TSTP Solution File: NUM386+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n013.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 : Wed Aug 31 18:04:57 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   49 (   8 unt;   0 def)
%            Number of atoms       :  223 (  70 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  276 ( 102   ~; 115   |;  47   &)
%                                         (   8 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   95 (  78   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f281,plain,
    $false,
    inference(subsumption_resolution,[],[f277,f164]) ).

fof(f164,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f163]) ).

fof(f163,plain,
    ! [X2,X1] :
      ( in(X2,X1)
      | singleton(X2) != X1 ),
    inference(equality_resolution,[],[f138]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( in(X2,X1)
      | X0 != X2
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ( ( ~ in(sK9(X0,X1),X1)
            | sK9(X0,X1) != X0 )
          & ( in(sK9(X0,X1),X1)
            | sK9(X0,X1) = X0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f87,f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | X0 != X3 )
          & ( in(X3,X1)
            | X0 = X3 ) )
     => ( ( ~ in(sK9(X0,X1),X1)
          | sK9(X0,X1) != X0 )
        & ( in(sK9(X0,X1),X1)
          | sK9(X0,X1) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | X0 != X3 )
            & ( in(X3,X1)
              | X0 = X3 ) ) ) ),
    inference(rectify,[],[f86]) ).

fof(f86,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | X1 != X2 )
            & ( in(X2,X0)
              | X1 = X2 ) ) ) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( X1 = X2
        <=> in(X2,X0) )
    <=> singleton(X1) = X0 ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f277,plain,
    ~ in(sK0,singleton(sK0)),
    inference(backward_demodulation,[],[f257,f269]) ).

fof(f269,plain,
    sK0 = sK1,
    inference(subsumption_resolution,[],[f268,f257]) ).

fof(f268,plain,
    ( sK0 = sK1
    | in(sK1,singleton(sK0)) ),
    inference(subsumption_resolution,[],[f267,f239]) ).

fof(f239,plain,
    ~ in(sK1,sK0),
    inference(duplicate_literal_removal,[],[f232]) ).

fof(f232,plain,
    ( ~ in(sK1,sK0)
    | ~ in(sK1,sK0) ),
    inference(resolution,[],[f166,f159]) ).

fof(f159,plain,
    ( ~ in(sK1,set_union2(sK0,singleton(sK0)))
    | ~ in(sK1,sK0) ),
    inference(definition_unfolding,[],[f104,f133]) ).

fof(f133,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(f104,plain,
    ( ~ in(sK1,sK0)
    | ~ in(sK1,succ(sK0)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ( ( ( sK0 != sK1
        & ~ in(sK1,sK0) )
      | ~ in(sK1,succ(sK0)) )
    & ( sK0 = sK1
      | in(sK1,sK0)
      | in(sK1,succ(sK0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f63,f64]) ).

fof(f64,plain,
    ( ? [X0,X1] :
        ( ( ( X0 != X1
            & ~ in(X1,X0) )
          | ~ in(X1,succ(X0)) )
        & ( X0 = X1
          | in(X1,X0)
          | in(X1,succ(X0)) ) )
   => ( ( ( sK0 != sK1
          & ~ in(sK1,sK0) )
        | ~ in(sK1,succ(sK0)) )
      & ( sK0 = sK1
        | in(sK1,sK0)
        | in(sK1,succ(sK0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ? [X0,X1] :
      ( ( ( X0 != X1
          & ~ in(X1,X0) )
        | ~ in(X1,succ(X0)) )
      & ( X0 = X1
        | in(X1,X0)
        | in(X1,succ(X0)) ) ),
    inference(rectify,[],[f62]) ).

fof(f62,plain,
    ? [X1,X0] :
      ( ( ( X0 != X1
          & ~ in(X0,X1) )
        | ~ in(X0,succ(X1)) )
      & ( X0 = X1
        | in(X0,X1)
        | in(X0,succ(X1)) ) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ? [X1,X0] :
      ( ( ( X0 != X1
          & ~ in(X0,X1) )
        | ~ in(X0,succ(X1)) )
      & ( X0 = X1
        | in(X0,X1)
        | in(X0,succ(X1)) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f48,plain,
    ? [X1,X0] :
      ( in(X0,succ(X1))
    <~> ( X0 = X1
        | in(X0,X1) ) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X0,X1] :
        ( in(X0,succ(X1))
      <=> ( X0 = X1
          | in(X0,X1) ) ),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X0,X1] :
      ( in(X0,succ(X1))
    <=> ( X0 = X1
        | in(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).

fof(f166,plain,
    ! [X3,X0,X1] :
      ( in(X3,set_union2(X1,X0))
      | ~ in(X3,X1) ),
    inference(equality_resolution,[],[f151]) ).

