TSTP Solution File: SEU225+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU225+3 : TPTP v8.1.0. Released v3.2.0.
% 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 : n020.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 18:32:39 EDT 2022

% Result   : Theorem 0.20s 0.59s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   89 (  12 unt;   0 def)
%            Number of atoms       :  365 (  96 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  443 ( 167   ~; 171   |;  68   &)
%                                         (  16 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :  135 ( 119   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f702,plain,
    $false,
    inference(avatar_sat_refutation,[],[f477,f678,f691]) ).

fof(f691,plain,
    ( spl18_9
    | ~ spl18_12 ),
    inference(avatar_contradiction_clause,[],[f690]) ).

fof(f690,plain,
    ( $false
    | spl18_9
    | ~ spl18_12 ),
    inference(subsumption_resolution,[],[f689,f179]) ).

fof(f179,plain,
    in(sK10,sK9),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ( function(sK11)
    & relation(sK11)
    & apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10)
    & in(sK10,sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f124,f125]) ).

fof(f125,plain,
    ( ? [X0,X1,X2] :
        ( function(X2)
        & relation(X2)
        & apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
        & in(X1,X0) )
   => ( function(sK11)
      & relation(sK11)
      & apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10)
      & in(sK10,sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ? [X0,X1,X2] :
      ( function(X2)
      & relation(X2)
      & apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
      & in(X1,X0) ),
    inference(rectify,[],[f88]) ).

fof(f88,plain,
    ? [X1,X2,X0] :
      ( function(X0)
      & relation(X0)
      & apply(X0,X2) != apply(relation_dom_restriction(X0,X1),X2)
      & in(X2,X1) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ? [X2,X1,X0] :
      ( apply(X0,X2) != apply(relation_dom_restriction(X0,X1),X2)
      & in(X2,X1)
      & relation(X0)
      & function(X0) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,plain,
    ~ ! [X2,X1,X0] :
        ( ( relation(X0)
          & function(X0) )
       => ( in(X2,X1)
         => apply(X0,X2) = apply(relation_dom_restriction(X0,X1),X2) ) ),
    inference(rectify,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X2,X0,X1] :
        ( ( relation(X2)
          & function(X2) )
       => ( in(X1,X0)
         => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X2,X0,X1] :
      ( ( relation(X2)
        & function(X2) )
     => ( in(X1,X0)
       => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).

fof(f689,plain,
    ( ~ in(sK10,sK9)
    | spl18_9
    | ~ spl18_12 ),
    inference(subsumption_resolution,[],[f656,f431]) ).

fof(f431,plain,
    ( ~ in(sK10,relation_dom(sF15))
    | spl18_9 ),
    inference(avatar_component_clause,[],[f429]) ).

fof(f429,plain,
    ( spl18_9
  <=> in(sK10,relation_dom(sF15)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).

fof(f656,plain,
    ( in(sK10,relation_dom(sF15))
    | ~ in(sK10,sK9)
    | ~ spl18_12 ),
    inference(resolution,[],[f404,f448]) ).

fof(f448,plain,
    ( in(sK10,relation_dom(sK11))
    | ~ spl18_12 ),
    inference(avatar_component_clause,[],[f447]) ).

fof(f447,plain,
    ( spl18_12
  <=> in(sK10,relation_dom(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).

fof(f404,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sK11))
      | in(X0,relation_dom(sF15))
      | ~ in(X0,sK9) ),
    inference(subsumption_resolution,[],[f403,f182]) ).

fof(f182,plain,
    function(sK11),
    inference(cnf_transformation,[],[f126]) ).

fof(f403,plain,
    ! [X0] :
      ( in(X0,relation_dom(sF15))
      | ~ in(X0,sK9)
      | ~ in(X0,relation_dom(sK11))
      | ~ function(sK11) ),
    inference(subsumption_resolution,[],[f400,f181]) ).

fof(f181,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f126]) ).

fof(f400,plain,
    ! [X0] :
      ( in(X0,relation_dom(sF15))
      | ~ in(X0,relation_dom(sK11))
      | ~ relation(sK11)
      | ~ function(sK11)
      | ~ in(X0,sK9) ),
    inference(superposition,[],[f164,f223]) ).

fof(f223,plain,
    sF15 = relation_dom_restriction(sK11,sK9),
    introduced(function_definition,[]) ).

