TSTP Solution File: SET659+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET659+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 03:01:09 EDT 2024

% Result   : Theorem 35.74s 5.68s
% Output   : CNFRefutation 35.74s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f216)

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

fof(f3,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',p3) ).

fof(f7,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',p7) ).

fof(f9,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( X0 = X1
          <=> ( subset(X1,X0)
              & subset(X0,X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).

fof(f17,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',p17) ).

fof(f20,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( subset(X0,X1)
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).

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(f24,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',p24) ).

fof(f27,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',p27) ).

fof(f30,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',p30) ).

fof(f31,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',p31) ).

fof(f34,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).

fof(f35,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X1,X0))
             => ( ! [X3] :
                    ( ilf_type(X3,set_type)
                   => ( member(X3,X1)
                     => ? [X4] :
                          ( member(ordered_pair(X3,X4),X2)
                          & ilf_type(X4,set_type) ) ) )
              <=> domain(X1,X0,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_22) ).

fof(f36,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,relation_type(X1,X0))
               => ( ! [X3] :
                      ( ilf_type(X3,set_type)
                     => ( member(X3,X1)
                       => ? [X4] :
                            ( member(ordered_pair(X3,X4),X2)
                            & ilf_type(X4,set_type) ) ) )
                <=> domain(X1,X0,X2) = X1 ) ) ) ),
    inference(negated_conjecture,[],[f35]) ).

fof(f37,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,[],[f7]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X1,domain_of(X0))
          <=> ? [X2] :
                ( member(ordered_pair(X1,X2),X0)
                & ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f40,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,[],[f3]) ).

fof(f41,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,[],[f40]) ).

fof(f46,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,[],[f37]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( X0 = X1
          <=> ( subset(X1,X0)
              & subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f55,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,[],[f17]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,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,[],[f20]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,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,[],[f58]) ).

fof(f61,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(f62,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,[],[f61]) ).

fof(f63,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f64,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,[],[f24]) ).

fof(f65,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,[],[f64]) ).

fof(f70,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,[],[f27]) ).

fof(f74,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,[],[f30]) ).

fof(f75,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,[],[f31]) ).

fof(f78,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( ! [X3] :
                    ( ? [X4] :
                        ( member(ordered_pair(X3,X4),X2)
                        & ilf_type(X4,set_type) )
                    | ~ member(X3,X1)
                    | ~ ilf_type(X3,set_type) )
              <~> domain(X1,X0,X2) = X1 )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f79,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( ! [X3] :
                    ( ? [X4] :
                        ( member(ordered_pair(X3,X4),X2)
                        & ilf_type(X4,set_type) )
                    | ~ member(X3,X1)
                    | ~ ilf_type(X3,set_type) )
              <~> domain(X1,X0,X2) = X1 )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f78]) ).

fof(f80,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,domain_of(X0))
              | ! [X2] :
                  ( ~ member(ordered_pair(X1,X2),X0)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ? [X2] :
                  ( member(ordered_pair(X1,X2),X0)
                  & ilf_type(X2,set_type) )
              | ~ member(X1,domain_of(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f81,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,domain_of(X0))
              | ! [X2] :
                  ( ~ member(ordered_pair(X1,X2),X0)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ? [X3] :
                  ( member(ordered_pair(X1,X3),X0)
                  & ilf_type(X3,set_type) )
              | ~ member(X1,domain_of(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(rectify,[],[f80]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(ordered_pair(X1,X3),X0)
          & ilf_type(X3,set_type) )
     => ( member(ordered_pair(X1,sK0(X0,X1)),X0)
        & ilf_type(sK0(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,domain_of(X0))
              | ! [X2] :
                  ( ~ member(ordered_pair(X1,X2),X0)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ( member(ordered_pair(X1,sK0(X0,X1)),X0)
                & ilf_type(sK0(X0,X1),set_type) )
              | ~ member(X1,domain_of(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f81,f82]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( X0 = X1
              | ~ subset(X1,X0)
              | ~ subset(X0,X1) )
            & ( ( subset(X1,X0)
                & subset(X0,X1) )
              | X0 != X1 ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f92,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( X0 = X1
              | ~ subset(X1,X0)
              | ~ subset(X0,X1) )
            & ( ( subset(X1,X0)
                & subset(X0,X1) )
              | X0 != X1 ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f91]) ).

