TSTP Solution File: SET650+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:35:03 EDT 2023

% Result   : Theorem 0.18s 0.61s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   42
% Syntax   : Number of formulae    :  103 (   8 unt;  32 typ;   0 def)
%            Number of atoms       :  297 (   0 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  385 ( 159   ~; 165   |;  24   &)
%                                         (   5 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   41 (  26   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   27 (  27 usr;   6 con; 0-2 aty)
%            Number of variables   :  136 (   9 sgn;  56   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    set_type: $i ).

tff(decl_23,type,
    ilf_type: ( $i * $i ) > $o ).

tff(decl_24,type,
    binary_relation_type: $i ).

tff(decl_25,type,
    domain_of: $i > $i ).

tff(decl_26,type,
    member: ( $i * $i ) > $o ).

tff(decl_27,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_28,type,
    range_of: $i > $i ).

tff(decl_29,type,
    relation_type: ( $i * $i ) > $i ).

tff(decl_30,type,
    cross_product: ( $i * $i ) > $i ).

tff(decl_31,type,
    subset_type: $i > $i ).

tff(decl_32,type,
    subset: ( $i * $i ) > $o ).

tff(decl_33,type,
    relation_like: $i > $o ).

tff(decl_34,type,
    power_set: $i > $i ).

tff(decl_35,type,
    member_type: $i > $i ).

tff(decl_36,type,
    empty: $i > $o ).

tff(decl_37,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_41,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_42,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk7_0: $i ).

tff(decl_44,type,
    esk8_1: $i > $i ).

tff(decl_45,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk10_1: $i > $i ).

tff(decl_47,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk13_1: $i > $i ).

tff(decl_50,type,
    esk14_1: $i > $i ).

tff(decl_51,type,
    esk15_0: $i ).

tff(decl_52,type,
    esk16_0: $i ).

tff(decl_53,type,
    esk17_0: $i ).

fof(p3,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,set_type)
                 => ! [X5] :
                      ( ilf_type(X5,relation_type(X1,X2))
                     => ( member(ordered_pair(X3,X4),X5)
                       => ( member(X3,X1)
                          & member(X4,X2) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

fof(p26,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).

fof(prove_relset_1_12,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => ( subset(domain_of(X3),X1)
                & subset(range_of(X3),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_12) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,binary_relation_type)
         => ( member(X1,range_of(X2))
          <=> ? [X3] :
                ( ilf_type(X3,set_type)
                & member(ordered_pair(X3,X1),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(p18,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( member(X1,power_set(X2))
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).

fof(p1,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,binary_relation_type)
         => ( member(X1,domain_of(X2))
          <=> ? [X3] :
                ( ilf_type(X3,set_type)
                & member(ordered_pair(X1,X3),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(p10,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( subset(X1,X2)
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).

fof(p8,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X1,X2)))
               => ilf_type(X3,relation_type(X1,X2)) )
            & ! [X4] :
                ( ilf_type(X4,relation_type(X1,X2))
               => ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).

fof(p13,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ilf_type(X1,binary_relation_type)
      <=> ( relation_like(X1)
          & ilf_type(X1,set_type) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).

fof(p23,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,subset_type(cross_product(X1,X2)))
             => relation_like(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).

fof(c_0_10,plain,
    ! [X14,X15,X16,X17,X18] :
      ( ( member(X16,X14)
        | ~ member(ordered_pair(X16,X17),X18)
        | ~ ilf_type(X18,relation_type(X14,X15))
        | ~ ilf_type(X17,set_type)
        | ~ ilf_type(X16,set_type)
        | ~ ilf_type(X15,set_type)
        | ~ ilf_type(X14,set_type) )
      & ( member(X17,X15)
        | ~ member(ordered_pair(X16,X17),X18)
        | ~ ilf_type(X18,relation_type(X14,X15))
        | ~ ilf_type(X17,set_type)
        | ~ ilf_type(X16,set_type)
        | ~ ilf_type(X15,set_type)
        | ~ ilf_type(X14,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).

fof(c_0_11,plain,
    ! [X74] : ilf_type(X74,set_type),
    inference(variable_rename,[status(thm)],[p26]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,set_type)
           => ! [X3] :
                ( ilf_type(X3,relation_type(X1,X2))
               => ( subset(domain_of(X3),X1)
                  & subset(range_of(X3),X2) ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_12]) ).

