TSTP Solution File: SEU178+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU178+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : 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 : Sun May  5 09:20:46 EDT 2024

% Result   : Theorem 0.58s 0.78s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   71 (   8 unt;   0 def)
%            Number of atoms       :  304 (  34 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  386 ( 153   ~; 157   |;  48   &)
%                                         (  13 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   4 con; 0-2 aty)
%            Number of variables   :  215 ( 173   !;  42   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f324,plain,
    $false,
    inference(subsumption_resolution,[],[f321,f109]) ).

fof(f109,plain,
    ~ subset(sK0,sF14),
    inference(definition_folding,[],[f78,f108,f107,f106]) ).

fof(f106,plain,
    relation_dom(sK0) = sF12,
    introduced(function_definition,[new_symbols(definition,[sF12])]) ).

fof(f107,plain,
    relation_rng(sK0) = sF13,
    introduced(function_definition,[new_symbols(definition,[sF13])]) ).

fof(f108,plain,
    cartesian_product2(sF12,sF13) = sF14,
    introduced(function_definition,[new_symbols(definition,[sF14])]) ).

fof(f78,plain,
    ~ subset(sK0,cartesian_product2(relation_dom(sK0),relation_rng(sK0))),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ( ~ subset(sK0,cartesian_product2(relation_dom(sK0),relation_rng(sK0)))
    & relation(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f42,f49]) ).

fof(f49,plain,
    ( ? [X0] :
        ( ~ subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
        & relation(X0) )
   => ( ~ subset(sK0,cartesian_product2(relation_dom(sK0),relation_rng(sK0)))
      & relation(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ? [X0] :
      ( ~ subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
      & relation(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,negated_conjecture,
    ~ ! [X0] :
        ( relation(X0)
       => subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
    inference(negated_conjecture,[],[f32]) ).

fof(f32,conjecture,
    ! [X0] :
      ( relation(X0)
     => subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
    file('/export/starexec/sandbox2/tmp/tmp.BrindLcLTS/Vampire---4.8_26350',t21_relat_1) ).

fof(f321,plain,
    subset(sK0,sF14),
    inference(duplicate_literal_removal,[],[f320]) ).

fof(f320,plain,
    ( subset(sK0,sF14)
    | subset(sK0,sF14) ),
    inference(resolution,[],[f317,f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ~ in(sK8(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK8(X0,X1),X1)
          & in(sK8(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f66,f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK8(X0,X1),X1)
        & in(sK8(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f65,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BrindLcLTS/Vampire---4.8_26350',d3_tarski) ).

fof(f317,plain,
    ! [X0] :
      ( in(sK8(sK0,X0),sF14)
      | subset(sK0,X0) ),
    inference(subsumption_resolution,[],[f316,f77]) ).

fof(f77,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f50]) ).

fof(f316,plain,
    ! [X0] :
      ( in(sK8(sK0,X0),sF14)
      | ~ relation(sK0)
      | subset(sK0,X0) ),
    inference(duplicate_literal_removal,[],[f313]) ).

fof(f313,plain,
    ! [X0] :
      ( in(sK8(sK0,X0),sF14)
      | ~ relation(sK0)
      | subset(sK0,X0)
      | subset(sK0,X0) ),
    inference(resolution,[],[f306,f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( in(sK8(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f306,plain,
    ! [X0,X1] :
      ( ~ in(sK8(sK0,X1),X0)
      | in(sK8(sK0,X1),sF14)
      | ~ relation(X0)
      | subset(sK0,X1) ),
    inference(subsumption_resolution,[],[f305,f77]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | in(sK8(sK0,X1),sF14)
      | ~ in(sK8(sK0,X1),X0)
      | ~ relation(sK0)
      | subset(sK0,X1) ),
    inference(duplicate_literal_removal,[],[f302]) ).

