TSTP Solution File: SET669+3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %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 : Sat May  4 09:19:51 EDT 2024

% Result   : Theorem 0.22s 0.57s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   63 (  13 unt;   0 def)
%            Number of atoms       :  255 (  15 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  321 ( 129   ~; 127   |;  22   &)
%                                         (   5 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   4 con; 0-3 aty)
%            Number of variables   :  123 (   2 sgn  57   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(p22,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/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p22) ).

fof(p21,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ~ empty(power_set(X1))
        & ilf_type(power_set(X1),set_type) ) ),
    file('/export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p21) ).

fof(p20,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/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p20) ).

fof(p32,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p32) ).

fof(p30,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/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p30) ).

fof(prove_relset_1_32,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => ( subset(identity_relation_of(X2),X3)
               => ( subset(X2,domain(X1,X2,X3))
                  & X2 = range(X1,X2,X3) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',prove_relset_1_32) ).

fof(p16,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ilf_type(X2,subset_type(X1))
          <=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p16) ).

fof(p31,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p31) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X1,X2))
                 => ( subset(identity_relation_of(X3),X4)
                   => ( subset(X3,domain(X1,X2,X4))
                      & subset(X3,range(X1,X2,X4)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p2) ).

fof(p7,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/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p7) ).

fof(p1,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ( subset(X1,X2)
              & subset(X2,X1) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p',p1) ).

fof(c_0_11,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)],[p22]) ).

fof(c_0_12,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ~ empty(power_set(X1))
        & ilf_type(power_set(X1),set_type) ) ),
    inference(fof_simplification,[status(thm)],[p21]) ).

fof(c_0_13,plain,
    ! [X48,X49,X50] :
      ( ( ~ member(X48,power_set(X49))
        | ~ ilf_type(X50,set_type)
        | ~ member(X50,X48)
        | member(X50,X49)
        | ~ ilf_type(X49,set_type)
        | ~ ilf_type(X48,set_type) )
      & ( ilf_type(esk7_2(X48,X49),set_type)
        | member(X48,power_set(X49))
        | ~ ilf_type(X49,set_type)
        | ~ ilf_type(X48,set_type) )
      & ( member(esk7_2(X48,X49),X48)
        | member(X48,power_set(X49))
        | ~ ilf_type(X49,set_type)
        | ~ ilf_type(X48,set_type) )
      & ( ~ member(esk7_2(X48,X49),X49)
        | member(X48,power_set(X49))
        | ~ ilf_type(X49,set_type)
        | ~ ilf_type(X48,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)],[p20])])])])])]) ).

fof(c_0_14,plain,
    ! [X83] : ilf_type(X83,set_type),
    inference(variable_rename,[status(thm)],[p32]) ).

fof(c_0_15,plain,
    ! [X53,X54] :
      ( ( ~ ilf_type(X53,member_type(X54))
        | member(X53,X54)
        | empty(X54)
        | ~ ilf_type(X54,set_type)
        | ~ ilf_type(X53,set_type) )
      & ( ~ member(X53,X54)
        | ilf_type(X53,member_type(X54))
        | empty(X54)
        | ~ ilf_type(X54,set_type)
        | ~ ilf_type(X53,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_11])])])])]) ).

fof(c_0_16,plain,
    ! [X52] :
      ( ( ~ empty(power_set(X52))
        | ~ ilf_type(X52,set_type) )
      & ( ilf_type(power_set(X52),set_type)
        | ~ ilf_type(X52,set_type) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

fof(c_0_17,plain,
    ! [X77,X78,X79] :
      ( ~ ilf_type(X77,set_type)
      | ~ ilf_type(X78,set_type)
      | ~ ilf_type(X79,relation_type(X77,X78))
      | range(X77,X78,X79) = range_of(X79) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p30])])])]) ).

fof(c_0_18,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,set_type)
           => ! [X3] :
                ( ilf_type(X3,relation_type(X1,X2))
               => ( subset(identity_relation_of(X2),X3)
                 => ( subset(X2,domain(X1,X2,X3))
                    & X2 = range(X1,X2,X3) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_32]) ).

cnf(c_0_19,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_13]) ).

cnf(c_0_20,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,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_15]) ).

