TSTP Solution File: SEU293+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n005.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 : Fri May  3 03:05:21 EDT 2024

% Result   : Theorem 6.79s 1.66s
% Output   : CNFRefutation 6.79s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

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

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

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

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

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

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

fof(f45,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

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

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

fof(f66,plain,
    ! [X0,X1,X2] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f69]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ( ( ( quasi_total(X2,X0,X1)
          <=> empty_set = X2 )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ( ( ( quasi_total(X2,X0,X1)
          <=> empty_set = X2 )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(flattening,[],[f71]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f86,plain,
    ? [X0,X1,X2,X3] :
      ( ? [X4] :
          ( in(X4,relation_inverse_image(X3,X2))
        <~> ( in(apply(X3,X4),X2)
            & in(X4,X0) ) )
      & empty_set != X1
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f87,plain,
    ? [X0,X1,X2,X3] :
      ( ? [X4] :
          ( in(X4,relation_inverse_image(X3,X2))
        <~> ( in(apply(X3,X4),X2)
            & in(X4,X0) ) )
      & empty_set != X1
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(flattening,[],[f86]) ).

fof(f94,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f95,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f94]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X4] :
                ( ( in(X4,X2)
                  | ~ in(apply(X0,X4),X1)
                  | ~ in(X4,relation_dom(X0)) )
                & ( ( in(apply(X0,X4),X1)
                    & in(X4,relation_dom(X0)) )
                  | ~ in(X4,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f95]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(apply(X0,X3),X1)
            | ~ in(X3,relation_dom(X0))
            | ~ in(X3,X2) )
          & ( ( in(apply(X0,X3),X1)
              & in(X3,relation_dom(X0)) )
            | in(X3,X2) ) )
     => ( ( ~ in(apply(X0,sK0(X0,X1,X2)),X1)
          | ~ in(sK0(X0,X1,X2),relation_dom(X0))
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ( in(apply(X0,sK0(X0,X1,X2)),X1)
            & in(sK0(X0,X1,X2),relation_dom(X0)) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ( ( ~ in(apply(X0,sK0(X0,X1,X2)),X1)
                | ~ in(sK0(X0,X1,X2),relation_dom(X0))
                | ~ in(sK0(X0,X1,X2),X2) )
              & ( ( in(apply(X0,sK0(X0,X1,X2)),X1)
                  & in(sK0(X0,X1,X2),relation_dom(X0)) )
                | in(sK0(X0,X1,X2),X2) ) ) )
          & ( ! [X4] :
                ( ( in(X4,X2)
                  | ~ in(apply(X0,X4),X1)
                  | ~ in(X4,relation_dom(X0)) )
                & ( ( in(apply(X0,X4),X1)
                    & in(X4,relation_dom(X0)) )
                  | ~ in(X4,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f96,f97]) ).

fof(f99,plain,
    ! [X0,X1,X2] :
      ( ( ( ( ( quasi_total(X2,X0,X1)
              | empty_set != X2 )
            & ( empty_set = X2
              | ~ quasi_total(X2,X0,X1) ) )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( ( quasi_total(X2,X0,X1)
              | relation_dom_as_subset(X0,X1,X2) != X0 )
            & ( relation_dom_as_subset(X0,X1,X2) = X0
              | ~ quasi_total(X2,X0,X1) ) )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f134,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,[],[f43]) ).

fof(f135,plain,
    ? [X0,X1,X2,X3] :
      ( ? [X4] :
          ( ( ~ in(apply(X3,X4),X2)
            | ~ in(X4,X0)
            | ~ in(X4,relation_inverse_image(X3,X2)) )
          & ( ( in(apply(X3,X4),X2)
              & in(X4,X0) )
            | in(X4,relation_inverse_image(X3,X2)) ) )
      & empty_set != X1
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(nnf_transformation,[],[f87]) ).

fof(f136,plain,
    ? [X0,X1,X2,X3] :
      ( ? [X4] :
          ( ( ~ in(apply(X3,X4),X2)
            | ~ in(X4,X0)
            | ~ in(X4,relation_inverse_image(X3,X2)) )
          & ( ( in(apply(X3,X4),X2)
              & in(X4,X0) )
            | in(X4,relation_inverse_image(X3,X2)) ) )
      & empty_set != X1
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(flattening,[],[f135]) ).