fof(f97,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,[],[f55]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,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) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,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) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f105]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK6(X0,X1),X1)
        & member(sK6(X0,X1),X0)
        & ilf_type(sK6(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ( ~ member(sK6(X0,X1),X1)
                & member(sK6(X0,X1),X0)
                & ilf_type(sK6(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f106,f107]) ).

fof(f109,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,[],[f62]) ).

fof(f110,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,[],[f109]) ).

fof(f111,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(f112,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])],[f110,f111]) ).

fof(f113,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,[],[f65]) ).

fof(f126,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( domain(X1,X0,X2) != X1
                | ? [X3] :
                    ( ! [X4] :
                        ( ~ member(ordered_pair(X3,X4),X2)
                        | ~ ilf_type(X4,set_type) )
                    & member(X3,X1)
                    & ilf_type(X3,set_type) ) )
              & ( domain(X1,X0,X2) = X1
                | ! [X3] :
                    ( ? [X4] :
                        ( member(ordered_pair(X3,X4),X2)
                        & ilf_type(X4,set_type) )
                    | ~ member(X3,X1)
                    | ~ ilf_type(X3,set_type) ) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f79]) ).

fof(f127,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( domain(X1,X0,X2) != X1
                | ? [X3] :
                    ( ! [X4] :
                        ( ~ member(ordered_pair(X3,X4),X2)
                        | ~ ilf_type(X4,set_type) )
                    & member(X3,X1)
                    & ilf_type(X3,set_type) ) )
              & ( domain(X1,X0,X2) = X1
                | ! [X3] :
                    ( ? [X4] :
                        ( member(ordered_pair(X3,X4),X2)
                        & ilf_type(X4,set_type) )
                    | ~ member(X3,X1)
                    | ~ ilf_type(X3,set_type) ) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f126]) ).

fof(f128,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( domain(X1,X0,X2) != X1
                | ? [X3] :
                    ( ! [X4] :
                        ( ~ member(ordered_pair(X3,X4),X2)
                        | ~ ilf_type(X4,set_type) )
                    & member(X3,X1)
                    & ilf_type(X3,set_type) ) )
              & ( domain(X1,X0,X2) = X1
                | ! [X5] :
                    ( ? [X6] :
                        ( member(ordered_pair(X5,X6),X2)
                        & ilf_type(X6,set_type) )
                    | ~ member(X5,X1)
                    | ~ ilf_type(X5,set_type) ) )
              & ilf_type(X2,relation_type(X1,X0)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(rectify,[],[f127]) ).

