TSTP Solution File: SET681+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET681+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Fri May  3 03:01:13 EDT 2024

% Result   : Theorem 7.44s 1.71s
% Output   : CNFRefutation 7.44s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f187)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,binary_relation_type)
         => ( member(X0,range_of(X1))
          <=> ? [X2] :
                ( member(ordered_pair(X2,X0),X1)
                & ilf_type(X2,set_type) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,binary_relation_type)
             => ( member(ordered_pair(X0,X1),X2)
               => ( member(X1,range_of(X2))
                  & member(X0,domain_of(X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f6,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',p6) ).

fof(f8,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',p8) ).

fof(f10,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',p10) ).

fof(f19,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',p19) ).

fof(f22,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',p22) ).

fof(f23,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',p23) ).

fof(f26,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',p26) ).

fof(f27,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => domain_of(X2) = domain(X0,X1,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).

fof(f28,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).

fof(f29,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => range_of(X2) = range(X0,X1,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).

fof(f31,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).

fof(f32,conjecture,
    ! [X0] :
      ( ( ilf_type(X0,set_type)
        & ~ empty(X0) )
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ! [X2] :
              ( ilf_type(X2,relation_type(X1,X0))
             => ! [X3] :
                  ( ilf_type(X3,member_type(X0))
                 => ( member(X3,range(X1,X0,X2))
                  <=> ? [X4] :
                        ( member(ordered_pair(X4,X3),X2)
                        & ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_48) ).

fof(f33,negated_conjecture,
    ~ ! [X0] :
        ( ( ilf_type(X0,set_type)
          & ~ empty(X0) )
       => ! [X1] :
            ( ( ilf_type(X1,set_type)
              & ~ empty(X1) )
           => ! [X2] :
                ( ilf_type(X2,relation_type(X1,X0))
               => ! [X3] :
                    ( ilf_type(X3,member_type(X0))
                   => ( member(X3,range(X1,X0,X2))
                    <=> ? [X4] :
                          ( member(ordered_pair(X4,X3),X2)
                          & ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f32]) ).

fof(f34,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,[],[f6]) ).

fof(f35,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,range_of(X1))
          <=> ? [X2] :
                ( member(ordered_pair(X2,X0),X1)
                & ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,binary_relation_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f36,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( member(X1,range_of(X2))
                & member(X0,domain_of(X2)) )
              | ~ member(ordered_pair(X0,X1),X2)
              | ~ ilf_type(X2,binary_relation_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f37,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( member(X1,range_of(X2))
                & member(X0,domain_of(X2)) )
              | ~ member(ordered_pair(X0,X1),X2)
              | ~ ilf_type(X2,binary_relation_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f36]) ).

fof(f42,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,[],[f34]) ).

fof(f44,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,[],[f8]) ).

fof(f45,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,[],[f44]) ).

fof(f48,plain,
    ! [X0] :
      ( ( empty(X0)
      <=> ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f56,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,[],[f19]) ).

fof(f59,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,[],[f22]) ).

fof(f60,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,[],[f59]) ).

fof(f61,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f66,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,[],[f26]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( domain_of(X2) = domain(X0,X1,X2)
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f68,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(domain(X0,X1,X2),subset_type(X0))
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( range_of(X2) = range(X0,X1,X2)
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f71,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( member(X3,range(X1,X0,X2))
                  <~> ? [X4] :
                        ( member(ordered_pair(X4,X3),X2)
                        & ilf_type(X4,member_type(X1)) ) )
                  & ilf_type(X3,member_type(X0)) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f72,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( member(X3,range(X1,X0,X2))
                  <~> ? [X4] :
                        ( member(ordered_pair(X4,X3),X2)
                        & ilf_type(X4,member_type(X1)) ) )
                  & ilf_type(X3,member_type(X0)) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(flattening,[],[f71]) ).

