TSTP Solution File: SEU265+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n023.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 : Thu Aug 31 17:57:27 EDT 2023

% Result   : Theorem 0.22s 0.46s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  124 (  20 unt;   0 def)
%            Number of atoms       :  362 (  65 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  392 ( 154   ~; 163   |;  44   &)
%                                         (  10 <=>;  19  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :  256 (; 210   !;  46   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f625,plain,
    $false,
    inference(subsumption_resolution,[],[f624,f550]) ).

fof(f550,plain,
    in(sK3,sK1),
    inference(subsumption_resolution,[],[f132,f549]) ).

fof(f549,plain,
    sK1 = sF15,
    inference(subsumption_resolution,[],[f547,f506]) ).

fof(f506,plain,
    ( in(sK9(sK1,sF15),sK1)
    | sK1 = sF15 ),
    inference(factoring,[],[f491]) ).

fof(f491,plain,
    ! [X0] :
      ( in(sK9(X0,sF15),sK1)
      | sF15 = X0
      | in(sK9(X0,sF15),X0) ),
    inference(subsumption_resolution,[],[f488,f395]) ).

fof(f395,plain,
    ~ empty(sK1),
    inference(subsumption_resolution,[],[f394,f289]) ).

fof(f289,plain,
    ( ~ empty(sK1)
    | empty(sF15) ),
    inference(forward_literal_rewriting,[],[f285,f145]) ).

fof(f145,plain,
    ! [X2] :
      ( ~ sP14(X2)
      | empty(X2) ),
    inference(resolution,[],[f140,f129]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ sP14(X1) ),
    inference(general_splitting,[],[f123,f128_D]) ).

fof(f128,plain,
    ! [X2,X1] :
      ( ~ element(X1,powerset(X2))
      | ~ empty(X2)
      | sP14(X1) ),
    inference(cnf_transformation,[],[f128_D]) ).

fof(f128_D,plain,
    ! [X1] :
      ( ! [X2] :
          ( ~ element(X1,powerset(X2))
          | ~ empty(X2) )
    <=> ~ sP14(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP14])]) ).

fof(f123,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t5_subset) ).

fof(f140,plain,
    ! [X0] :
      ( in(sK8(X0),X0)
      | empty(X0) ),
    inference(resolution,[],[f106,f99]) ).

fof(f99,plain,
    ! [X0] : element(sK8(X0),X0),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0] : element(sK8(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK8(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f19,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',existence_m1_subset_1) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t2_subset) ).

fof(f285,plain,
    ( ~ empty(sK1)
    | sP14(sF15) ),
    inference(resolution,[],[f283,f128]) ).

fof(f283,plain,
    element(sF15,powerset(sK1)),
    inference(subsumption_resolution,[],[f279,f178]) ).

fof(f178,plain,
    relation_of2(sK2,sK1,sK0),
    inference(resolution,[],[f121,f89]) ).

fof(f89,plain,
    relation_of2_as_subset(sK2,sK1,sK0),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ( ( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
      | ( ! [X4] : ~ in(ordered_pair(sK3,X4),sK2)
        & in(sK3,sK1) ) )
    & ( sK1 = relation_dom_as_subset(sK1,sK0,sK2)
      | ! [X5] :
          ( in(ordered_pair(X5,sK4(X5)),sK2)
          | ~ in(X5,sK1) ) )
    & relation_of2_as_subset(sK2,sK1,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f64,f67,f66,f65]) ).

