TSTP Solution File: ITP010+5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP010+5 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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  : 300s
% DateTime : Sun May  5 06:57:42 EDT 2024

% Result   : Theorem 31.46s 5.73s
% Output   : Refutation 31.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (   3 unt;   0 def)
%            Number of atoms       :  107 (   0 equ)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :  126 (  35   ~;  24   |;  47   &)
%                                         (   3 <=>;  16  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   40 (  12   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f116641,plain,
    $false,
    inference(subsumption_resolution,[],[f116621,f116622]) ).

fof(f116622,plain,
    p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)),
    inference(duplicate_literal_removal,[],[f68636]) ).

fof(f68636,plain,
    ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
    | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) ),
    inference(cnf_transformation,[],[f36122]) ).

fof(f36122,plain,
    ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
      | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
    & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
      | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
    & mem(sK6913,arr(sK6911,bool))
    & mem(sK6912,arr(sK6910,bool))
    & ne(sK6911)
    & ne(sK6910) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6910,sK6911,sK6912,sK6913])],[f36117,f36121,f36120,f36119,f36118]) ).

fof(f36118,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                      | p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
                    & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                      | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
                    & mem(X3,arr(X1,bool)) )
                & mem(X2,arr(X0,bool)) )
            & ne(X1) )
        & ne(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
                    | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
                  & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
                    | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
                  & mem(X3,arr(X1,bool)) )
              & mem(X2,arr(sK6910,bool)) )
          & ne(X1) )
      & ne(sK6910) ) ),
    introduced(choice_axiom,[]) ).

fof(f36119,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
                  | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
                & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
                  | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
                & mem(X3,arr(X1,bool)) )
            & mem(X2,arr(sK6910,bool)) )
        & ne(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
                | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
              & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
                | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
              & mem(X3,arr(sK6911,bool)) )
          & mem(X2,arr(sK6910,bool)) )
      & ne(sK6911) ) ),
    introduced(choice_axiom,[]) ).

fof(f36120,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
              | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
            & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
              | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
            & mem(X3,arr(sK6911,bool)) )
        & mem(X2,arr(sK6910,bool)) )
   => ( ? [X3] :
          ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
            | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
          & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
            | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
          & mem(X3,arr(sK6911,bool)) )
      & mem(sK6912,arr(sK6910,bool)) ) ),
    introduced(choice_axiom,[]) ).

fof(f36121,plain,
    ( ? [X3] :
        ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
          | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
        & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
          | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
        & mem(X3,arr(sK6911,bool)) )
   => ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
        | p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
      & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
        | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
      & mem(sK6913,arr(sK6911,bool)) ) ),
    introduced(choice_axiom,[]) ).

fof(f36117,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                    | p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
                  & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                    | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
                  & mem(X3,arr(X1,bool)) )
              & mem(X2,arr(X0,bool)) )
          & ne(X1) )
      & ne(X0) ),
    inference(flattening,[],[f36116]) ).

fof(f36116,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                    | p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
                  & ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                    | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
                  & mem(X3,arr(X1,bool)) )
              & mem(X2,arr(X0,bool)) )
          & ne(X1) )
      & ne(X0) ),
    inference(nnf_transformation,[],[f17046]) ).

fof(f17046,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                  <~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
                  & mem(X3,arr(X1,bool)) )
              & mem(X2,arr(X0,bool)) )
          & ne(X1) )
      & ne(X0) ),
    inference(ennf_transformation,[],[f8600]) ).

fof(f8600,plain,
    ~ ! [X0] :
        ( ne(X0)
       => ! [X1] :
            ( ne(X1)
           => ! [X2] :
                ( mem(X2,arr(X0,bool))
               => ! [X3] :
                    ( mem(X3,arr(X1,bool))
                   => ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
                    <=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ) ) ),
    inference(rectify,[],[f8599]) ).

fof(f8599,negated_conjecture,
    ~ ! [X8] :
        ( ne(X8)
       => ! [X10] :
            ( ne(X10)
           => ! [X167] :
                ( mem(X167,arr(X8,bool))
               => ! [X41] :
                    ( mem(X41,arr(X10,bool))
                   => ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41))
                    <=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41)) ) ) ) ) ),
    inference(negated_conjecture,[],[f8598]) ).

fof(f8598,conjecture,
    ! [X8] :
      ( ne(X8)
     => ! [X10] :
          ( ne(X10)
         => ! [X167] :
              ( mem(X167,arr(X8,bool))
             => ! [X41] :
                  ( mem(X41,arr(X10,bool))
                 => ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41))
                  <=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).

fof(f116621,plain,
    ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)),
    inference(duplicate_literal_removal,[],[f68635]) ).

fof(f68635,plain,
    ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
    | ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) ),
    inference(cnf_transformation,[],[f36122]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ITP010+5 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 19:03:39 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.36  % (19053)Running in auto input_syntax mode. Trying TPTP
% 1.09/1.29  % (19054)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.09/1.29  % (19056)WARNING: value z3 for option sas not known
% 1.09/1.29  % (19055)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 1.09/1.29  % (19056)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 1.09/1.29  % (19057)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 1.09/1.29  % (19059)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 1.09/1.29  % (19060)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.09/1.29  % (19058)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 31.46/5.70  % (19060)First to succeed.
% 31.46/5.71  % (19060)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19053"
% 31.46/5.73  % (19060)Refutation found. Thanks to Tanya!
% 31.46/5.73  % SZS status Theorem for theBenchmark
% 31.46/5.73  % SZS output start Proof for theBenchmark
% See solution above
% 31.46/5.74  % (19060)------------------------------
% 31.46/5.74  % (19060)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 31.46/5.74  % (19060)Termination reason: Refutation
% 31.46/5.74  
% 31.46/5.74  % (19060)Memory used [KB]: 160654
% 31.46/5.74  % (19060)Time elapsed: 4.412 s
% 31.46/5.74  % (19060)Instructions burned: 10121 (million)
% 31.46/5.74  % (19053)Success in time 5.372 s
%------------------------------------------------------------------------------