fof(f302,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | in(sK8(sK0,X1),sF14)
      | ~ in(sK8(sK0,X1),X0)
      | ~ relation(sK0)
      | subset(sK0,X1)
      | subset(sK0,X1) ),
    inference(resolution,[],[f288,f92]) ).

fof(f288,plain,
    ! [X2,X0,X1] :
      ( ~ in(sK8(sK0,X0),X2)
      | ~ relation(X1)
      | in(sK8(sK0,X0),sF14)
      | ~ in(sK8(sK0,X0),X1)
      | ~ relation(X2)
      | subset(sK0,X0) ),
    inference(resolution,[],[f281,f92]) ).

fof(f281,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,sK0)
      | ~ in(X0,X1)
      | ~ relation(X1)
      | in(X0,sF14)
      | ~ in(X0,X2)
      | ~ relation(X2) ),
    inference(subsumption_resolution,[],[f279,f256]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( in(sK3(X0),sF12)
      | ~ in(X0,sK0)
      | ~ in(X0,X1)
      | ~ relation(X1) ),
    inference(subsumption_resolution,[],[f254,f77]) ).

fof(f254,plain,
    ! [X0,X1] :
      ( in(sK3(X0),sF12)
      | ~ in(X0,sK0)
      | ~ relation(sK0)
      | ~ in(X0,X1)
      | ~ relation(X1) ),
    inference(superposition,[],[f133,f106]) ).

fof(f133,plain,
    ! [X2,X0,X1] :
      ( in(sK3(X0),relation_dom(X1))
      | ~ in(X0,X1)
      | ~ relation(X1)
      | ~ in(X0,X2)
      | ~ relation(X2) ),
    inference(superposition,[],[f102,f81]) ).

fof(f81,plain,
    ! [X0,X4] :
      ( ordered_pair(sK3(X4),sK4(X4)) = X4
      | ~ in(X4,X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ( relation(X0)
        | ( ! [X2,X3] : ordered_pair(X2,X3) != sK2(X0)
          & in(sK2(X0),X0) ) )
      & ( ! [X4] :
            ( ordered_pair(sK3(X4),sK4(X4)) = X4
            | ~ in(X4,X0) )
        | ~ relation(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f54,f56,f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2,X3] : ordered_pair(X2,X3) != X1
          & in(X1,X0) )
     => ( ! [X3,X2] : ordered_pair(X2,X3) != sK2(X0)
        & in(sK2(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X4] :
      ( ? [X5,X6] : ordered_pair(X5,X6) = X4
     => ordered_pair(sK3(X4),sK4(X4)) = X4 ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ! [X0] :
      ( ( relation(X0)
        | ? [X1] :
            ( ! [X2,X3] : ordered_pair(X2,X3) != X1
            & in(X1,X0) ) )
      & ( ! [X4] :
            ( ? [X5,X6] : ordered_pair(X5,X6) = X4
            | ~ in(X4,X0) )
        | ~ relation(X0) ) ),
    inference(rectify,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ( relation(X0)
        | ? [X1] :
            ( ! [X2,X3] : ordered_pair(X2,X3) != X1
            & in(X1,X0) ) )
      & ( ! [X1] :
            ( ? [X2,X3] : ordered_pair(X2,X3) = X1
            | ~ in(X1,X0) )
        | ~ relation(X0) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( relation(X0)
    <=> ! [X1] :
          ( ? [X2,X3] : ordered_pair(X2,X3) = X1
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( relation(X0)
    <=> ! [X1] :
          ~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
            & in(X1,X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BrindLcLTS/Vampire---4.8_26350',d1_relat_1) ).

