[bind(X_6,$fot(implies(X_137,X_137)))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(not(X_136),X_136),X_136)),
inference(subst,[],[cn_2:[bind(X,$fot(X_136))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(not(X_136),X_136),X_136))
| is_a_theorem(implies(X_136,X_136)) ),
inference(subst,[],[refute_0_7:[bind(X_45,$fot(X_136)),bind(X_46,$fot(X_136)),bind(X_47,$fot(X_136))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_136,X_136)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_136),X_136),X_136)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(X_137,X_137)),
inference(subst,[],[refute_0_53:[bind(X_136,$fot(X_137))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(not(implies(X_137,X_137)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_137,X_137)) )],[refute_0_54,refute_0_50]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(not(implies(X_139,X_139)),X_138)),
inference(subst,[],[refute_0_55:[bind(Y,$fot(X_138)),bind(X_137,$fot(X_139))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(X_138,Z),implies(not(implies(X_139,X_139)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_139,X_139)),X_138)) )],[refute_0_56,refute_0_46]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(not(X_46),X_159),implies(not(implies(X_161,X_161)),X_159))),
inference(subst,[],[refute_0_57:[bind(Z,$fot(X_159)),bind(X_138,$fot(not(X_46))),bind(X_139,$fot(X_161))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(X_46,implies(not(implies(X_161,X_161)),X_159))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_46),X_159),implies(not(implies(X_161,X_161)),X_159))) )],[refute_0_58,refute_0_45]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(X_164,implies(not(implies(X_163,X_163)),X_162))),
inference(subst,[],[refute_0_59:[bind(X_159,$fot(X_162)),bind(X_161,$fot(X_163)),bind(X_46,$fot(X_164))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(not(implies(X_163,X_163)),X_162),Z),implies(X_164,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_164,implies(not(implies(X_163,X_163)),X_162))) )],[refute_0_60,refute_0_44]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(implies(not(implies(X_204,X_204)),X_203),X_202),implies(X_205,X_202))),
inference(subst,[],[refute_0_61:[bind(Z,$fot(X_202)),bind(X_162,$fot(X_203)),bind(X_163,$fot(X_204)),bind(X_164,$fot(X_205))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_204,X_204)),X_203),X_202))
| is_a_theorem(implies(X_205,X_202)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_204,X_204)),X_203),X_202),implies(X_205,X_202))) )],[refute_0_62,refute_0_43]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_1415,X_1415)),implies(X_1415,X_1415)),implies(implies(implies(not(implies(X_1417,X_1417)),X_1416),X_1415),X_1415)))
| is_a_theorem(implies(X_205,implies(implies(implies(not(implies(X_1417,X_1417)),X_1416),X_1415),X_1415))) ),
inference(subst,[],[refute_0_63:[bind(X_202,$fot(implies(implies(implies(not(implies(X_1417,X_1417)),X_1416),X_1415),X_1415))),bind(X_203,$fot(implies(X_1415,X_1415))),bind(X_204,$fot(X_1415))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(X_30,X_31))
| ~ is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31)))
| is_a_theorem(implies(implies(not(X_30),X_30),X_31)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_30,X_31))),bind(Y,$fot(implies(implies(not(X_30),X_30),X_31)))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(X_30,X_31))
| is_a_theorem(implies(implies(not(X_30),X_30),X_31)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) )],[refute_0_21,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(X_1410,X_1411),implies(implies(implies(not(implies(X_1413,X_1413)),X_1412),X_1410),X_1411)))
| is_a_theorem(implies(implies(not(implies(X_1410,X_1411)),implies(X_1410,X_1411)),implies(implies(implies(not(implies(X_1413,X_1413)),X_1412),X_1410),X_1411))) ),
inference(subst,[],[refute_0_66:[bind(X_30,$fot(implies(X_1410,X_1411))),bind(X_31,$fot(implies(implies(implies(not(implies(X_1413,X_1413)),X_1412),X_1410),X_1411)))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_204,X_204)),X_203),X_202),implies(X_205,X_202)))
| is_a_theorem(implies(implies(implies(X_205,X_202),Z),implies(implies(implies(not(implies(X_204,X_204)),X_203),X_202),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(implies(X_204,X_204)),X_203),X_202))),bind(Y,$fot(implies(X_205,X_202)))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(implies(X_205,X_202),Z),implies(implies(implies(not(implies(X_204,X_204)),X_203),X_202),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_204,X_204)),X_203),X_202),implies(X_205,X_202))) )],[refute_0_62,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(not(X_1338),X_1338),X_1339),implies(implies(implies(not(implies(X_204,X_204)),X_203),X_1338),X_1339))),
inference(subst,[],[refute_0_69:[bind(Z,$fot(X_1339)),bind(X_202,$fot(X_1338)),bind(X_205,$fot(not(X_1338)))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1338),X_1338),X_1339),implies(implies(implies(not(implies(X_204,X_204)),X_203),X_1338),X_1339)))
| is_a_theorem(implies(implies(X_1338,X_1339),implies(implies(implies(not(implies(X_204,X_204)),X_203),X_1338),X_1339))) ),
