TSTP Solution File: NUM385+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM385+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 : n026.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 14:21:56 EDT 2024

% Result   : Theorem 0.10s 0.37s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   52 (  19 unt;   0 def)
%            Number of atoms       :  172 (  45 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  193 (  73   ~;  69   |;  34   &)
%                                         (  11 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :  105 (  95   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2250,plain,
    $false,
    inference(subsumption_resolution,[],[f2244,f2158]) ).

fof(f2158,plain,
    sP1(singleton(sK4),sK3,sK4),
    inference(unit_resulting_resolution,[],[f110,f309,f135]) ).

fof(f135,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | ~ in(X4,X2)
      | sP1(X1,X4,X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
            | ~ in(sK7(X0,X1,X2),X2) )
          & ( sP1(X1,sK7(X0,X1,X2),X0)
            | in(sK7(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP1(X1,X4,X0) )
            & ( sP1(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f75,f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP1(X1,X3,X0)
            | ~ in(X3,X2) )
          & ( sP1(X1,X3,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
          | ~ in(sK7(X0,X1,X2),X2) )
        & ( sP1(X1,sK7(X0,X1,X2),X0)
          | in(sK7(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP1(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP1(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP1(X1,X4,X0) )
            & ( sP1(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP1(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP1(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ sP1(X1,X3,X0) )
            & ( sP1(X1,X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( sP2(X0,X1,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> sP1(X1,X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f309,plain,
    sP2(sK4,singleton(sK4),succ(sK3)),
    inference(superposition,[],[f294,f102]) ).

fof(f102,plain,
    succ(sK3) = succ(sK4),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ( sK3 != sK4
    & succ(sK3) = succ(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f44,f65]) ).

fof(f65,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & succ(X0) = succ(X1) )
   => ( sK3 != sK4
      & succ(sK3) = succ(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ? [X0,X1] :
      ( X0 != X1
      & succ(X0) = succ(X1) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ! [X0,X1] :
        ( succ(X0) = succ(X1)
       => X0 = X1 ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ! [X0,X1] :
      ( succ(X0) = succ(X1)
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_ordinal1) ).

fof(f294,plain,
    ! [X0] : sP2(X0,singleton(X0),succ(X0)),
    inference(superposition,[],[f164,f112]) ).

fof(f112,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(f164,plain,
    ! [X0,X1] : sP2(X0,X1,set_union2(X0,X1)),
    inference(equality_resolution,[],[f142]) ).

fof(f142,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ~ sP2(X0,X1,X2) )
      & ( sP2(X0,X1,X2)
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> sP2(X0,X1,X2) ),
    inference(definition_folding,[],[f8,f63,f62]) ).

fof(f62,plain,
    ! [X1,X3,X0] :
      ( sP1(X1,X3,X0)
    <=> ( in(X3,X1)
        | in(X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

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

fof(f110,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).

fof(f2244,plain,
    ~ sP1(singleton(sK4),sK3,sK4),
    inference(unit_resulting_resolution,[],[f1066,f2215,f139]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,X2)
      | in(X1,X2)
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ~ in(X1,X0)
          & ~ in(X1,X2) ) )
      & ( in(X1,X0)
        | in(X1,X2)
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f79]) ).

fof(f79,plain,
    ! [X1,X3,X0] :
      ( ( sP1(X1,X3,X0)
        | ( ~ in(X3,X1)
          & ~ in(X3,X0) ) )
      & ( in(X3,X1)
        | in(X3,X0)
        | ~ sP1(X1,X3,X0) ) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X1,X3,X0] :
      ( ( sP1(X1,X3,X0)
        | ( ~ in(X3,X1)
          & ~ in(X3,X0) ) )
      & ( in(X3,X1)
        | in(X3,X0)
        | ~ sP1(X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f2215,plain,
    ~ in(sK3,sK4),
    inference(unit_resulting_resolution,[],[f2212,f124]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f2212,plain,
    in(sK4,sK3),
    inference(unit_resulting_resolution,[],[f1067,f2126,f139]) ).

fof(f2126,plain,
    sP1(singleton(sK3),sK4,sK3),
    inference(unit_resulting_resolution,[],[f166,f294,f135]) ).

fof(f166,plain,
    in(sK4,succ(sK3)),
    inference(superposition,[],[f110,f102]) ).

fof(f1067,plain,
    ~ in(sK4,singleton(sK3)),
    inference(unit_resulting_resolution,[],[f103,f163,f127]) ).

fof(f127,plain,
    ! [X3,X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ in(X3,X1)
      | X0 = X3 ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( sK6(X0,X1) != X0
            | ~ in(sK6(X0,X1),X1) )
          & ( sK6(X0,X1) = X0
            | in(sK6(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f70,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK6(X0,X1) != X0
          | ~ in(sK6(X0,X1),X1) )
        & ( sK6(X0,X1) = X0
          | in(sK6(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f69,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f163,plain,
    ! [X0] : sP0(X0,singleton(X0)),
    inference(equality_resolution,[],[f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f7,f60]) ).

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

fof(f103,plain,
    sK3 != sK4,
    inference(cnf_transformation,[],[f66]) ).

fof(f1066,plain,
    ~ in(sK3,singleton(sK4)),
    inference(unit_resulting_resolution,[],[f103,f163,f127]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n026.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Mon Apr 29 23:31:19 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (13425)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33  % (13428)WARNING: value z3 for option sas not known
% 0.10/0.33  % (13427)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.33  % (13432)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)
% 0.10/0.33  % (13429)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.33  % (13430)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)
% 0.10/0.34  % (13431)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)
% 0.10/0.34  % (13428)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)
% 0.10/0.34  % (13426)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34  TRYING [1]
% 0.10/0.34  TRYING [2]
% 0.10/0.34  TRYING [3]
% 0.10/0.34  TRYING [4]
% 0.10/0.34  TRYING [1]
% 0.10/0.34  TRYING [2]
% 0.10/0.35  TRYING [5]
% 0.10/0.35  TRYING [3]
% 0.10/0.37  % (13432)First to succeed.
% 0.10/0.37  % (13432)Refutation found. Thanks to Tanya!
% 0.10/0.37  % SZS status Theorem for theBenchmark
% 0.10/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.37  % (13432)------------------------------
% 0.10/0.37  % (13432)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.37  % (13432)Termination reason: Refutation
% 0.10/0.37  
% 0.10/0.37  % (13432)Memory used [KB]: 1368
% 0.10/0.37  % (13432)Time elapsed: 0.037 s
% 0.10/0.37  % (13432)Instructions burned: 71 (million)
% 0.10/0.37  % (13432)------------------------------
% 0.10/0.37  % (13432)------------------------------
% 0.10/0.37  % (13425)Success in time 0.052 s
%------------------------------------------------------------------------------