TSTP Solution File: SET682+3 by Vampire-SAT---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.9
% Problem  : SET682+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d SAT

% Computer : n019.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 : Mon Jun 24 14:59:24 EDT 2024

% Result   : Theorem 0.20s 0.46s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  102 (  13 unt;   0 def)
%            Number of atoms       :  340 (  12 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  402 ( 164   ~; 148   |;  31   &)
%                                         (  14 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   6 con; 0-3 aty)
%            Number of variables   :  201 ( 188   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1054,plain,
    $false,
    inference(avatar_sat_refutation,[],[f297,f308,f1029]) ).

fof(f1029,plain,
    ~ spl14_11,
    inference(avatar_contradiction_clause,[],[f1028]) ).

fof(f1028,plain,
    ( $false
    | ~ spl14_11 ),
    inference(subsumption_resolution,[],[f990,f348]) ).

fof(f348,plain,
    ( ~ member(sK8(sK2),sK1)
    | ~ spl14_11 ),
    inference(resolution,[],[f310,f152]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1) ),
    inference(subsumption_resolution,[],[f151,f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ~ member(X1,X0)
      | ~ empty(X0) ),
    inference(subsumption_resolution,[],[f114,f66]) ).

fof(f66,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ member(X1,X0)
      | ~ empty(X0) ),
    inference(subsumption_resolution,[],[f77,f66]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ member(X1,X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ( empty(X0)
      <=> ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( empty(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ~ member(X1,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f151,plain,
    ! [X0,X1] :
      ( empty(X1)
      | ~ member(X0,X1)
      | ilf_type(X0,member_type(X1)) ),
    inference(subsumption_resolution,[],[f150,f66]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( empty(X1)
      | ~ ilf_type(X1,set_type)
      | ~ member(X0,X1)
      | ilf_type(X0,member_type(X1)) ),
    inference(subsumption_resolution,[],[f100,f66]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | empty(X1)
      | ~ ilf_type(X1,set_type)
      | ~ member(X0,X1)
      | ilf_type(X0,member_type(X1)) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f310,plain,
    ( ~ ilf_type(sK8(sK2),member_type(sK1))
    | ~ spl14_11 ),
    inference(resolution,[],[f292,f270]) ).

fof(f270,plain,
    ! [X4] :
      ( ~ member(X4,range_of(sK2))
      | ~ ilf_type(X4,member_type(sK1)) ),
    inference(backward_demodulation,[],[f58,f264]) ).

fof(f264,plain,
    range(sK0,sK1,sK2) = range_of(sK2),
    inference(resolution,[],[f135,f61]) ).

fof(f61,plain,
    ilf_type(sK2,relation_type(sK0,sK1)),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ! [X4] :
                      ( ~ member(X4,range(X0,X1,X2))
                      | ~ ilf_type(X4,member_type(X1)) )
                  & member(X3,domain(X0,X1,X2))
                  & ilf_type(X3,member_type(X0)) )
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ! [X4] :
                      ( ~ member(X4,range(X0,X1,X2))
                      | ~ ilf_type(X4,member_type(X1)) )
                  & member(X3,domain(X0,X1,X2))
                  & ilf_type(X3,member_type(X0)) )
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,negated_conjecture,
    ~ ! [X0] :
        ( ( ilf_type(X0,set_type)
          & ~ empty(X0) )
       => ! [X1] :
            ( ( ilf_type(X1,set_type)
              & ~ empty(X1) )
           => ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ! [X3] :
                    ( ilf_type(X3,member_type(X0))
                   => ( member(X3,domain(X0,X1,X2))
                     => ? [X4] :
                          ( member(X4,range(X0,X1,X2))
                          & ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f25]) ).

fof(f25,conjecture,
    ! [X0] :
      ( ( ilf_type(X0,set_type)
        & ~ empty(X0) )
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ! [X3] :
                  ( ilf_type(X3,member_type(X0))
                 => ( member(X3,domain(X0,X1,X2))
                   => ? [X4] :
                        ( member(X4,range(X0,X1,X2))
                        & ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f135,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | range(X0,X1,X2) = range_of(X2) ),
    inference(subsumption_resolution,[],[f134,f66]) ).

fof(f134,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | range(X0,X1,X2) = range_of(X2) ),
    inference(subsumption_resolution,[],[f94,f66]) ).

fof(f94,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | range(X0,X1,X2) = range_of(X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( range(X0,X1,X2) = range_of(X2)
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => range(X0,X1,X2) = range_of(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f58,plain,
    ! [X4] :
      ( ~ member(X4,range(sK0,sK1,sK2))
      | ~ ilf_type(X4,member_type(sK1)) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f292,plain,
    ( member(sK8(sK2),range_of(sK2))
    | ~ spl14_11 ),
    inference(avatar_component_clause,[],[f290]) ).

