TSTP Solution File: LCL076-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL076-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:49:14 EDT 2022

% Result   : Unsatisfiable 0.19s 0.52s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   46 (  26 unt;   0 nHn;  20 RR)
%            Number of literals    :   72 (   0 equ;  27 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   97 (  17 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
    ( ~ is_a_theorem(implies(X,Y))
    | ~ is_a_theorem(X)
    | is_a_theorem(Y) ) ).

cnf(cn_18,axiom,
    is_a_theorem(implies(X,implies(Y,X))) ).

cnf(cn_35,axiom,
    is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).

cnf(cn_49,axiom,
    is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).

cnf(prove_cn_40,negated_conjecture,
    ~ is_a_theorem(implies(a,not(not(a)))) ).

cnf(refute_0_0,plain,
    ( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
    | ~ is_a_theorem(implies(not(X),not(Y)))
    | is_a_theorem(implies(Y,X)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).

cnf(refute_0_1,plain,
    ( ~ is_a_theorem(implies(not(X),not(Y)))
    | is_a_theorem(implies(Y,X)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ is_a_theorem(implies(not(not(not(Y))),not(Y)))
    | is_a_theorem(implies(Y,not(not(Y)))) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(not(not(Y))))]]) ).

cnf(refute_0_3,plain,
    is_a_theorem(implies(X_7,implies(Y,X_7))),
    inference(subst,[],[cn_18:[bind(X,$fot(X_7))]]) ).

cnf(refute_0_4,plain,
    ( ~ is_a_theorem(X_7)
    | ~ is_a_theorem(implies(X_7,implies(Y,X_7)))
    | is_a_theorem(implies(Y,X_7)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(X_7)),bind(Y,$fot(implies(Y,X_7)))]]) ).

cnf(refute_0_5,plain,
    ( ~ is_a_theorem(X_7)
    | is_a_theorem(implies(Y,X_7)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(X_7,implies(Y,X_7))) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ is_a_theorem(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))
    | is_a_theorem(implies(Y,implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))) ),
    inference(subst,[],[refute_0_5:[bind(X_7,$fot(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))))]]) ).

cnf(refute_0_7,plain,
    is_a_theorem(implies(implies(not(X_30),not(X_29)),implies(X_29,X_30))),
    inference(subst,[],[cn_49:[bind(X,$fot(X_30)),bind(Y,$fot(X_29))]]) ).

cnf(refute_0_8,plain,
    ( ~ is_a_theorem(implies(X,implies(Y,Z)))
    | ~ is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z))))
    | is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,implies(Y,Z)))),bind(Y,$fot(implies(implies(X,Y),implies(X,Z))))]]) ).

cnf(refute_0_9,plain,
    ( ~ is_a_theorem(implies(X,implies(Y,Z)))
    | is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) )],[cn_35,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ is_a_theorem(implies(implies(not(X_30),not(X_29)),implies(X_29,X_30)))
    | is_a_theorem(implies(implies(implies(not(X_30),not(X_29)),X_29),implies(implies(not(X_30),not(X_29)),X_30))) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(implies(not(X_30),not(X_29)))),bind(Y,$fot(X_29)),bind(Z,$fot(X_30))]]) ).

cnf(refute_0_11,plain,
    is_a_theorem(implies(implies(implies(not(X_30),not(X_29)),X_29),implies(implies(not(X_30),not(X_29)),X_30))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_30),not(X_29)),implies(X_29,X_30))) )],[refute_0_7,refute_0_10]) ).

cnf(refute_0_12,plain,
    is_a_theorem(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))),
    inference(subst,[],[refute_0_11:[bind(X_29,$fot(X_41)),bind(X_30,$fot(X_42))]]) ).

cnf(refute_0_13,plain,
    is_a_theorem(implies(Y,implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))) )],[refute_0_12,refute_0_6]) ).

cnf(refute_0_14,plain,
    is_a_theorem(implies(not(not(X_529)),implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))),
    inference(subst,[],[refute_0_13:[bind(Y,$fot(not(not(X_529))))]]) ).

cnf(refute_0_15,plain,
    ( ~ is_a_theorem(implies(implies(not(not(X_420)),X_421),implies(not(not(X_420)),X_420)))
    | ~ is_a_theorem(implies(not(not(X_420)),X_421))
    | is_a_theorem(implies(not(not(X_420)),X_420)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(not(X_420)),X_421))),bind(Y,$fot(implies(not(not(X_420)),X_420)))]]) ).

cnf(refute_0_16,plain,
    ( ~ is_a_theorem(implies(not(not(X_395)),implies(X_396,X_395)))
    | is_a_theorem(implies(implies(not(not(X_395)),X_396),implies(not(not(X_395)),X_395))) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(not(not(X_395)))),bind(Y,$fot(X_396)),bind(Z,$fot(X_395))]]) ).

cnf(refute_0_17,plain,
    ( ~ is_a_theorem(implies(X_53,implies(not(X_51),not(X_52))))
    | ~ is_a_theorem(implies(implies(X_53,implies(not(X_51),not(X_52))),implies(X_53,implies(X_52,X_51))))
    | is_a_theorem(implies(X_53,implies(X_52,X_51))) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_53,implies(not(X_51),not(X_52))))),bind(Y,$fot(implies(X_53,implies(X_52,X_51))))]]) ).

cnf(refute_0_18,plain,
    ( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
    | is_a_theorem(implies(X_9,implies(implies(not(X),not(Y)),implies(Y,X)))) ),
    inference(subst,[],[refute_0_5:[bind(Y,$fot(X_9)),bind(X_7,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).

cnf(refute_0_19,plain,
    is_a_theorem(implies(X_9,implies(implies(not(X),not(Y)),implies(Y,X)))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_18]) ).

