TSTP Solution File: SWV196+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV196+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 : Wed Jul 20 20:30:27 EDT 2022

% Result   : Theorem 9.19s 9.38s
% Output   : CNFRefutation 9.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   26 (  14 unt;   0 def)
%            Number of atoms       :  244 ( 152 equ)
%            Maximal formula atoms :   52 (   9 avg)
%            Number of connectives :  260 (  42   ~;  23   |; 181   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   44 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  16 con; 0-3 aty)
%            Number of variables   :   32 (   0 sgn  28   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
    ! [X] : ~ gt(X,X) ).

fof(quaternion_ds1_inuse_0007,conjecture,
    ( ( a_select2(rho_defuse,n0) = use
      & a_select2(rho_defuse,n1) = use
      & a_select2(rho_defuse,n2) = use
      & a_select2(sigma_defuse,n0) = use
      & a_select2(sigma_defuse,n1) = use
      & a_select2(sigma_defuse,n2) = use
      & a_select2(sigma_defuse,n3) = use
      & a_select2(sigma_defuse,n4) = use
      & a_select2(sigma_defuse,n5) = use
      & a_select3(u_defuse,n0,n0) = use
      & a_select3(u_defuse,n1,n0) = use
      & a_select3(u_defuse,n2,n0) = use
      & a_select2(xinit_defuse,n3) = use
      & a_select2(xinit_defuse,n4) = use
      & a_select2(xinit_defuse,n5) = use
      & a_select2(xinit_mean_defuse,n0) = use
      & a_select2(xinit_mean_defuse,n1) = use
      & a_select2(xinit_mean_defuse,n2) = use
      & a_select2(xinit_mean_defuse,n3) = use
      & a_select2(xinit_mean_defuse,n4) = use
      & a_select2(xinit_mean_defuse,n5) = use
      & a_select2(xinit_noise_defuse,n0) = use
      & a_select2(xinit_noise_defuse,n1) = use
      & a_select2(xinit_noise_defuse,n2) = use
      & a_select2(xinit_noise_defuse,n3) = use
      & a_select2(xinit_noise_defuse,n4) = use
      & a_select2(xinit_noise_defuse,n5) = use
      & leq(n0,pv5)
      & leq(pv5,n0)
      & leq(pv5,n998)
      & gt(pv5,n0)
      & ! [A,B] :
          ( ( leq(n0,A)
            & leq(n0,B)
            & leq(A,n2)
            & leq(B,pred(pv5)) )
         => a_select3(u_defuse,A,B) = use )
      & ! [C,D] :
          ( ( leq(n0,C)
            & leq(n0,D)
            & leq(C,n2)
            & leq(D,pred(pv5)) )
         => a_select3(z_defuse,C,D) = use ) )
   => ! [E,F] :
        ( ( leq(n0,E)
          & leq(n0,F)
          & leq(E,n2)
          & leq(F,pv5) )
       => ( ( ~ ( n0 = E
                & pv5 = F )
            & ~ ( n1 = E
                & pv5 = F )
            & ~ ( n2 = E
                & pv5 = F ) )
         => a_select3(z_defuse,E,F) = use ) ) ) ).

fof(finite_domain_0,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n0) )
     => X = n0 ) ).

