TSTP Solution File: LCL080-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL080-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 12:49:17 EDT 2022
% Result : Unsatisfiable 2.72s 2.90s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of clauses : 69 ( 39 unt; 0 nHn; 20 RR)
% Number of literals : 107 ( 0 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 223 ( 60 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(ic_2,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(ic_3,axiom,
is_a_theorem(implies(implies(implies(X,Y),X),X)) ).
cnf(ic_4,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(prove_ic_JLukasiewicz,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(X_1211,implies(X_1211,X_1212)))
| ~ is_a_theorem(implies(implies(X_1211,implies(X_1211,X_1212)),implies(X_1211,X_1212)))
| is_a_theorem(implies(X_1211,X_1212)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1211,implies(X_1211,X_1212)))),bind(Y,$fot(implies(X_1211,X_1212)))]]) ).
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,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[ic_4,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X_69,X_70),implies(implies(implies(X_69,X_68),X_69),X_70)))
| is_a_theorem(implies(implies(implies(implies(implies(X_69,X_68),X_69),X_70),Z),implies(implies(X_69,X_70),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_69,X_70))),bind(Y,$fot(implies(implies(implies(X_69,X_68),X_69),X_70)))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(X_52,Y),X_52),X_52)),
inference(subst,[],[ic_3:[bind(X,$fot(X_52))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(X_52,Y),X_52),X_52))
| is_a_theorem(implies(implies(X_52,X_53),implies(implies(implies(X_52,Y),X_52),X_53))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(X_52,Y),X_52))),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(X_52,X_53),implies(implies(implies(X_52,Y),X_52),X_53))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_52,Y),X_52),X_52)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(X_69,X_70),implies(implies(implies(X_69,X_68),X_69),X_70))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(X_68)),bind(X_52,$fot(X_69)),bind(X_53,$fot(X_70))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_69,X_68),X_69),X_70),Z),implies(implies(X_69,X_70),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_69,X_70),implies(implies(implies(X_69,X_68),X_69),X_70))) )],[refute_0_7,refute_0_3]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_1210,X_68),X_1210),implies(X_1210,X_68)),implies(X_1210,X_68)),implies(implies(X_1210,implies(X_1210,X_68)),implies(X_1210,X_68)))),
inference(subst,[],[refute_0_8:[bind(Z,$fot(implies(X_1210,X_68))),bind(X_69,$fot(X_1210)),bind(X_70,$fot(implies(X_1210,X_68)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_473,X_474),X_473),X_473),X_472))
| ~ is_a_theorem(implies(implies(implies(implies(implies(X_473,X_474),X_473),X_473),X_472),X_472))
| is_a_theorem(X_472) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_473,X_474),X_473),X_473),X_472))),bind(Y,$fot(X_472))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(X_9,Y),X_9),X_9)),
inference(subst,[],[ic_3:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(X_9,Y),X_9))
| ~ is_a_theorem(implies(implies(implies(X_9,Y),X_9),X_9))
| is_a_theorem(X_9) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_9,Y),X_9))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(X_9,Y),X_9))
| is_a_theorem(X_9) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_9,Y),X_9),X_9)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467),X_467),implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467)))
| is_a_theorem(implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467)) ),
inference(subst,[],[refute_0_13:[bind(Y,$fot(X_467)),bind(X_9,$fot(implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467)))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_61,X_62),X_61),X_61),X_64),implies(X_63,X_64)))
| is_a_theorem(implies(implies(implies(X_63,X_64),Z),implies(implies(implies(implies(implies(X_61,X_62),X_61),X_61),X_64),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(implies(implies(X_61,X_62),X_61),X_61),X_64))),bind(Y,$fot(implies(X_63,X_64)))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_8,implies(Y,X_8))),