fof(f290,plain,
    ( spl14_11
  <=> member(sK8(sK2),range_of(sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).

fof(f990,plain,
    ( member(sK8(sK2),sK1)
    | ~ spl14_11 ),
    inference(resolution,[],[f532,f292]) ).

fof(f532,plain,
    ! [X0] :
      ( ~ member(X0,range_of(sK2))
      | member(X0,sK1) ),
    inference(resolution,[],[f333,f219]) ).

fof(f219,plain,
    ilf_type(range_of(sK2),subset_type(sK1)),
    inference(resolution,[],[f143,f61]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(range_of(X2),subset_type(X1)) ),
    inference(forward_subsumption_demodulation,[],[f142,f135]) ).

fof(f142,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(range(X0,X1,X2),subset_type(X1)) ),
    inference(subsumption_resolution,[],[f141,f66]) ).

fof(f141,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(range(X0,X1,X2),subset_type(X1)) ),
    inference(subsumption_resolution,[],[f97,f66]) ).

fof(f97,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(range(X0,X1,X2),subset_type(X1)) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(range(X0,X1,X2),subset_type(X1))
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f333,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,subset_type(X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(resolution,[],[f178,f129]) ).

fof(f129,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(subsumption_resolution,[],[f128,f66]) ).

fof(f128,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | member(X2,X1)
      | ~ member(X0,power_set(X1)) ),
    inference(subsumption_resolution,[],[f127,f66]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | member(X2,X1)
      | ~ member(X0,power_set(X1)) ),
    inference(subsumption_resolution,[],[f88,f66]) ).

fof(f88,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | member(X2,X1)
      | ~ member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f178,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ ilf_type(X0,subset_type(X1)) ),
    inference(subsumption_resolution,[],[f174,f106]) ).

fof(f106,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(subsumption_resolution,[],[f69,f66]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ~ empty(power_set(X0)) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f174,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | empty(power_set(X1))
      | ~ ilf_type(X0,subset_type(X1)) ),
    inference(resolution,[],[f149,f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(subsumption_resolution,[],[f130,f66]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(subsumption_resolution,[],[f93,f66]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f149,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,member_type(X1))
      | member(X0,X1)
      | empty(X1) ),
    inference(subsumption_resolution,[],[f148,f66]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( empty(X1)
      | ~ ilf_type(X1,set_type)
      | member(X0,X1)
      | ~ ilf_type(X0,member_type(X1)) ),
    inference(subsumption_resolution,[],[f101,f66]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | empty(X1)
      | ~ ilf_type(X1,set_type)
      | member(X0,X1)
      | ~ ilf_type(X0,member_type(X1)) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f308,plain,
    spl14_12,
    inference(avatar_contradiction_clause,[],[f307]) ).

fof(f307,plain,
    ( $false
    | spl14_12 ),
    inference(subsumption_resolution,[],[f305,f298]) ).

fof(f298,plain,
    ( ~ relation_like(sK2)
    | spl14_12 ),
    inference(resolution,[],[f296,f116]) ).

fof(f116,plain,
    ! [X0] :
      ( ilf_type(X0,binary_relation_type)
      | ~ relation_like(X0) ),
    inference(subsumption_resolution,[],[f81,f66]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ relation_like(X0)
      | ~ ilf_type(X0,set_type)
      | ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ( ilf_type(X0,binary_relation_type)
      <=> ( ilf_type(X0,set_type)
          & relation_like(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(X0,binary_relation_type)
      <=> ( ilf_type(X0,set_type)
          & relation_like(X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f296,plain,
    ( ~ ilf_type(sK2,binary_relation_type)
    | spl14_12 ),
    inference(avatar_component_clause,[],[f294]) ).

fof(f294,plain,
    ( spl14_12
  <=> ilf_type(sK2,binary_relation_type) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_12])]) ).

fof(f305,plain,
    relation_like(sK2),
    inference(resolution,[],[f224,f61]) ).

fof(f224,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,relation_type(X1,X2))
      | relation_like(X0) ),
    inference(resolution,[],[f122,f145]) ).

fof(f145,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | relation_like(X2) ),
    inference(subsumption_resolution,[],[f144,f66]) ).

fof(f144,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | relation_like(X2) ),
    inference(subsumption_resolution,[],[f98,f66]) ).