fof(subgoal_0,plain,
    ( ( a_select2(rho_defuse,n0) = use
      & a_select2(rho_defuse,n1) = use
      & a_select2(rho_defuse,n2) = use
      & a_select2(sigma_defuse,n0) = use
      & a_select2(sigma_defuse,n1) = use
      & a_select2(sigma_defuse,n2) = use
      & a_select2(sigma_defuse,n3) = use
      & a_select2(sigma_defuse,n4) = use
      & a_select2(sigma_defuse,n5) = use
      & a_select3(u_defuse,n0,n0) = use
      & a_select3(u_defuse,n1,n0) = use
      & a_select3(u_defuse,n2,n0) = use
      & a_select2(xinit_defuse,n3) = use
      & a_select2(xinit_defuse,n4) = use
      & a_select2(xinit_defuse,n5) = use
      & a_select2(xinit_mean_defuse,n0) = use
      & a_select2(xinit_mean_defuse,n1) = use
      & a_select2(xinit_mean_defuse,n2) = use
      & a_select2(xinit_mean_defuse,n3) = use
      & a_select2(xinit_mean_defuse,n4) = use
      & a_select2(xinit_mean_defuse,n5) = use
      & a_select2(xinit_noise_defuse,n0) = use
      & a_select2(xinit_noise_defuse,n1) = use
      & a_select2(xinit_noise_defuse,n2) = use
      & a_select2(xinit_noise_defuse,n3) = use
      & a_select2(xinit_noise_defuse,n4) = use
      & a_select2(xinit_noise_defuse,n5) = use
      & leq(n0,pv5)
      & leq(pv5,n0)
      & leq(pv5,n998)
      & gt(pv5,n0)
      & ! [A,B] :
          ( ( leq(n0,A)
            & leq(n0,B)
            & leq(A,n2)
            & leq(B,pred(pv5)) )
         => a_select3(u_defuse,A,B) = use )
      & ! [C,D] :
          ( ( leq(n0,C)
            & leq(n0,D)
            & leq(C,n2)
            & leq(D,pred(pv5)) )
         => a_select3(z_defuse,C,D) = use ) )
   => ! [E,F] :
        ( ( leq(n0,E)
          & leq(n0,F)
          & leq(E,n2)
          & leq(F,pv5)
          & ~ ( n0 = E
              & pv5 = F )
          & ~ ( n1 = E
              & pv5 = F )
          & ~ ( n2 = E
              & pv5 = F ) )
       => a_select3(z_defuse,E,F) = use ) ),
    inference(strip,[],[quaternion_ds1_inuse_0007]) ).

fof(negate_0_0,plain,
    ~ ( ( a_select2(rho_defuse,n0) = use
        & a_select2(rho_defuse,n1) = use
        & a_select2(rho_defuse,n2) = use
        & a_select2(sigma_defuse,n0) = use
        & a_select2(sigma_defuse,n1) = use
        & a_select2(sigma_defuse,n2) = use
        & a_select2(sigma_defuse,n3) = use
        & a_select2(sigma_defuse,n4) = use
        & a_select2(sigma_defuse,n5) = use
        & a_select3(u_defuse,n0,n0) = use
        & a_select3(u_defuse,n1,n0) = use
        & a_select3(u_defuse,n2,n0) = use
        & a_select2(xinit_defuse,n3) = use
        & a_select2(xinit_defuse,n4) = use
        & a_select2(xinit_defuse,n5) = use
        & a_select2(xinit_mean_defuse,n0) = use
        & a_select2(xinit_mean_defuse,n1) = use
        & a_select2(xinit_mean_defuse,n2) = use
        & a_select2(xinit_mean_defuse,n3) = use
        & a_select2(xinit_mean_defuse,n4) = use
        & a_select2(xinit_mean_defuse,n5) = use
        & a_select2(xinit_noise_defuse,n0) = use
        & a_select2(xinit_noise_defuse,n1) = use
        & a_select2(xinit_noise_defuse,n2) = use
        & a_select2(xinit_noise_defuse,n3) = use
        & a_select2(xinit_noise_defuse,n4) = use
        & a_select2(xinit_noise_defuse,n5) = use
        & leq(n0,pv5)
        & leq(pv5,n0)
        & leq(pv5,n998)
        & gt(pv5,n0)
        & ! [A,B] :
            ( ( leq(n0,A)
              & leq(n0,B)
              & leq(A,n2)
              & leq(B,pred(pv5)) )
           => a_select3(u_defuse,A,B) = use )
        & ! [C,D] :
            ( ( leq(n0,C)
              & leq(n0,D)
              & leq(C,n2)
              & leq(D,pred(pv5)) )
           => a_select3(z_defuse,C,D) = use ) )
     => ! [E,F] :
          ( ( leq(n0,E)
            & leq(n0,F)
            & leq(E,n2)
            & leq(F,pv5)
            & ~ ( n0 = E
                & pv5 = F )
            & ~ ( n1 = E
                & pv5 = F )
            & ~ ( n2 = E
                & pv5 = F ) )
         => a_select3(z_defuse,E,F) = use ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( a_select2(rho_defuse,n0) = use
    & a_select2(rho_defuse,n1) = use
    & a_select2(rho_defuse,n2) = use
    & a_select2(sigma_defuse,n0) = use
    & a_select2(sigma_defuse,n1) = use
    & a_select2(sigma_defuse,n2) = use
    & a_select2(sigma_defuse,n3) = use
    & a_select2(sigma_defuse,n4) = use
    & a_select2(sigma_defuse,n5) = use
    & a_select2(xinit_defuse,n3) = use
    & a_select2(xinit_defuse,n4) = use
    & a_select2(xinit_defuse,n5) = use
    & a_select2(xinit_mean_defuse,n0) = use
    & a_select2(xinit_mean_defuse,n1) = use
    & a_select2(xinit_mean_defuse,n2) = use
    & a_select2(xinit_mean_defuse,n3) = use
    & a_select2(xinit_mean_defuse,n4) = use
    & a_select2(xinit_mean_defuse,n5) = use
    & a_select2(xinit_noise_defuse,n0) = use
    & a_select2(xinit_noise_defuse,n1) = use
    & a_select2(xinit_noise_defuse,n2) = use
    & a_select2(xinit_noise_defuse,n3) = use
    & a_select2(xinit_noise_defuse,n4) = use
    & a_select2(xinit_noise_defuse,n5) = use
    & a_select3(u_defuse,n0,n0) = use
    & a_select3(u_defuse,n1,n0) = use
    & a_select3(u_defuse,n2,n0) = use
    & gt(pv5,n0)
    & leq(n0,pv5)
    & leq(pv5,n0)
    & leq(pv5,n998)
    & ? [E,F] :
        ( a_select3(z_defuse,E,F) != use
        & leq(E,n2)
        & leq(F,pv5)
        & leq(n0,E)
        & leq(n0,F)
        & ( n0 != E
          | pv5 != F )
        & ( n1 != E
          | pv5 != F )
        & ( n2 != E
          | pv5 != F ) )
    & ! [A,B] :
        ( ~ leq(A,n2)
        | ~ leq(B,pred(pv5))
        | ~ leq(n0,A)
        | ~ leq(n0,B)
        | a_select3(u_defuse,A,B) = use )
    & ! [C,D] :
        ( ~ leq(C,n2)
        | ~ leq(D,pred(pv5))
        | ~ leq(n0,C)
        | ~ leq(n0,D)
        | a_select3(z_defuse,C,D) = use ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    gt(pv5,n0),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    leq(pv5,n0),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ~ leq(X,n0)
      | ~ leq(n0,X)
      | X = n0 ),
    inference(canonicalize,[],[finite_domain_0]) ).