fof(f164,plain,
    ! [X2,X0,X1] :
      ( in(X2,relation_dom(relation_dom_restriction(X1,X0)))
      | ~ relation(X1)
      | ~ in(X2,relation_dom(X1))
      | ~ in(X2,X0)
      | ~ function(X1) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( ( ( ( in(X2,X0)
            & in(X2,relation_dom(X1)) )
          | ~ in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
        & ( in(X2,relation_dom(relation_dom_restriction(X1,X0)))
          | ~ in(X2,X0)
          | ~ in(X2,relation_dom(X1)) ) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(flattening,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( ( ( ( in(X2,X0)
            & in(X2,relation_dom(X1)) )
          | ~ in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
        & ( in(X2,relation_dom(relation_dom_restriction(X1,X0)))
          | ~ in(X2,X0)
          | ~ in(X2,relation_dom(X1)) ) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X2,X0)
          & in(X2,relation_dom(X1)) )
      <=> in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ! [X1,X0,X2] :
      ( ( ( in(X2,X0)
          & in(X2,relation_dom(X1)) )
      <=> in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X1,X0,X2] :
      ( ( relation(X1)
        & function(X1) )
     => ( ( in(X2,X0)
          & in(X2,relation_dom(X1)) )
      <=> in(X2,relation_dom(relation_dom_restriction(X1,X0))) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X0,X2,X1] :
      ( ( relation(X2)
        & function(X2) )
     => ( ( in(X1,X0)
          & in(X1,relation_dom(X2)) )
      <=> in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).

fof(f678,plain,
    ~ spl18_9,
    inference(avatar_contradiction_clause,[],[f677]) ).

fof(f677,plain,
    ( $false
    | ~ spl18_9 ),
    inference(subsumption_resolution,[],[f676,f226]) ).

fof(f226,plain,
    sF17 != sF16,
    inference(definition_folding,[],[f180,f225,f224,f223]) ).

fof(f224,plain,
    apply(sF15,sK10) = sF16,
    introduced(function_definition,[]) ).

fof(f225,plain,
    apply(sK11,sK10) = sF17,
    introduced(function_definition,[]) ).

fof(f180,plain,
    apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10),
    inference(cnf_transformation,[],[f126]) ).

fof(f676,plain,
    ( sF17 = sF16
    | ~ spl18_9 ),
    inference(backward_demodulation,[],[f225,f675]) ).

fof(f675,plain,
    ( apply(sK11,sK10) = sF16
    | ~ spl18_9 ),
    inference(forward_demodulation,[],[f672,f224]) ).

fof(f672,plain,
    ( apply(sK11,sK10) = apply(sF15,sK10)
    | ~ spl18_9 ),
    inference(resolution,[],[f460,f430]) ).

fof(f430,plain,
    ( in(sK10,relation_dom(sF15))
    | ~ spl18_9 ),
    inference(avatar_component_clause,[],[f429]) ).

fof(f460,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sF15,X0) = apply(sK11,X0) ),
    inference(subsumption_resolution,[],[f459,f181]) ).

fof(f459,plain,
    ! [X0] :
      ( apply(sF15,X0) = apply(sK11,X0)
      | ~ relation(sK11)
      | ~ in(X0,relation_dom(sF15)) ),
    inference(subsumption_resolution,[],[f455,f182]) ).

fof(f455,plain,
    ! [X0] :
      ( apply(sF15,X0) = apply(sK11,X0)
      | ~ function(sK11)
      | ~ in(X0,relation_dom(sF15))
      | ~ relation(sK11) ),
    inference(superposition,[],[f231,f223]) ).

fof(f231,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ function(X2)
      | apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3)
      | ~ relation(X2) ),
    inference(subsumption_resolution,[],[f230,f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X1,X0))
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X1,X0))
        & relation(relation_dom_restriction(X1,X0)) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f77]) ).

fof(f77,plain,
    ! [X1,X0] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(f230,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ function(relation_dom_restriction(X2,X0))
      | apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3)
      | ~ relation(X2)
      | ~ function(X2) ),
    inference(subsumption_resolution,[],[f219,f206]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | relation(relation_dom_restriction(X0,X1)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(f219,plain,
    ! [X2,X3,X0] :
      ( ~ relation(relation_dom_restriction(X2,X0))
      | ~ relation(X2)
      | ~ function(relation_dom_restriction(X2,X0))
      | ~ in(X3,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ function(X2)
      | apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
    inference(equality_resolution,[],[f173]) ).