fof(f137,plain,
    ( ? [X0,X1,X2,X3] :
        ( ? [X4] :
            ( ( ~ in(apply(X3,X4),X2)
              | ~ in(X4,X0)
              | ~ in(X4,relation_inverse_image(X3,X2)) )
            & ( ( in(apply(X3,X4),X2)
                & in(X4,X0) )
              | in(X4,relation_inverse_image(X3,X2)) ) )
        & empty_set != X1
        & relation_of2_as_subset(X3,X0,X1)
        & quasi_total(X3,X0,X1)
        & function(X3) )
   => ( ? [X4] :
          ( ( ~ in(apply(sK21,X4),sK20)
            | ~ in(X4,sK18)
            | ~ in(X4,relation_inverse_image(sK21,sK20)) )
          & ( ( in(apply(sK21,X4),sK20)
              & in(X4,sK18) )
            | in(X4,relation_inverse_image(sK21,sK20)) ) )
      & empty_set != sK19
      & relation_of2_as_subset(sK21,sK18,sK19)
      & quasi_total(sK21,sK18,sK19)
      & function(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ( ? [X4] :
        ( ( ~ in(apply(sK21,X4),sK20)
          | ~ in(X4,sK18)
          | ~ in(X4,relation_inverse_image(sK21,sK20)) )
        & ( ( in(apply(sK21,X4),sK20)
            & in(X4,sK18) )
          | in(X4,relation_inverse_image(sK21,sK20)) ) )
   => ( ( ~ in(apply(sK21,sK22),sK20)
        | ~ in(sK22,sK18)
        | ~ in(sK22,relation_inverse_image(sK21,sK20)) )
      & ( ( in(apply(sK21,sK22),sK20)
          & in(sK22,sK18) )
        | in(sK22,relation_inverse_image(sK21,sK20)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f139,plain,
    ( ( ~ in(apply(sK21,sK22),sK20)
      | ~ in(sK22,sK18)
      | ~ in(sK22,relation_inverse_image(sK21,sK20)) )
    & ( ( in(apply(sK21,sK22),sK20)
        & in(sK22,sK18) )
      | in(sK22,relation_inverse_image(sK21,sK20)) )
    & empty_set != sK19
    & relation_of2_as_subset(sK21,sK18,sK19)
    & quasi_total(sK21,sK18,sK19)
    & function(sK21) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f136,f138,f137]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f146,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,relation_dom(X0))
      | ~ in(X4,X2)
      | relation_inverse_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f147,plain,
    ! [X2,X0,X1,X4] :
      ( in(apply(X0,X4),X1)
      | ~ in(X4,X2)
      | relation_inverse_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f148,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(apply(X0,X4),X1)
      | ~ in(X4,relation_dom(X0))
      | relation_inverse_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X1,X2) = X0
      | ~ quasi_total(X2,X0,X1)
      | empty_set = X1
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f159,plain,
    ! [X2,X0,X1] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f203,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f204,plain,
    ! [X2,X0,X1] :
      ( relation_of2(X2,X0,X1)
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f205,plain,
    ! [X2,X0,X1] :
      ( relation_of2_as_subset(X2,X0,X1)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f210,plain,
    function(sK21),
    inference(cnf_transformation,[],[f139]) ).

fof(f211,plain,
    quasi_total(sK21,sK18,sK19),
    inference(cnf_transformation,[],[f139]) ).

fof(f212,plain,
    relation_of2_as_subset(sK21,sK18,sK19),
    inference(cnf_transformation,[],[f139]) ).

fof(f213,plain,
    empty_set != sK19,
    inference(cnf_transformation,[],[f139]) ).

fof(f214,plain,
    ( in(sK22,sK18)
    | in(sK22,relation_inverse_image(sK21,sK20)) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f215,plain,
    ( in(apply(sK21,sK22),sK20)
    | in(sK22,relation_inverse_image(sK21,sK20)) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f216,plain,
    ( ~ in(apply(sK21,sK22),sK20)
    | ~ in(sK22,sK18)
    | ~ in(sK22,relation_inverse_image(sK21,sK20)) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f222,plain,
    ! [X0,X1,X4] :
      ( in(X4,relation_inverse_image(X0,X1))
      | ~ in(apply(X0,X4),X1)
      | ~ in(X4,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f148]) ).

fof(f223,plain,
    ! [X0,X1,X4] :
      ( in(apply(X0,X4),X1)
      | ~ in(X4,relation_inverse_image(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f147]) ).

fof(f224,plain,
    ! [X0,X1,X4] :
      ( in(X4,relation_dom(X0))
      | ~ in(X4,relation_inverse_image(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f146]) ).

