TSTP Solution File: SET681+3 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SET681+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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 : Tue May 21 02:59:12 EDT 2024

% Result   : Theorem 0.53s 0.53s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   75 (  12 unt;   0 def)
%            Number of atoms       :  284 (   5 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  344 ( 135   ~; 137   |;  29   &)
%                                         (   8 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-3 aty)
%            Number of variables   :  127 (   9 sgn  60   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(p6,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',p6) ).

fof(p31,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).

fof(prove_relset_1_48,conjecture,
    ! [X1] :
      ( ( ~ empty(X1)
        & ilf_type(X1,set_type) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ! [X3] :
              ( ilf_type(X3,relation_type(X2,X1))
             => ! [X4] :
                  ( ilf_type(X4,member_type(X1))
                 => ( member(X4,range(X2,X1,X3))
                  <=> ? [X5] :
                        ( ilf_type(X5,member_type(X2))
                        & member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_48) ).

fof(p17,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',p17) ).

fof(p26,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',p26) ).

fof(p29,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => range(X1,X2,X3) = range_of(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).

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

fof(p1,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',p1) ).

fof(p8,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).

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(c_0_10,plain,
    ! [X25,X26,X27,X28] :
      ( ( ~ ilf_type(X27,subset_type(cross_product(X25,X26)))
        | ilf_type(X27,relation_type(X25,X26))
        | ~ ilf_type(X26,set_type)
        | ~ ilf_type(X25,set_type) )
      & ( ~ ilf_type(X28,relation_type(X25,X26))
        | ilf_type(X28,subset_type(cross_product(X25,X26)))
        | ~ ilf_type(X26,set_type)
        | ~ ilf_type(X25,set_type) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])]) ).

fof(c_0_11,plain,
    ! [X86] : ilf_type(X86,set_type),
    inference(variable_rename,[status(thm)],[p31]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty(X1)
          & ilf_type(X1,set_type) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & ilf_type(X2,set_type) )
           => ! [X3] :
                ( ilf_type(X3,relation_type(X2,X1))
               => ! [X4] :
                    ( ilf_type(X4,member_type(X1))
                   => ( member(X4,range(X2,X1,X3))
                    <=> ? [X5] :
                          ( ilf_type(X5,member_type(X2))
                          & member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_48])]) ).

fof(c_0_13,plain,
    ! [X48] :
      ( ( relation_like(X48)
        | ~ ilf_type(X48,binary_relation_type)
        | ~ ilf_type(X48,set_type) )
      & ( ilf_type(X48,set_type)
        | ~ ilf_type(X48,binary_relation_type)
        | ~ ilf_type(X48,set_type) )
      & ( ~ relation_like(X48)
        | ~ ilf_type(X48,set_type)
        | ilf_type(X48,binary_relation_type)
        | ~ ilf_type(X48,set_type) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])]) ).

fof(c_0_14,plain,
    ! [X71,X72,X73] :
      ( ~ ilf_type(X71,set_type)
      | ~ ilf_type(X72,set_type)
      | ~ ilf_type(X73,subset_type(cross_product(X71,X72)))
      | relation_like(X73) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])])]) ).

cnf(c_0_15,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_10]) ).

cnf(c_0_16,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_17,negated_conjecture,
    ! [X91] :
      ( ~ empty(esk12_0)
      & ilf_type(esk12_0,set_type)
      & ~ empty(esk13_0)
      & ilf_type(esk13_0,set_type)
      & ilf_type(esk14_0,relation_type(esk13_0,esk12_0))
      & ilf_type(esk15_0,member_type(esk12_0))
      & ( ~ member(esk15_0,range(esk13_0,esk12_0,esk14_0))
        | ~ ilf_type(X91,member_type(esk13_0))
        | ~ member(ordered_pair(X91,esk15_0),esk14_0) )
      & ( ilf_type(esk16_0,member_type(esk13_0))
        | member(esk15_0,range(esk13_0,esk12_0,esk14_0)) )
      & ( member(ordered_pair(esk16_0,esk15_0),esk14_0)
        | member(esk15_0,range(esk13_0,esk12_0,esk14_0)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])])]) ).

