TSTP Solution File: SEU293+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n004.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 : Wed Aug 31 18:33:03 EDT 2022

% Result   : Theorem 1.80s 0.60s
% Output   : Refutation 1.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  114 (  13 unt;   0 def)
%            Number of atoms       :  495 (  80 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  604 ( 223   ~; 227   |; 103   &)
%                                         (  25 <=>;  24  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   7 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   8 con; 0-3 aty)
%            Number of variables   :  198 ( 162   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f609,plain,
    $false,
    inference(avatar_sat_refutation,[],[f277,f278,f279,f396,f408,f413,f503,f535,f608]) ).

fof(f608,plain,
    ( ~ spl25_1
    | spl25_2
    | ~ spl25_3
    | ~ spl25_6 ),
    inference(avatar_contradiction_clause,[],[f607]) ).

fof(f607,plain,
    ( $false
    | ~ spl25_1
    | spl25_2
    | ~ spl25_3
    | ~ spl25_6 ),
    inference(subsumption_resolution,[],[f606,f267]) ).

fof(f267,plain,
    ( in(sF23,sK20)
    | ~ spl25_1 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f266,plain,
    ( spl25_1
  <=> in(sF23,sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_1])]) ).

fof(f606,plain,
    ( ~ in(sF23,sK20)
    | spl25_2
    | ~ spl25_3
    | ~ spl25_6 ),
    inference(subsumption_resolution,[],[f600,f272]) ).

fof(f272,plain,
    ( ~ in(sK21,sF24)
    | spl25_2 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f270,plain,
    ( spl25_2
  <=> in(sK21,sF24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_2])]) ).

fof(f600,plain,
    ( in(sK21,sF24)
    | ~ in(sF23,sK20)
    | ~ spl25_3
    | ~ spl25_6 ),
    inference(superposition,[],[f504,f261]) ).

fof(f261,plain,
    sF24 = relation_inverse_image(sK19,sK20),
    introduced(function_definition,[]) ).

fof(f504,plain,
    ( ! [X0] :
        ( in(sK21,relation_inverse_image(sK19,X0))
        | ~ in(sF23,X0) )
    | ~ spl25_3
    | ~ spl25_6 ),
    inference(subsumption_resolution,[],[f450,f275]) ).

fof(f275,plain,
    ( in(sK21,sK17)
    | ~ spl25_3 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f274,plain,
    ( spl25_3
  <=> in(sK21,sK17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).

fof(f450,plain,
    ( ! [X0] :
        ( ~ in(sK21,sK17)
        | in(sK21,relation_inverse_image(sK19,X0))
        | ~ in(sF23,X0) )
    | ~ spl25_6 ),
    inference(forward_demodulation,[],[f449,f438]) ).

fof(f438,plain,
    sK17 = relation_dom(sK19),
    inference(backward_demodulation,[],[f385,f437]) ).

fof(f437,plain,
    sK17 = relation_dom_as_subset(sK17,sK18,sK19),
    inference(subsumption_resolution,[],[f436,f245]) ).

fof(f245,plain,
    relation_of2_as_subset(sK19,sK17,sK18),
    inference(cnf_transformation,[],[f165]) ).

fof(f165,plain,
    ( relation_of2_as_subset(sK19,sK17,sK18)
    & ( ~ in(apply(sK19,sK21),sK20)
      | ~ in(sK21,sK17)
      | ~ in(sK21,relation_inverse_image(sK19,sK20)) )
    & ( ( in(apply(sK19,sK21),sK20)
        & in(sK21,sK17) )
      | in(sK21,relation_inverse_image(sK19,sK20)) )
    & quasi_total(sK19,sK17,sK18)
    & empty_set != sK18
    & function(sK19) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20,sK21])],[f162,f164,f163]) ).

