TSTP Solution File: KRS196+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KRS196+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 03:19:07 EDT 2022

% Result   : Theorem 0.92s 1.11s
% Output   : CNFRefutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   69 (   7 unt;   0 def)
%            Number of atoms       :  179 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  192 (  82   ~;  69   |;  19   &)
%                                         (  20 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :  147 (   6 sgn  89   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(sat,axiom,
    ! [Ax,C] :
      ( ? [I1] :
          ( model(I1,Ax)
          & model(I1,C) )
    <=> status(Ax,C,sat) ) ).

fof(thm,axiom,
    ! [Ax,C] :
      ( ! [I1] :
          ( model(I1,Ax)
         => model(I1,C) )
    <=> status(Ax,C,thm) ) ).

fof(cax,axiom,
    ! [Ax,C] :
      ( ~ ? [I1] : model(I1,Ax)
    <=> status(Ax,C,cax) ) ).

fof(sca,axiom,
    ! [Ax,C] :
      ( ( ~ ? [I1] : model(I1,Ax)
        & ? [I2] : model(I2,C) )
    <=> status(Ax,C,sca) ) ).

fof(wca,axiom,
    ! [Ax,C] :
      ( ( ~ ? [I1] : model(I1,Ax)
        & ? [I2] : model(I2,C)
        & ? [I3] : ~ model(I3,C) )
    <=> status(Ax,C,wca) ) ).

fof(isa,axiom,
    ! [S1,S2] :
      ( ! [Ax,C] :
          ( status(Ax,C,S1)
         => status(Ax,C,S2) )
    <=> isa(S1,S2) ) ).

fof(isa_wca_thm,conjecture,
    isa(wca,thm) ).

fof(subgoal_0,plain,
    isa(wca,thm),
    inference(strip,[],[isa_wca_thm]) ).

fof(negate_0_0,plain,
    ~ isa(wca,thm),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,sca)
    <=> ( ? [I1] : model(I1,Ax)
        | ! [I2] : ~ model(I2,C) ) ),
    inference(canonicalize,[],[sca]) ).

fof(normalize_0_1,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,cax)
    <=> ? [I1] : model(I1,Ax) ),
    inference(canonicalize,[],[cax]) ).

fof(normalize_0_2,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,cax)
    <=> ? [I1] : model(I1,Ax) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,sca)
    <=> ( ~ status(Ax,C,cax)
        | ! [I2] : ~ model(I2,C) ) ),
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,sca)
    <=> ( ~ status(Ax,C,cax)
        | ! [I2] : ~ model(I2,C) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Ax,C,I2] :
      ( ( ~ status(Ax,C,sca)
        | model(skolemFOFtoCNF_I2_9(C),C) )
      & ( ~ status(Ax,C,sca)
        | status(Ax,C,cax) )
      & ( ~ model(I2,C)
        | ~ status(Ax,C,cax)
        | status(Ax,C,sca) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,sca)
      | status(Ax,C,cax) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,wca)
    <=> ( ? [I1] : model(I1,Ax)
        | ! [I2] : ~ model(I2,C)
        | ! [I3] : model(I3,C) ) ),
    inference(canonicalize,[],[wca]) ).

fof(normalize_0_8,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,wca)
    <=> ( ~ status(Ax,C,sca)
        | ! [I3] : model(I3,C) ) ),
    inference(simplify,[],[normalize_0_7,normalize_0_4,normalize_0_2]) ).

fof(normalize_0_9,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,wca)
    <=> ( ~ status(Ax,C,sca)
        | ! [I3] : model(I3,C) ) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [Ax,C,I3] :
      ( ( ~ model(skolemFOFtoCNF_I3_3(C),C)
        | ~ status(Ax,C,wca) )
      & ( ~ status(Ax,C,wca)
        | status(Ax,C,sca) )
      & ( ~ status(Ax,C,sca)
        | model(I3,C)
        | status(Ax,C,wca) ) ),
    inference(clausify,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,wca)
      | status(Ax,C,sca) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [S1,S2] :
      ( ~ isa(S1,S2)
    <=> ? [Ax,C] :
          ( ~ status(Ax,C,S2)
          & status(Ax,C,S1) ) ),
    inference(canonicalize,[],[isa]) ).

fof(normalize_0_13,plain,
    ! [S1,S2] :
      ( ~ isa(S1,S2)
    <=> ? [Ax,C] :
          ( ~ status(Ax,C,S2)
          & status(Ax,C,S1) ) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [Ax,C,S1,S2] :
      ( ( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
        | isa(S1,S2) )
      & ( isa(S1,S2)
        | status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) )
      & ( ~ isa(S1,S2)
        | ~ status(Ax,C,S1)
        | status(Ax,C,S2) ) ),
    inference(clausify,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [S1,S2] :
      ( isa(S1,S2)
      | status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
    inference(conjunct,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [Ax,C,I1] :
      ( ( ~ model(I1,Ax)
        | ~ status(Ax,C,cax) )
      & ( model(skolemFOFtoCNF_I1_13(Ax),Ax)
        | status(Ax,C,cax) ) ),
    inference(clausify,[],[normalize_0_2]) ).