cnf(c_52,plain,
    ( ~ element(X0,powerset(cartesian_product2(X1,X2)))
    | relation(X0) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_56,plain,
    ( ~ in(apply(X0,X1),X2)
    | ~ in(X1,relation_dom(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | in(X1,relation_inverse_image(X0,X2)) ),
    inference(cnf_transformation,[],[f222]) ).

cnf(c_57,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ function(X1)
    | ~ relation(X1)
    | in(apply(X1,X0),X2) ),
    inference(cnf_transformation,[],[f223]) ).

cnf(c_58,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ function(X1)
    | ~ relation(X1)
    | in(X0,relation_dom(X1)) ),
    inference(cnf_transformation,[],[f224]) ).

cnf(c_64,plain,
    ( ~ quasi_total(X0,X1,X2)
    | ~ relation_of2_as_subset(X0,X1,X2)
    | relation_dom_as_subset(X1,X2,X0) = X1
    | X2 = empty_set ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_66,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | element(X0,powerset(cartesian_product2(X1,X2))) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_110,plain,
    ( ~ relation_of2(X0,X1,X2)
    | relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_111,plain,
    ( ~ relation_of2(X0,X1,X2)
    | relation_of2_as_subset(X0,X1,X2) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_112,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | relation_of2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f204]) ).

cnf(c_114,plain,
    ( ~ in(X0,X1)
    | element(X0,X1) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_117,negated_conjecture,
    ( ~ in(apply(sK21,sK22),sK20)
    | ~ in(sK22,relation_inverse_image(sK21,sK20))
    | ~ in(sK22,sK18) ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_118,negated_conjecture,
    ( in(apply(sK21,sK22),sK20)
    | in(sK22,relation_inverse_image(sK21,sK20)) ),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_119,negated_conjecture,
    ( in(sK22,relation_inverse_image(sK21,sK20))
    | in(sK22,sK18) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_120,negated_conjecture,
    empty_set != sK19,
    inference(cnf_transformation,[],[f213]) ).

cnf(c_121,negated_conjecture,
    relation_of2_as_subset(sK21,sK18,sK19),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_122,negated_conjecture,
    quasi_total(sK21,sK18,sK19),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_123,negated_conjecture,
    function(sK21),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_166,plain,
    ( relation_of2(X0,X1,X2)
    | ~ relation_of2_as_subset(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_112]) ).

cnf(c_167,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | relation_of2(X0,X1,X2) ),
    inference(renaming,[status(thm)],[c_166]) ).

cnf(c_168,plain,
    ( ~ relation_of2(X0,X1,X2)
    | relation_of2_as_subset(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_111]) ).

cnf(c_196,plain,
    ( element(X0,powerset(cartesian_product2(X1,X2)))
    | ~ relation_of2(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_111,c_66]) ).

cnf(c_197,plain,
    ( ~ relation_of2(X0,X1,X2)
    | element(X0,powerset(cartesian_product2(X1,X2))) ),
    inference(renaming,[status(thm)],[c_196]) ).

cnf(c_351,plain,
    ( ~ quasi_total(X0,X1,X2)
    | ~ relation_of2(X0,X1,X2)
    | relation_dom_as_subset(X1,X2,X0) = X1
    | X2 = empty_set ),
    inference(bin_hyper_res,[status(thm)],[c_64,c_168]) ).

cnf(c_1222,plain,
    ( X0 != sK21
    | X1 != sK18
    | X2 != sK19
    | relation_of2(X0,X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_167,c_121]) ).

cnf(c_1223,plain,
    relation_of2(sK21,sK18,sK19),
    inference(unflattening,[status(thm)],[c_1222]) ).

cnf(c_1327,plain,
    ( X0 != sK21
    | X1 != sK18
    | X2 != sK19
    | ~ relation_of2(X0,X1,X2)
    | relation_dom_as_subset(X1,X2,X0) = X1
    | X2 = empty_set ),
    inference(resolution_lifted,[status(thm)],[c_351,c_122]) ).

cnf(c_1328,plain,
    ( ~ relation_of2(sK21,sK18,sK19)
    | relation_dom_as_subset(sK18,sK19,sK21) = sK18
    | sK19 = empty_set ),
    inference(unflattening,[status(thm)],[c_1327]) ).

cnf(c_1329,plain,
    ( relation_dom_as_subset(sK18,sK19,sK21) = sK18
    | sK19 = empty_set ),
    inference(global_subsumption_just,[status(thm)],[c_1328,c_1223,c_1328]) ).