cnf(c_0_18,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_13]) ).

cnf(c_0_19,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_14]) ).

cnf(c_0_20,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_15,c_0_16]),c_0_16])]) ).

cnf(c_0_21,negated_conjecture,
    ilf_type(esk14_0,relation_type(esk13_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_22,plain,
    ! [X80,X81,X82] :
      ( ~ ilf_type(X80,set_type)
      | ~ ilf_type(X81,set_type)
      | ~ ilf_type(X82,relation_type(X80,X81))
      | range(X80,X81,X82) = range_of(X82) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p29])])])]) ).

fof(c_0_23,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[p10]) ).

fof(c_0_24,plain,
    ! [X6,X7,X9] :
      ( ( ilf_type(esk1_2(X6,X7),set_type)
        | ~ member(X6,range_of(X7))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type) )
      & ( member(ordered_pair(esk1_2(X6,X7),X6),X7)
        | ~ member(X6,range_of(X7))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type) )
      & ( ~ ilf_type(X9,set_type)
        | ~ member(ordered_pair(X9,X6),X7)
        | member(X6,range_of(X7))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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_25,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1)
    | ~ ilf_type(X1,set_type) ),
    inference(cn,[status(thm)],[c_0_18]) ).

cnf(c_0_26,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_19,c_0_16]),c_0_16])]) ).

cnf(c_0_27,negated_conjecture,
    ilf_type(esk14_0,subset_type(cross_product(esk13_0,esk12_0))),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,plain,
    ( range(X1,X2,X3) = range_of(X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_29,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[p8]) ).

fof(c_0_30,plain,
    ! [X36,X37] :
      ( ( ~ empty(X36)
        | ~ ilf_type(X37,set_type)
        | ~ member(X37,X36)
        | ~ ilf_type(X36,set_type) )
      & ( ilf_type(esk4_1(X36),set_type)
        | empty(X36)
        | ~ ilf_type(X36,set_type) )
      & ( member(esk4_1(X36),X36)
        | empty(X36)
        | ~ ilf_type(X36,set_type) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])])]) ).

fof(c_0_31,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ( member(X15,X13)
        | ~ member(ordered_pair(X15,X16),X17)
        | ~ ilf_type(X17,relation_type(X13,X14))
        | ~ ilf_type(X16,set_type)
        | ~ ilf_type(X15,set_type)
        | ~ ilf_type(X14,set_type)
        | ~ ilf_type(X13,set_type) )
      & ( member(X16,X14)
        | ~ member(ordered_pair(X15,X16),X17)
        | ~ ilf_type(X17,relation_type(X13,X14))
        | ~ ilf_type(X16,set_type)
        | ~ ilf_type(X15,set_type)
        | ~ ilf_type(X14,set_type)
        | ~ ilf_type(X13,set_type) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])]) ).

cnf(c_0_32,plain,
    ( member(ordered_pair(esk1_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_24]) ).

cnf(c_0_33,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_16])]) ).

cnf(c_0_34,negated_conjecture,
    relation_like(esk14_0),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_35,plain,
    ( range(X1,X2,X3) = range_of(X3)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_16]),c_0_16])]) ).

fof(c_0_36,plain,
    ! [X32,X33] :
      ( ( ~ ilf_type(X32,member_type(X33))
        | member(X32,X33)
        | empty(X33)
        | ~ ilf_type(X33,set_type)
        | ~ ilf_type(X32,set_type) )
      & ( ~ member(X32,X33)
        | ilf_type(X32,member_type(X33))
        | empty(X33)
        | ~ ilf_type(X33,set_type)
        | ~ ilf_type(X32,set_type) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])]) ).

cnf(c_0_37,plain,
    ( ~ empty(X1)
    | ~ ilf_type(X2,set_type)
    | ~ member(X2,X1)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_38,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_31]) ).

cnf(c_0_39,plain,
    ( member(ordered_pair(esk1_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_32,c_0_16])]) ).