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,range_of(X1))
              | ! [X2] :
                  ( ~ member(ordered_pair(X2,X0),X1)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ? [X2] :
                  ( member(ordered_pair(X2,X0),X1)
                  & ilf_type(X2,set_type) )
              | ~ member(X0,range_of(X1)) ) )
          | ~ ilf_type(X1,binary_relation_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,range_of(X1))
              | ! [X2] :
                  ( ~ member(ordered_pair(X2,X0),X1)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ? [X3] :
                  ( member(ordered_pair(X3,X0),X1)
                  & ilf_type(X3,set_type) )
              | ~ member(X0,range_of(X1)) ) )
          | ~ ilf_type(X1,binary_relation_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f73]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(ordered_pair(X3,X0),X1)
          & ilf_type(X3,set_type) )
     => ( member(ordered_pair(sK0(X0,X1),X0),X1)
        & ilf_type(sK0(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,range_of(X1))
              | ! [X2] :
                  ( ~ member(ordered_pair(X2,X0),X1)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ( member(ordered_pair(sK0(X0,X1),X0),X1)
                & ilf_type(sK0(X0,X1),set_type) )
              | ~ member(X0,range_of(X1)) ) )
          | ~ ilf_type(X1,binary_relation_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f74,f75]) ).

fof(f80,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f83,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f84,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f83]) ).

fof(f85,plain,
    ! [X0] :
      ( ? [X1] :
          ( member(X1,X0)
          & ilf_type(X1,set_type) )
     => ( member(sK3(X0),X0)
        & ilf_type(sK3(X0),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ( member(sK3(X0),X0)
            & ilf_type(sK3(X0),set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f84,f85]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X1,subset_type(X0))
              | ~ ilf_type(X1,member_type(power_set(X0))) )
            & ( ilf_type(X1,member_type(power_set(X0)))
              | ~ ilf_type(X1,subset_type(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f99]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK7(X0,X1),X1)
        & member(sK7(X0,X1),X0)
        & ilf_type(sK7(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ( ~ member(sK7(X0,X1),X1)
                & member(sK7(X0,X1),X0)
                & ilf_type(sK7(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f100,f101]) ).

fof(f109,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ! [X4] :
                        ( ~ member(ordered_pair(X4,X3),X2)
                        | ~ ilf_type(X4,member_type(X1)) )
                    | ~ member(X3,range(X1,X0,X2)) )
                  & ( ? [X4] :
                        ( member(ordered_pair(X4,X3),X2)
                        & ilf_type(X4,member_type(X1)) )
                    | member(X3,range(X1,X0,X2)) )
                  & ilf_type(X3,member_type(X0)) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f110,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ! [X4] :
                        ( ~ member(ordered_pair(X4,X3),X2)
                        | ~ ilf_type(X4,member_type(X1)) )
                    | ~ member(X3,range(X1,X0,X2)) )
                  & ( ? [X4] :
                        ( member(ordered_pair(X4,X3),X2)
                        & ilf_type(X4,member_type(X1)) )
                    | member(X3,range(X1,X0,X2)) )
                  & ilf_type(X3,member_type(X0)) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(flattening,[],[f109]) ).

fof(f111,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ! [X4] :
                        ( ~ member(ordered_pair(X4,X3),X2)
                        | ~ ilf_type(X4,member_type(X1)) )
                    | ~ member(X3,range(X1,X0,X2)) )
                  & ( ? [X5] :
                        ( member(ordered_pair(X5,X3),X2)
                        & ilf_type(X5,member_type(X1)) )
                    | member(X3,range(X1,X0,X2)) )
                  & ilf_type(X3,member_type(X0)) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(rectify,[],[f110]) ).

