TSTP Solution File: NUM409+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM409+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n042.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan  8 15:21:15 EST 2018

% Result   : Theorem 0.07s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  102 (  32 unt;   0 def)
%            Number of atoms       :  320 (  14 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  376 ( 158   ~; 165   |;  41   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   18 (  16 usr;   3 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   2 con; 0-3 aty)
%            Number of variables   :  170 (  23 sgn  83   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t5_subset) ).

fof(10,axiom,
    ! [X1,X2] :
      ( transfinite_sequence_of(X2,X1)
     => ( relation(X2)
        & function(X2)
        & transfinite_sequence(X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',dt_m1_ordinal1) ).

fof(12,axiom,
    ( relation(empty_set)
    & relation_empty_yielding(empty_set)
    & function(empty_set)
    & one_to_one(empty_set)
    & empty(empty_set)
    & epsilon_transitive(empty_set)
    & epsilon_connected(empty_set)
    & ordinal(empty_set) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',fc2_ordinal1) ).

fof(20,axiom,
    ! [X1,X2] : equal(unordered_pair(X1,X2),unordered_pair(X2,X1)),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',commutativity_k2_tarski) ).

fof(21,axiom,
    ! [X1] :
    ? [X2] : transfinite_sequence_of(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',existence_m1_ordinal1) ).

fof(30,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( equal(X2,relation_dom(X1))
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',d4_relat_1) ).

fof(33,axiom,
    ! [X1] :
      ( ( ~ empty(X1)
        & relation(X1) )
     => ~ empty(relation_rng(X1)) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',fc6_relat_1) ).

fof(34,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t3_subset) ).

fof(36,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2)
        & transfinite_sequence(X2) )
     => ( transfinite_sequence_of(X2,X1)
      <=> subset(relation_rng(X2),X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',d8_ordinal1) ).

fof(38,axiom,
    ! [X1,X2] : equal(ordered_pair(X1,X2),unordered_pair(unordered_pair(X1,X2),singleton(X1))),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',d5_tarski) ).

fof(39,axiom,
    ! [X1] :
      ( empty(X1)
     => equal(X1,empty_set) ),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t6_boole) ).

fof(44,conjecture,
    ! [X1] : transfinite_sequence_of(empty_set,X1),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t45_ordinal1) ).

fof(51,axiom,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t2_xboole_1) ).

fof(52,negated_conjecture,
    ~ ! [X1] : transfinite_sequence_of(empty_set,X1),
    inference(assume_negation,[status(cth)],[44]) ).

fof(58,plain,
    ! [X1] :
      ( ( ~ empty(X1)
        & relation(X1) )
     => ~ empty(relation_rng(X1)) ),
    inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).

fof(73,plain,
    ! [X1,X2,X3] :
      ( ~ in(X1,X2)
      | ~ element(X2,powerset(X3))
      | ~ empty(X3) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(74,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | ~ empty(X6) ),
    inference(variable_rename,[status(thm)],[73]) ).

cnf(75,plain,
    ( ~ empty(X1)
    | ~ element(X2,powerset(X1))
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(100,plain,
    ! [X1,X2] :
      ( ~ transfinite_sequence_of(X2,X1)
      | ( relation(X2)
        & function(X2)
        & transfinite_sequence(X2) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(101,plain,
    ! [X3,X4] :
      ( ~ transfinite_sequence_of(X4,X3)
      | ( relation(X4)
        & function(X4)
        & transfinite_sequence(X4) ) ),
    inference(variable_rename,[status(thm)],[100]) ).

fof(102,plain,
    ! [X3,X4] :
      ( ( relation(X4)
        | ~ transfinite_sequence_of(X4,X3) )
      & ( function(X4)
        | ~ transfinite_sequence_of(X4,X3) )
      & ( transfinite_sequence(X4)
        | ~ transfinite_sequence_of(X4,X3) ) ),
    inference(distribute,[status(thm)],[101]) ).