cnf(c_1464,plain,
    ( X0 != sK21
    | X1 != sK18
    | X2 != sK19
    | relation_of2(X0,X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_167,c_121]) ).

cnf(c_1465,plain,
    relation_of2(sK21,sK18,sK19),
    inference(unflattening,[status(thm)],[c_1464]) ).

cnf(c_10027,plain,
    relation_inverse_image(sK21,sK20) = sP0_iProver_def,
    definition ).

cnf(c_10028,plain,
    apply(sK21,sK22) = sP1_iProver_def,
    definition ).

cnf(c_10029,negated_conjecture,
    function(sK21),
    inference(demodulation,[status(thm)],[c_123]) ).

cnf(c_10030,negated_conjecture,
    empty_set != sK19,
    inference(demodulation,[status(thm)],[c_120]) ).

cnf(c_10031,negated_conjecture,
    ( in(sK22,sK18)
    | in(sK22,sP0_iProver_def) ),
    inference(demodulation,[status(thm)],[c_119,c_10027]) ).

cnf(c_10032,negated_conjecture,
    ( in(sK22,sP0_iProver_def)
    | in(sP1_iProver_def,sK20) ),
    inference(demodulation,[status(thm)],[c_118,c_10028]) ).

cnf(c_10033,negated_conjecture,
    ( ~ in(sK22,sK18)
    | ~ in(sK22,sP0_iProver_def)
    | ~ in(sP1_iProver_def,sK20) ),
    inference(demodulation,[status(thm)],[c_117]) ).

cnf(c_11279,plain,
    relation_dom_as_subset(sK18,sK19,sK21) = relation_dom(sK21),
    inference(superposition,[status(thm)],[c_1465,c_110]) ).

cnf(c_11287,plain,
    ( relation_dom(sK21) = sK18
    | empty_set = sK19 ),
    inference(demodulation,[status(thm)],[c_1329,c_11279]) ).

cnf(c_11288,plain,
    relation_dom(sK21) = sK18,
    inference(forward_subsumption_resolution,[status(thm)],[c_11287,c_10030]) ).

cnf(c_11301,plain,
    ( ~ in(X0,sP0_iProver_def)
    | ~ function(sK21)
    | ~ relation(sK21)
    | in(X0,relation_dom(sK21)) ),
    inference(superposition,[status(thm)],[c_10027,c_58]) ).

cnf(c_11302,plain,
    ( ~ in(X0,sP0_iProver_def)
    | ~ function(sK21)
    | ~ relation(sK21)
    | in(X0,sK18) ),
    inference(light_normalisation,[status(thm)],[c_11301,c_11288]) ).

cnf(c_11303,plain,
    ( ~ in(X0,sP0_iProver_def)
    | ~ relation(sK21)
    | in(X0,sK18) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11302,c_10029]) ).

cnf(c_11340,plain,
    ( ~ in(X0,sP0_iProver_def)
    | ~ function(sK21)
    | ~ relation(sK21)
    | in(apply(sK21,X0),sK20) ),
    inference(superposition,[status(thm)],[c_10027,c_57]) ).

cnf(c_11341,plain,
    ( ~ in(X0,sP0_iProver_def)
    | ~ relation(sK21)
    | in(apply(sK21,X0),sK20) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11340,c_10029]) ).

cnf(c_11379,plain,
    ( ~ in(sK22,relation_dom(sK21))
    | ~ in(sP1_iProver_def,X0)
    | ~ function(sK21)
    | ~ relation(sK21)
    | in(sK22,relation_inverse_image(sK21,X0)) ),
    inference(superposition,[status(thm)],[c_10028,c_56]) ).

cnf(c_11384,plain,
    ( ~ in(sP1_iProver_def,X0)
    | ~ in(sK22,sK18)
    | ~ function(sK21)
    | ~ relation(sK21)
    | in(sK22,relation_inverse_image(sK21,X0)) ),
    inference(light_normalisation,[status(thm)],[c_11379,c_11288]) ).

cnf(c_11385,plain,
    ( ~ in(sP1_iProver_def,X0)
    | ~ in(sK22,sK18)
    | ~ relation(sK21)
    | in(sK22,relation_inverse_image(sK21,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11384,c_10029]) ).

cnf(c_11433,plain,
    ( ~ relation(sK21)
    | in(sK22,sK18)
    | in(sP1_iProver_def,sK20) ),
    inference(superposition,[status(thm)],[c_10032,c_11303]) ).