fof(f129,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ( domain(X1,X0,X2) != X1
                  | ? [X3] :
                      ( ! [X4] :
                          ( ~ member(ordered_pair(X3,X4),X2)
                          | ~ ilf_type(X4,set_type) )
                      & member(X3,X1)
                      & ilf_type(X3,set_type) ) )
                & ( domain(X1,X0,X2) = X1
                  | ! [X5] :
                      ( ? [X6] :
                          ( member(ordered_pair(X5,X6),X2)
                          & ilf_type(X6,set_type) )
                      | ~ member(X5,X1)
                      | ~ ilf_type(X5,set_type) ) )
                & ilf_type(X2,relation_type(X1,X0)) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ( domain(X1,sK13,X2) != X1
                | ? [X3] :
                    ( ! [X4] :
                        ( ~ member(ordered_pair(X3,X4),X2)
                        | ~ ilf_type(X4,set_type) )
                    & member(X3,X1)
                    & ilf_type(X3,set_type) ) )
              & ( domain(X1,sK13,X2) = X1
                | ! [X5] :
                    ( ? [X6] :
                        ( member(ordered_pair(X5,X6),X2)
                        & ilf_type(X6,set_type) )
                    | ~ member(X5,X1)
                    | ~ ilf_type(X5,set_type) ) )
              & ilf_type(X2,relation_type(X1,sK13)) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK13,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( domain(X1,sK13,X2) != X1
              | ? [X3] :
                  ( ! [X4] :
                      ( ~ member(ordered_pair(X3,X4),X2)
                      | ~ ilf_type(X4,set_type) )
                  & member(X3,X1)
                  & ilf_type(X3,set_type) ) )
            & ( domain(X1,sK13,X2) = X1
              | ! [X5] :
                  ( ? [X6] :
                      ( member(ordered_pair(X5,X6),X2)
                      & ilf_type(X6,set_type) )
                  | ~ member(X5,X1)
                  | ~ ilf_type(X5,set_type) ) )
            & ilf_type(X2,relation_type(X1,sK13)) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ( sK14 != domain(sK14,sK13,X2)
            | ? [X3] :
                ( ! [X4] :
                    ( ~ member(ordered_pair(X3,X4),X2)
                    | ~ ilf_type(X4,set_type) )
                & member(X3,sK14)
                & ilf_type(X3,set_type) ) )
          & ( sK14 = domain(sK14,sK13,X2)
            | ! [X5] :
                ( ? [X6] :
                    ( member(ordered_pair(X5,X6),X2)
                    & ilf_type(X6,set_type) )
                | ~ member(X5,sK14)
                | ~ ilf_type(X5,set_type) ) )
          & ilf_type(X2,relation_type(sK14,sK13)) )
      & ilf_type(sK14,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ( ? [X2] :
        ( ( sK14 != domain(sK14,sK13,X2)
          | ? [X3] :
              ( ! [X4] :
                  ( ~ member(ordered_pair(X3,X4),X2)
                  | ~ ilf_type(X4,set_type) )
              & member(X3,sK14)
              & ilf_type(X3,set_type) ) )
        & ( sK14 = domain(sK14,sK13,X2)
          | ! [X5] :
              ( ? [X6] :
                  ( member(ordered_pair(X5,X6),X2)
                  & ilf_type(X6,set_type) )
              | ~ member(X5,sK14)
              | ~ ilf_type(X5,set_type) ) )
        & ilf_type(X2,relation_type(sK14,sK13)) )
   => ( ( sK14 != domain(sK14,sK13,sK15)
        | ? [X3] :
            ( ! [X4] :
                ( ~ member(ordered_pair(X3,X4),sK15)
                | ~ ilf_type(X4,set_type) )
            & member(X3,sK14)
            & ilf_type(X3,set_type) ) )
      & ( sK14 = domain(sK14,sK13,sK15)
        | ! [X5] :
            ( ? [X6] :
                ( member(ordered_pair(X5,X6),sK15)
                & ilf_type(X6,set_type) )
            | ~ member(X5,sK14)
            | ~ ilf_type(X5,set_type) ) )
      & ilf_type(sK15,relation_type(sK14,sK13)) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X3] :
        ( ! [X4] :
            ( ~ member(ordered_pair(X3,X4),sK15)
            | ~ ilf_type(X4,set_type) )
        & member(X3,sK14)
        & ilf_type(X3,set_type) )
   => ( ! [X4] :
          ( ~ member(ordered_pair(sK16,X4),sK15)
          | ~ ilf_type(X4,set_type) )
      & member(sK16,sK14)
      & ilf_type(sK16,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ! [X5] :
      ( ? [X6] :
          ( member(ordered_pair(X5,X6),sK15)
          & ilf_type(X6,set_type) )
     => ( member(ordered_pair(X5,sK17(X5)),sK15)
        & ilf_type(sK17(X5),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ( sK14 != domain(sK14,sK13,sK15)
      | ( ! [X4] :
            ( ~ member(ordered_pair(sK16,X4),sK15)
            | ~ ilf_type(X4,set_type) )
        & member(sK16,sK14)
        & ilf_type(sK16,set_type) ) )
    & ( sK14 = domain(sK14,sK13,sK15)
      | ! [X5] :
          ( ( member(ordered_pair(X5,sK17(X5)),sK15)
            & ilf_type(sK17(X5),set_type) )
          | ~ member(X5,sK14)
          | ~ ilf_type(X5,set_type) ) )
    & ilf_type(sK15,relation_type(sK14,sK13))
    & ilf_type(sK14,set_type)
    & ilf_type(sK13,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17])],[f128,f133,f132,f131,f130,f129]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( member(ordered_pair(X1,sK0(X0,X1)),X0)
      | ~ member(X1,domain_of(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( member(X1,domain_of(X0))
      | ~ member(ordered_pair(X1,X2),X0)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f139,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,[],[f41]) ).

