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  
%------------------------------------------------------------------------------