TSTP Solution File: LCL035-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL035-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 12:48:55 EDT 2022

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   36 (  20 unt;   0 nHn;  13 RR)
%            Number of literals    :   57 (   0 equ;  22 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;   2 con; 0-2 aty)
%            Number of variables   :  120 (  62 sgn)

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

cnf(c0_CAMerideth,axiom,
    is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))) ).

cnf(prove_c0_4,negated_conjecture,
    ~ is_a_theorem(implies(falsehood,a)) ).

cnf(refute_0_0,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3))
    | ~ is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3),implies(implies(X_3,X_4),implies(X_6,X_4))))
    | is_a_theorem(implies(implies(X_3,X_4),implies(X_6,X_4))) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3))),bind(Y,$fot(implies(implies(X_3,X_4),implies(X_6,X_4))))]]) ).

cnf(refute_0_1,plain,
    is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3),implies(implies(X_3,X_4),implies(X_6,X_4)))),
    inference(subst,[],[c0_CAMerideth:[bind(U,$fot(X_2)),bind(V,$fot(X_3)),bind(X,$fot(X_4)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_2,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3))
    | is_a_theorem(implies(implies(X_3,X_4),implies(X_6,X_4))) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3),implies(implies(X_3,X_4),implies(X_6,X_4)))) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_23),implies(falsehood,X_23)))
    | is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))) ),
    inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_23)),bind(X_3,$fot(implies(falsehood,X_23)))]]) ).

cnf(refute_0_4,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(falsehood,falsehood)),X_20),implies(X_18,X_20)))
    | is_a_theorem(implies(implies(implies(X_18,X_20),X_4),implies(falsehood,X_4))) ),
    inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_20)),bind(X_3,$fot(implies(X_18,X_20))),bind(X_6,$fot(falsehood))]]) ).

cnf(refute_0_5,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_16,falsehood),implies(X_14,falsehood)),implies(falsehood,X_13)),implies(X_15,implies(falsehood,X_13))))
    | is_a_theorem(implies(implies(implies(X_15,implies(falsehood,X_13)),X_16),implies(X_14,X_16))) ),
    inference(subst,[],[refute_0_2:[bind(X_2,$fot(implies(falsehood,X_13))),bind(X_3,$fot(implies(X_15,implies(falsehood,X_13)))),bind(X_4,$fot(X_16)),bind(X_5,$fot(falsehood)),bind(X_6,$fot(X_14))]]) ).

cnf(refute_0_6,plain,
    is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),implies(X_11,falsehood)),X_7),implies(implies(X_7,X),implies(Z,X)))),
    inference(subst,[],[c0_CAMerideth:[bind(U,$fot(implies(X_11,falsehood))),bind(V,$fot(X_7))]]) ).

cnf(refute_0_7,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),implies(X_11,falsehood)),X_7),implies(implies(X_7,X),implies(Z,X))))
    | is_a_theorem(implies(implies(implies(implies(X_7,X),implies(Z,X)),implies(X,Y)),implies(X_11,implies(X,Y)))) ),
    inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_7)),bind(X_3,$fot(implies(implies(X_7,X),implies(Z,X)))),bind(X_4,$fot(implies(X,Y))),bind(X_5,$fot(implies(Z,falsehood))),bind(X_6,$fot(X_11))]]) ).

cnf(refute_0_8,plain,
    is_a_theorem(implies(implies(implies(implies(X_7,X),implies(Z,X)),implies(X,Y)),implies(X_11,implies(X,Y)))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),implies(X_11,falsehood)),X_7),implies(implies(X_7,X),implies(Z,X)))) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    is_a_theorem(implies(implies(implies(implies(X_16,falsehood),implies(X_14,falsehood)),implies(falsehood,X_13)),implies(X_15,implies(falsehood,X_13)))),
    inference(subst,[],[refute_0_8:[bind(X,$fot(falsehood)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14)),bind(X_11,$fot(X_15)),bind(X_7,$fot(X_16))]]) ).

cnf(refute_0_10,plain,
    is_a_theorem(implies(implies(implies(X_15,implies(falsehood,X_13)),X_16),implies(X_14,X_16))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_16,falsehood),implies(X_14,falsehood)),implies(falsehood,X_13)),implies(X_15,implies(falsehood,X_13)))) )],[refute_0_9,refute_0_5]) ).

cnf(refute_0_11,plain,
    is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(falsehood,falsehood)),X_20),implies(X_18,X_20))),
    inference(subst,[],[refute_0_10:[bind(X_13,$fot(falsehood)),bind(X_14,$fot(X_18)),bind(X_15,$fot(implies(X_4,X_5))),bind(X_16,$fot(X_20))]]) ).

cnf(refute_0_12,plain,
    is_a_theorem(implies(implies(implies(X_18,X_20),X_4),implies(falsehood,X_4))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(falsehood,falsehood)),X_20),implies(X_18,X_20))) )],[refute_0_11,refute_0_4]) ).

cnf(refute_0_13,plain,
    is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_23),implies(falsehood,X_23))),
    inference(subst,[],[refute_0_12:[bind(X_18,$fot(implies(X_4,X_5))),bind(X_20,$fot(implies(X_6,falsehood))),bind(X_4,$fot(X_23))]]) ).

cnf(refute_0_14,plain,
    is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_23),implies(falsehood,X_23))) )],[refute_0_13,refute_0_3]) ).