fof(f112,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ! [X4] :
                          ( ~ member(ordered_pair(X4,X3),X2)
                          | ~ ilf_type(X4,member_type(X1)) )
                      | ~ member(X3,range(X1,X0,X2)) )
                    & ( ? [X5] :
                          ( member(ordered_pair(X5,X3),X2)
                          & ilf_type(X5,member_type(X1)) )
                      | member(X3,range(X1,X0,X2)) )
                    & ilf_type(X3,member_type(X0)) )
                & ilf_type(X2,relation_type(X1,X0)) )
            & ilf_type(X1,set_type)
            & ~ empty(X1) )
        & ilf_type(X0,set_type)
        & ~ empty(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ! [X4] :
                        ( ~ member(ordered_pair(X4,X3),X2)
                        | ~ ilf_type(X4,member_type(X1)) )
                    | ~ member(X3,range(X1,sK11,X2)) )
                  & ( ? [X5] :
                        ( member(ordered_pair(X5,X3),X2)
                        & ilf_type(X5,member_type(X1)) )
                    | member(X3,range(X1,sK11,X2)) )
                  & ilf_type(X3,member_type(sK11)) )
              & ilf_type(X2,relation_type(X1,sK11)) )
          & ilf_type(X1,set_type)
          & ~ empty(X1) )
      & ilf_type(sK11,set_type)
      & ~ empty(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ! [X4] :
                      ( ~ member(ordered_pair(X4,X3),X2)
                      | ~ ilf_type(X4,member_type(X1)) )
                  | ~ member(X3,range(X1,sK11,X2)) )
                & ( ? [X5] :
                      ( member(ordered_pair(X5,X3),X2)
                      & ilf_type(X5,member_type(X1)) )
                  | member(X3,range(X1,sK11,X2)) )
                & ilf_type(X3,member_type(sK11)) )
            & ilf_type(X2,relation_type(X1,sK11)) )
        & ilf_type(X1,set_type)
        & ~ empty(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ! [X4] :
                    ( ~ member(ordered_pair(X4,X3),X2)
                    | ~ ilf_type(X4,member_type(sK12)) )
                | ~ member(X3,range(sK12,sK11,X2)) )
              & ( ? [X5] :
                    ( member(ordered_pair(X5,X3),X2)
                    & ilf_type(X5,member_type(sK12)) )
                | member(X3,range(sK12,sK11,X2)) )
              & ilf_type(X3,member_type(sK11)) )
          & ilf_type(X2,relation_type(sK12,sK11)) )
      & ilf_type(sK12,set_type)
      & ~ empty(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ! [X4] :
                  ( ~ member(ordered_pair(X4,X3),X2)
                  | ~ ilf_type(X4,member_type(sK12)) )
              | ~ member(X3,range(sK12,sK11,X2)) )
            & ( ? [X5] :
                  ( member(ordered_pair(X5,X3),X2)
                  & ilf_type(X5,member_type(sK12)) )
              | member(X3,range(sK12,sK11,X2)) )
            & ilf_type(X3,member_type(sK11)) )
        & ilf_type(X2,relation_type(sK12,sK11)) )
   => ( ? [X3] :
          ( ( ! [X4] :
                ( ~ member(ordered_pair(X4,X3),sK13)
                | ~ ilf_type(X4,member_type(sK12)) )
            | ~ member(X3,range(sK12,sK11,sK13)) )
          & ( ? [X5] :
                ( member(ordered_pair(X5,X3),sK13)
                & ilf_type(X5,member_type(sK12)) )
            | member(X3,range(sK12,sK11,sK13)) )
          & ilf_type(X3,member_type(sK11)) )
      & ilf_type(sK13,relation_type(sK12,sK11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ( ? [X3] :
        ( ( ! [X4] :
              ( ~ member(ordered_pair(X4,X3),sK13)
              | ~ ilf_type(X4,member_type(sK12)) )
          | ~ member(X3,range(sK12,sK11,sK13)) )
        & ( ? [X5] :
              ( member(ordered_pair(X5,X3),sK13)
              & ilf_type(X5,member_type(sK12)) )
          | member(X3,range(sK12,sK11,sK13)) )
        & ilf_type(X3,member_type(sK11)) )
   => ( ( ! [X4] :
            ( ~ member(ordered_pair(X4,sK14),sK13)
            | ~ ilf_type(X4,member_type(sK12)) )
        | ~ member(sK14,range(sK12,sK11,sK13)) )
      & ( ? [X5] :
            ( member(ordered_pair(X5,sK14),sK13)
            & ilf_type(X5,member_type(sK12)) )
        | member(sK14,range(sK12,sK11,sK13)) )
      & ilf_type(sK14,member_type(sK11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ( ? [X5] :
        ( member(ordered_pair(X5,sK14),sK13)
        & ilf_type(X5,member_type(sK12)) )
   => ( member(ordered_pair(sK15,sK14),sK13)
      & ilf_type(sK15,member_type(sK12)) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ( ( ! [X4] :
          ( ~ member(ordered_pair(X4,sK14),sK13)
          | ~ ilf_type(X4,member_type(sK12)) )
      | ~ member(sK14,range(sK12,sK11,sK13)) )
    & ( ( member(ordered_pair(sK15,sK14),sK13)
        & ilf_type(sK15,member_type(sK12)) )
      | member(sK14,range(sK12,sK11,sK13)) )
    & ilf_type(sK14,member_type(sK11))
    & ilf_type(sK13,relation_type(sK12,sK11))
    & ilf_type(sK12,set_type)
    & ~ empty(sK12)
    & ilf_type(sK11,set_type)
    & ~ empty(sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15])],[f111,f116,f115,f114,f113,f112]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( member(ordered_pair(sK0(X0,X1),X0),X1)
      | ~ member(X0,range_of(X1))
      | ~ ilf_type(X1,binary_relation_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f120,plain,
    ! [X2,X0,X1] :
      ( member(X0,range_of(X1))
      | ~ member(ordered_pair(X2,X0),X1)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,binary_relation_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( member(X0,domain_of(X2))
      | ~ member(ordered_pair(X0,X1),X2)
      | ~ ilf_type(X2,binary_relation_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( member(X1,range_of(X2))
      | ~ member(ordered_pair(X0,X1),X2)
      | ~ ilf_type(X2,binary_relation_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f129,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f132,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(cnf_transformation,[],[f80]) ).