fof(f173,plain,
    ! [X2,X3,X0,X1] :
      ( ~ relation(X2)
      | ~ in(X3,relation_dom(X1))
      | apply(X1,X3) = apply(X2,X3)
      | relation_dom_restriction(X2,X0) != X1
      | ~ function(X2)
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
                & ! [X3] :
                    ( ~ in(X3,relation_dom(X1))
                    | apply(X1,X3) = apply(X2,X3) ) )
              | relation_dom_restriction(X2,X0) != X1 )
            & ( relation_dom_restriction(X2,X0) = X1
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
              | ( in(sK7(X1,X2),relation_dom(X1))
                & apply(X2,sK7(X1,X2)) != apply(X1,sK7(X1,X2)) ) ) )
          | ~ function(X2) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f119,f120]) ).

fof(f120,plain,
    ! [X1,X2] :
      ( ? [X4] :
          ( in(X4,relation_dom(X1))
          & apply(X2,X4) != apply(X1,X4) )
     => ( in(sK7(X1,X2),relation_dom(X1))
        & apply(X2,sK7(X1,X2)) != apply(X1,sK7(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
                & ! [X3] :
                    ( ~ in(X3,relation_dom(X1))
                    | apply(X1,X3) = apply(X2,X3) ) )
              | relation_dom_restriction(X2,X0) != X1 )
            & ( relation_dom_restriction(X2,X0) = X1
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
              | ? [X4] :
                  ( in(X4,relation_dom(X1))
                  & apply(X2,X4) != apply(X1,X4) ) ) )
          | ~ function(X2) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(rectify,[],[f118]) ).

fof(f118,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
                & ! [X3] :
                    ( ~ in(X3,relation_dom(X0))
                    | apply(X2,X3) = apply(X0,X3) ) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1)
              | ? [X3] :
                  ( in(X3,relation_dom(X0))
                  & apply(X2,X3) != apply(X0,X3) ) ) )
          | ~ function(X2) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(flattening,[],[f117]) ).

fof(f117,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
                & ! [X3] :
                    ( ~ in(X3,relation_dom(X0))
                    | apply(X2,X3) = apply(X0,X3) ) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1)
              | ? [X3] :
                  ( in(X3,relation_dom(X0))
                  & apply(X2,X3) != apply(X0,X3) ) ) )
          | ~ function(X2) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(nnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
              & ! [X3] :
                  ( ~ in(X3,relation_dom(X0))
                  | apply(X2,X3) = apply(X0,X3) ) )
          <=> relation_dom_restriction(X2,X1) = X0 )
          | ~ function(X2) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
              & ! [X3] :
                  ( ~ in(X3,relation_dom(X0))
                  | apply(X2,X3) = apply(X0,X3) ) )
          <=> relation_dom_restriction(X2,X1) = X0 )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X1,X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( relation_dom_restriction(X2,X1) = X0
          <=> ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
              & ! [X3] :
                  ( in(X3,relation_dom(X0))
                 => apply(X2,X3) = apply(X0,X3) ) ) ) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,axiom,
    ! [X1,X0] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
          <=> relation_dom_restriction(X2,X0) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).

fof(f477,plain,
    ( spl18_9
    | spl18_12 ),
    inference(avatar_contradiction_clause,[],[f476]) ).

fof(f476,plain,
    ( $false
    | spl18_9
    | spl18_12 ),
    inference(subsumption_resolution,[],[f475,f471]) ).

fof(f471,plain,
    ( empty_set != sF17
    | spl18_9 ),
    inference(backward_demodulation,[],[f226,f470]) ).

fof(f470,plain,
    ( empty_set = sF16
    | spl18_9 ),
    inference(backward_demodulation,[],[f224,f469]) ).

fof(f469,plain,
    ( empty_set = apply(sF15,sK10)
    | spl18_9 ),
    inference(subsumption_resolution,[],[f468,f269]) ).

fof(f269,plain,
    relation(sF15),
    inference(subsumption_resolution,[],[f268,f181]) ).

fof(f268,plain,
    ( ~ relation(sK11)
    | relation(sF15) ),
    inference(superposition,[],[f206,f223]) ).

fof(f468,plain,
    ( ~ relation(sF15)
    | empty_set = apply(sF15,sK10)
    | spl18_9 ),
    inference(subsumption_resolution,[],[f467,f314]) ).

fof(f314,plain,
    function(sF15),
    inference(subsumption_resolution,[],[f313,f181]) ).

fof(f313,plain,
    ( function(sF15)
    | ~ relation(sK11) ),
    inference(subsumption_resolution,[],[f312,f182]) ).

fof(f312,plain,
    ( ~ function(sK11)
    | function(sF15)
    | ~ relation(sK11) ),
    inference(superposition,[],[f203,f223]) ).

fof(f467,plain,
    ( ~ function(sF15)
    | empty_set = apply(sF15,sK10)
    | ~ relation(sF15)
    | spl18_9 ),
    inference(resolution,[],[f431,f221]) ).

