TSTP Solution File: SET894+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET894+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n011.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 09:08:58 EDT 2024

% Result   : Theorem 0.60s 0.79s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   76 (  16 unt;   0 def)
%            Number of atoms       :  273 (  96 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  330 ( 133   ~; 130   |;  52   &)
%                                         (   7 <=>;   7  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   2 con; 0-3 aty)
%            Number of variables   :  182 ( 151   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f347,plain,
    $false,
    inference(avatar_sat_refutation,[],[f108,f225,f340]) ).

fof(f340,plain,
    ~ spl11_1,
    inference(avatar_contradiction_clause,[],[f339]) ).

fof(f339,plain,
    ( $false
    | ~ spl11_1 ),
    inference(subsumption_resolution,[],[f331,f76]) ).

fof(f76,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f75]) ).

fof(f75,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f50]) ).

fof(f50,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( singleton(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) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f28,f29]) ).

fof(f29,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(f28,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,[],[f27]) ).

fof(f27,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/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',d1_tarski) ).

fof(f331,plain,
    ( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | ~ spl11_1 ),
    inference(backward_demodulation,[],[f243,f328]) ).

fof(f328,plain,
    ( unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)) = sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | ~ spl11_1 ),
    inference(backward_demodulation,[],[f298,f321]) ).

fof(f321,plain,
    ( sK1 = sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))
    | ~ spl11_1 ),
    inference(resolution,[],[f251,f77]) ).

fof(f77,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f49]) ).

fof(f49,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f251,plain,
    ( in(sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))),singleton(sK1))
    | ~ spl11_1 ),
    inference(resolution,[],[f104,f73]) ).

fof(f73,plain,
    ! [X0,X1,X8] :
      ( ~ in(X8,cartesian_product2(X0,X1))
      | in(sK7(X0,X1,X8),X1) ),
    inference(equality_resolution,[],[f42]) ).

fof(f42,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK7(X0,X1,X8),X1)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != sK3(X0,X1,X2)
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(sK3(X0,X1,X2),X2) )
          & ( ( sK3(X0,X1,X2) = ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2))
              & in(sK5(X0,X1,X2),X1)
              & in(sK4(X0,X1,X2),X0) )
            | in(sK3(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
                & in(sK7(X0,X1,X8),X1)
                & in(sK6(X0,X1,X8),X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f22,f25,f24,f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != X3
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(X3,X2) )
          & ( ? [X6,X7] :
                ( ordered_pair(X6,X7) = X3
                & in(X7,X1)
                & in(X6,X0) )
            | in(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( ordered_pair(X4,X5) != sK3(X0,X1,X2)
              | ~ in(X5,X1)
              | ~ in(X4,X0) )
          | ~ in(sK3(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ordered_pair(X6,X7) = sK3(X0,X1,X2)
              & in(X7,X1)
              & in(X6,X0) )
          | in(sK3(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ordered_pair(X6,X7) = sK3(X0,X1,X2)
          & in(X7,X1)
          & in(X6,X0) )
     => ( sK3(X0,X1,X2) = ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2))
        & in(sK5(X0,X1,X2),X1)
        & in(sK4(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ordered_pair(X11,X12) = X8
          & in(X12,X1)
          & in(X11,X0) )
     => ( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
        & in(sK7(X0,X1,X8),X1)
        & in(sK6(X0,X1,X8),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X6,X7] :
                  ( ordered_pair(X6,X7) = X3
                  & in(X7,X1)
                  & in(X6,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ? [X11,X12] :
                  ( ordered_pair(X11,X12) = X8
                  & in(X12,X1)
                  & in(X11,X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | ~ in(X3,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',d2_zfmisc_1) ).

fof(f104,plain,
    ( in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1)))
    | ~ spl11_1 ),
    inference(avatar_component_clause,[],[f103]) ).

fof(f103,plain,
    ( spl11_1
  <=> in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).

fof(f298,plain,
    ( sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))) = unordered_pair(singleton(sK0),unordered_pair(sK0,sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))))
    | ~ spl11_1 ),
    inference(backward_demodulation,[],[f249,f290]) ).

fof(f290,plain,
    ( sK0 = sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))
    | ~ spl11_1 ),
    inference(resolution,[],[f250,f77]) ).

fof(f250,plain,
    ( in(sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))),singleton(sK0))
    | ~ spl11_1 ),
    inference(resolution,[],[f104,f74]) ).

fof(f74,plain,
    ! [X0,X1,X8] :
      ( ~ in(X8,cartesian_product2(X0,X1))
      | in(sK6(X0,X1,X8),X0) ),
    inference(equality_resolution,[],[f41]) ).

