TSTP Solution File: SET919+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET919+1 : TPTP v8.2.0. 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 : Tue May 21 03:24:48 EDT 2024

% Result   : Theorem 4.25s 0.98s
% Output   : Refutation 4.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   91 (  34 unt;   0 def)
%            Number of atoms       :  304 (  83 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  341 ( 128   ~; 128   |;  62   &)
%                                         (  17 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  200 ( 182   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f33343,plain,
    $false,
    inference(subsumption_resolution,[],[f33304,f24916]) ).

fof(f24916,plain,
    ! [X0] : ~ in(sK7,set_intersection2(sK6,X0)),
    inference(unit_resulting_resolution,[],[f89,f24709,f73]) ).

fof(f73,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP4(X0,X1,X2)
      | ~ in(X4,X2)
      | sP3(X1,X4,X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ( ( ~ sP3(X1,sK10(X0,X1,X2),X0)
            | ~ in(sK10(X0,X1,X2),X2) )
          & ( sP3(X1,sK10(X0,X1,X2),X0)
            | in(sK10(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP3(X1,X4,X0) )
            & ( sP3(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f40,f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP3(X1,X3,X0)
            | ~ in(X3,X2) )
          & ( sP3(X1,X3,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP3(X1,sK10(X0,X1,X2),X0)
          | ~ in(sK10(X0,X1,X2),X2) )
        & ( sP3(X1,sK10(X0,X1,X2),X0)
          | in(sK10(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP3(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP3(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP3(X1,X4,X0) )
            & ( sP3(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP3(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP3(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ sP3(X1,X3,X0) )
            & ( sP3(X1,X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( sP4(X0,X1,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> sP3(X1,X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f24709,plain,
    ! [X0] : ~ sP3(X0,sK7,sK6),
    inference(unit_resulting_resolution,[],[f24617,f77]) ).

fof(f77,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0,X1,X2)
      | in(X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ( sP3(X0,X1,X2)
        | ~ in(X1,X0)
        | ~ in(X1,X2) )
      & ( ( in(X1,X0)
          & in(X1,X2) )
        | ~ sP3(X0,X1,X2) ) ),
    inference(rectify,[],[f44]) ).

fof(f44,plain,
    ! [X1,X3,X0] :
      ( ( sP3(X1,X3,X0)
        | ~ in(X3,X1)
        | ~ in(X3,X0) )
      & ( ( in(X3,X1)
          & in(X3,X0) )
        | ~ sP3(X1,X3,X0) ) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X1,X3,X0] :
      ( ( sP3(X1,X3,X0)
        | ~ in(X3,X1)
        | ~ in(X3,X0) )
      & ( ( in(X3,X1)
          & in(X3,X0) )
        | ~ sP3(X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X1,X3,X0] :
      ( sP3(X1,X3,X0)
    <=> ( in(X3,X1)
        & in(X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f24617,plain,
    ~ in(sK7,sK6),
    inference(unit_resulting_resolution,[],[f24604,f52]) ).

fof(f52,plain,
    ( ~ in(sK7,sK6)
    | sK5 = sK7 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6)
    & ( sK5 = sK7
      | ~ in(sK7,sK6) )
    & in(sK5,sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f14,f24]) ).

fof(f24,plain,
    ( ? [X0,X1,X2] :
        ( singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
        & ( X0 = X2
          | ~ in(X2,X1) )
        & in(X0,X1) )
   => ( singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6)
      & ( sK5 = sK7
        | ~ in(sK7,sK6) )
      & in(sK5,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
      & ( X0 = X2
        | ~ in(X2,X1) )
      & in(X0,X1) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ? [X0,X1,X2] :
      ( singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
      & ( X0 = X2
        | ~ in(X2,X1) )
      & in(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( in(X0,X1)
       => ( singleton(X0) = set_intersection2(unordered_pair(X0,X2),X1)
          | ( X0 != X2
            & in(X2,X1) ) ) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X0,X1,X2] :
      ( in(X0,X1)
     => ( singleton(X0) = set_intersection2(unordered_pair(X0,X2),X1)
        | ( X0 != X2
          & in(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).

fof(f24604,plain,
    sK5 != sK7,
    inference(superposition,[],[f24310,f24594]) ).

fof(f24594,plain,
    sK7 = sK8(sK5,unordered_pair(sK5,sK7)),
    inference(unit_resulting_resolution,[],[f24310,f24547,f68]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,X2)
      | X0 = X2
      | X0 = X1 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( X0 != X1
          & X0 != X2 ) )
      & ( X0 = X1
        | X0 = X2
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X3,X1,X0] :
      ( ( sP1(X3,X1,X0)
        | ( X1 != X3
          & X0 != X3 ) )
      & ( X1 = X3
        | X0 = X3
        | ~ sP1(X3,X1,X0) ) ),
    inference(flattening,[],[f35]) ).