fof(f163,plain,
    ( ? [X0,X1,X2,X3] :
        ( relation_of2_as_subset(X2,X0,X1)
        & ? [X4] :
            ( ( ~ in(apply(X2,X4),X3)
              | ~ in(X4,X0)
              | ~ in(X4,relation_inverse_image(X2,X3)) )
            & ( ( in(apply(X2,X4),X3)
                & in(X4,X0) )
              | in(X4,relation_inverse_image(X2,X3)) ) )
        & quasi_total(X2,X0,X1)
        & empty_set != X1
        & function(X2) )
   => ( relation_of2_as_subset(sK19,sK17,sK18)
      & ? [X4] :
          ( ( ~ in(apply(sK19,X4),sK20)
            | ~ in(X4,sK17)
            | ~ in(X4,relation_inverse_image(sK19,sK20)) )
          & ( ( in(apply(sK19,X4),sK20)
              & in(X4,sK17) )
            | in(X4,relation_inverse_image(sK19,sK20)) ) )
      & quasi_total(sK19,sK17,sK18)
      & empty_set != sK18
      & function(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f164,plain,
    ( ? [X4] :
        ( ( ~ in(apply(sK19,X4),sK20)
          | ~ in(X4,sK17)
          | ~ in(X4,relation_inverse_image(sK19,sK20)) )
        & ( ( in(apply(sK19,X4),sK20)
            & in(X4,sK17) )
          | in(X4,relation_inverse_image(sK19,sK20)) ) )
   => ( ( ~ in(apply(sK19,sK21),sK20)
        | ~ in(sK21,sK17)
        | ~ in(sK21,relation_inverse_image(sK19,sK20)) )
      & ( ( in(apply(sK19,sK21),sK20)
          & in(sK21,sK17) )
        | in(sK21,relation_inverse_image(sK19,sK20)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f162,plain,
    ? [X0,X1,X2,X3] :
      ( relation_of2_as_subset(X2,X0,X1)
      & ? [X4] :
          ( ( ~ in(apply(X2,X4),X3)
            | ~ in(X4,X0)
            | ~ in(X4,relation_inverse_image(X2,X3)) )
          & ( ( in(apply(X2,X4),X3)
              & in(X4,X0) )
            | in(X4,relation_inverse_image(X2,X3)) ) )
      & quasi_total(X2,X0,X1)
      & empty_set != X1
      & function(X2) ),
    inference(rectify,[],[f161]) ).

fof(f161,plain,
    ? [X1,X3,X2,X0] :
      ( relation_of2_as_subset(X2,X1,X3)
      & ? [X4] :
          ( ( ~ in(apply(X2,X4),X0)
            | ~ in(X4,X1)
            | ~ in(X4,relation_inverse_image(X2,X0)) )
          & ( ( in(apply(X2,X4),X0)
              & in(X4,X1) )
            | in(X4,relation_inverse_image(X2,X0)) ) )
      & quasi_total(X2,X1,X3)
      & empty_set != X3
      & function(X2) ),
    inference(flattening,[],[f160]) ).

fof(f160,plain,
    ? [X1,X3,X2,X0] :
      ( relation_of2_as_subset(X2,X1,X3)
      & ? [X4] :
          ( ( ~ in(apply(X2,X4),X0)
            | ~ in(X4,X1)
            | ~ in(X4,relation_inverse_image(X2,X0)) )
          & ( ( in(apply(X2,X4),X0)
              & in(X4,X1) )
            | in(X4,relation_inverse_image(X2,X0)) ) )
      & quasi_total(X2,X1,X3)
      & empty_set != X3
      & function(X2) ),
    inference(nnf_transformation,[],[f91]) ).

fof(f91,plain,
    ? [X1,X3,X2,X0] :
      ( relation_of2_as_subset(X2,X1,X3)
      & ? [X4] :
          ( in(X4,relation_inverse_image(X2,X0))
        <~> ( in(apply(X2,X4),X0)
            & in(X4,X1) ) )
      & quasi_total(X2,X1,X3)
      & empty_set != X3
      & function(X2) ),
    inference(flattening,[],[f90]) ).

fof(f90,plain,
    ? [X3,X0,X2,X1] :
      ( ? [X4] :
          ( in(X4,relation_inverse_image(X2,X0))
        <~> ( in(apply(X2,X4),X0)
            & in(X4,X1) ) )
      & empty_set != X3
      & relation_of2_as_subset(X2,X1,X3)
      & quasi_total(X2,X1,X3)
      & function(X2) ),
    inference(ennf_transformation,[],[f66]) ).

