TSTP Solution File: SET650+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 03:01:07 EDT 2024

% Result   : Theorem 0.46s 1.16s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f170)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,set_type)
                 => ! [X4] :
                      ( ilf_type(X4,relation_type(X0,X1))
                     => ( member(ordered_pair(X2,X3),X4)
                       => ( member(X3,X1)
                          & member(X2,X0) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

fof(f4,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',p4) ).

fof(f6,axiom,
    ! [X0] :
      ( ilf_type(X0,binary_relation_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X1,range_of(X0))
          <=> ? [X2] :
                ( member(ordered_pair(X2,X1),X0)
                & ilf_type(X2,set_type) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).

fof(f8,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',p8) ).

fof(f10,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',p10) ).

fof(f23,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',p23) ).

fof(f26,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).

fof(f27,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ( subset(range_of(X2),X1)
                & subset(domain_of(X2),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_12) ).

fof(f28,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ( subset(range_of(X2),X1)
                  & subset(domain_of(X2),X0) ) ) ) ),
    inference(negated_conjecture,[],[f27]) ).

fof(f29,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,[],[f8]) ).

fof(f32,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ( member(X3,X1)
                        & member(X2,X0) )
                      | ~ member(ordered_pair(X2,X3),X4)
                      | ~ ilf_type(X4,relation_type(X0,X1)) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f33,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ( member(X3,X1)
                        & member(X2,X0) )
                      | ~ member(ordered_pair(X2,X3),X4)
                      | ~ ilf_type(X4,relation_type(X0,X1)) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f32]) ).

fof(f34,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,[],[f4]) ).

fof(f36,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X1,range_of(X0))
          <=> ? [X2] :
                ( member(ordered_pair(X2,X1),X0)
                & ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f38,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,[],[f29]) ).

fof(f40,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,[],[f10]) ).

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

fof(f57,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,[],[f23]) ).

fof(f61,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( ~ subset(range_of(X2),X1)
                | ~ subset(domain_of(X2),X0) )
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f70,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,[],[f34]) ).

fof(f71,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,[],[f70]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(ordered_pair(X1,X3),X0)
          & ilf_type(X3,set_type) )
     => ( member(ordered_pair(X1,sK2(X0,X1)),X0)
        & ilf_type(sK2(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,domain_of(X0))
              | ! [X2] :
                  ( ~ member(ordered_pair(X1,X2),X0)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ( member(ordered_pair(X1,sK2(X0,X1)),X0)
                & ilf_type(sK2(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,[sK2])],[f71,f72]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,range_of(X0))
              | ! [X2] :
                  ( ~ member(ordered_pair(X2,X1),X0)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ? [X2] :
                  ( member(ordered_pair(X2,X1),X0)
                  & ilf_type(X2,set_type) )
              | ~ member(X1,range_of(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,range_of(X0))
              | ! [X2] :
                  ( ~ member(ordered_pair(X2,X1),X0)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ? [X3] :
                  ( member(ordered_pair(X3,X1),X0)
                  & ilf_type(X3,set_type) )
              | ~ member(X1,range_of(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(rectify,[],[f74]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(ordered_pair(X3,X1),X0)
          & ilf_type(X3,set_type) )
     => ( member(ordered_pair(sK3(X0,X1),X1),X0)
        & ilf_type(sK3(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,range_of(X0))
              | ! [X2] :
                  ( ~ member(ordered_pair(X2,X1),X0)
                  | ~ ilf_type(X2,set_type) ) )
            & ( ( member(ordered_pair(sK3(X0,X1),X1),X0)
                & ilf_type(sK3(X0,X1),set_type) )
              | ~ member(X1,range_of(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f75,f76]) ).

fof(f80,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,[],[f41]) ).

fof(f81,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,[],[f80]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK5(X0,X1),X1)
        & member(sK5(X0,X1),X0)
        & ilf_type(sK5(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ( ~ member(sK5(X0,X1),X1)
                & member(sK5(X0,X1),X0)
                & ilf_type(sK5(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,[sK5])],[f81,f82]) ).

fof(f108,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ( ~ subset(range_of(X2),X1)
                  | ~ subset(domain_of(X2),X0) )
                & ilf_type(X2,relation_type(X0,X1)) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ( ~ subset(range_of(X2),X1)
                | ~ subset(domain_of(X2),sK14) )
              & ilf_type(X2,relation_type(sK14,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK14,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( ~ subset(range_of(X2),X1)
              | ~ subset(domain_of(X2),sK14) )
            & ilf_type(X2,relation_type(sK14,X1)) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ( ~ subset(range_of(X2),sK15)
            | ~ subset(domain_of(X2),sK14) )
          & ilf_type(X2,relation_type(sK14,sK15)) )
      & ilf_type(sK15,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ( ? [X2] :
        ( ( ~ subset(range_of(X2),sK15)
          | ~ subset(domain_of(X2),sK14) )
        & ilf_type(X2,relation_type(sK14,sK15)) )
   => ( ( ~ subset(range_of(sK16),sK15)
        | ~ subset(domain_of(sK16),sK14) )
      & ilf_type(sK16,relation_type(sK14,sK15)) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ( ( ~ subset(range_of(sK16),sK15)
      | ~ subset(domain_of(sK16),sK14) )
    & ilf_type(sK16,relation_type(sK14,sK15))
    & ilf_type(sK15,set_type)
    & ilf_type(sK14,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f61,f110,f109,f108]) ).