fof(f102,plain,
    ! [X0,X6,X5] :
      ( ~ in(ordered_pair(X5,X6),X0)
      | in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X5,X6),X0)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(sK5(X0,X1),X3),X0)
                | ~ in(sK5(X0,X1),X1) )
              & ( in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
                | in(sK5(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( in(ordered_pair(X5,sK7(X0,X5)),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f59,f62,f61,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X2,X4),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(sK5(X0,X1),X3),X0)
          | ~ in(sK5(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(sK5(X0,X1),X4),X0)
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(sK5(X0,X1),X4),X0)
     => in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X5,X7),X0)
     => in(ordered_pair(X5,sK7(X0,X5)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X2,X4),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( ? [X7] : in(ordered_pair(X5,X7),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BrindLcLTS/Vampire---4.8_26350',d4_relat_1) ).

fof(f279,plain,
    ! [X2,X0,X1] :
      ( in(X0,sF14)
      | ~ in(sK3(X0),sF12)
      | ~ in(X0,X1)
      | ~ relation(X1)
      | ~ in(X0,sK0)
      | ~ in(X0,X2)
      | ~ relation(X2) ),
    inference(resolution,[],[f150,f260]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( in(sK4(X0),sF13)
      | ~ in(X0,sK0)
      | ~ in(X0,X1)
      | ~ relation(X1) ),
    inference(subsumption_resolution,[],[f258,f77]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( in(sK4(X0),sF13)
      | ~ in(X0,sK0)
      | ~ relation(sK0)
      | ~ in(X0,X1)
      | ~ relation(X1) ),
    inference(superposition,[],[f134,f107]) ).

fof(f134,plain,
    ! [X2,X0,X1] :
      ( in(sK4(X0),relation_rng(X1))
      | ~ in(X0,X1)
      | ~ relation(X1)
      | ~ in(X0,X2)
      | ~ relation(X2) ),
    inference(superposition,[],[f104,f81]) ).

fof(f104,plain,
    ! [X0,X6,X5] :
      ( ~ in(ordered_pair(X6,X5),X0)
      | in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X6,X5),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK9(X0,X1)),X0)
                | ~ in(sK9(X0,X1),X1) )
              & ( in(ordered_pair(sK10(X0,X1),sK9(X0,X1)),X0)
                | in(sK9(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK11(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f70,f73,f72,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X4,X2),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(X3,sK9(X0,X1)),X0)
          | ~ in(sK9(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK9(X0,X1)),X0)
          | in(sK9(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK9(X0,X1)),X0)
     => in(ordered_pair(sK10(X0,X1),sK9(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK11(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BrindLcLTS/Vampire---4.8_26350',d5_relat_1) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0),sF13)
      | in(X0,sF14)
      | ~ in(sK3(X0),sF12)
      | ~ in(X0,X1)
      | ~ relation(X1) ),
    inference(superposition,[],[f143,f81]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X1),sF14)
      | ~ in(X1,sF13)
      | ~ in(X0,sF12) ),
    inference(superposition,[],[f100,f108]) ).