fof(f66,plain,
    ~ ! [X3,X0,X2,X1] :
        ( ( relation_of2_as_subset(X2,X1,X3)
          & quasi_total(X2,X1,X3)
          & function(X2) )
       => ( empty_set != X3
         => ! [X4] :
              ( ( in(apply(X2,X4),X0)
                & in(X4,X1) )
            <=> in(X4,relation_inverse_image(X2,X0)) ) ) ),
    inference(rectify,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ! [X2,X0,X3,X1] :
        ( ( function(X3)
          & quasi_total(X3,X0,X1)
          & relation_of2_as_subset(X3,X0,X1) )
       => ( empty_set != X1
         => ! [X4] :
              ( ( in(X4,X0)
                & in(apply(X3,X4),X2) )
            <=> in(X4,relation_inverse_image(X3,X2)) ) ) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ! [X2,X0,X3,X1] :
      ( ( function(X3)
        & quasi_total(X3,X0,X1)
        & relation_of2_as_subset(X3,X0,X1) )
     => ( empty_set != X1
       => ! [X4] :
            ( ( in(X4,X0)
              & in(apply(X3,X4),X2) )
          <=> in(X4,relation_inverse_image(X3,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).

fof(f436,plain,
    ( ~ relation_of2_as_subset(sK19,sK17,sK18)
    | sK17 = relation_dom_as_subset(sK17,sK18,sK19) ),
    inference(subsumption_resolution,[],[f433,f240]) ).

fof(f240,plain,
    empty_set != sK18,
    inference(cnf_transformation,[],[f165]) ).

fof(f433,plain,
    ( empty_set = sK18
    | ~ relation_of2_as_subset(sK19,sK17,sK18)
    | sK17 = relation_dom_as_subset(sK17,sK18,sK19) ),
    inference(resolution,[],[f221,f241]) ).

fof(f241,plain,
    quasi_total(sK19,sK17,sK18),
    inference(cnf_transformation,[],[f165]) ).

fof(f221,plain,
    ! [X2,X0,X1] :
      ( ~ quasi_total(X2,X1,X0)
      | ~ relation_of2_as_subset(X2,X1,X0)
      | empty_set = X0
      | relation_dom_as_subset(X1,X0,X2) = X1 ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0,X1,X2] :
      ( ( ( ( ( relation_dom_as_subset(X1,X0,X2) = X1
              | ~ quasi_total(X2,X1,X0) )
            & ( quasi_total(X2,X1,X0)
              | relation_dom_as_subset(X1,X0,X2) != X1 ) )
          | ( empty_set = X0
            & empty_set != X1 ) )
        & ( empty_set != X0
          | ( ( empty_set = X2
              | ~ quasi_total(X2,X1,X0) )
            & ( quasi_total(X2,X1,X0)
              | empty_set != X2 ) )
          | empty_set = X1 ) )
      | ~ relation_of2_as_subset(X2,X1,X0) ),
    inference(rectify,[],[f142]) ).

fof(f142,plain,
    ! [X1,X2,X0] :
      ( ( ( ( ( relation_dom_as_subset(X2,X1,X0) = X2
              | ~ quasi_total(X0,X2,X1) )
            & ( quasi_total(X0,X2,X1)
              | relation_dom_as_subset(X2,X1,X0) != X2 ) )
          | ( empty_set = X1
            & empty_set != X2 ) )
        & ( empty_set != X1
          | ( ( empty_set = X0
              | ~ quasi_total(X0,X2,X1) )
            & ( quasi_total(X0,X2,X1)
              | empty_set != X0 ) )
          | empty_set = X2 ) )
      | ~ relation_of2_as_subset(X0,X2,X1) ),
    inference(nnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X1,X2,X0] :
      ( ( ( ( relation_dom_as_subset(X2,X1,X0) = X2
          <=> quasi_total(X0,X2,X1) )
          | ( empty_set = X1
            & empty_set != X2 ) )
        & ( empty_set != X1
          | ( empty_set = X0
          <=> quasi_total(X0,X2,X1) )
          | empty_set = X2 ) )
      | ~ relation_of2_as_subset(X0,X2,X1) ),
    inference(flattening,[],[f94]) ).