fof(f118,plain,
    ! [X2,X3,X0,X1,X4] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),X4)
      | ~ ilf_type(X4,relation_type(X0,X1))
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f119,plain,
    ! [X2,X3,X0,X1,X4] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),X4)
      | ~ ilf_type(X4,relation_type(X0,X1))
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( member(ordered_pair(X1,sK2(X0,X1)),X0)
      | ~ member(X1,domain_of(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( member(ordered_pair(sK3(X0,X1),X1),X0)
      | ~ member(X1,range_of(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f77]) ).

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,[],[f38]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK5(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK5(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f160,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,[],[f57]) ).

fof(f165,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f26]) ).

fof(f168,plain,
    ilf_type(sK16,relation_type(sK14,sK15)),
    inference(cnf_transformation,[],[f111]) ).

fof(f169,plain,
    ( ~ subset(range_of(sK16),sK15)
    | ~ subset(domain_of(sK16),sK14) ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_55,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X1,X4) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_56,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X0,X3) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_58,plain,
    ( ~ member(X0,domain_of(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(X0,sK2(X1,X0)),X1) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_62,plain,
    ( ~ member(X0,range_of(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(sK3(X1,X0),X0),X1) ),
    inference(cnf_transformation,[],[f125]) ).

cnf(c_65,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_68,plain,
    ( ~ member(sK5(X0,X1),X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_69,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(sK5(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_74,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_96,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,[],[f160]) ).

cnf(c_101,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_102,negated_conjecture,
    ( ~ subset(domain_of(sK16),sK14)
    | ~ subset(range_of(sK16),sK15) ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_103,negated_conjecture,
    ilf_type(sK16,relation_type(sK14,sK15)),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_180,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(global_subsumption_just,[status(thm)],[c_74,c_101,c_74]) ).

cnf(c_207,plain,
    ( ~ ilf_type(X1,set_type)
    | member(sK5(X0,X1),X0)
    | subset(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_69,c_101,c_69]) ).

cnf(c_208,plain,
    ( ~ ilf_type(X0,set_type)
    | member(sK5(X1,X0),X1)
    | subset(X1,X0) ),
    inference(renaming,[status(thm)],[c_207]) ).

cnf(c_209,plain,
    ( member(sK5(X1,X0),X1)
    | subset(X1,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_208,c_101,c_208]) ).

cnf(c_210,plain,
    ( member(sK5(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_209]) ).

cnf(c_221,plain,
    ( ~ member(sK5(X0,X1),X1)
    | ~ ilf_type(X1,set_type)
    | subset(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_68,c_101,c_68]) ).

cnf(c_250,plain,
    ( ~ member(X0,range_of(X1))
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(sK3(X1,X0),X0),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_62,c_101,c_62]) ).

cnf(c_253,plain,
    ( ~ member(X0,domain_of(X1))
    | ~ ilf_type(X1,binary_relation_type)
    | member(ordered_pair(X0,sK2(X1,X0)),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_58,c_101,c_58]) ).

cnf(c_278,plain,
    ( ~ ilf_type(X2,relation_type(X3,X4))
    | ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X0,X3) ),
    inference(global_subsumption_just,[status(thm)],[c_56,c_101,c_56]) ).

cnf(c_279,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X0,X3) ),
    inference(renaming,[status(thm)],[c_278]) ).

cnf(c_280,plain,
    ( ~ ilf_type(X2,relation_type(X3,X4))
    | ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X1,X4) ),
    inference(global_subsumption_just,[status(thm)],[c_55,c_101,c_55]) ).

cnf(c_281,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X1,X4) ),
    inference(renaming,[status(thm)],[c_280]) ).

cnf(c_430,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X1,X4) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_281,c_101]) ).

cnf(c_431,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | member(X0,X3) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_279,c_101]) ).

cnf(c_437,plain,
    ( ~ member(sK5(X0,X1),X1)
    | subset(X0,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_221,c_101]) ).

cnf(c_443,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_96,c_101]) ).

cnf(c_445,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_65,c_101]) ).

cnf(c_534,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | relation_like(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_443,c_101]) ).

cnf(c_609,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_445,c_101]) ).

cnf(c_650,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | member(X1,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_430,c_101,c_101]) ).

