TSTP Solution File: SEU230+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU230+3 : 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 : n014.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 : Tue Apr 30 15:24:52 EDT 2024

% Result   : Theorem 0.23s 0.40s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   32 (  12 unt;   0 def)
%            Number of atoms       :  149 (  34 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  185 (  68   ~;  71   |;  36   &)
%                                         (   7 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-3 aty)
%            Number of variables   :   79 (  70   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f411,plain,
    $false,
    inference(resolution,[],[f402,f95]) ).

fof(f95,plain,
    ~ in(sK1,succ(sK1)),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ~ in(sK1,succ(sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f43,f61]) ).

fof(f61,plain,
    ( ? [X0] : ~ in(X0,succ(X0))
   => ~ in(sK1,succ(sK1)) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ? [X0] : ~ in(X0,succ(X0)),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X0] : in(X0,succ(X0)),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).

fof(f402,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(resolution,[],[f272,f151]) ).

fof(f151,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f150]) ).

fof(f150,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f119]) ).

fof(f119,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK3(X0,X1) != X0
            | ~ in(sK3(X0,X1),X1) )
          & ( sK3(X0,X1) = X0
            | in(sK3(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f66,f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK3(X0,X1) != X0
          | ~ in(sK3(X0,X1),X1) )
        & ( sK3(X0,X1) = X0
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

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

fof(f272,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | in(X0,succ(X1)) ),
    inference(resolution,[],[f126,f170]) ).

fof(f170,plain,
    ! [X0] : sP0(singleton(X0),X0,succ(X0)),
    inference(superposition,[],[f153,f103]) ).

fof(f103,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/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(f153,plain,
    ! [X0,X1] : sP0(X1,X0,set_union2(X0,X1)),
    inference(equality_resolution,[],[f130]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ~ sP0(X1,X0,X2) )
      & ( sP0(X1,X0,X2)
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> sP0(X1,X0,X2) ),
    inference(definition_folding,[],[f8,f59]) ).

fof(f59,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

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

fof(f126,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP0(X0,X1,X2)
      | ~ in(X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ( ~ in(sK4(X0,X1,X2),X0)
              & ~ in(sK4(X0,X1,X2),X1) )
            | ~ in(sK4(X0,X1,X2),X2) )
          & ( in(sK4(X0,X1,X2),X0)
            | in(sK4(X0,X1,X2),X1)
            | in(sK4(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X0)
                & ~ in(X4,X1) ) )
            & ( in(X4,X0)
              | in(X4,X1)
              | ~ in(X4,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f71,f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X0)
              & ~ in(X3,X1) )
            | ~ in(X3,X2) )
          & ( in(X3,X0)
            | in(X3,X1)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK4(X0,X1,X2),X0)
            & ~ in(sK4(X0,X1,X2),X1) )
          | ~ in(sK4(X0,X1,X2),X2) )
        & ( in(sK4(X0,X1,X2),X0)
          | in(sK4(X0,X1,X2),X1)
          | in(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ( ~ in(X3,X0)
                & ~ in(X3,X1) )
              | ~ in(X3,X2) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X0)
                & ~ in(X4,X1) ) )
            & ( in(X4,X0)
              | in(X4,X1)
              | ~ in(X4,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f70]) ).

fof(f70,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f69]) ).

fof(f69,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU230+3 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Apr 29 20:19:34 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (16131)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.38  % (16134)WARNING: value z3 for option sas not known
% 0.23/0.38  % (16132)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.39  % (16133)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.39  % (16134)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)
% 0.23/0.39  % (16135)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.39  % (16136)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)
% 0.23/0.39  % (16138)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)
% 0.23/0.39  % (16137)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)
% 0.23/0.39  TRYING [1]
% 0.23/0.39  TRYING [2]
% 0.23/0.39  TRYING [3]
% 0.23/0.39  TRYING [4]
% 0.23/0.39  TRYING [1]
% 0.23/0.39  TRYING [2]
% 0.23/0.40  TRYING [1]
% 0.23/0.40  % (16134)First to succeed.
% 0.23/0.40  TRYING [2]
% 0.23/0.40  TRYING [3]
% 0.23/0.40  % (16134)Refutation found. Thanks to Tanya!
% 0.23/0.40  % SZS status Theorem for theBenchmark
% 0.23/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.40  % (16134)------------------------------
% 0.23/0.40  % (16134)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.23/0.40  % (16134)Termination reason: Refutation
% 0.23/0.40  
% 0.23/0.40  % (16134)Memory used [KB]: 946
% 0.23/0.40  % (16134)Time elapsed: 0.013 s
% 0.23/0.40  % (16134)Instructions burned: 15 (million)
% 0.23/0.40  % (16134)------------------------------
% 0.23/0.40  % (16134)------------------------------
% 0.23/0.40  % (16131)Success in time 0.028 s
%------------------------------------------------------------------------------