inference(subst,[],[refute_0_29:[bind(X_68,$fot(implies(implies(implies(not(implies(X_204,X_204)),X_203),X_1338),X_1339))),bind(X_69,$fot(X_1338)),bind(X_70,$fot(X_1339))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(X_1338,X_1339),implies(implies(implies(not(implies(X_204,X_204)),X_203),X_1338),X_1339))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1338),X_1338),X_1339),implies(implies(implies(not(implies(X_204,X_204)),X_203),X_1338),X_1339))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(X_1410,X_1411),implies(implies(implies(not(implies(X_1413,X_1413)),X_1412),X_1410),X_1411))),
inference(subst,[],[refute_0_72:[bind(X_1338,$fot(X_1410)),bind(X_1339,$fot(X_1411)),bind(X_203,$fot(X_1412)),bind(X_204,$fot(X_1413))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(not(implies(X_1410,X_1411)),implies(X_1410,X_1411)),implies(implies(implies(not(implies(X_1413,X_1413)),X_1412),X_1410),X_1411))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1410,X_1411),implies(implies(implies(not(implies(X_1413,X_1413)),X_1412),X_1410),X_1411))) )],[refute_0_73,refute_0_67]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(not(implies(X_1415,X_1415)),implies(X_1415,X_1415)),implies(implies(implies(not(implies(X_1417,X_1417)),X_1416),X_1415),X_1415))),
inference(subst,[],[refute_0_74:[bind(X_1410,$fot(X_1415)),bind(X_1411,$fot(X_1415)),bind(X_1412,$fot(X_1416)),bind(X_1413,$fot(X_1417))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(X_205,implies(implies(implies(not(implies(X_1417,X_1417)),X_1416),X_1415),X_1415))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(X_1415,X_1415)),implies(X_1415,X_1415)),implies(implies(implies(not(implies(X_1417,X_1417)),X_1416),X_1415),X_1415))) )],[refute_0_75,refute_0_64]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418))),X_314),implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418))),
inference(subst,[],[refute_0_76:[bind(X_1415,$fot(X_1418)),bind(X_1416,$fot(X_1419)),bind(X_1417,$fot(X_1420)),bind(X_205,$fot(implies(not(not(implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418))),X_314)))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418))),X_314),implies(implies(implies(not(implies(X_1420,X_1420)),X_1419),X_1418),X_1418))) )],[refute_0_77,refute_0_42]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(implies(not(implies(X_1424,X_1424)),implies(X_1424,X_1424)),X_1422),X_1422)),
inference(subst,[],[refute_0_78:[bind(X_1418,$fot(X_1422)),bind(X_1419,$fot(implies(X_1424,X_1424))),bind(X_1420,$fot(X_1424))]]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(implies(implies(X_1424,X_1424),X_1422),X_1422)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_1424,X_1424)),implies(X_1424,X_1424)),X_1422),X_1422)) )],[refute_0_79,refute_0_30]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(implies(X_1426,X_1426),X_1425),X_1425)),
inference(subst,[],[refute_0_80:[bind(X_1422,$fot(X_1425)),bind(X_1424,$fot(X_1426))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1426),X_1426),X_1426),X_1425),X_1425)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1426,X_1426),X_1425),X_1425)) )],[refute_0_81,refute_0_27]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(implies(implies(not(X_2345),X_2345),X_2345),implies(X_2343,X_2345)),implies(X_2343,X_2345))),
inference(subst,[],[refute_0_82:[bind(X_1425,$fot(implies(X_2343,X_2345))),bind(X_1426,$fot(X_2345))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_2345),X_2345),X_2345),implies(X_2343,X_2345)),implies(X_2343,X_2345)))
| is_a_theorem(implies(implies(X_2343,implies(not(X_2345),X_2345)),implies(X_2343,X_2345))) ),
inference(subst,[],[refute_0_13:[bind(X_87,$fot(X_2343)),bind(X_88,$fot(implies(not(X_2345),X_2345))),bind(X_89,$fot(X_2345)),bind(X_90,$fot(implies(X_2343,X_2345)))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(X_2343,implies(not(X_2345),X_2345)),implies(X_2343,X_2345))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_2345),X_2345),X_2345),implies(X_2343,X_2345)),implies(X_2343,X_2345))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(implies(X_88,X_2348),implies(not(X_2348),X_2348)),implies(implies(X_88,X_2348),X_2348))),
inference(subst,[],[refute_0_85:[bind(X_2343,$fot(implies(X_88,X_2348))),bind(X_2345,$fot(X_2348))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(implies(not(X_2348),X_88),implies(implies(X_88,X_2348),X_2348))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_88,X_2348),implies(not(X_2348),X_2348)),implies(implies(X_88,X_2348),X_2348))) )],[refute_0_86,refute_0_14]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(implies(not(X_2371),X_2372),implies(implies(X_2372,X_2371),X_2371))),
inference(subst,[],[refute_0_87:[bind(X_2348,$fot(X_2371)),bind(X_88,$fot(X_2372))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(X_2371,implies(implies(X_2372,X_2371),X_2371))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_2371),X_2372),implies(implies(X_2372,X_2371),X_2371))) )],[refute_0_88,refute_0_8]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(x,implies(implies(y,x),x))),
inference(subst,[],[refute_0_89:[bind(X_2371,$fot(x)),bind(X_2372,$fot(y))]]) ).
cnf(refute_0_91,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(x,implies(implies(y,x),x))) )],[refute_0_90,prove_cn_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL367-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.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 : Mon Jul 4 20:18:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.22/1.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.22/1.42
% 1.22/1.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.22/1.43
%------------------------------------------------------------------------------