fof(f94,plain,
    ! [X0,X2,X1] :
      ( ( ( empty_set = X2
          | ( empty_set = X0
          <=> quasi_total(X0,X2,X1) )
          | empty_set != X1 )
        & ( ( relation_dom_as_subset(X2,X1,X0) = X2
          <=> quasi_total(X0,X2,X1) )
          | ( empty_set = X1
            & empty_set != X2 ) ) )
      | ~ relation_of2_as_subset(X0,X2,X1) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X2,X1] :
      ( relation_of2_as_subset(X0,X2,X1)
     => ( ( empty_set = X1
         => ( empty_set = X2
            | ( empty_set = X0
            <=> quasi_total(X0,X2,X1) ) ) )
        & ( ( empty_set = X1
           => empty_set = X2 )
         => ( relation_dom_as_subset(X2,X1,X0) = X2
          <=> quasi_total(X0,X2,X1) ) ) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X2,X1,X0] :
      ( relation_of2_as_subset(X2,X0,X1)
     => ( ( empty_set = X1
         => ( ( empty_set = X2
            <=> quasi_total(X2,X0,X1) )
            | empty_set = X0 ) )
        & ( ( empty_set = X1
           => empty_set = X0 )
         => ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).

fof(f385,plain,
    relation_dom_as_subset(sK17,sK18,sK19) = relation_dom(sK19),
    inference(resolution,[],[f247,f347]) ).

fof(f347,plain,
    relation_of2(sK19,sK17,sK18),
    inference(resolution,[],[f248,f245]) ).

fof(f248,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2_as_subset(X1,X2,X0)
      | relation_of2(X1,X2,X0) ),
    inference(cnf_transformation,[],[f167]) ).

fof(f167,plain,
    ! [X0,X1,X2] :
      ( ( relation_of2_as_subset(X1,X2,X0)
        | ~ relation_of2(X1,X2,X0) )
      & ( relation_of2(X1,X2,X0)
        | ~ relation_of2_as_subset(X1,X2,X0) ) ),
    inference(rectify,[],[f166]) ).

fof(f166,plain,
    ! [X0,X2,X1] :
      ( ( relation_of2_as_subset(X2,X1,X0)
        | ~ relation_of2(X2,X1,X0) )
      & ( relation_of2(X2,X1,X0)
        | ~ relation_of2_as_subset(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X2,X1] :
      ( relation_of2_as_subset(X2,X1,X0)
    <=> relation_of2(X2,X1,X0) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ! [X1,X0,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
    <=> relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

fof(f247,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2(X1,X0,X2)
      | relation_dom_as_subset(X0,X2,X1) = relation_dom(X1) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ~ relation_of2(X1,X0,X2)
      | relation_dom_as_subset(X0,X2,X1) = relation_dom(X1) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X2,X1] :
      ( relation_of2(X1,X0,X2)
     => relation_dom_as_subset(X0,X2,X1) = relation_dom(X1) ),
    inference(rectify,[],[f42]) ).

fof(f42,axiom,
    ! [X0,X2,X1] :
      ( relation_of2(X2,X0,X1)
     => relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).

fof(f449,plain,
    ( ! [X0] :
        ( ~ in(sK21,relation_dom(sK19))
        | in(sK21,relation_inverse_image(sK19,X0))
        | ~ in(sF23,X0) )
    | ~ spl25_6 ),
    inference(subsumption_resolution,[],[f448,f391]) ).

fof(f391,plain,
    ( relation(sK19)
    | ~ spl25_6 ),
    inference(avatar_component_clause,[],[f390]) ).

fof(f390,plain,
    ( spl25_6
  <=> relation(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_6])]) ).

fof(f448,plain,
    ! [X0] :
      ( ~ in(sF23,X0)
      | in(sK21,relation_inverse_image(sK19,X0))
      | ~ in(sK21,relation_dom(sK19))
      | ~ relation(sK19) ),
    inference(subsumption_resolution,[],[f447,f239]) ).

fof(f239,plain,
    function(sK19),
    inference(cnf_transformation,[],[f165]) ).

fof(f447,plain,
    ! [X0] :
      ( ~ function(sK19)
      | ~ relation(sK19)
      | ~ in(sK21,relation_dom(sK19))
      | ~ in(sF23,X0)
      | in(sK21,relation_inverse_image(sK19,X0)) ),
    inference(superposition,[],[f252,f260]) ).

fof(f260,plain,
    sF23 = apply(sK19,sK21),
    introduced(function_definition,[]) ).

fof(f252,plain,
    ! [X2,X3,X0] :
      ( ~ in(apply(X0,X3),X2)
      | ~ function(X0)
      | in(X3,relation_inverse_image(X0,X2))
      | ~ in(X3,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f195]) ).