fof(f151,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | ~ in(X3,X1)
      | set_union2(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) ) )
        | set_union2(X1,X0) != X2 )
      & ( set_union2(X1,X0) = X2
        | ( ( ~ in(sK13(X0,X1,X2),X2)
            | ( ~ in(sK13(X0,X1,X2),X1)
              & ~ in(sK13(X0,X1,X2),X0) ) )
          & ( in(sK13(X0,X1,X2),X2)
            | in(sK13(X0,X1,X2),X1)
            | in(sK13(X0,X1,X2),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f98,f99]) ).

fof(f99,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X2)
            | ( ~ in(X4,X1)
              & ~ in(X4,X0) ) )
          & ( in(X4,X2)
            | in(X4,X1)
            | in(X4,X0) ) )
     => ( ( ~ in(sK13(X0,X1,X2),X2)
          | ( ~ in(sK13(X0,X1,X2),X1)
            & ~ in(sK13(X0,X1,X2),X0) ) )
        & ( in(sK13(X0,X1,X2),X2)
          | in(sK13(X0,X1,X2),X1)
          | in(sK13(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) ) )
        | set_union2(X1,X0) != X2 )
      & ( set_union2(X1,X0) = X2
        | ? [X4] :
            ( ( ~ in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X2)
              | in(X4,X1)
              | in(X4,X0) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,plain,
    ! [X1,X0,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | in(X3,X1)
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( ~ in(X3,X0)
                & ~ in(X3,X1) ) ) )
        | set_union2(X0,X1) != X2 )
      & ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ( ~ in(X3,X0)
                & ~ in(X3,X1) ) )
            & ( in(X3,X2)
              | in(X3,X0)
              | in(X3,X1) ) ) ) ),
    inference(flattening,[],[f96]) ).

fof(f96,plain,
    ! [X1,X0,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | in(X3,X1)
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( ~ in(X3,X0)
                & ~ in(X3,X1) ) ) )
        | set_union2(X0,X1) != X2 )
      & ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ( ~ in(X3,X0)
                & ~ in(X3,X1) ) )
            & ( in(X3,X2)
              | in(X3,X0)
              | in(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( ( in(X3,X0)
            | in(X3,X1) )
        <=> in(X3,X2) )
    <=> set_union2(X0,X1) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f267,plain,
    ( sK0 = sK1
    | in(sK1,sK0)
    | in(sK1,singleton(sK0)) ),
    inference(duplicate_literal_removal,[],[f258]) ).

fof(f258,plain,
    ( in(sK1,sK0)
    | in(sK1,singleton(sK0))
    | in(sK1,sK0)
    | sK0 = sK1 ),
    inference(resolution,[],[f165,f160]) ).

fof(f160,plain,
    ( in(sK1,set_union2(sK0,singleton(sK0)))
    | in(sK1,sK0)
    | sK0 = sK1 ),
    inference(definition_unfolding,[],[f103,f133]) ).

fof(f103,plain,
    ( sK0 = sK1
    | in(sK1,sK0)
    | in(sK1,succ(sK0)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f165,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,set_union2(X1,X0))
      | in(X3,X1)
      | in(X3,X0) ),
    inference(equality_resolution,[],[f152]) ).

fof(f152,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | in(X3,X0)
      | ~ in(X3,X2)
      | set_union2(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f100]) ).

fof(f257,plain,
    ~ in(sK1,singleton(sK0)),
    inference(subsumption_resolution,[],[f251,f162]) ).

fof(f162,plain,
    ! [X2,X0] :
      ( ~ in(X2,singleton(X0))
      | X0 = X2 ),
    inference(equality_resolution,[],[f139]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | ~ in(X2,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f89]) ).

fof(f251,plain,
    ( sK0 != sK1
    | ~ in(sK1,singleton(sK0)) ),
    inference(resolution,[],[f167,f158]) ).

fof(f158,plain,
    ( ~ in(sK1,set_union2(sK0,singleton(sK0)))
    | sK0 != sK1 ),
    inference(definition_unfolding,[],[f105,f133]) ).

fof(f105,plain,
    ( sK0 != sK1
    | ~ in(sK1,succ(sK0)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f167,plain,
    ! [X3,X0,X1] :
      ( in(X3,set_union2(X1,X0))
      | ~ in(X3,X0) ),
    inference(equality_resolution,[],[f150]) ).

fof(f150,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | ~ in(X3,X0)
      | set_union2(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n013.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    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 06:35:17 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (27844)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.51  % (27845)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.51  % (27836)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51  % (27822)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.51  % (27834)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52  % (27845)First to succeed.
% 0.20/0.53  % (27825)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (27845)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (27845)------------------------------
% 0.20/0.53  % (27845)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (27845)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (27845)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (27845)Memory used [KB]: 1023
% 0.20/0.53  % (27845)Time elapsed: 0.110 s
% 0.20/0.53  % (27845)Instructions burned: 7 (million)
% 0.20/0.53  % (27845)------------------------------
% 0.20/0.53  % (27845)------------------------------
% 0.20/0.53  % (27820)Success in time 0.173 s
%------------------------------------------------------------------------------