cnf(c_0_40,negated_conjecture,
    ilf_type(esk14_0,binary_relation_type),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_41,negated_conjecture,
    ( member(ordered_pair(esk16_0,esk15_0),esk14_0)
    | member(esk15_0,range(esk13_0,esk12_0,esk14_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_42,negated_conjecture,
    range(esk13_0,esk12_0,esk14_0) = range_of(esk14_0),
    inference(spm,[status(thm)],[c_0_35,c_0_21]) ).

cnf(c_0_43,plain,
    ( ilf_type(X1,member_type(X2))
    | empty(X2)
    | ~ member(X1,X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_44,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_16]),c_0_16])]) ).

cnf(c_0_45,negated_conjecture,
    ( ilf_type(esk16_0,member_type(esk13_0))
    | member(esk15_0,range(esk13_0,esk12_0,esk14_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_46,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_38,c_0_16]),c_0_16]),c_0_16]),c_0_16])]) ).

cnf(c_0_47,negated_conjecture,
    ( member(ordered_pair(esk1_2(X1,esk14_0),X1),esk14_0)
    | ~ member(X1,range_of(esk14_0)) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_48,negated_conjecture,
    ( member(ordered_pair(esk16_0,esk15_0),esk14_0)
    | member(esk15_0,range_of(esk14_0)) ),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_49,plain,
    ( member(X1,X2)
    | empty(X2)
    | ~ ilf_type(X1,member_type(X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_50,plain,
    ( ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_16]),c_0_16])]),c_0_44]) ).

cnf(c_0_51,negated_conjecture,
    ( ilf_type(esk16_0,member_type(esk13_0))
    | ~ empty(range(esk13_0,esk12_0,esk14_0)) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_52,negated_conjecture,
    ( ~ member(esk15_0,range(esk13_0,esk12_0,esk14_0))
    | ~ ilf_type(X1,member_type(esk13_0))
    | ~ member(ordered_pair(X1,esk15_0),esk14_0) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_53,negated_conjecture,
    ( member(X1,esk13_0)
    | ~ member(ordered_pair(X1,X2),esk14_0) ),
    inference(spm,[status(thm)],[c_0_46,c_0_21]) ).

cnf(c_0_54,negated_conjecture,
    ( member(ordered_pair(esk1_2(esk15_0,esk14_0),esk15_0),esk14_0)
    | member(ordered_pair(esk16_0,esk15_0),esk14_0) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_55,plain,
    ( empty(X1)
    | member(X2,X1)
    | ~ ilf_type(X2,member_type(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_16]),c_0_16])]) ).

cnf(c_0_56,negated_conjecture,
    ( ilf_type(esk15_0,member_type(range(esk13_0,esk12_0,esk14_0)))
    | ilf_type(esk16_0,member_type(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_50,c_0_45]) ).

cnf(c_0_57,negated_conjecture,
    ( ilf_type(esk16_0,member_type(esk13_0))
    | ~ empty(range_of(esk14_0)) ),
    inference(rw,[status(thm)],[c_0_51,c_0_42]) ).

cnf(c_0_58,plain,
    ( member(X2,range_of(X3))
    | ~ ilf_type(X1,set_type)
    | ~ member(ordered_pair(X1,X2),X3)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_59,negated_conjecture,
    ( ~ member(ordered_pair(X1,esk15_0),esk14_0)
    | ~ member(esk15_0,range_of(esk14_0))
    | ~ ilf_type(X1,member_type(esk13_0)) ),
    inference(rw,[status(thm)],[c_0_52,c_0_42]) ).

cnf(c_0_60,negated_conjecture,
    ( member(ordered_pair(esk16_0,esk15_0),esk14_0)
    | member(esk1_2(esk15_0,esk14_0),esk13_0) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_61,negated_conjecture,
    ( member(esk15_0,range_of(esk14_0))
    | ilf_type(esk16_0,member_type(esk13_0)) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_42]),c_0_42]),c_0_57]) ).