fof(normalize_0_17,plain,
    ! [Ax,C,I1] :
      ( ~ model(I1,Ax)
      | ~ status(Ax,C,cax) ),
    inference(conjunct,[],[normalize_0_16]) ).

fof(normalize_0_18,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,sat)
    <=> ! [I1] :
          ( ~ model(I1,Ax)
          | ~ model(I1,C) ) ),
    inference(canonicalize,[],[sat]) ).

fof(normalize_0_19,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,sat)
    <=> ! [I1] :
          ( ~ model(I1,Ax)
          | ~ model(I1,C) ) ),
    inference(specialize,[],[normalize_0_18]) ).

fof(normalize_0_20,plain,
    ! [Ax,C,I1] :
      ( ( ~ status(Ax,C,sat)
        | model(skolemFOFtoCNF_I1_4(Ax,C),Ax) )
      & ( ~ status(Ax,C,sat)
        | model(skolemFOFtoCNF_I1_4(Ax,C),C) )
      & ( ~ model(I1,Ax)
        | ~ model(I1,C)
        | status(Ax,C,sat) ) ),
    inference(clausify,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,sat)
      | model(skolemFOFtoCNF_I1_4(Ax,C),Ax) ),
    inference(conjunct,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    ! [Ax,C,I1] :
      ( ~ model(I1,Ax)
      | ~ model(I1,C)
      | status(Ax,C,sat) ),
    inference(conjunct,[],[normalize_0_20]) ).

fof(normalize_0_23,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,thm)
    <=> ? [I1] :
          ( ~ model(I1,C)
          & model(I1,Ax) ) ),
    inference(canonicalize,[],[thm]) ).

fof(normalize_0_24,plain,
    ! [Ax,C] :
      ( ~ status(Ax,C,thm)
    <=> ? [I1] :
          ( ~ model(I1,C)
          & model(I1,Ax) ) ),
    inference(specialize,[],[normalize_0_23]) ).

fof(normalize_0_25,plain,
    ! [Ax,C,I1] :
      ( ( ~ model(skolemFOFtoCNF_I1_5(Ax,C),C)
        | status(Ax,C,thm) )
      & ( model(skolemFOFtoCNF_I1_5(Ax,C),Ax)
        | status(Ax,C,thm) )
      & ( ~ model(I1,Ax)
        | ~ status(Ax,C,thm)
        | model(I1,C) ) ),
    inference(clausify,[],[normalize_0_24]) ).

fof(normalize_0_26,plain,
    ! [Ax,C] :
      ( model(skolemFOFtoCNF_I1_5(Ax,C),Ax)
      | status(Ax,C,thm) ),
    inference(conjunct,[],[normalize_0_25]) ).

fof(normalize_0_27,plain,
    ! [S1,S2] :
      ( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
      | isa(S1,S2) ),
    inference(conjunct,[],[normalize_0_14]) ).

fof(normalize_0_28,plain,
    ~ isa(wca,thm),
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    ( ~ status(Ax,C,sca)
    | status(Ax,C,cax) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_1,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),sca)
    | status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),cax) ),
    inference(subst,[],[refute_0_0:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(wca,X_446))),bind(C,$fot(skolemFOFtoCNF_C_1(wca,X_446)))]]) ).

cnf(refute_0_2,plain,
    ( ~ status(Ax,C,wca)
    | status(Ax,C,sca) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_3,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),wca)
    | status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),sca) ),
    inference(subst,[],[refute_0_2:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(wca,X_407))),bind(C,$fot(skolemFOFtoCNF_C_1(wca,X_407)))]]) ).

cnf(refute_0_4,plain,
    ( isa(S1,S2)
    | status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_5,plain,
    ( isa(wca,X_407)
    | status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),wca) ),
    inference(subst,[],[refute_0_4:[bind(S1,$fot(wca)),bind(S2,$fot(X_407))]]) ).

cnf(refute_0_6,plain,
    ( isa(wca,X_407)
    | status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),sca) ),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),wca) )],[refute_0_5,refute_0_3]) ).

cnf(refute_0_7,plain,
    ( isa(wca,X_446)
    | status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),sca) ),
    inference(subst,[],[refute_0_6:[bind(X_407,$fot(X_446))]]) ).

cnf(refute_0_8,plain,
    ( isa(wca,X_446)
    | status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),cax) ),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),sca) )],[refute_0_7,refute_0_1]) ).

cnf(refute_0_9,plain,
    ( isa(wca,thm)
    | status(skolemFOFtoCNF_Ax_1(wca,thm),skolemFOFtoCNF_C_1(wca,thm),cax) ),
    inference(subst,[],[refute_0_8:[bind(X_446,$fot(thm))]]) ).