fof(c_0_13,plain,
    ! [X10,X11,X13] :
      ( ( ilf_type(esk2_2(X10,X11),set_type)
        | ~ member(X10,range_of(X11))
        | ~ ilf_type(X11,binary_relation_type)
        | ~ ilf_type(X10,set_type) )
      & ( member(ordered_pair(esk2_2(X10,X11),X10),X11)
        | ~ member(X10,range_of(X11))
        | ~ ilf_type(X11,binary_relation_type)
        | ~ ilf_type(X10,set_type) )
      & ( ~ ilf_type(X13,set_type)
        | ~ member(ordered_pair(X13,X10),X11)
        | member(X10,range_of(X11))
        | ~ ilf_type(X11,binary_relation_type)
        | ~ ilf_type(X10,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])]) ).

fof(c_0_14,plain,
    ! [X51,X52,X53] :
      ( ( ~ member(X51,power_set(X52))
        | ~ ilf_type(X53,set_type)
        | ~ member(X53,X51)
        | member(X53,X52)
        | ~ ilf_type(X52,set_type)
        | ~ ilf_type(X51,set_type) )
      & ( ilf_type(esk9_2(X51,X52),set_type)
        | member(X51,power_set(X52))
        | ~ ilf_type(X52,set_type)
        | ~ ilf_type(X51,set_type) )
      & ( member(esk9_2(X51,X52),X51)
        | member(X51,power_set(X52))
        | ~ ilf_type(X52,set_type)
        | ~ ilf_type(X51,set_type) )
      & ( ~ member(esk9_2(X51,X52),X52)
        | member(X51,power_set(X52))
        | ~ ilf_type(X52,set_type)
        | ~ ilf_type(X51,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])])]) ).

fof(c_0_15,plain,
    ! [X6,X7,X9] :
      ( ( ilf_type(esk1_2(X6,X7),set_type)
        | ~ member(X6,domain_of(X7))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type) )
      & ( member(ordered_pair(X6,esk1_2(X6,X7)),X7)
        | ~ member(X6,domain_of(X7))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type) )
      & ( ~ ilf_type(X9,set_type)
        | ~ member(ordered_pair(X6,X9),X7)
        | member(X6,domain_of(X7))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])]) ).

cnf(c_0_16,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ ilf_type(X4,relation_type(X5,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X5,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_18,negated_conjecture,
    ( ilf_type(esk15_0,set_type)
    & ilf_type(esk16_0,set_type)
    & ilf_type(esk17_0,relation_type(esk15_0,esk16_0))
    & ( ~ subset(domain_of(esk17_0),esk15_0)
      | ~ subset(range_of(esk17_0),esk16_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

cnf(c_0_19,plain,
    ( member(ordered_pair(esk2_2(X1,X2),X1),X2)
    | ~ member(X1,range_of(X2))
    | ~ ilf_type(X2,binary_relation_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( member(esk9_2(X1,X2),X1)
    | member(X1,power_set(X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X3),X4)
    | ~ ilf_type(X4,relation_type(X2,X5))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X5,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_22,plain,
    ( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
    | ~ member(X1,domain_of(X2))
    | ~ ilf_type(X2,binary_relation_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ ilf_type(X4,relation_type(X5,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).

cnf(c_0_24,negated_conjecture,
    ilf_type(esk17_0,relation_type(esk15_0,esk16_0)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,plain,
    ( member(ordered_pair(esk2_2(X1,X2),X1),X2)
    | ~ member(X1,range_of(X2))
    | ~ ilf_type(X2,binary_relation_type) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17])]) ).

cnf(c_0_26,plain,
    ( member(esk9_2(X1,X2),X1)
    | member(X1,power_set(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_17])]) ).

fof(c_0_27,plain,
    ! [X36,X37,X38] :
      ( ( ~ subset(X36,X37)
        | ~ ilf_type(X38,set_type)
        | ~ member(X38,X36)
        | member(X38,X37)
        | ~ ilf_type(X37,set_type)
        | ~ ilf_type(X36,set_type) )
      & ( ilf_type(esk6_2(X36,X37),set_type)
        | subset(X36,X37)
        | ~ ilf_type(X37,set_type)
        | ~ ilf_type(X36,set_type) )
      & ( member(esk6_2(X36,X37),X36)
        | subset(X36,X37)
        | ~ ilf_type(X37,set_type)
        | ~ ilf_type(X36,set_type) )
      & ( ~ member(esk6_2(X36,X37),X37)
        | subset(X36,X37)
        | ~ ilf_type(X37,set_type)
        | ~ ilf_type(X36,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])])]) ).