cnf(c_0_62,plain,
    ( member(X1,range_of(X2))
    | ~ member(ordered_pair(X3,X1),X2)
    | ~ ilf_type(X2,binary_relation_type) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_16]),c_0_16])]) ).

cnf(c_0_63,negated_conjecture,
    ( member(ordered_pair(esk16_0,esk15_0),esk14_0)
    | ~ member(ordered_pair(X1,esk15_0),esk14_0)
    | ~ ilf_type(X1,member_type(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_48]) ).

cnf(c_0_64,negated_conjecture,
    ( member(ordered_pair(esk16_0,esk15_0),esk14_0)
    | ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_50,c_0_60]) ).

cnf(c_0_65,negated_conjecture,
    ( member(ordered_pair(esk1_2(esk15_0,esk14_0),esk15_0),esk14_0)
    | ilf_type(esk16_0,member_type(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_61]) ).

cnf(c_0_66,negated_conjecture,
    ( member(X1,range_of(esk14_0))
    | ~ member(ordered_pair(X2,X1),esk14_0) ),
    inference(spm,[status(thm)],[c_0_62,c_0_40]) ).

cnf(c_0_67,negated_conjecture,
    member(ordered_pair(esk16_0,esk15_0),esk14_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_54]) ).

cnf(c_0_68,negated_conjecture,
    ( member(esk1_2(esk15_0,esk14_0),esk13_0)
    | ilf_type(esk16_0,member_type(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_53,c_0_65]) ).

cnf(c_0_69,negated_conjecture,
    member(esk15_0,range_of(esk14_0)),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_70,negated_conjecture,
    ( ilf_type(esk16_0,member_type(esk13_0))
    | ~ member(ordered_pair(X1,esk15_0),esk14_0)
    | ~ ilf_type(X1,member_type(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_61]) ).

cnf(c_0_71,negated_conjecture,
    ( ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0))
    | ilf_type(esk16_0,member_type(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_50,c_0_68]) ).

cnf(c_0_72,negated_conjecture,
    ( ~ member(ordered_pair(X1,esk15_0),esk14_0)
    | ~ ilf_type(X1,member_type(esk13_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_69])]) ).

cnf(c_0_73,negated_conjecture,
    ilf_type(esk16_0,member_type(esk13_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_65]) ).