fof(f98,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | relation_like(X2) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( relation_like(X2)
              | ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,subset_type(cross_product(X0,X1)))
             => relation_like(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1)) ),
    inference(subsumption_resolution,[],[f121,f66]) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(X2,subset_type(cross_product(X0,X1))) ),
    inference(subsumption_resolution,[],[f86,f66]) ).

fof(f86,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(X2,subset_type(cross_product(X0,X1))) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
                | ~ ilf_type(X2,relation_type(X0,X1)) )
            & ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
                | ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ilf_type(X2,subset_type(cross_product(X0,X1))) )
            & ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X0,X1)))
               => ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
               => ilf_type(X3,subset_type(cross_product(X0,X1))) )
            & ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
               => ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f297,plain,
    ( spl14_11
    | ~ spl14_12 ),
    inference(avatar_split_clause,[],[f286,f294,f290]) ).

fof(f286,plain,
    ( ~ ilf_type(sK2,binary_relation_type)
    | member(sK8(sK2),range_of(sK2)) ),
    inference(resolution,[],[f283,f118]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ member(X0,domain_of(X1))
      | ~ ilf_type(X1,binary_relation_type)
      | member(sK8(X1),range_of(X1)) ),
    inference(subsumption_resolution,[],[f83,f66]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,binary_relation_type)
      | ~ member(X0,domain_of(X1))
      | member(sK8(X1),range_of(X1)) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( member(X2,range_of(X1))
              & ilf_type(X2,set_type) )
          | ~ member(X0,domain_of(X1))
          | ~ ilf_type(X1,binary_relation_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( member(X2,range_of(X1))
              & ilf_type(X2,set_type) )
          | ~ member(X0,domain_of(X1))
          | ~ ilf_type(X1,binary_relation_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,binary_relation_type)
         => ( member(X0,domain_of(X1))
           => ? [X2] :
                ( member(X2,range_of(X1))
                & ilf_type(X2,set_type) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f283,plain,
    member(sK3,domain_of(sK2)),
    inference(backward_demodulation,[],[f60,f278]) ).

fof(f278,plain,
    domain(sK0,sK1,sK2) = domain_of(sK2),
    inference(resolution,[],[f137,f61]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | domain(X0,X1,X2) = domain_of(X2) ),
    inference(subsumption_resolution,[],[f136,f66]) ).

fof(f136,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | domain(X0,X1,X2) = domain_of(X2) ),
    inference(subsumption_resolution,[],[f95,f66]) ).

fof(f95,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | domain(X0,X1,X2) = domain_of(X2) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( domain(X0,X1,X2) = domain_of(X2)
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => domain(X0,X1,X2) = domain_of(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f60,plain,
    member(sK3,domain(sK0,sK1,sK2)),
    inference(cnf_transformation,[],[f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET682+3 : TPTP v8.2.0. Released v2.2.0.
% 0.12/0.12  % Command    : run_vampire %s %d SAT
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun Jun 23 17:53:09 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.35  Running first-order model finding
% 0.12/0.35  Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.41  % (3474)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency:i=99418_0 on theBenchmark for (3000ds/99418Mi)
% 0.12/0.41  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.41  % (3478)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (3000ds/146Mi)
% 0.12/0.41  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.41  % (3476)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (3000ds/152523Mi)
% 0.12/0.41  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.41  % (3475)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (3000ds/214858Mi)
% 0.20/0.42  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (3473)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (3000ds/98885Mi)
% 0.20/0.42  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (3479)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (3000ds/115Mi)
% 0.20/0.42  TRYING [1]
% 0.20/0.42  TRYING [2]
% 0.20/0.43  TRYING [3]
% 0.20/0.43  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (3477)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (3000ds/104Mi)
% 0.20/0.43  TRYING [10]
% 0.20/0.45  TRYING [4]
% 0.20/0.46  % (3477)First to succeed.
% 0.20/0.46  % (3477)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3472"
% 0.20/0.46  % (3472)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.46  % (3477)Refutation found. Thanks to Tanya!
% 0.20/0.46  % SZS status Theorem for theBenchmark
% 0.20/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.46  % (3477)------------------------------
% 0.20/0.46  % (3477)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.46  % (3477)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.46  % (3477)Termination reason: Refutation
% 0.20/0.46  
% 0.20/0.46  % (3477)Memory used [KB]: 1348
% 0.20/0.46  % (3477)Time elapsed: 0.033 s
% 0.20/0.46  % (3477)Instructions burned: 47 (million)
% 0.20/0.46  % (3477)------------------------------
% 0.20/0.46  % (3477)------------------------------
% 0.20/0.46  % (3472)Success in time 0.103 s
%------------------------------------------------------------------------------