cnf(c_0_22,plain,
    ( ~ empty(power_set(X1))
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_23,plain,
    ! [X42,X43] :
      ( ( ~ ilf_type(X43,subset_type(X42))
        | ilf_type(X43,member_type(power_set(X42)))
        | ~ ilf_type(X43,set_type)
        | ~ ilf_type(X42,set_type) )
      & ( ~ ilf_type(X43,member_type(power_set(X42)))
        | ilf_type(X43,subset_type(X42))
        | ~ ilf_type(X43,set_type)
        | ~ ilf_type(X42,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)],[p16])])])])]) ).

fof(c_0_24,plain,
    ! [X80,X81,X82] :
      ( ~ ilf_type(X80,set_type)
      | ~ ilf_type(X81,set_type)
      | ~ ilf_type(X82,relation_type(X80,X81))
      | ilf_type(range(X80,X81,X82),subset_type(X81)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p31])])])]) ).

cnf(c_0_25,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_17]) ).

fof(c_0_26,negated_conjecture,
    ( ilf_type(esk13_0,set_type)
    & ilf_type(esk14_0,set_type)
    & ilf_type(esk15_0,relation_type(esk13_0,esk14_0))
    & subset(identity_relation_of(esk14_0),esk15_0)
    & ( ~ subset(esk14_0,domain(esk13_0,esk14_0,esk15_0))
      | esk14_0 != range(esk13_0,esk14_0,esk15_0) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).

fof(c_0_27,plain,
    ! [X7,X8,X9,X10] :
      ( ( subset(X9,domain(X7,X8,X10))
        | ~ subset(identity_relation_of(X9),X10)
        | ~ ilf_type(X10,relation_type(X7,X8))
        | ~ ilf_type(X9,set_type)
        | ~ ilf_type(X8,set_type)
        | ~ ilf_type(X7,set_type) )
      & ( subset(X9,range(X7,X8,X10))
        | ~ subset(identity_relation_of(X9),X10)
        | ~ ilf_type(X10,relation_type(X7,X8))
        | ~ ilf_type(X9,set_type)
        | ~ ilf_type(X8,set_type)
        | ~ ilf_type(X7,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)],[p2])])])])]) ).

cnf(c_0_28,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_19,c_0_20]),c_0_20]),c_0_20])]) ).

cnf(c_0_29,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_21,c_0_20]),c_0_20])]) ).

cnf(c_0_30,plain,
    ~ empty(power_set(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_20])]) ).

cnf(c_0_31,plain,
    ( ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X1,subset_type(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_32,plain,
    ( ilf_type(range(X1,X2,X3),subset_type(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,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_25,c_0_20]),c_0_20])]) ).

cnf(c_0_34,negated_conjecture,
    ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_35,plain,
    ( subset(X1,range(X2,X3,X4))
    | ~ subset(identity_relation_of(X1),X4)
    | ~ ilf_type(X4,relation_type(X2,X3))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,plain,
    ( subset(X1,domain(X2,X3,X4))
    | ~ subset(identity_relation_of(X1),X4)
    | ~ ilf_type(X4,relation_type(X2,X3))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ ilf_type(X3,member_type(power_set(X2))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_38,plain,
    ( ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X1,subset_type(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_20]),c_0_20])]) ).

cnf(c_0_39,plain,
    ( ilf_type(range(X1,X2,X3),subset_type(X2))
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_20]),c_0_20])]) ).

cnf(c_0_40,negated_conjecture,
    range(esk13_0,esk14_0,esk15_0) = range_of(esk15_0),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

fof(c_0_41,plain,
    ! [X22,X23,X24] :
      ( ( ~ subset(X22,X23)
        | ~ ilf_type(X24,set_type)
        | ~ member(X24,X22)
        | member(X24,X23)
        | ~ ilf_type(X23,set_type)
        | ~ ilf_type(X22,set_type) )
      & ( ilf_type(esk2_2(X22,X23),set_type)
        | subset(X22,X23)
        | ~ ilf_type(X23,set_type)
        | ~ ilf_type(X22,set_type) )
      & ( member(esk2_2(X22,X23),X22)
        | subset(X22,X23)
        | ~ ilf_type(X23,set_type)
        | ~ ilf_type(X22,set_type) )
      & ( ~ member(esk2_2(X22,X23),X23)
        | subset(X22,X23)
        | ~ ilf_type(X23,set_type)
        | ~ ilf_type(X22,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)],[p7])])])])])]) ).