cnf(c_0_28,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X3),X4)
    | ~ ilf_type(X4,relation_type(X2,X5)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).

cnf(c_0_29,plain,
    ( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
    | ~ member(X1,domain_of(X2))
    | ~ ilf_type(X2,binary_relation_type) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_17])]) ).

cnf(c_0_30,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk9_2(X1,X2),X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_31,negated_conjecture,
    ( member(X1,esk16_0)
    | ~ member(ordered_pair(X2,X1),esk17_0) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_32,plain,
    ( member(ordered_pair(esk2_2(esk9_2(range_of(X1),X2),X1),esk9_2(range_of(X1),X2)),X1)
    | member(range_of(X1),power_set(X2))
    | ~ ilf_type(X1,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_33,plain,
    ( member(esk6_2(X1,X2),X1)
    | subset(X1,X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_34,plain,
    ( subset(X1,X2)
    | ~ member(esk6_2(X1,X2),X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,negated_conjecture,
    ( member(X1,esk15_0)
    | ~ member(ordered_pair(X1,X2),esk17_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_24]) ).

cnf(c_0_36,plain,
    ( member(ordered_pair(esk9_2(domain_of(X1),X2),esk1_2(esk9_2(domain_of(X1),X2),X1)),X1)
    | member(domain_of(X1),power_set(X2))
    | ~ ilf_type(X1,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_29,c_0_26]) ).

cnf(c_0_37,plain,
    ( member(X3,X2)
    | ~ member(X1,power_set(X2))
    | ~ ilf_type(X3,set_type)
    | ~ member(X3,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_38,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk9_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_17]),c_0_17])]) ).

cnf(c_0_39,negated_conjecture,
    ( member(esk9_2(range_of(esk17_0),X1),esk16_0)
    | member(range_of(esk17_0),power_set(X1))
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ subset(domain_of(esk17_0),esk15_0)
    | ~ subset(range_of(esk17_0),esk16_0) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_41,plain,
    ( subset(X1,X2)
    | member(esk6_2(X1,X2),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_17]),c_0_17])]) ).

cnf(c_0_42,plain,
    ( subset(X1,X2)
    | ~ member(esk6_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17]),c_0_17])]) ).

fof(c_0_43,plain,
    ! [X29,X30,X31,X32] :
      ( ( ~ ilf_type(X31,subset_type(cross_product(X29,X30)))
        | ilf_type(X31,relation_type(X29,X30))
        | ~ ilf_type(X30,set_type)
        | ~ ilf_type(X29,set_type) )
      & ( ~ ilf_type(X32,relation_type(X29,X30))
        | ilf_type(X32,subset_type(cross_product(X29,X30)))
        | ~ ilf_type(X30,set_type)
        | ~ ilf_type(X29,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p8])])])]) ).

cnf(c_0_44,negated_conjecture,
    ( member(esk9_2(domain_of(esk17_0),X1),esk15_0)
    | member(domain_of(esk17_0),power_set(X1))
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_45,plain,
    ( member(X1,X2)
    | ~ member(X3,power_set(X2))
    | ~ member(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_17]),c_0_17]),c_0_17])]) ).

cnf(c_0_46,negated_conjecture,
    ( member(range_of(esk17_0),power_set(esk16_0))
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_47,negated_conjecture,
    ( member(esk6_2(range_of(esk17_0),esk16_0),range_of(esk17_0))
    | ~ subset(domain_of(esk17_0),esk15_0) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_48,negated_conjecture,
    ( ~ subset(domain_of(esk17_0),esk15_0)
    | ~ member(esk6_2(range_of(esk17_0),esk16_0),esk16_0) ),
    inference(spm,[status(thm)],[c_0_40,c_0_42]) ).