cnf(refute_0_20,plain,
    is_a_theorem(implies(X_28,implies(implies(not(X),not(Y)),implies(Y,X)))),
    inference(subst,[],[refute_0_19:[bind(X_9,$fot(X_28))]]) ).

cnf(refute_0_21,plain,
    ( ~ is_a_theorem(implies(X_28,implies(implies(not(X),not(Y)),implies(Y,X))))
    | is_a_theorem(implies(implies(X_28,implies(not(X),not(Y))),implies(X_28,implies(Y,X)))) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(X_28)),bind(Y,$fot(implies(not(X),not(Y)))),bind(Z,$fot(implies(Y,X)))]]) ).

cnf(refute_0_22,plain,
    is_a_theorem(implies(implies(X_28,implies(not(X),not(Y))),implies(X_28,implies(Y,X)))),
    inference(resolve,[$cnf( is_a_theorem(implies(X_28,implies(implies(not(X),not(Y)),implies(Y,X)))) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    is_a_theorem(implies(implies(X_53,implies(not(X_51),not(X_52))),implies(X_53,implies(X_52,X_51)))),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(X_28,$fot(X_53))]]) ).

cnf(refute_0_24,plain,
    ( ~ is_a_theorem(implies(X_53,implies(not(X_51),not(X_52))))
    | is_a_theorem(implies(X_53,implies(X_52,X_51))) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(X_53,implies(not(X_51),not(X_52))),implies(X_53,implies(X_52,X_51)))) )],[refute_0_23,refute_0_17]) ).

cnf(refute_0_25,plain,
    ( ~ is_a_theorem(implies(not(not(X_51)),implies(not(X_51),not(X_52))))
    | is_a_theorem(implies(not(not(X_51)),implies(X_52,X_51))) ),
    inference(subst,[],[refute_0_24:[bind(X_53,$fot(not(not(X_51))))]]) ).

cnf(refute_0_26,plain,
    is_a_theorem(implies(not(X_389),implies(not(X_388),not(X_389)))),
    inference(subst,[],[cn_18:[bind(X,$fot(not(X_389))),bind(Y,$fot(not(X_388)))]]) ).

cnf(refute_0_27,plain,
    ( ~ is_a_theorem(implies(not(X_389),implies(not(X_388),not(X_389))))
    | is_a_theorem(implies(not(X_389),implies(X_389,X_388))) ),
    inference(subst,[],[refute_0_24:[bind(X_51,$fot(X_388)),bind(X_52,$fot(X_389)),bind(X_53,$fot(not(X_389)))]]) ).

cnf(refute_0_28,plain,
    is_a_theorem(implies(not(X_389),implies(X_389,X_388))),
    inference(resolve,[$cnf( is_a_theorem(implies(not(X_389),implies(not(X_388),not(X_389)))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    is_a_theorem(implies(not(not(X_51)),implies(not(X_51),not(X_52)))),
    inference(subst,[],[refute_0_28:[bind(X_388,$fot(not(X_52))),bind(X_389,$fot(not(X_51)))]]) ).

cnf(refute_0_30,plain,
    is_a_theorem(implies(not(not(X_51)),implies(X_52,X_51))),
    inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_51)),implies(not(X_51),not(X_52)))) )],[refute_0_29,refute_0_25]) ).

cnf(refute_0_31,plain,
    is_a_theorem(implies(not(not(X_395)),implies(X_396,X_395))),
    inference(subst,[],[refute_0_30:[bind(X_51,$fot(X_395)),bind(X_52,$fot(X_396))]]) ).

cnf(refute_0_32,plain,
    is_a_theorem(implies(implies(not(not(X_395)),X_396),implies(not(not(X_395)),X_395))),
    inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_395)),implies(X_396,X_395))) )],[refute_0_31,refute_0_16]) ).

cnf(refute_0_33,plain,
    is_a_theorem(implies(implies(not(not(X_420)),X_421),implies(not(not(X_420)),X_420))),
    inference(subst,[],[refute_0_32:[bind(X_395,$fot(X_420)),bind(X_396,$fot(X_421))]]) ).

cnf(refute_0_34,plain,
    ( ~ is_a_theorem(implies(not(not(X_420)),X_421))
    | is_a_theorem(implies(not(not(X_420)),X_420)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_420)),X_421),implies(not(not(X_420)),X_420))) )],[refute_0_33,refute_0_15]) ).

cnf(refute_0_35,plain,
    ( ~ is_a_theorem(implies(not(not(X_529)),implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))))
    | is_a_theorem(implies(not(not(X_529)),X_529)) ),
    inference(subst,[],[refute_0_34:[bind(X_420,$fot(X_529)),bind(X_421,$fot(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))))]]) ).

cnf(refute_0_36,plain,
    is_a_theorem(implies(not(not(X_529)),X_529)),
    inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_529)),implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))) )],[refute_0_14,refute_0_35]) ).

cnf(refute_0_37,plain,
    is_a_theorem(implies(not(not(not(Y))),not(Y))),
    inference(subst,[],[refute_0_36:[bind(X_529,$fot(not(Y)))]]) ).

cnf(refute_0_38,plain,
    is_a_theorem(implies(Y,not(not(Y)))),
    inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(Y))),not(Y))) )],[refute_0_37,refute_0_2]) ).

cnf(refute_0_39,plain,
    is_a_theorem(implies(a,not(not(a)))),
    inference(subst,[],[refute_0_38:[bind(Y,$fot(a))]]) ).

cnf(refute_0_40,plain,
    $false,
    inference(resolve,[$cnf( is_a_theorem(implies(a,not(not(a)))) )],[refute_0_39,prove_cn_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL076-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul  3 15:06:59 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52  
% 0.19/0.52  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52  
%------------------------------------------------------------------------------