fof(f134,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ ilf_type(X2,set_type)
      | ~ empty(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f155,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f159,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f168,plain,
    ! [X2,X0,X1] :
      ( relation_like(X2)
      | ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f169,plain,
    ! [X2,X0,X1] :
      ( domain_of(X2) = domain(X0,X1,X2)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f170,plain,
    ! [X2,X0,X1] :
      ( ilf_type(domain(X0,X1,X2),subset_type(X0))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f171,plain,
    ! [X2,X0,X1] :
      ( range_of(X2) = range(X0,X1,X2)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f173,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f31]) ).

fof(f178,plain,
    ilf_type(sK13,relation_type(sK12,sK11)),
    inference(cnf_transformation,[],[f117]) ).

fof(f181,plain,
    ( member(ordered_pair(sK15,sK14),sK13)
    | member(sK14,range(sK12,sK11,sK13)) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f182,plain,
    ! [X4] :
      ( ~ member(ordered_pair(X4,sK14),sK13)
      | ~ ilf_type(X4,member_type(sK12))
      | ~ member(sK14,range(sK12,sK11,sK13)) ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_49,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,binary_relation_type)
    | member(X1,range_of(X2)) ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_50,plain,
    ( ~ member(X0,range_of(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(sK0(X0,X1),X0),X1) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_52,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,binary_relation_type)
    | member(X1,range_of(X2)) ),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_53,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,binary_relation_type)
    | member(X0,domain_of(X2)) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_59,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(cnf_transformation,[],[f129]) ).

cnf(c_62,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(X1))
    | empty(X1) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_63,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_67,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_74,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f187]) ).

cnf(c_78,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_88,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_90,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ empty(power_set(X0)) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_98,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | relation_like(X0) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_99,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | domain(X1,X2,X0) = domain_of(X0) ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_100,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_101,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | range(X1,X2,X0) = range_of(X0) ),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_103,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_104,negated_conjecture,
    ( ~ member(sK14,range(sK12,sK11,sK13))
    | ~ member(ordered_pair(X0,sK14),sK13)
    | ~ ilf_type(X0,member_type(sK12)) ),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_105,negated_conjecture,
    ( member(sK14,range(sK12,sK11,sK13))
    | member(ordered_pair(sK15,sK14),sK13) ),
    inference(cnf_transformation,[],[f181]) ).

cnf(c_108,negated_conjecture,
    ilf_type(sK13,relation_type(sK12,sK11)),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_163,plain,
    ~ empty(power_set(X0)),
    inference(global_subsumption_just,[status(thm)],[c_90,c_103,c_90]) ).

cnf(c_187,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(global_subsumption_just,[status(thm)],[c_74,c_103,c_74]) ).

cnf(c_243,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_78,c_103,c_78]) ).

cnf(c_247,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | ~ ilf_type(X1,set_type)
    | member(X0,X1)
    | empty(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_63,c_103,c_63]) ).

cnf(c_249,plain,
    ( ilf_type(X0,member_type(X1))
    | ~ ilf_type(X1,set_type)
    | ~ member(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_62,c_103,c_67,c_62]) ).