fof(f148,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,[],[f46]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f162,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,[],[f97]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK6(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK6(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f175,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,[],[f112]) ).

fof(f179,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f181,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,[],[f113]) ).

fof(f190,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,[],[f70]) ).

fof(f195,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,[],[f74]) ).

fof(f196,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,[],[f75]) ).

fof(f199,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f34]) ).

fof(f202,plain,
    ilf_type(sK15,relation_type(sK14,sK13)),
    inference(cnf_transformation,[],[f134]) ).

fof(f204,plain,
    ! [X5] :
      ( sK14 = domain(sK14,sK13,sK15)
      | member(ordered_pair(X5,sK17(X5)),sK15)
      | ~ member(X5,sK14)
      | ~ ilf_type(X5,set_type) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f206,plain,
    ( sK14 != domain(sK14,sK13,sK15)
    | member(sK16,sK14) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f207,plain,
    ! [X4] :
      ( sK14 != domain(sK14,sK13,sK15)
      | ~ member(ordered_pair(sK16,X4),sK15)
      | ~ ilf_type(X4,set_type) ),
    inference(cnf_transformation,[],[f134]) ).

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(X0,domain_of(X2)) ),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_50,plain,
    ( ~ member(X0,domain_of(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(X0,sK0(X1,X0)),X1) ),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_54,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,[],[f139]) ).

cnf(c_61,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,[],[f148]) ).

cnf(c_64,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_72,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_76,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,[],[f162]) ).

cnf(c_83,plain,
    ( ~ member(sK6(X0,X1),X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_84,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(sK6(X1,X0),X1)
    | subset(X1,X0) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_91,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,[],[f175]) ).

cnf(c_93,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ empty(power_set(X0)) ),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_95,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,[],[f181]) ).

cnf(c_103,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,[],[f190]) ).

cnf(c_108,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,[],[f195]) ).

cnf(c_109,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,[],[f196]) ).

cnf(c_112,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_113,negated_conjecture,
    ( domain(sK14,sK13,sK15) != sK14
    | ~ member(ordered_pair(sK16,X0),sK15)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_114,negated_conjecture,
    ( domain(sK14,sK13,sK15) != sK14
    | member(sK16,sK14) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_116,negated_conjecture,
    ( ~ member(X0,sK14)
    | ~ ilf_type(X0,set_type)
    | domain(sK14,sK13,sK15) = sK14
    | member(ordered_pair(X0,sK17(X0)),sK15) ),
    inference(cnf_transformation,[],[f204]) ).

cnf(c_118,negated_conjecture,
    ilf_type(sK15,relation_type(sK14,sK13)),
    inference(cnf_transformation,[],[f202]) ).

cnf(c_184,plain,
    ~ empty(power_set(X0)),
    inference(global_subsumption_just,[status(thm)],[c_93,c_112,c_93]) ).

cnf(c_214,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(global_subsumption_just,[status(thm)],[c_72,c_112,c_72]) ).

cnf(c_246,plain,
    ( ~ ilf_type(X1,set_type)
    | member(sK6(X1,X0),X1)
    | subset(X1,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_84,c_112,c_84]) ).

cnf(c_247,plain,
    ( ~ ilf_type(X0,set_type)
    | member(sK6(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_246]) ).

cnf(c_265,plain,
    ( ~ member(sK6(X0,X1),X1)
    | ~ ilf_type(X1,set_type)
    | subset(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_83,c_112,c_83]) ).