fof(c_0_49,plain,
    ! [X44] :
      ( ( relation_like(X44)
        | ~ ilf_type(X44,binary_relation_type)
        | ~ ilf_type(X44,set_type) )
      & ( ilf_type(X44,set_type)
        | ~ ilf_type(X44,binary_relation_type)
        | ~ ilf_type(X44,set_type) )
      & ( ~ relation_like(X44)
        | ~ ilf_type(X44,set_type)
        | ilf_type(X44,binary_relation_type)
        | ~ ilf_type(X44,set_type) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).

fof(c_0_50,plain,
    ! [X67,X68,X69] :
      ( ~ ilf_type(X67,set_type)
      | ~ ilf_type(X68,set_type)
      | ~ ilf_type(X69,subset_type(cross_product(X67,X68)))
      | relation_like(X69) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).

cnf(c_0_51,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_52,negated_conjecture,
    ( member(domain_of(esk17_0),power_set(esk15_0))
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_38,c_0_44]) ).

cnf(c_0_53,negated_conjecture,
    ( member(X1,esk16_0)
    | ~ member(X1,range_of(esk17_0))
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_54,negated_conjecture,
    ( member(esk6_2(domain_of(esk17_0),esk15_0),domain_of(esk17_0))
    | member(esk6_2(range_of(esk17_0),esk16_0),range_of(esk17_0)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_41]) ).

cnf(c_0_55,negated_conjecture,
    ( member(esk6_2(domain_of(esk17_0),esk15_0),domain_of(esk17_0))
    | ~ member(esk6_2(range_of(esk17_0),esk16_0),esk16_0) ),
    inference(spm,[status(thm)],[c_0_48,c_0_41]) ).

cnf(c_0_56,negated_conjecture,
    ( member(esk6_2(range_of(esk17_0),esk16_0),range_of(esk17_0))
    | ~ member(esk6_2(domain_of(esk17_0),esk15_0),esk15_0) ),
    inference(spm,[status(thm)],[c_0_47,c_0_42]) ).

cnf(c_0_57,negated_conjecture,
    ( ~ member(esk6_2(range_of(esk17_0),esk16_0),esk16_0)
    | ~ member(esk6_2(domain_of(esk17_0),esk15_0),esk15_0) ),
    inference(spm,[status(thm)],[c_0_48,c_0_42]) ).

cnf(c_0_58,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_59,plain,
    ( relation_like(X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_60,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_17]),c_0_17])]) ).

cnf(c_0_61,negated_conjecture,
    ( member(X1,esk15_0)
    | ~ member(X1,domain_of(esk17_0))
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_45,c_0_52]) ).

cnf(c_0_62,negated_conjecture,
    ( member(esk6_2(domain_of(esk17_0),esk15_0),domain_of(esk17_0))
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).

cnf(c_0_63,negated_conjecture,
    ( ~ member(esk6_2(domain_of(esk17_0),esk15_0),esk15_0)
    | ~ ilf_type(esk17_0,binary_relation_type) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_56]),c_0_57]) ).

cnf(c_0_64,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1)
    | ~ ilf_type(X1,set_type) ),
    inference(cn,[status(thm)],[c_0_58]) ).

cnf(c_0_65,plain,
    ( relation_like(X1)
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_17]),c_0_17])]) ).

cnf(c_0_66,negated_conjecture,
    ilf_type(esk17_0,subset_type(cross_product(esk15_0,esk16_0))),
    inference(spm,[status(thm)],[c_0_60,c_0_24]) ).

cnf(c_0_67,negated_conjecture,
    ~ ilf_type(esk17_0,binary_relation_type),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).

cnf(c_0_68,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_17])]) ).

cnf(c_0_69,negated_conjecture,
    relation_like(esk17_0),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_70,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.32  % Computer : n003.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Sat Aug 26 16:19:39 EDT 2023
% 0.13/0.32  % CPUTime  : 
% 0.18/0.54  start to proof: theBenchmark
% 0.18/0.61  % Version  : CSE_E---1.5
% 0.18/0.61  % Problem  : theBenchmark.p
% 0.18/0.61  % Proof found
% 0.18/0.61  % SZS status Theorem for theBenchmark.p
% 0.18/0.61  % SZS output start Proof
% See solution above
% 0.18/0.61  % Total time : 0.055000 s
% 0.18/0.61  % SZS output end Proof
% 0.18/0.61  % Total time : 0.059000 s
%------------------------------------------------------------------------------