fof(f65,plain,
    ( ? [X0,X1,X2] :
        ( ( relation_dom_as_subset(X1,X0,X2) != X1
          | ? [X3] :
              ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
              & in(X3,X1) ) )
        & ( relation_dom_as_subset(X1,X0,X2) = X1
          | ! [X5] :
              ( ? [X6] : in(ordered_pair(X5,X6),X2)
              | ~ in(X5,X1) ) )
        & relation_of2_as_subset(X2,X1,X0) )
   => ( ( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
        | ? [X3] :
            ( ! [X4] : ~ in(ordered_pair(X3,X4),sK2)
            & in(X3,sK1) ) )
      & ( sK1 = relation_dom_as_subset(sK1,sK0,sK2)
        | ! [X5] :
            ( ? [X6] : in(ordered_pair(X5,X6),sK2)
            | ~ in(X5,sK1) ) )
      & relation_of2_as_subset(sK2,sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ( ? [X3] :
        ( ! [X4] : ~ in(ordered_pair(X3,X4),sK2)
        & in(X3,sK1) )
   => ( ! [X4] : ~ in(ordered_pair(sK3,X4),sK2)
      & in(sK3,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X5] :
      ( ? [X6] : in(ordered_pair(X5,X6),sK2)
     => in(ordered_pair(X5,sK4(X5)),sK2) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ? [X0,X1,X2] :
      ( ( relation_dom_as_subset(X1,X0,X2) != X1
        | ? [X3] :
            ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
            & in(X3,X1) ) )
      & ( relation_dom_as_subset(X1,X0,X2) = X1
        | ! [X5] :
            ( ? [X6] : in(ordered_pair(X5,X6),X2)
            | ~ in(X5,X1) ) )
      & relation_of2_as_subset(X2,X1,X0) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ? [X0,X1,X2] :
      ( ( relation_dom_as_subset(X1,X0,X2) != X1
        | ? [X3] :
            ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
            & in(X3,X1) ) )
      & ( relation_dom_as_subset(X1,X0,X2) = X1
        | ! [X3] :
            ( ? [X4] : in(ordered_pair(X3,X4),X2)
            | ~ in(X3,X1) ) )
      & relation_of2_as_subset(X2,X1,X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ? [X0,X1,X2] :
      ( ( relation_dom_as_subset(X1,X0,X2) != X1
        | ? [X3] :
            ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
            & in(X3,X1) ) )
      & ( relation_dom_as_subset(X1,X0,X2) = X1
        | ! [X3] :
            ( ? [X4] : in(ordered_pair(X3,X4),X2)
            | ~ in(X3,X1) ) )
      & relation_of2_as_subset(X2,X1,X0) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f42,plain,
    ? [X0,X1,X2] :
      ( ( ! [X3] :
            ( ? [X4] : in(ordered_pair(X3,X4),X2)
            | ~ in(X3,X1) )
      <~> relation_dom_as_subset(X1,X0,X2) = X1 )
      & relation_of2_as_subset(X2,X1,X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( relation_of2_as_subset(X2,X1,X0)
       => ( ! [X3] :
              ~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
                & in(X3,X1) )
        <=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
    inference(negated_conjecture,[],[f30]) ).

fof(f30,conjecture,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X1,X0)
     => ( ! [X3] :
            ~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
              & in(X3,X1) )
      <=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t22_relset_1) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2_as_subset(X2,X0,X1)
      | relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( relation_of2_as_subset(X2,X0,X1)
        | ~ relation_of2(X2,X0,X1) )
      & ( relation_of2(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
    <=> relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',redefinition_m2_relset_1) ).

fof(f279,plain,
    ( element(sF15,powerset(sK1))
    | ~ relation_of2(sK2,sK1,sK0) ),
    inference(superposition,[],[f117,f130]) ).

fof(f130,plain,
    relation_dom_as_subset(sK1,sK0,sK2) = sF15,
    introduced(function_definition,[]) ).

fof(f117,plain,
    ! [X2,X0,X1] :
      ( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
      | ~ relation_of2(X2,X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2] :
      ( relation_of2(X2,X0,X1)
     => element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',dt_k4_relset_1) ).

fof(f394,plain,
    ( ~ empty(sK1)
    | ~ empty(sF15) ),
    inference(forward_literal_rewriting,[],[f392,f187]) ).

fof(f187,plain,
    ! [X0] :
      ( ~ empty(X0)
      | sP14(X0) ),
    inference(resolution,[],[f184,f100]) ).

fof(f100,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',reflexivity_r1_tarski) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | sP14(X1)
      | ~ empty(X0) ),
    inference(resolution,[],[f128,f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
     => element(X0,powerset(X1)) ),
    inference(unused_predicate_definition_removal,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t3_subset) ).

fof(f392,plain,
    ( ~ empty(sF15)
    | ~ sP14(sK1) ),
    inference(resolution,[],[f385,f129]) ).

fof(f385,plain,
    ( in(sK3,sK1)
    | ~ empty(sF15) ),
    inference(trivial_inequality_removal,[],[f376]) ).

fof(f376,plain,
    ( sK1 != sK1
    | in(sK3,sK1)
    | ~ empty(sF15) ),
    inference(superposition,[],[f132,f374]) ).

