TSTP Solution File: SET947+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n010.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 09:19:46 EDT 2024

% Result   : Theorem 0.16s 0.32s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   32 (  10 unt;   0 def)
%            Number of atoms       :  105 (   5 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  119 (  46   ~;  41   |;  20   &)
%                                         (   7 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   64 (  56   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f77,plain,
    $false,
    inference(unit_resulting_resolution,[],[f52,f57,f47,f40]) ).

fof(f40,plain,
    ! [X3,X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ subset(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ subset(sK3(X0,X1),X0)
            | ~ in(sK3(X0,X1),X1) )
          & ( subset(sK3(X0,X1),X0)
            | in(sK3(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK3(X0,X1),X0)
          | ~ in(sK3(X0,X1),X1) )
        & ( subset(sK3(X0,X1),X0)
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f47,plain,
    ! [X0] : sP0(X0,powerset(X0)),
    inference(equality_resolution,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f2,f15]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f57,plain,
    ~ in(sK2(sK1,powerset(union(sK1))),powerset(union(sK1))),
    inference(unit_resulting_resolution,[],[f32,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ in(sK2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK2(X0,X1),X1)
          & in(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK2(X0,X1),X1)
        & in(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f32,plain,
    ~ subset(sK1,powerset(union(sK1))),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ~ subset(sK1,powerset(union(sK1))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f17]) ).

fof(f17,plain,
    ( ? [X0] : ~ subset(X0,powerset(union(X0)))
   => ~ subset(sK1,powerset(union(sK1))) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0] : ~ subset(X0,powerset(union(X0))),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : subset(X0,powerset(union(X0))),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0] : subset(X0,powerset(union(X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).

fof(f52,plain,
    subset(sK2(sK1,powerset(union(sK1))),union(sK1)),
    inference(unit_resulting_resolution,[],[f50,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | subset(X0,union(X1)) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => subset(X0,union(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).

fof(f50,plain,
    in(sK2(sK1,powerset(union(sK1))),sK1),
    inference(unit_resulting_resolution,[],[f32,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30  % Computer : n010.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Fri May  3 16:55:07 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.09/0.31  % (17979)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32  % (17982)WARNING: value z3 for option sas not known
% 0.16/0.32  % (17983)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.32  % (17982)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)
% 0.16/0.32  % (17985)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)
% 0.16/0.32  % (17984)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)
% 0.16/0.32  % (17981)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.32  % (17986)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)
% 0.16/0.32  TRYING [1]
% 0.16/0.32  % (17980)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.32  TRYING [2]
% 0.16/0.32  TRYING [3]
% 0.16/0.32  % (17986)First to succeed.
% 0.16/0.32  % (17985)Also succeeded, but the first one will report.
% 0.16/0.32  TRYING [4]
% 0.16/0.32  % (17986)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17979"
% 0.16/0.32  % (17986)Refutation found. Thanks to Tanya!
% 0.16/0.32  % SZS status Theorem for theBenchmark
% 0.16/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.32  % (17986)------------------------------
% 0.16/0.32  % (17986)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.32  % (17986)Termination reason: Refutation
% 0.16/0.32  
% 0.16/0.32  % (17986)Memory used [KB]: 759
% 0.16/0.32  % (17986)Time elapsed: 0.004 s
% 0.16/0.32  % (17986)Instructions burned: 4 (million)
% 0.16/0.32  % (17979)Success in time 0.014 s
%------------------------------------------------------------------------------