inference(subst,[],[ic_2:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(X_8)
| ~ is_a_theorem(implies(X_8,implies(Y,X_8)))
| is_a_theorem(implies(Y,X_8)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_8)),bind(Y,$fot(implies(Y,X_8)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X_8)
| is_a_theorem(implies(Y,X_8)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_8,implies(Y,X_8))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X),X))
| is_a_theorem(implies(X_12,implies(implies(implies(X,Y),X),X))) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(X_12)),bind(X_8,$fot(implies(implies(implies(X,Y),X),X)))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(X_12,implies(implies(implies(X,Y),X),X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X),X)) )],[ic_3,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_51,implies(implies(implies(X,Y),X),X))),
inference(subst,[],[refute_0_20:[bind(X_12,$fot(X_51))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(X_51,implies(implies(implies(X,Y),X),X)))
| is_a_theorem(implies(implies(implies(implies(implies(X,Y),X),X),X_53),implies(X_51,X_53))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_51)),bind(Y,$fot(implies(implies(implies(X,Y),X),X))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),X),X),X_53),implies(X_51,X_53))),
inference(resolve,[$cnf( is_a_theorem(implies(X_51,implies(implies(implies(X,Y),X),X))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_61,X_62),X_61),X_61),X_64),implies(X_63,X_64))),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_61)),bind(Y,$fot(X_62)),bind(X_51,$fot(X_63)),bind(X_53,$fot(X_64))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(implies(X_63,X_64),Z),implies(implies(implies(implies(implies(X_61,X_62),X_61),X_61),X_64),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_61,X_62),X_61),X_61),X_64),implies(X_63,X_64))) )],[refute_0_24,refute_0_15]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467),X_467),implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467))),
inference(subst,[],[refute_0_25:[bind(Z,$fot(X_467)),bind(X_61,$fot(X_468)),bind(X_62,$fot(X_469)),bind(X_63,$fot(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467))),bind(X_64,$fot(X_467))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467),X_467),implies(implies(implies(implies(implies(X_468,X_469),X_468),X_468),X_467),X_467))) )],[refute_0_26,refute_0_14]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_473,X_474),X_473),X_473),X_472),X_472)),
inference(subst,[],[refute_0_27:[bind(X_467,$fot(X_472)),bind(X_468,$fot(X_473)),bind(X_469,$fot(X_474))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_473,X_474),X_473),X_473),X_472))
| is_a_theorem(X_472) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_473,X_474),X_473),X_473),X_472),X_472)) )],[refute_0_28,refute_0_10]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_1210,X_68),X_1210),implies(X_1210,X_68)),implies(X_1210,X_68)),implies(implies(X_1210,implies(X_1210,X_68)),implies(X_1210,X_68))))
| is_a_theorem(implies(implies(X_1210,implies(X_1210,X_68)),implies(X_1210,X_68))) ),
inference(subst,[],[refute_0_29:[bind(X_472,$fot(implies(implies(X_1210,implies(X_1210,X_68)),implies(X_1210,X_68)))),bind(X_473,$fot(implies(X_1210,X_68))),bind(X_474,$fot(X_1210))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(X_1210,implies(X_1210,X_68)),implies(X_1210,X_68))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_1210,X_68),X_1210),implies(X_1210,X_68)),implies(X_1210,X_68)),implies(implies(X_1210,implies(X_1210,X_68)),implies(X_1210,X_68)))) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(X_1211,implies(X_1211,X_1212)),implies(X_1211,X_1212))),
inference(subst,[],[refute_0_31:[bind(X_1210,$fot(X_1211)),bind(X_68,$fot(X_1212))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(X_1211,implies(X_1211,X_1212)))
| is_a_theorem(implies(X_1211,X_1212)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1211,implies(X_1211,X_1212)),implies(X_1211,X_1212))) )],[refute_0_32,refute_0_0]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(X_4607,X_4609),implies(X_4610,X_4609)))))
| is_a_theorem(implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(X_4607,X_4609),implies(X_4610,X_4609)))) ),