fof(c_0_42,plain,
    ! [X5,X6] :
      ( ~ ilf_type(X5,set_type)
      | ~ ilf_type(X6,set_type)
      | ~ subset(X5,X6)
      | ~ subset(X6,X5)
      | X5 = X6 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).

cnf(c_0_43,plain,
    ( subset(X1,range(X2,X3,X4))
    | ~ subset(identity_relation_of(X1),X4)
    | ~ ilf_type(X4,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_20]),c_0_20]),c_0_20])]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ subset(esk14_0,domain(esk13_0,esk14_0,esk15_0))
    | esk14_0 != range(esk13_0,esk14_0,esk15_0) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_45,plain,
    ( subset(X1,domain(X2,X3,X4))
    | ~ subset(identity_relation_of(X1),X4)
    | ~ ilf_type(X4,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_20]),c_0_20]),c_0_20])]) ).

cnf(c_0_46,negated_conjecture,
    subset(identity_relation_of(esk14_0),esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_47,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ ilf_type(X3,subset_type(X2)) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_48,negated_conjecture,
    ilf_type(range_of(esk15_0),subset_type(esk14_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_34])]) ).

cnf(c_0_49,plain,
    ( member(esk2_2(X1,X2),X1)
    | subset(X1,X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_50,plain,
    ( X1 = X2
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_51,negated_conjecture,
    ( subset(X1,range_of(esk15_0))
    | ~ subset(identity_relation_of(X1),esk15_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_34])]) ).

cnf(c_0_52,negated_conjecture,
    range(esk13_0,esk14_0,esk15_0) != esk14_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_34])]) ).

cnf(c_0_53,plain,
    ( subset(X1,X2)
    | ~ member(esk2_2(X1,X2),X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_54,negated_conjecture,
    ( member(X1,esk14_0)
    | ~ member(X1,range_of(esk15_0)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_55,plain,
    ( member(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_20]),c_0_20])]) ).

cnf(c_0_56,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_20]),c_0_20])]) ).

cnf(c_0_57,negated_conjecture,
    subset(esk14_0,range_of(esk15_0)),
    inference(spm,[status(thm)],[c_0_51,c_0_46]) ).

cnf(c_0_58,negated_conjecture,
    range_of(esk15_0) != esk14_0,
    inference(rw,[status(thm)],[c_0_52,c_0_40]) ).

cnf(c_0_59,plain,
    ( subset(X1,X2)
    | ~ member(esk2_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_20]),c_0_20])]) ).

cnf(c_0_60,negated_conjecture,
    ( member(esk2_2(range_of(esk15_0),X1),esk14_0)
    | subset(range_of(esk15_0),X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_61,negated_conjecture,
    ~ subset(range_of(esk15_0),esk14_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).