cnf(c_250,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(X1)) ),
    inference(renaming,[status(thm)],[c_249]) ).

cnf(c_259,plain,
    ( ~ member(X0,range_of(X1))
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(sK0(X0,X1),X0),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_103,c_50]) ).

cnf(c_269,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,binary_relation_type)
    | member(X0,domain_of(X2)) ),
    inference(global_subsumption_just,[status(thm)],[c_53,c_103,c_53]) ).

cnf(c_273,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,binary_relation_type)
    | member(X1,range_of(X2)) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_103,c_52]) ).

cnf(c_277,plain,
    ( ~ member(X2,X0)
    | ~ member(X0,power_set(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_88,c_103,c_88]) ).

cnf(c_278,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(renaming,[status(thm)],[c_277]) ).

cnf(c_451,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_59,c_103]) ).

cnf(c_452,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X2,set_type)
    | ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_100,c_103]) ).

cnf(c_453,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X2,set_type)
    | domain(X1,X2,X0) = domain_of(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_99,c_103]) ).

cnf(c_455,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X2,set_type)
    | range(X1,X2,X0) = range_of(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_101,c_103]) ).

cnf(c_458,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_278,c_103]) ).

cnf(c_459,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | member(X0,X1)
    | empty(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_247,c_103]) ).

cnf(c_460,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,binary_relation_type)
    | member(X1,range_of(X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_273,c_103]) ).

cnf(c_461,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,binary_relation_type)
    | member(X0,domain_of(X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_269,c_103]) ).

cnf(c_465,plain,
    ( ~ member(X0,X1)
    | ilf_type(X0,member_type(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_250,c_103]) ).

cnf(c_467,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X2,set_type)
    | relation_like(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_98,c_103]) ).

cnf(c_470,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_243,c_103]) ).

cnf(c_564,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | relation_like(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_467,c_103]) ).

cnf(c_627,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_451,c_103]) ).

cnf(c_644,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_452,c_103]) ).

cnf(c_672,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | domain(X1,X2,X0) = domain_of(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_453,c_103]) ).

cnf(c_683,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | range(X1,X2,X0) = range_of(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_455,c_103]) ).

cnf(c_695,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_458,c_103]) ).

cnf(c_1160,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(prop_impl_just,[status(thm)],[c_187]) ).

cnf(c_1164,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_470]) ).

cnf(c_1166,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | relation_like(X0) ),
    inference(prop_impl_just,[status(thm)],[c_564,c_627]) ).

cnf(c_1168,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | domain(X1,X2,X0) = domain_of(X0) ),
    inference(prop_impl_just,[status(thm)],[c_672]) ).

cnf(c_1170,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_644]) ).

cnf(c_1172,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | range(X1,X2,X0) = range_of(X0) ),
    inference(prop_impl_just,[status(thm)],[c_683]) ).

cnf(c_1176,plain,
    ( ~ member(X0,X1)
    | ilf_type(X0,member_type(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_465]) ).

cnf(c_1882,plain,
    relation_type(sK12,sK11) = sP0_iProver_def,
    definition ).

cnf(c_1884,plain,
    range(sK12,sK11,sK13) = sP2_iProver_def,
    definition ).

cnf(c_1885,plain,
    member_type(sK12) = sP3_iProver_def,
    definition ).

cnf(c_1886,plain,
    ordered_pair(sK15,sK14) = sP4_iProver_def,
    definition ).

cnf(c_1889,negated_conjecture,
    ilf_type(sK13,sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_108,c_1882]) ).

cnf(c_1892,negated_conjecture,
    ( member(sK14,sP2_iProver_def)
    | member(sP4_iProver_def,sK13) ),
    inference(demodulation,[status(thm)],[c_105,c_1886]) ).

cnf(c_1893,negated_conjecture,
    ( ~ member(ordered_pair(X0,sK14),sK13)
    | ~ ilf_type(X0,sP3_iProver_def)
    | ~ member(sK14,sP2_iProver_def) ),
    inference(demodulation,[status(thm)],[c_104]) ).