fof(f195,plain,
    ! [X2,X3,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(X3,X1)
      | ~ in(apply(X0,X3),X2)
      | ~ in(X3,relation_dom(X0))
      | relation_inverse_image(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( ( ! [X3] :
                ( ( in(X3,X1)
                  | ~ in(apply(X0,X3),X2)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X2)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X1) ) )
            | relation_inverse_image(X0,X2) != X1 )
          & ( relation_inverse_image(X0,X2) = X1
            | ( ( ~ in(apply(X0,sK4(X0,X1,X2)),X2)
                | ~ in(sK4(X0,X1,X2),relation_dom(X0))
                | ~ in(sK4(X0,X1,X2),X1) )
              & ( ( in(apply(X0,sK4(X0,X1,X2)),X2)
                  & in(sK4(X0,X1,X2),relation_dom(X0)) )
                | in(sK4(X0,X1,X2),X1) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f125,f126]) ).

fof(f126,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(apply(X0,X4),X2)
            | ~ in(X4,relation_dom(X0))
            | ~ in(X4,X1) )
          & ( ( in(apply(X0,X4),X2)
              & in(X4,relation_dom(X0)) )
            | in(X4,X1) ) )
     => ( ( ~ in(apply(X0,sK4(X0,X1,X2)),X2)
          | ~ in(sK4(X0,X1,X2),relation_dom(X0))
          | ~ in(sK4(X0,X1,X2),X1) )
        & ( ( in(apply(X0,sK4(X0,X1,X2)),X2)
            & in(sK4(X0,X1,X2),relation_dom(X0)) )
          | in(sK4(X0,X1,X2),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( ( ! [X3] :
                ( ( in(X3,X1)
                  | ~ in(apply(X0,X3),X2)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X2)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X1) ) )
            | relation_inverse_image(X0,X2) != X1 )
          & ( relation_inverse_image(X0,X2) = X1
            | ? [X4] :
                ( ( ~ in(apply(X0,X4),X2)
                  | ~ in(X4,relation_dom(X0))
                  | ~ in(X4,X1) )
                & ( ( in(apply(X0,X4),X2)
                    & in(X4,relation_dom(X0)) )
                  | in(X4,X1) ) ) ) ) ),
    inference(rectify,[],[f124]) ).

fof(f124,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X2,X1] :
          ( ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 )
          & ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) ) ) ),
    inference(flattening,[],[f123]) ).

fof(f123,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X2,X1] :
          ( ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 )
          & ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) ) ) ),
    inference(nnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) )
        <=> relation_inverse_image(X0,X1) = X2 ) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) )
        <=> relation_inverse_image(X0,X1) = X2 )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) )
        <=> relation_inverse_image(X0,X1) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).

fof(f535,plain,
    ( spl25_1
    | ~ spl25_2
    | ~ spl25_8 ),
    inference(avatar_contradiction_clause,[],[f534]) ).

fof(f534,plain,
    ( $false
    | spl25_1
    | ~ spl25_2
    | ~ spl25_8 ),
    inference(subsumption_resolution,[],[f533,f271]) ).

fof(f271,plain,
    ( in(sK21,sF24)
    | ~ spl25_2 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f533,plain,
    ( ~ in(sK21,sF24)
    | spl25_1
    | ~ spl25_8 ),
    inference(subsumption_resolution,[],[f527,f268]) ).

fof(f268,plain,
    ( ~ in(sF23,sK20)
    | spl25_1 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f527,plain,
    ( in(sF23,sK20)
    | ~ in(sK21,sF24)
    | ~ spl25_8 ),
    inference(superposition,[],[f412,f260]) ).

fof(f412,plain,
    ( ! [X0] :
        ( in(apply(sK19,X0),sK20)
        | ~ in(X0,sF24) )
    | ~ spl25_8 ),
    inference(avatar_component_clause,[],[f411]) ).

fof(f411,plain,
    ( spl25_8
  <=> ! [X0] :
        ( ~ in(X0,sF24)
        | in(apply(sK19,X0),sK20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_8])]) ).

fof(f503,plain,
    ( ~ spl25_2
    | spl25_3
    | ~ spl25_7 ),
    inference(avatar_contradiction_clause,[],[f502]) ).

fof(f502,plain,
    ( $false
    | ~ spl25_2
    | spl25_3
    | ~ spl25_7 ),
    inference(subsumption_resolution,[],[f500,f276]) ).