inference(subst,[],[refute_0_33:[bind(X_1211,$fot(implies(implies(X_4609,X_4608),X_4607))),bind(X_1212,$fot(implies(implies(X_4607,X_4609),implies(X_4610,X_4609))))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(X_132,X_133),implies(X_131,X_133)),X_134))
| ~ is_a_theorem(implies(implies(implies(implies(X_132,X_133),implies(X_131,X_133)),X_134),implies(implies(X_131,X_132),X_134)))
| is_a_theorem(implies(implies(X_131,X_132),X_134)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_132,X_133),implies(X_131,X_133)),X_134))),bind(Y,$fot(implies(implies(X_131,X_132),X_134)))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_53),implies(implies(X,Y),X_53))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_53),implies(implies(X,Y),X_53))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[ic_4,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(implies(X_132,X_133),implies(X_131,X_133)),X_134),implies(implies(X_131,X_132),X_134))),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_131)),bind(Y,$fot(X_132)),bind(Z,$fot(X_133)),bind(X_53,$fot(X_134))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(implies(X_132,X_133),implies(X_131,X_133)),X_134))
| is_a_theorem(implies(implies(X_131,X_132),X_134)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_132,X_133),implies(X_131,X_133)),X_134),implies(implies(X_131,X_132),X_134))) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(implies(X_132,X_4078),implies(implies(X_4078,X_4077),X_4078)),implies(X_4080,implies(implies(X_132,X_4078),implies(X_4079,X_4078)))))
| is_a_theorem(implies(implies(implies(X_4078,X_4077),X_132),implies(X_4080,implies(implies(X_132,X_4078),implies(X_4079,X_4078))))) ),
inference(subst,[],[refute_0_39:[bind(X_131,$fot(implies(X_4078,X_4077))),bind(X_133,$fot(X_4078)),bind(X_134,$fot(implies(X_4080,implies(implies(X_132,X_4078),implies(X_4079,X_4078)))))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(X_173,implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171))))
| is_a_theorem(implies(implies(implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171)),Z),implies(X_173,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_173)),bind(Y,$fot(implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171))))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(X_109,implies(X_110,X_109)),implies(implies(implies(X_109,Y),X_109),implies(X_110,X_109)))),
inference(subst,[],[refute_0_6:[bind(X_52,$fot(X_109)),bind(X_53,$fot(implies(X_110,X_109)))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(X_87,implies(X_88,X_87)),X_90))
| ~ is_a_theorem(implies(implies(implies(X_87,implies(X_88,X_87)),X_90),implies(X_89,X_90)))
| is_a_theorem(implies(X_89,X_90)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_87,implies(X_88,X_87)),X_90))),bind(Y,$fot(implies(X_89,X_90)))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(X,implies(Y,X)))
| is_a_theorem(implies(X_12,implies(X,implies(Y,X)))) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(X_12)),bind(X_8,$fot(implies(X,implies(Y,X))))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(X_12,implies(X,implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(X,implies(Y,X))) )],[ic_2,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(X_51,implies(X,implies(Y,X)))),
inference(subst,[],[refute_0_45:[bind(X_12,$fot(X_51))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(X_51,implies(X,implies(Y,X))))
| is_a_theorem(implies(implies(implies(X,implies(Y,X)),X_53),implies(X_51,X_53))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_51)),bind(Y,$fot(implies(X,implies(Y,X)))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(implies(X,implies(Y,X)),X_53),implies(X_51,X_53))),
inference(resolve,[$cnf( is_a_theorem(implies(X_51,implies(X,implies(Y,X)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(X_87,implies(X_88,X_87)),X_90),implies(X_89,X_90))),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_87)),bind(Y,$fot(X_88)),bind(X_51,$fot(X_89)),bind(X_53,$fot(X_90))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(implies(X_87,implies(X_88,X_87)),X_90))