cnf(c_2857,plain,
    ( ~ ilf_type(X0,sP0_iProver_def)
    | relation_like(X0) ),
    inference(superposition,[status(thm)],[c_1882,c_1166]) ).

cnf(c_2866,plain,
    ( ~ member(X0,sK12)
    | ilf_type(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_1885,c_1176]) ).

cnf(c_2906,plain,
    relation_like(sK13),
    inference(superposition,[status(thm)],[c_1889,c_2857]) ).

cnf(c_2951,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1))
    | empty(power_set(X1)) ),
    inference(superposition,[status(thm)],[c_1164,c_459]) ).

cnf(c_2952,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2951,c_163]) ).

cnf(c_3057,plain,
    ( ~ member(sP4_iProver_def,X0)
    | ~ ilf_type(X0,binary_relation_type)
    | member(sK14,range_of(X0)) ),
    inference(superposition,[status(thm)],[c_1886,c_460]) ).

cnf(c_3078,plain,
    ( ~ ilf_type(X0,sP0_iProver_def)
    | domain(sK12,sK11,X0) = domain_of(X0) ),
    inference(superposition,[status(thm)],[c_1882,c_1168]) ).

cnf(c_3228,plain,
    ( ~ ilf_type(X0,sP0_iProver_def)
    | range(sK12,sK11,X0) = range_of(X0) ),
    inference(superposition,[status(thm)],[c_1882,c_1172]) ).

cnf(c_3327,plain,
    ( ~ member(X0,range_of(X1))
    | ~ ilf_type(X1,binary_relation_type)
    | member(sK0(X0,X1),domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_259,c_461]) ).

cnf(c_3332,plain,
    ( ~ ilf_type(sK0(sK14,sK13),sP3_iProver_def)
    | ~ member(sK14,range_of(sK13))
    | ~ member(sK14,sP2_iProver_def)
    | ~ ilf_type(sK13,binary_relation_type) ),
    inference(superposition,[status(thm)],[c_259,c_1893]) ).

cnf(c_4421,plain,
    domain(sK12,sK11,sK13) = domain_of(sK13),
    inference(superposition,[status(thm)],[c_1889,c_3078]) ).

cnf(c_4436,plain,
    ( ~ ilf_type(sK13,relation_type(sK12,sK11))
    | ilf_type(domain_of(sK13),subset_type(sK12)) ),
    inference(superposition,[status(thm)],[c_4421,c_1170]) ).

cnf(c_4437,plain,
    ( ~ ilf_type(sK13,sP0_iProver_def)
    | ilf_type(domain_of(sK13),subset_type(sK12)) ),
    inference(light_normalisation,[status(thm)],[c_4436,c_1882]) ).

cnf(c_4438,plain,
    ilf_type(domain_of(sK13),subset_type(sK12)),
    inference(forward_subsumption_resolution,[status(thm)],[c_4437,c_1889]) ).

cnf(c_4450,plain,
    member(domain_of(sK13),power_set(sK12)),
    inference(superposition,[status(thm)],[c_4438,c_2952]) ).

cnf(c_4495,plain,
    ( ~ member(X0,domain_of(sK13))
    | member(X0,sK12) ),
    inference(superposition,[status(thm)],[c_4450,c_695]) ).

cnf(c_4903,plain,
    range(sK12,sK11,sK13) = range_of(sK13),
    inference(superposition,[status(thm)],[c_1889,c_3228]) ).

cnf(c_4907,plain,
    range_of(sK13) = sP2_iProver_def,
    inference(light_normalisation,[status(thm)],[c_4903,c_1884]) ).

cnf(c_4908,plain,
    ( ~ ilf_type(sK0(sK14,sK13),sP3_iProver_def)
    | ~ member(sK14,sP2_iProver_def)
    | ~ ilf_type(sK13,binary_relation_type) ),
    inference(demodulation,[status(thm)],[c_3332,c_4907]) ).

cnf(c_4925,plain,
    ( ~ member(sP4_iProver_def,sK13)
    | ~ ilf_type(sK13,binary_relation_type)
    | member(sK14,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_4907,c_3057]) ).

cnf(c_5002,plain,
    ( ~ ilf_type(sK0(sK14,sK13),sP3_iProver_def)
    | ~ ilf_type(sK13,binary_relation_type) ),
    inference(global_subsumption_just,[status(thm)],[c_4908,c_1892,c_4908,c_4925]) ).