fof(f276,plain,
    ( ~ in(sK21,sK17)
    | spl25_3 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f500,plain,
    ( in(sK21,sK17)
    | ~ spl25_2
    | ~ spl25_7 ),
    inference(resolution,[],[f442,f271]) ).

fof(f442,plain,
    ( ! [X0] :
        ( ~ in(X0,sF24)
        | in(X0,sK17) )
    | ~ spl25_7 ),
    inference(backward_demodulation,[],[f395,f438]) ).

fof(f395,plain,
    ( ! [X0] :
        ( in(X0,relation_dom(sK19))
        | ~ in(X0,sF24) )
    | ~ spl25_7 ),
    inference(avatar_component_clause,[],[f394]) ).

fof(f394,plain,
    ( spl25_7
  <=> ! [X0] :
        ( in(X0,relation_dom(sK19))
        | ~ in(X0,sF24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_7])]) ).

fof(f413,plain,
    ( spl25_8
    | ~ spl25_6 ),
    inference(avatar_split_clause,[],[f409,f390,f411]) ).

fof(f409,plain,
    ! [X0] :
      ( ~ relation(sK19)
      | ~ in(X0,sF24)
      | in(apply(sK19,X0),sK20) ),
    inference(subsumption_resolution,[],[f399,f239]) ).

fof(f399,plain,
    ! [X0] :
      ( in(apply(sK19,X0),sK20)
      | ~ relation(sK19)
      | ~ function(sK19)
      | ~ in(X0,sF24) ),
    inference(superposition,[],[f253,f261]) ).

fof(f253,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,relation_inverse_image(X0,X2))
      | in(apply(X0,X3),X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f194]) ).

fof(f194,plain,
    ! [X2,X3,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(apply(X0,X3),X2)
      | ~ in(X3,X1)
      | relation_inverse_image(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f127]) ).

fof(f408,plain,
    spl25_6,
    inference(avatar_split_clause,[],[f405,f390]) ).

fof(f405,plain,
    relation(sK19),
    inference(resolution,[],[f363,f245]) ).

fof(f363,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2_as_subset(X0,X1,X2)
      | relation(X0) ),
    inference(resolution,[],[f181,f223]) ).

fof(f223,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,powerset(cartesian_product2(X0,X1)))
      | relation(X2) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0,X1,X2] :
      ( ~ element(X2,powerset(cartesian_product2(X0,X1)))
      | relation(X2) ),
    inference(rectify,[],[f96]) ).

fof(f96,plain,
    ! [X0,X2,X1] :
      ( ~ element(X1,powerset(cartesian_product2(X0,X2)))
      | relation(X1) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X2,X1] :
      ( element(X1,powerset(cartesian_product2(X0,X2)))
     => relation(X1) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X2,X1] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
     => relation(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

fof(f181,plain,
    ! [X2,X0,X1] :
      ( element(X1,powerset(cartesian_product2(X2,X0)))
      | ~ relation_of2_as_subset(X1,X2,X0) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0,X1,X2] :
      ( element(X1,powerset(cartesian_product2(X2,X0)))
      | ~ relation_of2_as_subset(X1,X2,X0) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X2,X0,X1] :
      ( element(X0,powerset(cartesian_product2(X1,X2)))
      | ~ relation_of2_as_subset(X0,X1,X2) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X0,X1,X2)
     => element(X0,powerset(cartesian_product2(X1,X2))) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X2,X0,X1] :
      ( relation_of2_as_subset(X2,X0,X1)
     => element(X2,powerset(cartesian_product2(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

fof(f396,plain,
    ( ~ spl25_6
    | spl25_7 ),
    inference(avatar_split_clause,[],[f388,f394,f390]) ).

fof(f388,plain,
    ! [X0] :
      ( in(X0,relation_dom(sK19))
      | ~ in(X0,sF24)
      | ~ relation(sK19) ),
    inference(subsumption_resolution,[],[f387,f239]) ).

fof(f387,plain,
    ! [X0] :
      ( ~ function(sK19)
      | ~ relation(sK19)
      | in(X0,relation_dom(sK19))
      | ~ in(X0,sF24) ),
    inference(superposition,[],[f254,f261]) ).

fof(f254,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,relation_inverse_image(X0,X2))
      | ~ relation(X0)
      | in(X3,relation_dom(X0))
      | ~ function(X0) ),
    inference(equality_resolution,[],[f193]) ).