cnf(refute_0_15,plain,
    ( ~ is_a_theorem(X_47)
    | ~ is_a_theorem(implies(X_47,implies(falsehood,X_46)))
    | is_a_theorem(implies(falsehood,X_46)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(X_47)),bind(Y,$fot(implies(falsehood,X_46)))]]) ).

cnf(refute_0_16,plain,
    ( ~ is_a_theorem(X_32)
    | ~ is_a_theorem(implies(X_32,implies(X_33,implies(falsehood,X_31))))
    | is_a_theorem(implies(X_33,implies(falsehood,X_31))) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(X_32)),bind(Y,$fot(implies(X_33,implies(falsehood,X_31))))]]) ).

cnf(refute_0_17,plain,
    is_a_theorem(implies(implies(implies(falsehood,X_23),implies(falsehood,X_27)),implies(X_6,implies(falsehood,X_27)))),
    inference(subst,[],[refute_0_14:[bind(X_4,$fot(implies(falsehood,X_27)))]]) ).

cnf(refute_0_18,plain,
    ( ~ is_a_theorem(implies(implies(X_19,implies(falsehood,X_17)),X_20))
    | ~ is_a_theorem(implies(implies(implies(X_19,implies(falsehood,X_17)),X_20),implies(X_18,X_20)))
    | is_a_theorem(implies(X_18,X_20)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_19,implies(falsehood,X_17)),X_20))),bind(Y,$fot(implies(X_18,X_20)))]]) ).

cnf(refute_0_19,plain,
    is_a_theorem(implies(implies(implies(X_19,implies(falsehood,X_17)),X_20),implies(X_18,X_20))),
    inference(subst,[],[refute_0_10:[bind(X_13,$fot(X_17)),bind(X_14,$fot(X_18)),bind(X_15,$fot(X_19)),bind(X_16,$fot(X_20))]]) ).

cnf(refute_0_20,plain,
    ( ~ is_a_theorem(implies(implies(X_19,implies(falsehood,X_17)),X_20))
    | is_a_theorem(implies(X_18,X_20)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_19,implies(falsehood,X_17)),X_20),implies(X_18,X_20))) )],[refute_0_19,refute_0_18]) ).

cnf(refute_0_21,plain,
    ( ~ is_a_theorem(implies(implies(implies(falsehood,X_23),implies(falsehood,X_27)),implies(X_6,implies(falsehood,X_27))))
    | is_a_theorem(implies(X_28,implies(X_6,implies(falsehood,X_27)))) ),
    inference(subst,[],[refute_0_20:[bind(X_17,$fot(X_27)),bind(X_18,$fot(X_28)),bind(X_19,$fot(implies(falsehood,X_23))),bind(X_20,$fot(implies(X_6,implies(falsehood,X_27))))]]) ).

cnf(refute_0_22,plain,
    is_a_theorem(implies(X_28,implies(X_6,implies(falsehood,X_27)))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_23),implies(falsehood,X_27)),implies(X_6,implies(falsehood,X_27)))) )],[refute_0_17,refute_0_21]) ).

cnf(refute_0_23,plain,
    is_a_theorem(implies(X_32,implies(X_33,implies(falsehood,X_31)))),
    inference(subst,[],[refute_0_22:[bind(X_27,$fot(X_31)),bind(X_28,$fot(X_32)),bind(X_6,$fot(X_33))]]) ).

cnf(refute_0_24,plain,
    ( ~ is_a_theorem(X_32)
    | is_a_theorem(implies(X_33,implies(falsehood,X_31))) ),
    inference(resolve,[$cnf( is_a_theorem(implies(X_32,implies(X_33,implies(falsehood,X_31)))) )],[refute_0_23,refute_0_16]) ).

cnf(refute_0_25,plain,
    ( ~ is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4)))
    | is_a_theorem(implies(X_45,implies(falsehood,X_43))) ),
    inference(subst,[],[refute_0_24:[bind(X_31,$fot(X_43)),bind(X_32,$fot(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4)))),bind(X_33,$fot(X_45))]]) ).

cnf(refute_0_26,plain,
    is_a_theorem(implies(X_45,implies(falsehood,X_43))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))) )],[refute_0_14,refute_0_25]) ).

cnf(refute_0_27,plain,
    is_a_theorem(implies(X_47,implies(falsehood,X_46))),
    inference(subst,[],[refute_0_26:[bind(X_43,$fot(X_46)),bind(X_45,$fot(X_47))]]) ).

cnf(refute_0_28,plain,
    ( ~ is_a_theorem(X_47)
    | is_a_theorem(implies(falsehood,X_46)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(X_47,implies(falsehood,X_46))) )],[refute_0_27,refute_0_15]) ).

cnf(refute_0_29,plain,
    ( ~ is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4)))
    | is_a_theorem(implies(falsehood,X_48)) ),
    inference(subst,[],[refute_0_28:[bind(X_46,$fot(X_48)),bind(X_47,$fot(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))))]]) ).

cnf(refute_0_30,plain,
    is_a_theorem(implies(falsehood,X_48)),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))) )],[refute_0_14,refute_0_29]) ).

cnf(refute_0_31,plain,
    is_a_theorem(implies(falsehood,a)),
    inference(subst,[],[refute_0_30:[bind(X_48,$fot(a))]]) ).

cnf(refute_0_32,plain,
    $false,
    inference(resolve,[$cnf( is_a_theorem(implies(falsehood,a)) )],[refute_0_31,prove_c0_4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL035-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n020.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 10:40:45 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------