cnf(c_280,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | ~ ilf_type(X1,set_type)
    | member(X0,X1)
    | empty(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_95,c_112,c_95]) ).

cnf(c_287,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_76,c_112,c_76]) ).

cnf(c_301,plain,
    ( ~ subset(X1,X0)
    | ~ subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_64,c_112,c_64]) ).

cnf(c_302,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | ~ ilf_type(X1,set_type)
    | X0 = X1 ),
    inference(renaming,[status(thm)],[c_301]) ).

cnf(c_303,plain,
    ( ~ member(X0,domain_of(X1))
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(X0,sK0(X1,X0)),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_112,c_50]) ).

cnf(c_306,negated_conjecture,
    ( ~ member(X0,sK14)
    | domain(sK14,sK13,sK15) = sK14
    | member(ordered_pair(X0,sK17(X0)),sK15) ),
    inference(global_subsumption_just,[status(thm)],[c_116,c_112,c_116]) ).

cnf(c_321,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_54,c_112,c_54]) ).

cnf(c_325,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_49,c_321]) ).

cnf(c_331,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_91,c_112,c_91]) ).

cnf(c_332,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_331]) ).

cnf(c_528,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_61,c_112]) ).

cnf(c_531,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | member(X0,X1)
    | empty(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_280,c_112]) ).

cnf(c_537,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_332,c_112]) ).

cnf(c_539,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_325,c_112]) ).

cnf(c_541,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_109,c_112]) ).

cnf(c_542,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_108,c_112]) ).

cnf(c_543,plain,
    ( ~ member(sK6(X0,X1),X1)
    | subset(X0,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_265,c_112]) ).

cnf(c_544,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_103,c_112]) ).

cnf(c_545,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_302,c_112]) ).

cnf(c_547,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_287,c_112]) ).

cnf(c_654,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | relation_like(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_544,c_112]) ).

cnf(c_723,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_528,c_112]) ).

cnf(c_763,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_541,c_112]) ).

cnf(c_785,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | domain(X1,X2,X0) = domain_of(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_542,c_112]) ).

cnf(c_811,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_537,c_112]) ).

cnf(c_1215,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(prop_impl_just,[status(thm)],[c_214]) ).

cnf(c_1223,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_547]) ).

cnf(c_1225,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | relation_like(X0) ),
    inference(prop_impl_just,[status(thm)],[c_654,c_723]) ).

cnf(c_1227,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | domain(X1,X2,X0) = domain_of(X0) ),
    inference(prop_impl_just,[status(thm)],[c_785]) ).

cnf(c_1229,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_763]) ).

cnf(c_1235,plain,
    ( subset(X0,X1)
    | ~ member(sK6(X0,X1),X1) ),
    inference(prop_impl_just,[status(thm)],[c_543]) ).

cnf(c_1236,plain,
    ( ~ member(sK6(X0,X1),X1)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_1235]) ).

cnf(c_1237,plain,
    ( subset(X0,X1)
    | member(sK6(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_112,c_247]) ).

cnf(c_1238,plain,
    ( member(sK6(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_1237]) ).

cnf(c_1269,plain,
    ( domain(sK14,sK13,sK15) != sK14
    | ~ member(ordered_pair(sK16,X0),sK15) ),
    inference(prop_impl_just,[status(thm)],[c_112,c_113]) ).

cnf(c_4453,plain,
    domain(sK14,sK13,sK15) = domain_of(sK15),
    inference(superposition,[status(thm)],[c_118,c_1227]) ).

cnf(c_4458,plain,
    ( ~ member(X0,sK14)
    | domain_of(sK15) = sK14
    | member(ordered_pair(X0,sK17(X0)),sK15) ),
    inference(demodulation,[status(thm)],[c_306,c_4453]) ).

cnf(c_4501,plain,
    ( ~ member(X0,sK14)
    | ~ ilf_type(sK15,binary_relation_type)
    | domain_of(sK15) = sK14
    | member(X0,domain_of(sK15)) ),
    inference(superposition,[status(thm)],[c_4458,c_539]) ).