fof(f221,plain,
    ! [X2,X0] :
      ( in(X2,relation_dom(X0))
      | ~ function(X0)
      | empty_set = apply(X0,X2)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f186]) ).

fof(f186,plain,
    ! [X2,X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | empty_set = X1
      | apply(X0,X2) != X1
      | in(X2,relation_dom(X0)) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ! [X1,X2] :
          ( ( ~ in(X2,relation_dom(X0))
            | ( ( in(ordered_pair(X2,X1),X0)
                | apply(X0,X2) != X1 )
              & ( apply(X0,X2) = X1
                | ~ in(ordered_pair(X2,X1),X0) ) ) )
          & ( ( ( empty_set = X1
                | apply(X0,X2) != X1 )
              & ( apply(X0,X2) = X1
                | empty_set != X1 ) )
            | in(X2,relation_dom(X0)) ) ) ),
    inference(rectify,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ! [X2,X1] :
          ( ( ~ in(X1,relation_dom(X0))
            | ( ( in(ordered_pair(X1,X2),X0)
                | apply(X0,X1) != X2 )
              & ( apply(X0,X1) = X2
                | ~ in(ordered_pair(X1,X2),X0) ) ) )
          & ( ( ( empty_set = X2
                | apply(X0,X1) != X2 )
              & ( apply(X0,X1) = X2
                | empty_set != X2 ) )
            | in(X1,relation_dom(X0)) ) ) ),
    inference(nnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ! [X2,X1] :
          ( ( ~ in(X1,relation_dom(X0))
            | ( in(ordered_pair(X1,X2),X0)
            <=> apply(X0,X1) = X2 ) )
          & ( ( empty_set = X2
            <=> apply(X0,X1) = X2 )
            | in(X1,relation_dom(X0)) ) ) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ( ~ in(X1,relation_dom(X0))
            | ( in(ordered_pair(X1,X2),X0)
            <=> apply(X0,X1) = X2 ) )
          & ( ( empty_set = X2
            <=> apply(X0,X1) = X2 )
            | in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2,X1] :
          ( ( ~ in(X1,relation_dom(X0))
           => ( empty_set = X2
            <=> apply(X0,X1) = X2 ) )
          & ( in(X1,relation_dom(X0))
           => ( in(ordered_pair(X1,X2),X0)
            <=> apply(X0,X1) = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

fof(f475,plain,
    ( empty_set = sF17
    | spl18_12 ),
    inference(backward_demodulation,[],[f225,f474]) ).

fof(f474,plain,
    ( empty_set = apply(sK11,sK10)
    | spl18_12 ),
    inference(subsumption_resolution,[],[f473,f181]) ).

fof(f473,plain,
    ( ~ relation(sK11)
    | empty_set = apply(sK11,sK10)
    | spl18_12 ),
    inference(subsumption_resolution,[],[f472,f182]) ).

fof(f472,plain,
    ( ~ function(sK11)
    | ~ relation(sK11)
    | empty_set = apply(sK11,sK10)
    | spl18_12 ),
    inference(resolution,[],[f449,f221]) ).