fof(f374,plain,
    ( sK1 = sF15
    | ~ empty(sF15) ),
    inference(subsumption_resolution,[],[f373,f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ empty(X1)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t8_boole) ).

fof(f373,plain,
    ( ~ empty(sF15)
    | sK1 = sF15
    | empty(sK1) ),
    inference(forward_literal_rewriting,[],[f368,f187]) ).

fof(f368,plain,
    ( sK1 = sF15
    | empty(sK1)
    | ~ sP14(sF15) ),
    inference(resolution,[],[f363,f129]) ).

fof(f363,plain,
    ( in(sK8(sK1),sF15)
    | sK1 = sF15
    | empty(sK1) ),
    inference(resolution,[],[f332,f140]) ).

fof(f332,plain,
    ! [X0] :
      ( ~ in(X0,sK1)
      | sK1 = sF15
      | in(X0,sF15) ),
    inference(forward_demodulation,[],[f331,f274]) ).

fof(f274,plain,
    sF15 = relation_dom(sK2),
    inference(subsumption_resolution,[],[f272,f178]) ).

fof(f272,plain,
    ( sF15 = relation_dom(sK2)
    | ~ relation_of2(sK2,sK1,sK0) ),
    inference(superposition,[],[f116,f130]) ).

fof(f116,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1,X2] :
      ( relation_of2(X2,X0,X1)
     => relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',redefinition_k4_relset_1) ).

fof(f331,plain,
    ! [X0] :
      ( in(X0,relation_dom(sK2))
      | sK1 = sF15
      | ~ in(X0,sK1) ),
    inference(subsumption_resolution,[],[f329,f208]) ).

fof(f208,plain,
    relation(sK2),
    inference(resolution,[],[f203,f178]) ).

fof(f203,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2(X0,X1,X2)
      | relation(X0) ),
    inference(forward_literal_rewriting,[],[f200,f122]) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2(X2,X0,X1)
      | relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f200,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2_as_subset(X0,X1,X2)
      | relation(X0) ),
    inference(resolution,[],[f118,f119]) ).

fof(f119,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,powerset(cartesian_product2(X0,X1)))
      | relation(X2) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
     => relation(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',cc1_relset_1) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => element(X2,powerset(cartesian_product2(X0,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',dt_m2_relset_1) ).

fof(f329,plain,
    ! [X0] :
      ( in(X0,relation_dom(sK2))
      | ~ relation(sK2)
      | sK1 = sF15
      | ~ in(X0,sK1) ),
    inference(resolution,[],[f126,f133]) ).

fof(f133,plain,
    ! [X5] :
      ( in(ordered_pair(X5,sK4(X5)),sK2)
      | sK1 = sF15
      | ~ in(X5,sK1) ),
    inference(definition_folding,[],[f90,f130]) ).

fof(f90,plain,
    ! [X5] :
      ( sK1 = relation_dom_as_subset(sK1,sK0,sK2)
      | in(ordered_pair(X5,sK4(X5)),sK2)
      | ~ in(X5,sK1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f126,plain,
    ! [X0,X6,X5] :
      ( ~ in(ordered_pair(X5,X6),X0)
      | in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f95]) ).

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

fof(f74,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])],[f70,f73,f72,f71]) ).

fof(f71,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(f72,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(f73,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X5,X7),X0)
     => in(ordered_pair(X5,sK7(X0,X5)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f70,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,[],[f69]) ).

fof(f69,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,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,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.n7tGbnab4b/Vampire---4.8_8778',d4_relat_1) ).

fof(f488,plain,
    ! [X0] :
      ( in(sK9(X0,sF15),X0)
      | sF15 = X0
      | empty(sK1)
      | in(sK9(X0,sF15),sK1) ),
    inference(resolution,[],[f454,f106]) ).

fof(f454,plain,
    ! [X12] :
      ( element(sK9(X12,sF15),sK1)
      | in(sK9(X12,sF15),X12)
      | sF15 = X12 ),
    inference(resolution,[],[f107,f284]) ).

fof(f284,plain,
    ! [X0] :
      ( ~ in(X0,sF15)
      | element(X0,sK1) ),
    inference(resolution,[],[f283,f120]) ).

fof(f120,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | element(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t4_subset) ).