fof(f35,plain,
    ! [X3,X1,X0] :
      ( ( sP1(X3,X1,X0)
        | ( X1 != X3
          & X0 != X3 ) )
      & ( X1 = X3
        | X0 = X3
        | ~ sP1(X3,X1,X0) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X3,X1,X0] :
      ( sP1(X3,X1,X0)
    <=> ( X1 = X3
        | X0 = X3 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f24547,plain,
    sP1(sK8(sK5,unordered_pair(sK5,sK7)),sK7,sK5),
    inference(unit_resulting_resolution,[],[f88,f24312,f64]) ).

fof(f64,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | ~ in(X4,X2)
      | sP1(X4,X1,X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ( ~ sP1(sK9(X0,X1,X2),X1,X0)
            | ~ in(sK9(X0,X1,X2),X2) )
          & ( sP1(sK9(X0,X1,X2),X1,X0)
            | in(sK9(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP1(X4,X1,X0) )
            & ( sP1(X4,X1,X0)
              | ~ in(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f32,f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP1(X3,X1,X0)
            | ~ in(X3,X2) )
          & ( sP1(X3,X1,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP1(sK9(X0,X1,X2),X1,X0)
          | ~ in(sK9(X0,X1,X2),X2) )
        & ( sP1(sK9(X0,X1,X2),X1,X0)
          | in(sK9(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP1(X3,X1,X0)
              | ~ in(X3,X2) )
            & ( sP1(X3,X1,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP1(X4,X1,X0) )
            & ( sP1(X4,X1,X0)
              | ~ in(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP1(X3,X1,X0)
              | ~ in(X3,X2) )
            & ( sP1(X3,X1,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ sP1(X3,X1,X0) )
            & ( sP1(X3,X1,X0)
              | ~ in(X3,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( sP2(X0,X1,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> sP1(X3,X1,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f24312,plain,
    in(sK8(sK5,unordered_pair(sK5,sK7)),unordered_pair(sK5,sK7)),
    inference(subsumption_resolution,[],[f24311,f24310]) ).

fof(f24311,plain,
    ( sK5 = sK8(sK5,unordered_pair(sK5,sK7))
    | in(sK8(sK5,unordered_pair(sK5,sK7)),unordered_pair(sK5,sK7)) ),
    inference(resolution,[],[f24260,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sK8(X0,X1) = X0
      | in(sK8(X0,X1),X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( sK8(X0,X1) != X0
            | ~ in(sK8(X0,X1),X1) )
          & ( sK8(X0,X1) = X0
            | in(sK8(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK8(X0,X1) != X0
          | ~ in(sK8(X0,X1),X1) )
        & ( sK8(X0,X1) = X0
          | in(sK8(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,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,[],[f26]) ).

fof(f26,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,[],[f16]) ).

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

fof(f24260,plain,
    ~ sP0(sK5,unordered_pair(sK5,sK7)),
    inference(unit_resulting_resolution,[],[f1419,f19396,f58]) ).

fof(f58,plain,
    ! [X3,X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ in(X3,X1)
      | X0 = X3 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f19396,plain,
    in(sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),unordered_pair(sK5,sK7)),
    inference(unit_resulting_resolution,[],[f19342,f78]) ).

fof(f78,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0,X1,X2)
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f19342,plain,
    sP3(unordered_pair(sK5,sK7),sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),sK6),
    inference(unit_resulting_resolution,[],[f89,f2330,f73]) ).

fof(f2330,plain,
    in(sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),set_intersection2(sK6,unordered_pair(sK5,sK7))),
    inference(subsumption_resolution,[],[f2322,f1419]) ).

fof(f2322,plain,
    ( sK5 = sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7)))
    | in(sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),set_intersection2(sK6,unordered_pair(sK5,sK7))) ),
    inference(resolution,[],[f60,f120]) ).

fof(f120,plain,
    ~ sP0(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),
    inference(forward_demodulation,[],[f117,f56]) ).

fof(f56,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f117,plain,
    ~ sP0(sK5,set_intersection2(unordered_pair(sK5,sK7),sK6)),
    inference(unit_resulting_resolution,[],[f53,f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | singleton(X0) = X1 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f17]) ).