cnf(c_0_74,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_67])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : SET681+3 : TPTP v8.2.0. Released v2.2.0.
% 0.08/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 12:39:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  Running first-order model finding
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.53  # Version: 3.1.0
% 0.53/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.53/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.53/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.53/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.53/0.53  # Starting sh5l with 300s (1) cores
% 0.53/0.53  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 24168 completed with status 0
% 0.53/0.53  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.53/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.53/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.53/0.53  # No SInE strategy applied
% 0.53/0.53  # Search class: FGHSF-FFMM31-SFFFFFNN
% 0.53/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.53/0.53  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 811s (1) cores
% 0.53/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.53/0.53  # Starting new_bool_3 with 136s (1) cores
% 0.53/0.53  # Starting new_bool_1 with 136s (1) cores
% 0.53/0.53  # Starting U----_212g_01_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.53/0.53  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 24175 completed with status 0
% 0.53/0.53  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.53/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.53/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.53/0.53  # No SInE strategy applied
% 0.53/0.53  # Search class: FGHSF-FFMM31-SFFFFFNN
% 0.53/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.53/0.53  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 811s (1) cores
% 0.53/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.53/0.53  # Preprocessing time       : 0.002 s
% 0.53/0.53  # Presaturation interreduction done
% 0.53/0.53  
% 0.53/0.53  # Proof found!
% 0.53/0.53  # SZS status Theorem
% 0.53/0.53  # SZS output start CNFRefutation
% See solution above
% 0.53/0.53  # Parsed axioms                        : 32
% 0.53/0.53  # Removed by relevancy pruning/SinE    : 0
% 0.53/0.53  # Initial clauses                      : 65
% 0.53/0.53  # Removed in clause preprocessing      : 3
% 0.53/0.53  # Initial clauses in saturation        : 62
% 0.53/0.53  # Processed clauses                    : 328
% 0.53/0.53  # ...of these trivial                  : 18
% 0.53/0.53  # ...subsumed                          : 74
% 0.53/0.53  # ...remaining for further processing  : 236
% 0.53/0.53  # Other redundant clauses eliminated   : 6
% 0.53/0.53  # Clauses deleted for lack of memory   : 0
% 0.53/0.53  # Backward-subsumed                    : 2
% 0.53/0.53  # Backward-rewritten                   : 34
% 0.53/0.53  # Generated clauses                    : 969
% 0.53/0.53  # ...of the previous two non-redundant : 889
% 0.53/0.53  # ...aggressively subsumed             : 0
% 0.53/0.53  # Contextual simplify-reflections      : 5
% 0.53/0.53  # Paramodulations                      : 949
% 0.53/0.53  # Factorizations                       : 2
% 0.53/0.53  # NegExts                              : 0
% 0.53/0.53  # Equation resolutions                 : 6
% 0.53/0.53  # Disequality decompositions           : 0
% 0.53/0.53  # Total rewrite steps                  : 216
% 0.53/0.53  # ...of those cached                   : 153
% 0.53/0.53  # Propositional unsat checks           : 0
% 0.53/0.53  #    Propositional check models        : 0
% 0.53/0.53  #    Propositional check unsatisfiable : 0
% 0.53/0.53  #    Propositional clauses             : 0
% 0.53/0.53  #    Propositional clauses after purity: 0
% 0.53/0.53  #    Propositional unsat core size     : 0
% 0.53/0.53  #    Propositional preprocessing time  : 0.000
% 0.53/0.53  #    Propositional encoding time       : 0.000
% 0.53/0.53  #    Propositional solver time         : 0.000
% 0.53/0.53  #    Success case prop preproc time    : 0.000
% 0.53/0.53  #    Success case prop encoding time   : 0.000
% 0.53/0.53  #    Success case prop solver time     : 0.000
% 0.53/0.53  # Current number of processed clauses  : 142
% 0.53/0.53  #    Positive orientable unit clauses  : 58
% 0.53/0.53  #    Positive unorientable unit clauses: 1
% 0.53/0.53  #    Negative unit clauses             : 7
% 0.53/0.53  #    Non-unit-clauses                  : 76
% 0.53/0.53  # Current number of unprocessed clauses: 656
% 0.53/0.53  # ...number of literals in the above   : 2069
% 0.53/0.53  # Current number of archived formulas  : 0
% 0.53/0.53  # Current number of archived clauses   : 92
% 0.53/0.53  # Clause-clause subsumption calls (NU) : 1657
% 0.53/0.53  # Rec. Clause-clause subsumption calls : 1460
% 0.53/0.53  # Non-unit clause-clause subsumptions  : 48
% 0.53/0.53  # Unit Clause-clause subsumption calls : 332
% 0.53/0.53  # Rewrite failures with RHS unbound    : 0
% 0.53/0.53  # BW rewrite match attempts            : 16
% 0.53/0.53  # BW rewrite match successes           : 6
% 0.53/0.53  # Condensation attempts                : 0
% 0.53/0.53  # Condensation successes               : 0
% 0.53/0.53  # Termbank termtop insertions          : 15723
% 0.53/0.53  # Search garbage collected termcells   : 1437
% 0.53/0.53  
% 0.53/0.53  # -------------------------------------------------
% 0.53/0.53  # User time                : 0.033 s
% 0.53/0.53  # System time              : 0.004 s
% 0.53/0.53  # Total time               : 0.037 s
% 0.53/0.53  # Maximum resident set size: 1908 pages
% 0.53/0.53  
% 0.53/0.53  # -------------------------------------------------
% 0.53/0.53  # User time                : 0.127 s
% 0.53/0.53  # System time              : 0.016 s
% 0.53/0.53  # Total time               : 0.143 s
% 0.53/0.53  # Maximum resident set size: 1752 pages
% 0.53/0.53  % E---3.1 exiting
%------------------------------------------------------------------------------