fof(f41,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK6(X0,X1,X8),X0)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f249,plain,
    ( sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))) = unordered_pair(singleton(sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))),unordered_pair(sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))),sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))))
    | ~ spl11_1 ),
    inference(resolution,[],[f104,f82]) ).

fof(f82,plain,
    ! [X0,X1,X8] :
      ( ~ in(X8,cartesian_product2(X0,X1))
      | unordered_pair(singleton(sK6(X0,X1,X8)),unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8))) = X8 ),
    inference(backward_demodulation,[],[f72,f53]) ).

fof(f53,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/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',commutativity_k2_tarski) ).

fof(f72,plain,
    ! [X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)),singleton(sK6(X0,X1,X8))) = X8
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f65]) ).

fof(f65,plain,
    ! [X2,X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)),singleton(sK6(X0,X1,X8))) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(definition_unfolding,[],[f43,f40]) ).

fof(f40,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',d5_tarski) ).

fof(f43,plain,
    ! [X2,X0,X1,X8] :
      ( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f243,plain,
    ( ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | ~ spl11_1 ),
    inference(subsumption_resolution,[],[f120,f104]) ).

fof(f120,plain,
    ( ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1))) ),
    inference(extensionality_resolution,[],[f39,f80]) ).

fof(f80,plain,
    cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
    inference(backward_demodulation,[],[f61,f53]) ).

fof(f61,plain,
    cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0))),
    inference(definition_unfolding,[],[f37,f40]) ).

fof(f37,plain,
    cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(ordered_pair(sK0,sK1)),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(ordered_pair(sK0,sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16]) ).

fof(f16,plain,
    ( ? [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) != singleton(ordered_pair(X0,X1))
   => cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(ordered_pair(sK0,sK1)) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) != singleton(ordered_pair(X0,X1)),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',t35_zfmisc_1) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ in(sK2(X0,X1),X1)
      | X0 = X1
      | ~ in(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK2(X0,X1),X1)
          | ~ in(sK2(X0,X1),X0) )
        & ( in(sK2(X0,X1),X1)
          | in(sK2(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f18,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK2(X0,X1),X1)
          | ~ in(sK2(X0,X1),X0) )
        & ( in(sK2(X0,X1),X1)
          | in(sK2(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',t2_tarski) ).

fof(f225,plain,
    ~ spl11_2,
    inference(avatar_contradiction_clause,[],[f210]) ).

fof(f210,plain,
    ( $false
    | ~ spl11_2 ),
    inference(resolution,[],[f188,f127]) ).

fof(f127,plain,
    ( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))
    | ~ spl11_2 ),
    inference(forward_demodulation,[],[f126,f116]) ).

fof(f116,plain,
    ( unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)) = sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | ~ spl11_2 ),
    inference(resolution,[],[f107,f77]) ).

fof(f107,plain,
    ( in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | ~ spl11_2 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f106,plain,
    ( spl11_2
  <=> in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).

fof(f126,plain,
    ( ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1)))
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f125,f76]) ).

fof(f125,plain,
    ( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1)))
    | ~ spl11_2 ),
    inference(forward_demodulation,[],[f120,f116]) ).

fof(f188,plain,
    ! [X0,X1] : in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(singleton(X0),singleton(X1))),
    inference(resolution,[],[f155,f76]) ).

fof(f155,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,X2)
      | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,singleton(X1))) ),
    inference(resolution,[],[f78,f76]) ).

fof(f78,plain,
    ! [X10,X0,X1,X9] :
      ( ~ in(X10,X1)
      | in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),cartesian_product2(X0,X1))
      | ~ in(X9,X0) ),
    inference(backward_demodulation,[],[f71,f53]) ).

fof(f71,plain,
    ! [X10,X0,X1,X9] :
      ( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),cartesian_product2(X0,X1))
      | ~ in(X10,X1)
      | ~ in(X9,X0) ),
    inference(equality_resolution,[],[f70]) ).

fof(f70,plain,
    ! [X2,X10,X0,X1,X9] :
      ( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(equality_resolution,[],[f64]) ).

fof(f64,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( in(X8,X2)
      | unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(definition_unfolding,[],[f44,f40]) ).

fof(f44,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( in(X8,X2)
      | ordered_pair(X9,X10) != X8
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f108,plain,
    ( spl11_1
    | spl11_2 ),
    inference(avatar_split_clause,[],[f96,f106,f103]) ).