cnf(c_4662,plain,
    ( ~ member(sK6(X0,domain_of(sK15)),sK14)
    | ~ ilf_type(sK15,binary_relation_type)
    | domain_of(sK15) = sK14
    | subset(X0,domain_of(sK15)) ),
    inference(superposition,[status(thm)],[c_4501,c_1236]) ).

cnf(c_4712,plain,
    ( ~ ilf_type(sK15,binary_relation_type)
    | domain_of(sK15) = sK14
    | subset(sK14,domain_of(sK15)) ),
    inference(superposition,[status(thm)],[c_1238,c_4662]) ).

cnf(c_4845,plain,
    ( ~ subset(domain_of(sK15),sK14)
    | ~ ilf_type(sK15,binary_relation_type)
    | domain_of(sK15) = sK14 ),
    inference(superposition,[status(thm)],[c_4712,c_545]) ).

cnf(c_6813,plain,
    relation_like(sK15),
    inference(superposition,[status(thm)],[c_118,c_1225]) ).

cnf(c_6845,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1))
    | empty(power_set(X1)) ),
    inference(superposition,[status(thm)],[c_1223,c_531]) ).

cnf(c_6846,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6845,c_184]) ).

cnf(c_6915,plain,
    domain(sK14,sK13,sK15) = domain_of(sK15),
    inference(superposition,[status(thm)],[c_118,c_1227]) ).

cnf(c_6922,plain,
    ( ~ member(X0,sK14)
    | domain_of(sK15) = sK14
    | member(ordered_pair(X0,sK17(X0)),sK15) ),
    inference(demodulation,[status(thm)],[c_306,c_6915]) ).

cnf(c_6923,plain,
    ( domain_of(sK15) != sK14
    | member(sK16,sK14) ),
    inference(demodulation,[status(thm)],[c_114,c_6915]) ).

cnf(c_6924,plain,
    ( ~ ilf_type(sK15,relation_type(sK14,sK13))
    | ilf_type(domain_of(sK15),subset_type(sK14)) ),
    inference(superposition,[status(thm)],[c_6915,c_1229]) ).

cnf(c_6925,plain,
    ilf_type(domain_of(sK15),subset_type(sK14)),
    inference(forward_subsumption_resolution,[status(thm)],[c_6924,c_118]) ).

cnf(c_6931,plain,
    ( ~ member(X0,sK14)
    | ~ ilf_type(sK15,binary_relation_type)
    | domain_of(sK15) = sK14
    | member(X0,domain_of(sK15)) ),
    inference(superposition,[status(thm)],[c_6922,c_539]) ).

cnf(c_6957,plain,
    ( domain_of(sK15) != sK14
    | ~ member(ordered_pair(sK16,X0),sK15) ),
    inference(light_normalisation,[status(thm)],[c_1269,c_6915]) ).

cnf(c_7037,plain,
    ( ~ member(sK6(X0,domain_of(sK15)),sK14)
    | ~ ilf_type(sK15,binary_relation_type)
    | domain_of(sK15) = sK14
    | subset(X0,domain_of(sK15)) ),
    inference(superposition,[status(thm)],[c_6931,c_1236]) ).

cnf(c_7060,plain,
    member(domain_of(sK15),power_set(sK14)),
    inference(superposition,[status(thm)],[c_6925,c_6846]) ).

cnf(c_7166,plain,
    ( ~ member(X0,domain_of(sK15))
    | member(X0,sK14) ),
    inference(superposition,[status(thm)],[c_7060,c_811]) ).

cnf(c_7246,plain,
    ( member(sK6(domain_of(sK15),X0),sK14)
    | subset(domain_of(sK15),X0) ),
    inference(superposition,[status(thm)],[c_1238,c_7166]) ).

cnf(c_7412,plain,
    subset(domain_of(sK15),sK14),
    inference(superposition,[status(thm)],[c_7246,c_1236]) ).

cnf(c_7450,plain,
    ( domain_of(sK15) = sK14
    | ~ ilf_type(sK15,binary_relation_type) ),
    inference(global_subsumption_just,[status(thm)],[c_7037,c_4845,c_7412]) ).