cnf(c_0_62,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n025.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
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 10:31:13 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.22/0.49  Running first-order theorem proving
% 0.22/0.49  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.BB3qG8sqTQ/E---3.1_26053.p
% 0.22/0.57  # Version: 3.1.0
% 0.22/0.57  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.57  # Starting new_bool_1 with 300s (1) cores
% 0.22/0.57  # Starting sh5l with 300s (1) cores
% 0.22/0.57  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 26136 completed with status 0
% 0.22/0.57  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.22/0.57  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57  # No SInE strategy applied
% 0.22/0.57  # Search class: FGHSF-FFMS31-SFFFFFNN
% 0.22/0.57  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.57  # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 737s (1) cores
% 0.22/0.57  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/0.57  # Starting new_bool_3 with 189s (1) cores
% 0.22/0.57  # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.22/0.57  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/0.57  # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 26145 completed with status 0
% 0.22/0.57  # Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 0.22/0.57  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57  # No SInE strategy applied
% 0.22/0.57  # Search class: FGHSF-FFMS31-SFFFFFNN
% 0.22/0.57  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.57  # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 737s (1) cores
% 0.22/0.57  # Preprocessing time       : 0.002 s
% 0.22/0.57  
% 0.22/0.57  # Proof found!
% 0.22/0.57  # SZS status Theorem
% 0.22/0.57  # SZS output start CNFRefutation
% See solution above
% 0.22/0.57  # Parsed axioms                        : 33
% 0.22/0.57  # Removed by relevancy pruning/SinE    : 0
% 0.22/0.57  # Initial clauses                      : 65
% 0.22/0.57  # Removed in clause preprocessing      : 1
% 0.22/0.57  # Initial clauses in saturation        : 64
% 0.22/0.57  # Processed clauses                    : 661
% 0.22/0.57  # ...of these trivial                  : 15
% 0.22/0.57  # ...subsumed                          : 272
% 0.22/0.57  # ...remaining for further processing  : 374
% 0.22/0.57  # Other redundant clauses eliminated   : 4
% 0.22/0.57  # Clauses deleted for lack of memory   : 0
% 0.22/0.57  # Backward-subsumed                    : 19
% 0.22/0.57  # Backward-rewritten                   : 4
% 0.22/0.57  # Generated clauses                    : 1460
% 0.22/0.57  # ...of the previous two non-redundant : 1358
% 0.22/0.57  # ...aggressively subsumed             : 0
% 0.22/0.57  # Contextual simplify-reflections      : 10
% 0.22/0.57  # Paramodulations                      : 1456
% 0.22/0.57  # Factorizations                       : 0
% 0.22/0.57  # NegExts                              : 0
% 0.22/0.57  # Equation resolutions                 : 4
% 0.22/0.57  # Disequality decompositions           : 0
% 0.22/0.57  # Total rewrite steps                  : 244
% 0.22/0.57  # ...of those cached                   : 172
% 0.22/0.57  # Propositional unsat checks           : 0
% 0.22/0.57  #    Propositional check models        : 0
% 0.22/0.57  #    Propositional check unsatisfiable : 0
% 0.22/0.57  #    Propositional clauses             : 0
% 0.22/0.57  #    Propositional clauses after purity: 0
% 0.22/0.57  #    Propositional unsat core size     : 0
% 0.22/0.57  #    Propositional preprocessing time  : 0.000
% 0.22/0.57  #    Propositional encoding time       : 0.000
% 0.22/0.57  #    Propositional solver time         : 0.000
% 0.22/0.57  #    Success case prop preproc time    : 0.000
% 0.22/0.57  #    Success case prop encoding time   : 0.000
% 0.22/0.57  #    Success case prop solver time     : 0.000
% 0.22/0.57  # Current number of processed clauses  : 348
% 0.22/0.57  #    Positive orientable unit clauses  : 73
% 0.22/0.57  #    Positive unorientable unit clauses: 0
% 0.22/0.57  #    Negative unit clauses             : 7
% 0.22/0.57  #    Non-unit-clauses                  : 268
% 0.22/0.57  # Current number of unprocessed clauses: 746
% 0.22/0.57  # ...number of literals in the above   : 2879
% 0.22/0.57  # Current number of archived formulas  : 0
% 0.22/0.57  # Current number of archived clauses   : 23
% 0.22/0.57  # Clause-clause subsumption calls (NU) : 7789
% 0.22/0.57  # Rec. Clause-clause subsumption calls : 5255
% 0.22/0.57  # Non-unit clause-clause subsumptions  : 229
% 0.22/0.57  # Unit Clause-clause subsumption calls : 736
% 0.22/0.57  # Rewrite failures with RHS unbound    : 0
% 0.22/0.57  # BW rewrite match attempts            : 35
% 0.22/0.57  # BW rewrite match successes           : 4
% 0.22/0.57  # Condensation attempts                : 0
% 0.22/0.57  # Condensation successes               : 0
% 0.22/0.57  # Termbank termtop insertions          : 25720
% 0.22/0.57  # Search garbage collected termcells   : 1370
% 0.22/0.57  
% 0.22/0.57  # -------------------------------------------------
% 0.22/0.57  # User time                : 0.056 s
% 0.22/0.57  # System time              : 0.005 s
% 0.22/0.57  # Total time               : 0.061 s
% 0.22/0.57  # Maximum resident set size: 1904 pages
% 0.22/0.57  
% 0.22/0.57  # -------------------------------------------------
% 0.22/0.57  # User time                : 0.253 s
% 0.22/0.57  # System time              : 0.025 s
% 0.22/0.57  # Total time               : 0.278 s
% 0.22/0.57  # Maximum resident set size: 1748 pages
% 0.22/0.57  % E---3.1 exiting
% 0.22/0.57  % E exiting
%------------------------------------------------------------------------------