TSTP Solution File: SEU262+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n016.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 17:05:17 EDT 2023

% Result   : Theorem 16.31s 3.18s
% Output   : CNFRefutation 16.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   96 (  10 unt;   0 def)
%            Number of atoms       :  313 (  28 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  362 ( 145   ~; 146   |;  43   &)
%                                         (  13 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   3 con; 0-2 aty)
%            Number of variables   :  269 (   6 sgn; 172   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
     => relation(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f7,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f18,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => element(X2,powerset(cartesian_product2(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

fof(f26,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
    <=> relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

fof(f28,axiom,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).

fof(f29,conjecture,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => ( subset(relation_rng(X2),X1)
        & subset(relation_dom(X2),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).

fof(f30,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( relation_of2_as_subset(X2,X0,X1)
       => ( subset(relation_rng(X2),X1)
          & subset(relation_dom(X2),X0) ) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

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,[],[f5]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f46,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(relation_rng(X2),X1)
        | ~ subset(relation_dom(X2),X0) )
      & relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK0(X0,X1),X1)
        & in(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK0(X0,X1),X1)
          & in(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f57,f58]) ).

fof(f60,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(f61,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,[],[f60]) ).

fof(f62,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(sK1(X0,X1),X3),X0)
          | ~ in(sK1(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(sK1(X0,X1),X4),X0)
          | in(sK1(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(sK1(X0,X1),X4),X0)
     => in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X5,X7),X0)
     => in(ordered_pair(X5,sK3(X0,X5)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(sK1(X0,X1),X3),X0)
                | ~ in(sK1(X0,X1),X1) )
              & ( in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
                | in(sK1(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( in(ordered_pair(X5,sK3(X0,X5)),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f61,f64,f63,f62]) ).

fof(f66,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f66]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X4,X2),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
          | ~ in(sK4(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
     => in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK6(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
                | ~ in(sK4(X0,X1),X1) )
              & ( in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0)
                | in(sK4(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK6(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f67,f70,f69,f68]) ).

fof(f82,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(f83,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f84,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(flattening,[],[f83]) ).

fof(f85,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ subset(relation_rng(X2),X1)
          | ~ subset(relation_dom(X2),X0) )
        & relation_of2_as_subset(X2,X0,X1) )
   => ( ( ~ subset(relation_rng(sK14),sK13)
        | ~ subset(relation_dom(sK14),sK12) )
      & relation_of2_as_subset(sK14,sK12,sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ( ( ~ subset(relation_rng(sK14),sK13)
      | ~ subset(relation_dom(sK14),sK12) )
    & relation_of2_as_subset(sK14,sK12,sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f46,f85]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f89,plain,
    ! [X2,X0,X1] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f91,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f94,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(X5,sK3(X0,X5)),X0)
      | ~ in(X5,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f98,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK6(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f102,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f7]) ).

fof(f103,plain,
    ! [X2,X0,X1] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f111,plain,
    ! [X2,X0,X1] :
      ( relation_of2(X2,X0,X1)
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f112,plain,
    ! [X2,X0,X1] :
      ( relation_of2_as_subset(X2,X0,X1)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f114,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,X2)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f115,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f117,plain,
    relation_of2_as_subset(sK14,sK12,sK13),
    inference(cnf_transformation,[],[f86]) ).

fof(f118,plain,
    ( ~ subset(relation_rng(sK14),sK13)
    | ~ subset(relation_dom(sK14),sK12) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f131,plain,
    ! [X0,X1,X5] :
      ( in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0)
      | ~ in(X5,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f94,f102]) ).

fof(f135,plain,
    ! [X0,X1,X5] :
      ( in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f98,f102]) ).

fof(f138,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
    inference(definition_unfolding,[],[f115,f102]) ).

fof(f139,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,X2)
      | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
    inference(definition_unfolding,[],[f114,f102]) ).

fof(f141,plain,
    ! [X0,X5] :
      ( in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0)
      | ~ in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f131]) ).

fof(f143,plain,
    ! [X0,X5] :
      ( in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0)
      | ~ in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f135]) ).

cnf(c_50,plain,
    ( ~ element(X0,powerset(cartesian_product2(X1,X2)))
    | relation(X0) ),
    inference(cnf_transformation,[],[f89]) ).

cnf(c_52,plain,
    ( ~ in(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_53,plain,
    ( in(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_54,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_58,plain,
    ( ~ in(X0,relation_dom(X1))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(X0,sK3(X1,X0)),singleton(X0)),X1) ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_62,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(sK6(X1,X0),X0),singleton(sK6(X1,X0))),X1) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_63,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | element(X0,powerset(cartesian_product2(X1,X2))) ),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_71,plain,
    ( ~ relation_of2(X0,X1,X2)
    | relation_of2_as_subset(X0,X1,X2) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_72,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | relation_of2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_75,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
    | in(X1,X3) ),
    inference(cnf_transformation,[],[f138]) ).

cnf(c_76,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_77,negated_conjecture,
    ( ~ subset(relation_dom(sK14),sK12)
    | ~ subset(relation_rng(sK14),sK13) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_78,negated_conjecture,
    relation_of2_as_subset(sK14,sK12,sK13),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_82,plain,
    ( ~ element(X0,powerset(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_114,plain,
    ( relation_of2(X0,X1,X2)
    | ~ relation_of2_as_subset(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_72]) ).

cnf(c_115,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | relation_of2(X0,X1,X2) ),
    inference(renaming,[status(thm)],[c_114]) ).

cnf(c_132,plain,
    ( element(X0,powerset(cartesian_product2(X1,X2)))
    | ~ relation_of2(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_71,c_63]) ).