fof(f449,plain,
    ( ~ in(sK10,relation_dom(sK11))
    | spl18_12 ),
    inference(avatar_component_clause,[],[f447]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SEU225+3 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13  % 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 : n020.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 14:54:45 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (31727)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.50  TRYING [1]
% 0.20/0.50  TRYING [2]
% 0.20/0.50  TRYING [3]
% 0.20/0.51  % (31711)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.51  TRYING [4]
% 0.20/0.51  % (31721)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.52  % (31713)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (31727)Instruction limit reached!
% 0.20/0.52  % (31727)------------------------------
% 0.20/0.52  % (31727)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (31727)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (31727)Termination reason: Unknown
% 0.20/0.52  % (31727)Termination phase: Finite model building SAT solving
% 0.20/0.52  
% 0.20/0.52  % (31727)Memory used [KB]: 7931
% 0.20/0.52  % (31727)Time elapsed: 0.111 s
% 0.20/0.52  % (31727)Instructions burned: 60 (million)
% 0.20/0.52  % (31727)------------------------------
% 0.20/0.52  % (31727)------------------------------
% 0.20/0.52  % (31730)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.52  % (31710)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (31715)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)
% 0.20/0.53  % (31731)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.53  % (31735)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.53  TRYING [1]
% 0.20/0.53  TRYING [2]
% 0.20/0.53  % (31733)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)
% 0.20/0.53  % (31724)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)
% 0.20/0.53  TRYING [3]
% 0.20/0.53  % (31736)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)
% 0.20/0.53  % (31712)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)
% 0.20/0.53  % (31734)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.54  % (31709)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.54  % (31738)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54  TRYING [1]
% 0.20/0.54  % (31726)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)
% 0.20/0.54  % (31729)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54  TRYING [2]
% 0.20/0.54  % (31728)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54  % (31716)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.55  % (31737)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.55  % (31720)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55  % (31716)Instruction limit reached!
% 0.20/0.55  % (31716)------------------------------
% 0.20/0.55  % (31716)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (31716)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (31716)Termination reason: Unknown
% 0.20/0.55  % (31716)Termination phase: Saturation
% 0.20/0.55  
% 0.20/0.55  % (31716)Memory used [KB]: 5500
% 0.20/0.55  % (31716)Time elapsed: 0.099 s
% 0.20/0.55  % (31716)Instructions burned: 7 (million)
% 0.20/0.55  % (31716)------------------------------
% 0.20/0.55  % (31716)------------------------------
% 0.20/0.55  % (31710)Refutation not found, incomplete strategy% (31710)------------------------------
% 0.20/0.55  % (31710)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (31710)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (31710)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.55  
% 0.20/0.55  % (31710)Memory used [KB]: 5628
% 0.20/0.55  % (31710)Time elapsed: 0.112 s
% 0.20/0.55  % (31710)Instructions burned: 9 (million)
% 0.20/0.55  % (31710)------------------------------
% 0.20/0.55  % (31710)------------------------------
% 0.20/0.55  % (31718)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55  % (31719)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.55  % (31722)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.55  % (31717)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55  % (31717)Instruction limit reached!
% 0.20/0.55  % (31717)------------------------------
% 0.20/0.55  % (31717)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (31717)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (31717)Termination reason: Unknown
% 0.20/0.55  % (31717)Termination phase: Property scanning
% 0.20/0.55  
% 0.20/0.55  % (31717)Memory used [KB]: 895
% 0.20/0.55  % (31717)Time elapsed: 0.002 s
% 0.20/0.55  % (31717)Instructions burned: 3 (million)
% 0.20/0.55  % (31717)------------------------------
% 0.20/0.55  % (31717)------------------------------
% 0.20/0.56  % (31723)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)
% 0.20/0.56  % (31830)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/388Mi)
% 0.20/0.56  % (31714)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)
% 0.20/0.57  % (31739)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.57  % (31732)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)
% 0.20/0.57  TRYING [3]
% 0.20/0.58  % (31728)First to succeed.
% 0.20/0.58  TRYING [4]
% 0.20/0.58  % (31715)Instruction limit reached!
% 0.20/0.58  % (31715)------------------------------
% 0.20/0.58  % (31715)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58  % (31715)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58  % (31715)Termination reason: Unknown
% 0.20/0.58  % (31715)Termination phase: Finite model building constraint generation
% 0.20/0.58  
% 0.20/0.58  % (31715)Memory used [KB]: 7419
% 0.20/0.58  % (31715)Time elapsed: 0.174 s
% 0.20/0.58  % (31715)Instructions burned: 51 (million)
% 0.20/0.58  % (31715)------------------------------
% 0.20/0.58  % (31715)------------------------------
% 0.20/0.59  % (31711)Instruction limit reached!
% 0.20/0.59  % (31711)------------------------------
% 0.20/0.59  % (31711)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.59  % (31711)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.59  % (31711)Termination reason: Unknown
% 0.20/0.59  % (31711)Termination phase: Saturation
% 0.20/0.59  
% 0.20/0.59  % (31711)Memory used [KB]: 1407
% 0.20/0.59  % (31711)Time elapsed: 0.190 s
% 0.20/0.59  % (31711)Instructions burned: 37 (million)
% 0.20/0.59  % (31711)------------------------------
% 0.20/0.59  % (31711)------------------------------
% 0.20/0.59  % (31728)Refutation found. Thanks to Tanya!
% 0.20/0.59  % SZS status Theorem for theBenchmark
% 0.20/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.59  % (31728)------------------------------
% 0.20/0.59  % (31728)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.59  % (31728)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.59  % (31728)Termination reason: Refutation
% 0.20/0.59  
% 0.20/0.59  % (31728)Memory used [KB]: 5884
% 0.20/0.59  % (31728)Time elapsed: 0.177 s
% 0.20/0.59  % (31728)Instructions burned: 21 (million)
% 0.20/0.59  % (31728)------------------------------
% 0.20/0.59  % (31728)------------------------------
% 0.20/0.59  % (31707)Success in time 0.235 s
%------------------------------------------------------------------------------