fof(normalize_0_4,plain,
    ! [X] :
      ( ~ leq(X,n0)
      | ~ leq(n0,X)
      | X = n0 ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    leq(n0,pv5),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_6,plain,
    ! [X] : ~ gt(X,X),
    inference(canonicalize,[],[irreflexivity_gt]) ).

fof(normalize_0_7,plain,
    ! [X] : ~ gt(X,X),
    inference(specialize,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    gt(pv5,n0),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    leq(pv5,n0),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_2,plain,
    ( ~ leq(X,n0)
    | ~ leq(n0,X)
    | X = n0 ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    ( ~ leq(n0,pv5)
    | ~ leq(pv5,n0)
    | pv5 = n0 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(pv5))]]) ).

cnf(refute_0_4,plain,
    ( ~ leq(n0,pv5)
    | pv5 = n0 ),
    inference(resolve,[$cnf( leq(pv5,n0) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    leq(n0,pv5),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_6,plain,
    pv5 = n0,
    inference(resolve,[$cnf( leq(n0,pv5) )],[refute_0_5,refute_0_4]) ).

cnf(refute_0_7,plain,
    ( pv5 != n0
    | ~ gt(pv5,n0)
    | gt(n0,n0) ),
    introduced(tautology,[equality,[$cnf( gt(pv5,n0) ),[0],$fot(n0)]]) ).

cnf(refute_0_8,plain,
    ( ~ gt(pv5,n0)
    | gt(n0,n0) ),
    inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    gt(n0,n0),
    inference(resolve,[$cnf( gt(pv5,n0) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ gt(X,X),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_11,plain,
    ~ gt(n0,n0),
    inference(subst,[],[refute_0_10:[bind(X,$fot(n0))]]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( gt(n0,n0) )],[refute_0_9,refute_0_11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV196+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n003.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 : Wed Jun 15 11:41:26 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.19/9.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.19/9.38  
% 9.19/9.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.19/9.38  
%------------------------------------------------------------------------------