fof(f193,plain,
    ! [X2,X3,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(X3,relation_dom(X0))
      | ~ in(X3,X1)
      | relation_inverse_image(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f127]) ).

fof(f279,plain,
    ( spl25_2
    | spl25_1 ),
    inference(avatar_split_clause,[],[f263,f266,f270]) ).

fof(f263,plain,
    ( in(sF23,sK20)
    | in(sK21,sF24) ),
    inference(definition_folding,[],[f243,f261,f260]) ).

fof(f243,plain,
    ( in(apply(sK19,sK21),sK20)
    | in(sK21,relation_inverse_image(sK19,sK20)) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f278,plain,
    ( spl25_2
    | spl25_3 ),
    inference(avatar_split_clause,[],[f264,f274,f270]) ).

fof(f264,plain,
    ( in(sK21,sK17)
    | in(sK21,sF24) ),
    inference(definition_folding,[],[f242,f261]) ).

fof(f242,plain,
    ( in(sK21,sK17)
    | in(sK21,relation_inverse_image(sK19,sK20)) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f277,plain,
    ( ~ spl25_1
    | ~ spl25_2
    | ~ spl25_3 ),
    inference(avatar_split_clause,[],[f262,f274,f270,f266]) ).

fof(f262,plain,
    ( ~ in(sK21,sK17)
    | ~ in(sK21,sF24)
    | ~ in(sF23,sK20) ),
    inference(definition_folding,[],[f244,f261,f260]) ).

fof(f244,plain,
    ( ~ in(apply(sK19,sK21),sK20)
    | ~ in(sK21,sK17)
    | ~ in(sK21,relation_inverse_image(sK19,sK20)) ),
    inference(cnf_transformation,[],[f165]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 15:04:20 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.53  % (21106)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.54  % (21089)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.54  % (21098)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.54  % (21090)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.54  % (21090)Instruction limit reached!
% 0.19/0.54  % (21090)------------------------------
% 0.19/0.54  % (21090)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54  % (21090)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54  % (21090)Termination reason: Unknown
% 0.19/0.54  % (21090)Termination phase: Preprocessing 3
% 0.19/0.54  
% 0.19/0.54  % (21090)Memory used [KB]: 895
% 0.19/0.54  % (21090)Time elapsed: 0.003 s
% 0.19/0.54  % (21090)Instructions burned: 2 (million)
% 0.19/0.54  % (21090)------------------------------
% 0.19/0.54  % (21090)------------------------------
% 0.19/0.54  % (21097)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.54  % (21088)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55  TRYING [1]
% 0.19/0.55  % (21105)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.55  % (21104)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.55  % (21096)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.55  TRYING [2]
% 0.19/0.55  % (21089)Instruction limit reached!
% 0.19/0.55  % (21089)------------------------------
% 0.19/0.55  % (21089)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56  % (21089)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56  % (21089)Termination reason: Unknown
% 0.19/0.56  % (21089)Termination phase: Saturation
% 0.19/0.56  
% 0.19/0.56  % (21089)Memory used [KB]: 5628
% 0.19/0.56  % (21089)Time elapsed: 0.128 s
% 0.19/0.56  % (21089)Instructions burned: 7 (million)
% 0.19/0.56  % (21089)------------------------------
% 0.19/0.56  % (21089)------------------------------
% 0.19/0.56  TRYING [3]
% 1.71/0.58  % (21106)First to succeed.
% 1.71/0.59  % (21087)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.71/0.59  % (21085)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.71/0.60  TRYING [4]
% 1.71/0.60  % (21097)Also succeeded, but the first one will report.
% 1.80/0.60  % (21106)Refutation found. Thanks to Tanya!
% 1.80/0.60  % SZS status Theorem for theBenchmark
% 1.80/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.80/0.60  % (21106)------------------------------
% 1.80/0.60  % (21106)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.80/0.60  % (21106)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.80/0.60  % (21106)Termination reason: Refutation
% 1.80/0.60  
% 1.80/0.60  % (21106)Memory used [KB]: 5756
% 1.80/0.60  % (21106)Time elapsed: 0.162 s
% 1.80/0.60  % (21106)Instructions burned: 17 (million)
% 1.80/0.60  % (21106)------------------------------
% 1.80/0.60  % (21106)------------------------------
% 1.80/0.60  % (21081)Success in time 0.246 s
%------------------------------------------------------------------------------