cnf(c_7451,plain,
    ( ~ ilf_type(sK15,binary_relation_type)
    | domain_of(sK15) = sK14 ),
    inference(renaming,[status(thm)],[c_7450]) ).

cnf(c_7454,plain,
    ( ~ relation_like(sK15)
    | domain_of(sK15) = sK14 ),
    inference(superposition,[status(thm)],[c_1215,c_7451]) ).

cnf(c_7455,plain,
    domain_of(sK15) = sK14,
    inference(forward_subsumption_resolution,[status(thm)],[c_7454,c_6813]) ).

cnf(c_7456,plain,
    member(sK16,sK14),
    inference(backward_subsumption_resolution,[status(thm)],[c_6923,c_7455]) ).

cnf(c_7457,plain,
    ~ member(ordered_pair(sK16,X0),sK15),
    inference(backward_subsumption_resolution,[status(thm)],[c_6957,c_7455]) ).

cnf(c_7480,plain,
    ( ~ member(sK16,domain_of(sK15))
    | ~ ilf_type(sK15,binary_relation_type) ),
    inference(superposition,[status(thm)],[c_303,c_7457]) ).

cnf(c_7531,plain,
    ( ~ member(sK16,sK14)
    | ~ ilf_type(sK15,binary_relation_type) ),
    inference(light_normalisation,[status(thm)],[c_7480,c_7455]) ).

cnf(c_7532,plain,
    ~ ilf_type(sK15,binary_relation_type),
    inference(forward_subsumption_resolution,[status(thm)],[c_7531,c_7456]) ).

cnf(c_7533,plain,
    ~ relation_like(sK15),
    inference(superposition,[status(thm)],[c_1215,c_7532]) ).

cnf(c_7534,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_7533,c_6813]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET659+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 20:50:13 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.43  Running first-order theorem proving
% 0.17/0.43  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
% 35.74/5.68  % SZS status Started for theBenchmark.p
% 35.74/5.68  % SZS status Theorem for theBenchmark.p
% 35.74/5.68  
% 35.74/5.68  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 35.74/5.68  
% 35.74/5.68  ------  iProver source info
% 35.74/5.68  
% 35.74/5.68  git: date: 2024-05-02 19:28:25 +0000
% 35.74/5.68  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 35.74/5.68  git: non_committed_changes: false
% 35.74/5.68  
% 35.74/5.68  ------ Parsing...
% 35.74/5.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 35.74/5.68  
% 35.74/5.68  ------ 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 
% 35.74/5.68  
% 35.74/5.68  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 35.74/5.68  
% 35.74/5.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 35.74/5.68  ------ Proving...
% 35.74/5.68  ------ Problem Properties 
% 35.74/5.68  
% 35.74/5.68  
% 35.74/5.68  clauses                                 46
% 35.74/5.68  conjectures                             3
% 35.74/5.68  EPR                                     9
% 35.74/5.68  Horn                                    37
% 35.74/5.68  unary                                   9
% 35.74/5.68  binary                                  24
% 35.74/5.68  lits                                    96
% 35.74/5.68  lits eq                                 14
% 35.74/5.68  fd_pure                                 0
% 35.74/5.68  fd_pseudo                               0
% 35.74/5.68  fd_cond                                 0
% 35.74/5.68  fd_pseudo_cond                          5
% 35.74/5.68  AC symbols                              0
% 35.74/5.68  
% 35.74/5.68  ------ Input Options Time Limit: Unbounded
% 35.74/5.68  
% 35.74/5.68  
% 35.74/5.68  ------ 
% 35.74/5.68  Current options:
% 35.74/5.68  ------ 
% 35.74/5.68  
% 35.74/5.68  
% 35.74/5.68  
% 35.74/5.68  
% 35.74/5.68  ------ Proving...
% 35.74/5.68  
% 35.74/5.68  
% 35.74/5.68  % SZS status Theorem for theBenchmark.p
% 35.74/5.68  
% 35.74/5.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.74/5.68  
% 35.74/5.69  
%------------------------------------------------------------------------------