fof(f96,plain,
    ( in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
    | in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1))) ),
    inference(extensionality_resolution,[],[f38,f80]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( in(sK2(X0,X1),X1)
      | X0 = X1
      | in(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SET894+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.08/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Fri May  3 16:45:38 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789
% 0.60/0.76  % (3077)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.76  % (3083)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.60/0.77  % (3079)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.77  % (3078)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.60/0.77  % (3080)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.60/0.77  % (3082)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.60/0.77  % (3081)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.77  % (3077)Refutation not found, incomplete strategy% (3077)------------------------------
% 0.60/0.77  % (3077)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77  % (3077)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77  
% 0.60/0.77  % (3077)Memory used [KB]: 1065
% 0.60/0.77  % (3077)Time elapsed: 0.003 s
% 0.60/0.77  % (3077)Instructions burned: 6 (million)
% 0.60/0.77  % (3077)------------------------------
% 0.60/0.77  % (3077)------------------------------
% 0.60/0.77  % (3082)Refutation not found, incomplete strategy% (3082)------------------------------
% 0.60/0.77  % (3082)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77  % (3082)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77  
% 0.60/0.77  % (3082)Memory used [KB]: 1024
% 0.60/0.77  % (3082)Time elapsed: 0.003 s
% 0.60/0.77  % (3082)Instructions burned: 3 (million)
% 0.60/0.77  % (3082)------------------------------
% 0.60/0.77  % (3082)------------------------------
% 0.60/0.77  % (3081)Refutation not found, incomplete strategy% (3081)------------------------------
% 0.60/0.77  % (3081)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77  % (3081)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77  
% 0.60/0.77  % (3081)Memory used [KB]: 1051
% 0.60/0.77  % (3081)Time elapsed: 0.004 s
% 0.60/0.77  % (3081)Instructions burned: 4 (million)
% 0.60/0.77  % (3081)------------------------------
% 0.60/0.77  % (3081)------------------------------
% 0.60/0.77  % (3084)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.60/0.77  % (3084)Refutation not found, incomplete strategy% (3084)------------------------------
% 0.60/0.77  % (3084)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77  % (3084)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77  
% 0.60/0.77  % (3084)Memory used [KB]: 1047
% 0.60/0.77  % (3084)Time elapsed: 0.002 s
% 0.60/0.77  % (3084)Instructions burned: 3 (million)
% 0.60/0.77  % (3084)------------------------------
% 0.60/0.77  % (3084)------------------------------
% 0.60/0.77  % (3086)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.60/0.77  % (3087)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.60/0.77  % (3088)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.60/0.77  % (3085)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.60/0.77  % (3086)Refutation not found, incomplete strategy% (3086)------------------------------
% 0.60/0.77  % (3086)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77  % (3086)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77  
% 0.60/0.77  % (3086)Memory used [KB]: 1034
% 0.60/0.77  % (3086)Time elapsed: 0.003 s
% 0.60/0.77  % (3086)Instructions burned: 3 (million)
% 0.60/0.77  % (3086)------------------------------
% 0.60/0.77  % (3086)------------------------------
% 0.60/0.78  % (3089)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2996ds/518Mi)
% 0.60/0.78  % (3089)Refutation not found, incomplete strategy% (3089)------------------------------
% 0.60/0.78  % (3089)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.78  % (3089)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.78  
% 0.60/0.78  % (3089)Memory used [KB]: 1033
% 0.60/0.78  % (3089)Time elapsed: 0.004 s
% 0.60/0.78  % (3089)Instructions burned: 4 (million)
% 0.60/0.78  % (3089)------------------------------
% 0.60/0.78  % (3089)------------------------------
% 0.60/0.78  % (3080)Instruction limit reached!
% 0.60/0.78  % (3080)------------------------------
% 0.60/0.78  % (3080)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.78  % (3080)Termination reason: Unknown
% 0.60/0.78  % (3080)Termination phase: Saturation
% 0.60/0.78  
% 0.60/0.78  % (3080)Memory used [KB]: 1363
% 0.60/0.78  % (3080)Time elapsed: 0.020 s
% 0.60/0.78  % (3080)Instructions burned: 33 (million)
% 0.60/0.78  % (3080)------------------------------
% 0.60/0.78  % (3080)------------------------------
% 0.60/0.78  % (3088)First to succeed.
% 0.60/0.78  % (3088)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3003"
% 0.60/0.79  % (3088)Refutation found. Thanks to Tanya!
% 0.60/0.79  % SZS status Theorem for Vampire---4
% 0.60/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.79  % (3088)------------------------------
% 0.60/0.79  % (3088)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (3088)Termination reason: Refutation
% 0.60/0.79  
% 0.60/0.79  % (3088)Memory used [KB]: 1243
% 0.60/0.79  % (3088)Time elapsed: 0.012 s
% 0.60/0.79  % (3088)Instructions burned: 32 (million)
% 0.60/0.79  % (3003)Success in time 0.401 s
% 0.60/0.79  % Vampire---4.8 exiting
%------------------------------------------------------------------------------