cnf(c_11467,plain,
    ( ~ relation(sK21)
    | in(sP1_iProver_def,sK20)
    | element(sK22,sK18) ),
    inference(superposition,[status(thm)],[c_11433,c_114]) ).

cnf(c_11488,plain,
    ( ~ in(sK22,sP0_iProver_def)
    | ~ relation(sK21)
    | in(sP1_iProver_def,sK20) ),
    inference(superposition,[status(thm)],[c_10028,c_11341]) ).

cnf(c_11534,plain,
    ( ~ in(sK22,sK18)
    | ~ in(sP1_iProver_def,sK20)
    | ~ relation(sK21)
    | in(sK22,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_10027,c_11385]) ).

cnf(c_11908,plain,
    ( in(sP1_iProver_def,sK20)
    | ~ relation(sK21) ),
    inference(global_subsumption_just,[status(thm)],[c_11467,c_10032,c_11488]) ).

cnf(c_11909,plain,
    ( ~ relation(sK21)
    | in(sP1_iProver_def,sK20) ),
    inference(renaming,[status(thm)],[c_11908]) ).

cnf(c_12023,plain,
    ( ~ relation(sK21)
    | in(sK22,sP0_iProver_def) ),
    inference(global_subsumption_just,[status(thm)],[c_11534,c_10031,c_11534,c_11909]) ).

cnf(c_12032,plain,
    ( ~ relation(sK21)
    | in(sK22,sK18) ),
    inference(superposition,[status(thm)],[c_12023,c_11303]) ).

cnf(c_12041,plain,
    ~ relation(sK21),
    inference(global_subsumption_just,[status(thm)],[c_12032,c_10033,c_11909,c_12023,c_12032]) ).

cnf(c_14489,plain,
    ( ~ relation_of2(X0,X1,X2)
    | relation(X0) ),
    inference(superposition,[status(thm)],[c_197,c_52]) ).

cnf(c_14535,plain,
    relation(sK21),
    inference(superposition,[status(thm)],[c_1465,c_14489]) ).

cnf(c_14537,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_14535,c_12041]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n005.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May  2 17:51:41 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.79/1.66  % SZS status Started for theBenchmark.p
% 6.79/1.66  % SZS status Theorem for theBenchmark.p
% 6.79/1.66  
% 6.79/1.66  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 6.79/1.66  
% 6.79/1.66  ------  iProver source info
% 6.79/1.66  
% 6.79/1.66  git: date: 2024-05-02 19:28:25 +0000
% 6.79/1.66  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 6.79/1.66  git: non_committed_changes: false
% 6.79/1.66  
% 6.79/1.66  ------ Parsing...
% 6.79/1.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 6.79/1.66  
% 6.79/1.66  ------ 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  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 6.79/1.66  
% 6.79/1.66  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 6.79/1.66  
% 6.79/1.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 6.79/1.66  ------ Proving...
% 6.79/1.66  ------ Problem Properties 
% 6.79/1.66  
% 6.79/1.66  
% 6.79/1.66  clauses                                 73
% 6.79/1.66  conjectures                             5
% 6.79/1.66  EPR                                     35
% 6.79/1.66  Horn                                    63
% 6.79/1.66  unary                                   40
% 6.79/1.66  binary                                  20
% 6.79/1.66  lits                                    130
% 6.79/1.66  lits eq                                 18
% 6.79/1.66  fd_pure                                 0
% 6.79/1.66  fd_pseudo                               0
% 6.79/1.66  fd_cond                                 2
% 6.79/1.66  fd_pseudo_cond                          4
% 6.79/1.66  AC symbols                              0
% 6.79/1.66  
% 6.79/1.66  ------ Schedule dynamic 5 is on 
% 6.79/1.66  
% 6.79/1.66  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.79/1.66  
% 6.79/1.66  
% 6.79/1.66  ------ 
% 6.79/1.66  Current options:
% 6.79/1.66  ------ 
% 6.79/1.66  
% 6.79/1.66  
% 6.79/1.66  
% 6.79/1.66  
% 6.79/1.66  ------ Proving...
% 6.79/1.66  
% 6.79/1.66  
% 6.79/1.66  % SZS status Theorem for theBenchmark.p
% 6.79/1.66  
% 6.79/1.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.79/1.66  
% 6.79/1.66  
%------------------------------------------------------------------------------