| is_a_theorem(implies(X_89,X_90)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_87,implies(X_88,X_87)),X_90),implies(X_89,X_90))) )],[refute_0_49,refute_0_43]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(X_109,implies(X_110,X_109)),implies(implies(implies(X_109,Y),X_109),implies(X_110,X_109))))
| is_a_theorem(implies(X_111,implies(implies(implies(X_109,Y),X_109),implies(X_110,X_109)))) ),
inference(subst,[],[refute_0_50:[bind(X_87,$fot(X_109)),bind(X_88,$fot(X_110)),bind(X_89,$fot(X_111)),bind(X_90,$fot(implies(implies(implies(X_109,Y),X_109),implies(X_110,X_109))))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(X_111,implies(implies(implies(X_109,Y),X_109),implies(X_110,X_109)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_109,implies(X_110,X_109)),implies(implies(implies(X_109,Y),X_109),implies(X_110,X_109)))) )],[refute_0_42,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_173,implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171)))),
inference(subst,[],[refute_0_52:[bind(Y,$fot(X_170)),bind(X_109,$fot(X_171)),bind(X_110,$fot(X_172)),bind(X_111,$fot(X_173))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171)),Z),implies(X_173,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_173,implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171)))) )],[refute_0_53,refute_0_41]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171)),implies(X_2654,implies(X_172,X_171))),implies(X_173,implies(X_2654,implies(X_172,X_171))))),
inference(subst,[],[refute_0_54:[bind(Z,$fot(implies(X_2654,implies(X_172,X_171))))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171)),implies(X_2654,implies(X_172,X_171))),implies(X_173,implies(X_2654,implies(X_172,X_171)))))
| is_a_theorem(implies(implies(X_2654,implies(implies(X_171,X_170),X_171)),implies(X_173,implies(X_2654,implies(X_172,X_171))))) ),
inference(subst,[],[refute_0_39:[bind(X_131,$fot(X_2654)),bind(X_132,$fot(implies(implies(X_171,X_170),X_171))),bind(X_133,$fot(implies(X_172,X_171))),bind(X_134,$fot(implies(X_173,implies(X_2654,implies(X_172,X_171)))))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(X_2654,implies(implies(X_171,X_170),X_171)),implies(X_173,implies(X_2654,implies(X_172,X_171))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_171,X_170),X_171),implies(X_172,X_171)),implies(X_2654,implies(X_172,X_171))),implies(X_173,implies(X_2654,implies(X_172,X_171))))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(X_132,X_4078),implies(implies(X_4078,X_4077),X_4078)),implies(X_4080,implies(implies(X_132,X_4078),implies(X_4079,X_4078))))),
inference(subst,[],[refute_0_57:[bind(X_170,$fot(X_4077)),bind(X_171,$fot(X_4078)),bind(X_172,$fot(X_4079)),bind(X_173,$fot(X_4080)),bind(X_2654,$fot(implies(X_132,X_4078)))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(implies(implies(X_4078,X_4077),X_132),implies(X_4080,implies(implies(X_132,X_4078),implies(X_4079,X_4078))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_132,X_4078),implies(implies(X_4078,X_4077),X_4078)),implies(X_4080,implies(implies(X_132,X_4078),implies(X_4079,X_4078))))) )],[refute_0_58,refute_0_40]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(X_4607,X_4609),implies(X_4610,X_4609))))),
inference(subst,[],[refute_0_59:[bind(X_132,$fot(X_4607)),bind(X_4077,$fot(X_4608)),bind(X_4078,$fot(X_4609)),bind(X_4079,$fot(X_4610)),bind(X_4080,$fot(implies(implies(X_4609,X_4608),X_4607)))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(X_4607,X_4609),implies(X_4610,X_4609)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(implies(X_4609,X_4608),X_4607),implies(implies(X_4607,X_4609),implies(X_4610,X_4609))))) )],[refute_0_60,refute_0_34]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
inference(subst,[],[refute_0_61:[bind(X_4607,$fot(c)),bind(X_4608,$fot(b)),bind(X_4609,$fot(a)),bind(X_4610,$fot(e))]]) ).
cnf(refute_0_63,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))) )],[refute_0_62,prove_ic_JLukasiewicz]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : LCL080-2 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 14:22:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.72/2.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.72/2.90
% 2.72/2.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.72/2.90
%------------------------------------------------------------------------------