cnf(c_133,plain,
    ( ~ relation_of2(X0,X1,X2)
    | element(X0,powerset(cartesian_product2(X1,X2))) ),
    inference(renaming,[status(thm)],[c_132]) ).

cnf(c_431,plain,
    ( X0 != sK14
    | X1 != sK12
    | X2 != sK13
    | relation_of2(X0,X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_115,c_78]) ).

cnf(c_432,plain,
    relation_of2(sK14,sK12,sK13),
    inference(unflattening,[status(thm)],[c_431]) ).

cnf(c_450,plain,
    ( X0 != sK14
    | X1 != sK12
    | X2 != sK13
    | element(X0,powerset(cartesian_product2(X1,X2))) ),
    inference(resolution_lifted,[status(thm)],[c_133,c_432]) ).

cnf(c_451,plain,
    element(sK14,powerset(cartesian_product2(sK12,sK13))),
    inference(unflattening,[status(thm)],[c_450]) ).

cnf(c_2175,plain,
    ( ~ element(sK14,powerset(cartesian_product2(sK12,sK13)))
    | relation(sK14) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_3738,plain,
    subset(sK14,cartesian_product2(sK12,sK13)),
    inference(resolution,[status(thm)],[c_82,c_451]) ).

cnf(c_3753,plain,
    ( ~ in(X0,sK14)
    | in(X0,cartesian_product2(sK12,sK13)) ),
    inference(resolution,[status(thm)],[c_54,c_3738]) ).

cnf(c_6120,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK14)
    | in(X1,sK13) ),
    inference(resolution,[status(thm)],[c_75,c_3753]) ).

cnf(c_6126,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK14)
    | in(X0,sK12) ),
    inference(resolution,[status(thm)],[c_76,c_3753]) ).

cnf(c_8399,plain,
    ( ~ in(X0,relation_dom(sK14))
    | ~ relation(sK14)
    | in(X0,sK12) ),
    inference(resolution,[status(thm)],[c_6126,c_58]) ).

cnf(c_8450,plain,
    ( ~ in(X0,relation_dom(sK14))
    | in(X0,sK12) ),
    inference(global_subsumption_just,[status(thm)],[c_8399,c_451,c_2175,c_8399]) ).

cnf(c_8461,plain,
    ( in(sK0(relation_dom(sK14),X0),sK12)
    | subset(relation_dom(sK14),X0) ),
    inference(resolution,[status(thm)],[c_8450,c_53]) ).

cnf(c_8596,plain,
    subset(relation_dom(sK14),sK12),
    inference(resolution,[status(thm)],[c_8461,c_52]) ).

cnf(c_9427,plain,
    ( ~ in(X0,relation_rng(sK14))
    | ~ relation(sK14)
    | in(X0,sK13) ),
    inference(resolution,[status(thm)],[c_62,c_6120]) ).

cnf(c_10244,plain,
    ( ~ in(X0,relation_rng(sK14))
    | in(X0,sK13) ),
    inference(global_subsumption_just,[status(thm)],[c_9427,c_451,c_2175,c_9427]) ).

cnf(c_10255,plain,
    ( in(sK0(relation_rng(sK14),X0),sK13)
    | subset(relation_rng(sK14),X0) ),
    inference(resolution,[status(thm)],[c_10244,c_53]) ).

cnf(c_10403,plain,
    subset(relation_rng(sK14),sK13),
    inference(resolution,[status(thm)],[c_10255,c_52]) ).

cnf(c_10404,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_10403,c_8596,c_77]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 01:58:08 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.31/3.18  % SZS status Started for theBenchmark.p
% 16.31/3.18  % SZS status Theorem for theBenchmark.p
% 16.31/3.18  
% 16.31/3.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 16.31/3.18  
% 16.31/3.18  ------  iProver source info
% 16.31/3.18  
% 16.31/3.18  git: date: 2023-05-31 18:12:56 +0000
% 16.31/3.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 16.31/3.18  git: non_committed_changes: false
% 16.31/3.18  git: last_make_outside_of_git: false
% 16.31/3.18  
% 16.31/3.18  ------ Parsing...
% 16.31/3.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 16.31/3.18  
% 16.31/3.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 16.31/3.18  
% 16.31/3.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 16.31/3.18  
% 16.31/3.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 16.31/3.18  ------ Proving...
% 16.31/3.18  ------ Problem Properties 
% 16.31/3.18  
% 16.31/3.18  
% 16.31/3.18  clauses                                 36
% 16.31/3.18  conjectures                             1
% 16.31/3.18  EPR                                     13
% 16.31/3.18  Horn                                    32
% 16.31/3.18  unary                                   10
% 16.31/3.18  binary                                  12
% 16.31/3.18  lits                                    80
% 16.31/3.18  lits eq                                 7
% 16.31/3.18  fd_pure                                 0
% 16.31/3.18  fd_pseudo                               0
% 16.31/3.18  fd_cond                                 1
% 16.31/3.18  fd_pseudo_cond                          5
% 16.31/3.18  AC symbols                              0
% 16.31/3.18  
% 16.31/3.18  ------ Input Options Time Limit: Unbounded
% 16.31/3.18  
% 16.31/3.18  
% 16.31/3.18  ------ 
% 16.31/3.18  Current options:
% 16.31/3.18  ------ 
% 16.31/3.18  
% 16.31/3.18  
% 16.31/3.18  
% 16.31/3.18  
% 16.31/3.18  ------ Proving...
% 16.31/3.18  
% 16.31/3.18  
% 16.31/3.18  % SZS status Theorem for theBenchmark.p
% 16.31/3.18  
% 16.31/3.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.31/3.18  
% 16.31/3.19  
%------------------------------------------------------------------------------