fof(f100,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | ~ in(X1,X3)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BrindLcLTS/Vampire---4.8_26350',t106_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SEU178+1 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.15/0.36  % 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   : Fri May  3 11:29:47 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  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.BrindLcLTS/Vampire---4.8_26350
% 0.58/0.75  % (26746)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)
% 0.58/0.75  % (26739)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)
% 0.58/0.75  % (26742)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)
% 0.58/0.75  % (26741)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.75  % (26740)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)
% 0.58/0.75  % (26744)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)
% 0.58/0.75  % (26743)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)
% 0.58/0.75  % (26745)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)
% 0.58/0.75  % (26744)Refutation not found, incomplete strategy% (26744)------------------------------
% 0.58/0.75  % (26744)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (26744)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.75  
% 0.58/0.75  % (26744)Memory used [KB]: 1038
% 0.58/0.75  % (26744)Time elapsed: 0.003 s
% 0.58/0.75  % (26744)Instructions burned: 4 (million)
% 0.58/0.76  % (26744)------------------------------
% 0.58/0.76  % (26744)------------------------------
% 0.58/0.76  % (26739)Refutation not found, incomplete strategy% (26739)------------------------------
% 0.58/0.76  % (26739)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.76  % (26739)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.76  
% 0.58/0.76  % (26739)Memory used [KB]: 1084
% 0.58/0.76  % (26739)Time elapsed: 0.008 s
% 0.58/0.76  % (26739)Instructions burned: 11 (million)
% 0.58/0.76  % (26749)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)
% 0.58/0.76  % (26739)------------------------------
% 0.58/0.76  % (26739)------------------------------
% 0.58/0.76  % (26752)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)
% 0.58/0.77  % (26746)Instruction limit reached!
% 0.58/0.77  % (26746)------------------------------
% 0.58/0.77  % (26746)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77  % (26746)Termination reason: Unknown
% 0.58/0.77  % (26746)Termination phase: Saturation
% 0.58/0.77  
% 0.58/0.77  % (26746)Memory used [KB]: 1796
% 0.58/0.77  % (26746)Time elapsed: 0.020 s
% 0.58/0.77  % (26746)Instructions burned: 57 (million)
% 0.58/0.77  % (26746)------------------------------
% 0.58/0.77  % (26746)------------------------------
% 0.58/0.77  % (26742)Instruction limit reached!
% 0.58/0.77  % (26742)------------------------------
% 0.58/0.77  % (26742)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77  % (26742)Termination reason: Unknown
% 0.58/0.77  % (26742)Termination phase: Saturation
% 0.58/0.77  
% 0.58/0.77  % (26742)Memory used [KB]: 1433
% 0.58/0.77  % (26742)Time elapsed: 0.021 s
% 0.58/0.77  % (26742)Instructions burned: 33 (million)
% 0.58/0.77  % (26742)------------------------------
% 0.58/0.77  % (26742)------------------------------
% 0.58/0.77  % (26757)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)
% 0.58/0.77  % (26743)Instruction limit reached!
% 0.58/0.77  % (26743)------------------------------
% 0.58/0.77  % (26743)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77  % (26743)Termination reason: Unknown
% 0.58/0.77  % (26743)Termination phase: Saturation
% 0.58/0.77  
% 0.58/0.77  % (26743)Memory used [KB]: 1368
% 0.58/0.77  % (26743)Time elapsed: 0.022 s
% 0.58/0.77  % (26743)Instructions burned: 35 (million)
% 0.58/0.77  % (26743)------------------------------
% 0.58/0.77  % (26743)------------------------------
% 0.58/0.78  % (26740)Instruction limit reached!
% 0.58/0.78  % (26740)------------------------------
% 0.58/0.78  % (26740)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (26740)Termination reason: Unknown
% 0.58/0.78  % (26740)Termination phase: Saturation
% 0.58/0.78  
% 0.58/0.78  % (26740)Memory used [KB]: 1316
% 0.58/0.78  % (26740)Time elapsed: 0.025 s
% 0.58/0.78  % (26740)Instructions burned: 51 (million)
% 0.58/0.78  % (26740)------------------------------
% 0.58/0.78  % (26740)------------------------------
% 0.58/0.78  % (26761)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 (2995ds/52Mi)
% 0.58/0.78  % (26762)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 (2995ds/518Mi)
% 0.58/0.78  % (26757)First to succeed.
% 0.58/0.78  % (26757)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26568"
% 0.58/0.78  % (26757)Refutation found. Thanks to Tanya!
% 0.58/0.78  % SZS status Theorem for Vampire---4
% 0.58/0.78  % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.78  % (26757)------------------------------
% 0.58/0.78  % (26757)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (26757)Termination reason: Refutation
% 0.58/0.78  
% 0.58/0.78  % (26757)Memory used [KB]: 1170
% 0.58/0.78  % (26757)Time elapsed: 0.006 s
% 0.58/0.78  % (26757)Instructions burned: 16 (million)
% 0.58/0.78  % (26568)Success in time 0.405 s
% 0.58/0.78  % Vampire---4.8 exiting
%------------------------------------------------------------------------------