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

fof(f4,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f53,plain,
    singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6),
    inference(cnf_transformation,[],[f25]) ).

fof(f1419,plain,
    sK5 != sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),
    inference(unit_resulting_resolution,[],[f120,f917,f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | sK8(X0,X1) != X0
      | sP0(X0,X1) ),
    inference(inner_rewriting,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sK8(X0,X1) != X0
      | ~ in(sK8(X0,X1),X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f917,plain,
    ! [X0] : in(sK5,set_intersection2(sK6,unordered_pair(sK5,X0))),
    inference(forward_demodulation,[],[f875,f56]) ).

fof(f875,plain,
    ! [X0] : in(sK5,set_intersection2(unordered_pair(sK5,X0),sK6)),
    inference(unit_resulting_resolution,[],[f350,f106,f74]) ).

fof(f74,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP4(X0,X1,X2)
      | ~ sP3(X1,X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f106,plain,
    ! [X0,X1] : sP4(X0,X1,set_intersection2(X1,X0)),
    inference(superposition,[],[f89,f56]) ).

fof(f350,plain,
    ! [X0] : sP3(unordered_pair(sK5,X0),sK5,sK6),
    inference(unit_resulting_resolution,[],[f51,f255,f79]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X0)
      | sP3(X0,X1,X2)
      | ~ in(X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f255,plain,
    ! [X0,X1] : in(X0,unordered_pair(X0,X1)),
    inference(unit_resulting_resolution,[],[f86,f102,f65]) ).

fof(f65,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | ~ sP1(X4,X1,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f102,plain,
    ! [X0,X1] : sP2(X0,X1,unordered_pair(X1,X0)),
    inference(superposition,[],[f88,f55]) ).

fof(f55,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f86,plain,
    ! [X2,X1] : sP1(X1,X1,X2),
    inference(equality_resolution,[],[f70]) ).

fof(f70,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X1,X2)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f51,plain,
    in(sK5,sK6),
    inference(cnf_transformation,[],[f25]) ).

fof(f88,plain,
    ! [X0,X1] : sP2(X0,X1,unordered_pair(X0,X1)),
    inference(equality_resolution,[],[f71]) ).

fof(f71,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ~ sP2(X0,X1,X2) )
      & ( sP2(X0,X1,X2)
        | unordered_pair(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> sP2(X0,X1,X2) ),
    inference(definition_folding,[],[f5,f19,f18]) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f24310,plain,
    sK5 != sK8(sK5,unordered_pair(sK5,sK7)),
    inference(unit_resulting_resolution,[],[f255,f24260,f90]) ).

fof(f89,plain,
    ! [X0,X1] : sP4(X0,X1,set_intersection2(X0,X1)),
    inference(equality_resolution,[],[f80]) ).

fof(f80,plain,
    ! [X2,X0,X1] :
      ( sP4(X0,X1,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ~ sP4(X0,X1,X2) )
      & ( sP4(X0,X1,X2)
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> sP4(X0,X1,X2) ),
    inference(definition_folding,[],[f6,f22,f21]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f33304,plain,
    in(sK7,set_intersection2(sK6,unordered_pair(sK5,sK7))),
    inference(superposition,[],[f2330,f33294]) ).

fof(f33294,plain,
    sK7 = sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),
    inference(unit_resulting_resolution,[],[f1419,f24261,f68]) ).

fof(f24261,plain,
    sP1(sK8(sK5,set_intersection2(sK6,unordered_pair(sK5,sK7))),sK7,sK5),
    inference(unit_resulting_resolution,[],[f88,f19396,f64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET919+1 : TPTP v8.2.0. Released v3.2.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 11:14:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (1709)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (1712)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (1713)WARNING: value z3 for option sas not known
% 0.14/0.37  % (1713)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)
% 0.14/0.37  % (1714)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (1715)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)
% 0.14/0.37  % (1710)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (1717)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)
% 0.14/0.37  % (1716)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)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.40  TRYING [5]
% 0.14/0.40  TRYING [3]
% 0.21/0.43  TRYING [6]
% 0.21/0.50  TRYING [7]
% 0.21/0.50  TRYING [4]
% 1.56/0.57  TRYING [8]
% 2.04/0.64  TRYING [5]
% 2.64/0.74  TRYING [9]
% 4.25/0.97  TRYING [6]
% 4.25/0.97  % (1717)First to succeed.
% 4.25/0.97  % (1717)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1709"
% 4.25/0.98  % (1717)Refutation found. Thanks to Tanya!
% 4.25/0.98  % SZS status Theorem for theBenchmark
% 4.25/0.98  % SZS output start Proof for theBenchmark
% See solution above
% 4.25/0.98  % (1717)------------------------------
% 4.25/0.98  % (1717)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.25/0.98  % (1717)Termination reason: Refutation
% 4.25/0.98  
% 4.25/0.98  % (1717)Memory used [KB]: 10171
% 4.25/0.98  % (1717)Time elapsed: 0.603 s
% 4.25/0.98  % (1717)Instructions burned: 1699 (million)
% 4.25/0.98  % (1709)Success in time 0.593 s
%------------------------------------------------------------------------------