cnf(c_5008,plain,
    ( ~ ilf_type(sK13,binary_relation_type)
    | member(sK14,sP2_iProver_def) ),
    inference(global_subsumption_just,[status(thm)],[c_4925,c_1892,c_4925]) ).

cnf(c_5014,plain,
    ( ~ relation_like(sK13)
    | member(sK14,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_1160,c_5008]) ).

cnf(c_5015,plain,
    member(sK14,sP2_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_5014,c_2906]) ).

cnf(c_12641,plain,
    ( ~ member(X0,range_of(sK13))
    | ~ ilf_type(sK13,binary_relation_type)
    | member(sK0(X0,sK13),sK12) ),
    inference(superposition,[status(thm)],[c_3327,c_4495]) ).

cnf(c_12645,plain,
    ( ~ member(X0,sP2_iProver_def)
    | ~ ilf_type(sK13,binary_relation_type)
    | member(sK0(X0,sK13),sK12) ),
    inference(light_normalisation,[status(thm)],[c_12641,c_4907]) ).

cnf(c_12739,plain,
    ( ~ member(X0,sP2_iProver_def)
    | ~ ilf_type(sK13,binary_relation_type)
    | ilf_type(sK0(X0,sK13),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_12645,c_2866]) ).

cnf(c_12756,plain,
    ( ~ member(sK14,sP2_iProver_def)
    | ~ ilf_type(sK13,binary_relation_type) ),
    inference(superposition,[status(thm)],[c_12739,c_5002]) ).

cnf(c_12757,plain,
    ~ ilf_type(sK13,binary_relation_type),
    inference(forward_subsumption_resolution,[status(thm)],[c_12756,c_5015]) ).

cnf(c_12758,plain,
    ~ relation_like(sK13),
    inference(superposition,[status(thm)],[c_1160,c_12757]) ).

cnf(c_12759,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_12758,c_2906]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET681+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n023.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 May  2 20:45:54 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.44/1.71  % SZS status Started for theBenchmark.p
% 7.44/1.71  % SZS status Theorem for theBenchmark.p
% 7.44/1.71  
% 7.44/1.71  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.44/1.71  
% 7.44/1.71  ------  iProver source info
% 7.44/1.71  
% 7.44/1.71  git: date: 2024-05-02 19:28:25 +0000
% 7.44/1.71  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.44/1.71  git: non_committed_changes: false
% 7.44/1.71  
% 7.44/1.71  ------ Parsing...
% 7.44/1.71  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.44/1.71  
% 7.44/1.71  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.44/1.71  
% 7.44/1.71  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.44/1.71  
% 7.44/1.71  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.44/1.71  ------ Proving...
% 7.44/1.71  ------ Problem Properties 
% 7.44/1.71  
% 7.44/1.71  
% 7.44/1.71  clauses                                 49
% 7.44/1.71  conjectures                             7
% 7.44/1.71  EPR                                     12
% 7.44/1.71  Horn                                    41
% 7.44/1.71  unary                                   16
% 7.44/1.71  binary                                  22
% 7.44/1.71  lits                                    93
% 7.44/1.71  lits eq                                 13
% 7.44/1.71  fd_pure                                 0
% 7.44/1.71  fd_pseudo                               0
% 7.44/1.71  fd_cond                                 0
% 7.44/1.71  fd_pseudo_cond                          2
% 7.44/1.71  AC symbols                              0
% 7.44/1.71  
% 7.44/1.71  ------ Schedule dynamic 5 is on 
% 7.44/1.71  
% 7.44/1.71  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.44/1.71  
% 7.44/1.71  
% 7.44/1.71  ------ 
% 7.44/1.71  Current options:
% 7.44/1.71  ------ 
% 7.44/1.71  
% 7.44/1.71  
% 7.44/1.71  
% 7.44/1.71  
% 7.44/1.71  ------ Proving...
% 7.44/1.71  
% 7.44/1.71  
% 7.44/1.71  % SZS status Theorem for theBenchmark.p
% 7.44/1.71  
% 7.44/1.71  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.44/1.71  
% 7.44/1.71  
%------------------------------------------------------------------------------