TSTP Solution File: SET884+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET884+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 : Sun May  5 09:19:36 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   38 (   7 unt;   0 def)
%            Number of atoms       :  181 (  99 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  228 (  85   ~;  81   |;  48   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   98 (  85   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f109,plain,
    $false,
    inference(subsumption_resolution,[],[f108,f35]) ).

fof(f35,plain,
    sK1 != sK2,
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ( sK1 != sK3
    & sK1 != sK2
    & subset(singleton(sK1),unordered_pair(sK2,sK3)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f13,f18]) ).

fof(f18,plain,
    ( ? [X0,X1,X2] :
        ( X0 != X2
        & X0 != X1
        & subset(singleton(X0),unordered_pair(X1,X2)) )
   => ( sK1 != sK3
      & sK1 != sK2
      & subset(singleton(sK1),unordered_pair(sK2,sK3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1,X2] :
      ( X0 != X2
      & X0 != X1
      & subset(singleton(X0),unordered_pair(X1,X2)) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ~ ( X0 != X2
          & X0 != X1
          & subset(singleton(X0),unordered_pair(X1,X2)) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ~ ( X0 != X2
        & X0 != X1
        & subset(singleton(X0),unordered_pair(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).

fof(f108,plain,
    sK1 = sK2,
    inference(subsumption_resolution,[],[f107,f36]) ).

fof(f36,plain,
    sK1 != sK3,
    inference(cnf_transformation,[],[f19]) ).

fof(f107,plain,
    ( sK1 = sK3
    | sK1 = sK2 ),
    inference(resolution,[],[f104,f56]) ).

fof(f56,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f55]) ).

fof(f55,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f42]) ).

fof(f42,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK4(X0,X1) != X0
            | ~ in(sK4(X0,X1),X1) )
          & ( sK4(X0,X1) = X0
            | in(sK4(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK4(X0,X1) != X0
          | ~ in(sK4(X0,X1),X1) )
        & ( sK4(X0,X1) = X0
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,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,[],[f20]) ).

fof(f20,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,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f104,plain,
    ! [X0] :
      ( ~ in(X0,singleton(sK1))
      | sK3 = X0
      | sK2 = X0 ),
    inference(resolution,[],[f100,f84]) ).

fof(f84,plain,
    ! [X0] :
      ( in(X0,unordered_pair(sK2,sK3))
      | ~ in(X0,singleton(sK1)) ),
    inference(resolution,[],[f40,f34]) ).

fof(f34,plain,
    subset(singleton(sK1),unordered_pair(sK2,sK3)),
    inference(cnf_transformation,[],[f19]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) )
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
     => ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f100,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,unordered_pair(X0,X2))
      | X0 = X1
      | X1 = X2 ),
    inference(resolution,[],[f45,f60]) ).

fof(f60,plain,
    ! [X0,X1] : sP0(X1,X0,unordered_pair(X0,X1)),
    inference(equality_resolution,[],[f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0,X2)
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ~ sP0(X1,X0,X2) )
      & ( sP0(X1,X0,X2)
        | unordered_pair(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> sP0(X1,X0,X2) ),
    inference(definition_folding,[],[f4,f16]) ).

fof(f16,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f45,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP0(X0,X1,X2)
      | X1 = X4
      | ~ in(X4,X2)
      | X0 = X4 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ( sK5(X0,X1,X2) != X0
              & sK5(X0,X1,X2) != X1 )
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( sK5(X0,X1,X2) = X0
            | sK5(X0,X1,X2) = X1
            | in(sK5(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X0 != X4
                & X1 != X4 ) )
            & ( X0 = X4
              | X1 = X4
              | ~ in(X4,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f26,f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X0 != X3
              & X1 != X3 )
            | ~ in(X3,X2) )
          & ( X0 = X3
            | X1 = X3
            | in(X3,X2) ) )
     => ( ( ( sK5(X0,X1,X2) != X0
            & sK5(X0,X1,X2) != X1 )
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( sK5(X0,X1,X2) = X0
          | sK5(X0,X1,X2) = X1
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ( X0 != X3
                & X1 != X3 )
              | ~ in(X3,X2) )
            & ( X0 = X3
              | X1 = X3
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X0 != X4
                & X1 != X4 ) )
            & ( X0 = X4
              | X1 = X4
              | ~ in(X4,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n026.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 17:01:23 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (21263)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (21266)WARNING: value z3 for option sas not known
% 0.15/0.37  % (21266)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)
% 0.15/0.37  % (21267)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (21269)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)
% 0.15/0.37  % (21268)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)
% 0.15/0.37  % (21270)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)
% 0.21/0.37  % (21265)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.37  TRYING [3]
% 0.21/0.37  % (21266)First to succeed.
% 0.21/0.37  % (21264)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37  TRYING [4]
% 0.21/0.38  % (21270)Also succeeded, but the first one will report.
% 0.21/0.38  % (21266)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21263"
% 0.21/0.38  % (21269)Also succeeded, but the first one will report.
% 0.21/0.38  % (21266)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (21266)------------------------------
% 0.21/0.38  % (21266)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (21266)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (21266)Memory used [KB]: 834
% 0.21/0.38  % (21266)Time elapsed: 0.005 s
% 0.21/0.38  % (21266)Instructions burned: 7 (million)
% 0.21/0.38  % (21263)Success in time 0.019 s
%------------------------------------------------------------------------------