cnf(refute_0_10,plain,
    ( ~ model(I1,Ax)
    | ~ status(Ax,C,cax) ),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_11,plain,
    ( ~ model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm)),skolemFOFtoCNF_Ax_1(X_529,thm))
    | ~ status(skolemFOFtoCNF_Ax_1(X_529,thm),C,cax) ),
    inference(subst,[],[refute_0_10:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(X_529,thm))),bind(I1,$fot(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm))))]]) ).

cnf(refute_0_12,plain,
    ( ~ status(Ax,C,sat)
    | model(skolemFOFtoCNF_I1_4(Ax,C),Ax) ),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_13,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm),sat)
    | model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm)),skolemFOFtoCNF_Ax_1(X_404,thm)) ),
    inference(subst,[],[refute_0_12:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(X_404,thm))),bind(C,$fot(skolemFOFtoCNF_Ax_1(X_404,thm)))]]) ).

cnf(refute_0_14,plain,
    ( ~ model(I1,Ax)
    | ~ model(I1,C)
    | status(Ax,C,sat) ),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_15,plain,
    ( ~ model(skolemFOFtoCNF_I1_5(X_112,X_113),X_112)
    | status(X_112,X_112,sat) ),
    inference(subst,[],[refute_0_14:[bind(Ax,$fot(X_112)),bind(C,$fot(X_112)),bind(I1,$fot(skolemFOFtoCNF_I1_5(X_112,X_113)))]]) ).

cnf(refute_0_16,plain,
    ( model(skolemFOFtoCNF_I1_5(Ax,C),Ax)
    | status(Ax,C,thm) ),
    inference(canonicalize,[],[normalize_0_26]) ).

cnf(refute_0_17,plain,
    ( model(skolemFOFtoCNF_I1_5(X_112,X_113),X_112)
    | status(X_112,X_113,thm) ),
    inference(subst,[],[refute_0_16:[bind(Ax,$fot(X_112)),bind(C,$fot(X_113))]]) ).

cnf(refute_0_18,plain,
    ( status(X_112,X_112,sat)
    | status(X_112,X_113,thm) ),
    inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_5(X_112,X_113),X_112) )],[refute_0_17,refute_0_15]) ).

cnf(refute_0_19,plain,
    ( status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_Ax_1(X_394,thm),sat)
    | status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_C_1(X_394,thm),thm) ),
    inference(subst,[],[refute_0_18:[bind(X_112,$fot(skolemFOFtoCNF_Ax_1(X_394,thm))),bind(X_113,$fot(skolemFOFtoCNF_C_1(X_394,thm)))]]) ).

cnf(refute_0_20,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
    | isa(S1,S2) ),
    inference(canonicalize,[],[normalize_0_27]) ).

cnf(refute_0_21,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_C_1(X_394,thm),thm)
    | isa(X_394,thm) ),
    inference(subst,[],[refute_0_20:[bind(S1,$fot(X_394)),bind(S2,$fot(thm))]]) ).

cnf(refute_0_22,plain,
    ( isa(X_394,thm)
    | status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_Ax_1(X_394,thm),sat) ),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_C_1(X_394,thm),thm) )],[refute_0_19,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( isa(X_404,thm)
    | status(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm),sat) ),
    inference(subst,[],[refute_0_22:[bind(X_394,$fot(X_404))]]) ).

cnf(refute_0_24,plain,
    ( isa(X_404,thm)
    | model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm)),skolemFOFtoCNF_Ax_1(X_404,thm)) ),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm),sat) )],[refute_0_23,refute_0_13]) ).

cnf(refute_0_25,plain,
    ( isa(X_529,thm)
    | model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm)),skolemFOFtoCNF_Ax_1(X_529,thm)) ),
    inference(subst,[],[refute_0_24:[bind(X_404,$fot(X_529))]]) ).

cnf(refute_0_26,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(X_529,thm),C,cax)
    | isa(X_529,thm) ),
    inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm)),skolemFOFtoCNF_Ax_1(X_529,thm)) )],[refute_0_25,refute_0_11]) ).

cnf(refute_0_27,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(wca,thm),skolemFOFtoCNF_C_1(wca,thm),cax)
    | isa(wca,thm) ),
    inference(subst,[],[refute_0_26:[bind(C,$fot(skolemFOFtoCNF_C_1(wca,thm))),bind(X_529,$fot(wca))]]) ).

cnf(refute_0_28,plain,
    isa(wca,thm),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wca,thm),skolemFOFtoCNF_C_1(wca,thm),cax) )],[refute_0_9,refute_0_27]) ).

cnf(refute_0_29,plain,
    ~ isa(wca,thm),
    inference(canonicalize,[],[normalize_0_28]) ).

cnf(refute_0_30,plain,
    $false,
    inference(resolve,[$cnf( isa(wca,thm) )],[refute_0_28,refute_0_29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS196+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jun  7 13:38:34 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.92/1.11  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.11  
% 0.92/1.11  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.92/1.12  
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