cnf(c_666,plain,
    ( ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | member(X0,X3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_431,c_101,c_101]) ).

cnf(c_897,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(prop_impl_just,[status(thm)],[c_180]) ).

cnf(c_907,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | relation_like(X0) ),
    inference(prop_impl_just,[status(thm)],[c_534,c_609]) ).

cnf(c_909,plain,
    ( ~ member(sK5(X0,X1),X1)
    | subset(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_437]) ).

cnf(c_913,plain,
    ( subset(X0,X1)
    | member(sK5(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_210]) ).

cnf(c_914,plain,
    ( member(sK5(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_913]) ).

cnf(c_2352,plain,
    ( ~ ilf_type(sK16,relation_type(sK14,sK15))
    | relation_like(sK16) ),
    inference(instantiation,[status(thm)],[c_907]) ).

cnf(c_3512,plain,
    ( ~ relation_like(sK16)
    | ilf_type(sK16,binary_relation_type) ),
    inference(instantiation,[status(thm)],[c_897]) ).

cnf(c_4400,plain,
    ( ~ member(ordered_pair(X0,X1),sK16)
    | member(X1,sK15) ),
    inference(resolution,[status(thm)],[c_650,c_103]) ).

cnf(c_4495,plain,
    ( ~ member(ordered_pair(X0,X1),sK16)
    | member(X0,sK14) ),
    inference(resolution,[status(thm)],[c_666,c_103]) ).

cnf(c_4645,plain,
    ( ~ member(X0,range_of(sK16))
    | ~ ilf_type(sK16,binary_relation_type)
    | member(X0,sK15) ),
    inference(resolution,[status(thm)],[c_4400,c_250]) ).

cnf(c_4960,plain,
    ( ~ member(X0,range_of(sK16))
    | member(X0,sK15) ),
    inference(global_subsumption_just,[status(thm)],[c_4645,c_103,c_2352,c_3512,c_4645]) ).

cnf(c_4984,plain,
    ( member(sK5(range_of(sK16),X0),sK15)
    | subset(range_of(sK16),X0) ),
    inference(resolution,[status(thm)],[c_4960,c_914]) ).

cnf(c_5306,plain,
    ( ~ member(X0,domain_of(sK16))
    | ~ ilf_type(sK16,binary_relation_type)
    | member(X0,sK14) ),
    inference(resolution,[status(thm)],[c_253,c_4495]) ).

cnf(c_5661,plain,
    ( ~ member(X0,domain_of(sK16))
    | member(X0,sK14) ),
    inference(global_subsumption_just,[status(thm)],[c_5306,c_103,c_2352,c_3512,c_5306]) ).

cnf(c_5678,plain,
    ( member(sK5(domain_of(sK16),X0),sK14)
    | subset(domain_of(sK16),X0) ),
    inference(resolution,[status(thm)],[c_5661,c_914]) ).

cnf(c_5812,plain,
    subset(range_of(sK16),sK15),
    inference(resolution,[status(thm)],[c_4984,c_909]) ).

cnf(c_5878,plain,
    subset(domain_of(sK16),sK14),
    inference(resolution,[status(thm)],[c_5678,c_909]) ).

cnf(c_5879,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_5878,c_5812,c_102]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem  : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n008.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 20:41:13 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
% 0.46/1.16  % SZS status Started for theBenchmark.p
% 0.46/1.16  % SZS status Theorem for theBenchmark.p
% 0.46/1.16  
% 0.46/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.16  
% 0.46/1.16  ------  iProver source info
% 0.46/1.16  
% 0.46/1.16  git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.16  git: non_committed_changes: false
% 0.46/1.16  
% 0.46/1.16  ------ Parsing...
% 0.46/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... sup_sim: 0  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 
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.46/1.16  ------ Proving...
% 0.46/1.16  ------ Problem Properties 
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  clauses                                 38
% 0.46/1.16  conjectures                             2
% 0.46/1.16  EPR                                     8
% 0.46/1.16  Horn                                    32
% 0.46/1.16  unary                                   7
% 0.46/1.16  binary                                  19
% 0.46/1.16  lits                                    81
% 0.46/1.16  lits eq                                 2
% 0.46/1.16  fd_pure                                 0
% 0.46/1.16  fd_pseudo                               0
% 0.46/1.16  fd_cond                                 0
% 0.46/1.16  fd_pseudo_cond                          0
% 0.46/1.16  AC symbols                              0
% 0.46/1.16  
% 0.46/1.16  ------ Input Options Time Limit: Unbounded
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  ------ 
% 0.46/1.16  Current options:
% 0.46/1.16  ------ 
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  ------ Proving...
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  % SZS status Theorem for theBenchmark.p
% 0.46/1.16  
% 0.46/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.16  
% 0.46/1.16  
%------------------------------------------------------------------------------