fof(f107,plain,
    ! [X0,X1] :
      ( in(sK9(X0,X1),X1)
      | X0 = X1
      | in(sK9(X0,X1),X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK9(X0,X1),X1)
          | ~ in(sK9(X0,X1),X0) )
        & ( in(sK9(X0,X1),X1)
          | in(sK9(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f77,f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK9(X0,X1),X1)
          | ~ in(sK9(X0,X1),X0) )
        & ( in(sK9(X0,X1),X1)
          | in(sK9(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t2_tarski) ).

fof(f547,plain,
    ( sK1 = sF15
    | ~ in(sK9(sK1,sF15),sK1) ),
    inference(duplicate_literal_removal,[],[f545]) ).

fof(f545,plain,
    ( sK1 = sF15
    | ~ in(sK9(sK1,sF15),sK1)
    | sK1 = sF15 ),
    inference(resolution,[],[f108,f520]) ).

fof(f520,plain,
    ( in(sK9(sK1,sF15),sF15)
    | sK1 = sF15 ),
    inference(duplicate_literal_removal,[],[f511]) ).

fof(f511,plain,
    ( sK1 = sF15
    | sK1 = sF15
    | in(sK9(sK1,sF15),sF15) ),
    inference(resolution,[],[f506,f332]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ~ in(sK9(X0,X1),X1)
      | X0 = X1
      | ~ in(sK9(X0,X1),X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f132,plain,
    ( sK1 != sF15
    | in(sK3,sK1) ),
    inference(definition_folding,[],[f91,f130]) ).

fof(f91,plain,
    ( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
    | in(sK3,sK1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f624,plain,
    ~ in(sK3,sK1),
    inference(forward_demodulation,[],[f623,f549]) ).

fof(f623,plain,
    ~ in(sK3,sF15),
    inference(forward_demodulation,[],[f622,f274]) ).

fof(f622,plain,
    ~ in(sK3,relation_dom(sK2)),
    inference(subsumption_resolution,[],[f613,f208]) ).

fof(f613,plain,
    ( ~ in(sK3,relation_dom(sK2))
    | ~ relation(sK2) ),
    inference(resolution,[],[f127,f551]) ).

fof(f551,plain,
    ! [X4] : ~ in(ordered_pair(sK3,X4),sK2),
    inference(subsumption_resolution,[],[f131,f549]) ).

fof(f131,plain,
    ! [X4] :
      ( sK1 != sF15
      | ~ in(ordered_pair(sK3,X4),sK2) ),
    inference(definition_folding,[],[f92,f130]) ).

fof(f92,plain,
    ! [X4] :
      ( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
      | ~ in(ordered_pair(sK3,X4),sK2) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f127,plain,
    ! [X0,X5] :
      ( in(ordered_pair(X5,sK7(X0,X5)),X0)
      | ~ in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(X5,sK7(X0,X5)),X0)
      | ~ in(X5,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.37  % Computer : n023.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Wed Aug 23 20:33:27 EDT 2023
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778
% 0.14/0.38  % (8885)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44  % (8889)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.44  % (8892)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.44  % (8891)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.44  % (8890)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.44  % (8887)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.44  % (8888)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.44  % (8886)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.44  % (8889)Refutation not found, incomplete strategy% (8889)------------------------------
% 0.22/0.44  % (8889)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.44  % (8889)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.44  % (8889)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44  
% 0.22/0.44  % (8889)Memory used [KB]: 10106
% 0.22/0.44  % (8889)Time elapsed: 0.007 s
% 0.22/0.44  % (8889)------------------------------
% 0.22/0.44  % (8889)------------------------------
% 0.22/0.45  % (8890)First to succeed.
% 0.22/0.46  % (8890)Refutation found. Thanks to Tanya!
% 0.22/0.46  % SZS status Theorem for Vampire---4
% 0.22/0.46  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.46  % (8890)------------------------------
% 0.22/0.46  % (8890)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.46  % (8890)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.46  % (8890)Termination reason: Refutation
% 0.22/0.46  
% 0.22/0.46  % (8890)Memory used [KB]: 1279
% 0.22/0.46  % (8890)Time elapsed: 0.021 s
% 0.22/0.46  % (8890)------------------------------
% 0.22/0.46  % (8890)------------------------------
% 0.22/0.46  % (8885)Success in time 0.079 s
% 0.22/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------