cnf(103,plain,
    ( transfinite_sequence(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[102]) ).

cnf(104,plain,
    ( function(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[102]) ).

cnf(105,plain,
    ( relation(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[102]) ).

cnf(112,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(116,plain,
    relation(empty_set),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(143,plain,
    ! [X3,X4] : equal(unordered_pair(X3,X4),unordered_pair(X4,X3)),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(144,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[143]) ).

fof(145,plain,
    ! [X3] :
    ? [X4] : transfinite_sequence_of(X4,X3),
    inference(variable_rename,[status(thm)],[21]) ).

fof(146,plain,
    ! [X3] : transfinite_sequence_of(esk8_1(X3),X3),
    inference(skolemize,[status(esa)],[145]) ).

cnf(147,plain,
    transfinite_sequence_of(esk8_1(X1),X1),
    inference(split_conjunct,[status(thm)],[146]) ).

fof(177,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ! [X2] :
          ( ( ~ equal(X2,relation_dom(X1))
            | ! [X3] :
                ( ( ~ in(X3,X2)
                  | ? [X4] : in(ordered_pair(X3,X4),X1) )
                & ( ! [X4] : ~ in(ordered_pair(X3,X4),X1)
                  | in(X3,X2) ) ) )
          & ( ? [X3] :
                ( ( ~ in(X3,X2)
                  | ! [X4] : ~ in(ordered_pair(X3,X4),X1) )
                & ( in(X3,X2)
                  | ? [X4] : in(ordered_pair(X3,X4),X1) ) )
            | equal(X2,relation_dom(X1)) ) ) ),
    inference(fof_nnf,[status(thm)],[30]) ).

fof(178,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ! [X6] :
          ( ( ~ equal(X6,relation_dom(X5))
            | ! [X7] :
                ( ( ~ in(X7,X6)
                  | ? [X8] : in(ordered_pair(X7,X8),X5) )
                & ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
                  | in(X7,X6) ) ) )
          & ( ? [X10] :
                ( ( ~ in(X10,X6)
                  | ! [X11] : ~ in(ordered_pair(X10,X11),X5) )
                & ( in(X10,X6)
                  | ? [X12] : in(ordered_pair(X10,X12),X5) ) )
            | equal(X6,relation_dom(X5)) ) ) ),
    inference(variable_rename,[status(thm)],[177]) ).

fof(179,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ! [X6] :
          ( ( ~ equal(X6,relation_dom(X5))
            | ! [X7] :
                ( ( ~ in(X7,X6)
                  | in(ordered_pair(X7,esk9_3(X5,X6,X7)),X5) )
                & ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
                  | in(X7,X6) ) ) )
          & ( ( ( ~ in(esk10_2(X5,X6),X6)
                | ! [X11] : ~ in(ordered_pair(esk10_2(X5,X6),X11),X5) )
              & ( in(esk10_2(X5,X6),X6)
                | in(ordered_pair(esk10_2(X5,X6),esk11_2(X5,X6)),X5) ) )
            | equal(X6,relation_dom(X5)) ) ) ),
    inference(skolemize,[status(esa)],[178]) ).

fof(180,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ( ~ in(ordered_pair(esk10_2(X5,X6),X11),X5)
              | ~ in(esk10_2(X5,X6),X6) )
            & ( in(esk10_2(X5,X6),X6)
              | in(ordered_pair(esk10_2(X5,X6),esk11_2(X5,X6)),X5) ) )
          | equal(X6,relation_dom(X5)) )
        & ( ( ( ~ in(ordered_pair(X7,X9),X5)
              | in(X7,X6) )
            & ( ~ in(X7,X6)
              | in(ordered_pair(X7,esk9_3(X5,X6,X7)),X5) ) )
          | ~ equal(X6,relation_dom(X5)) ) )
      | ~ relation(X5) ),
    inference(shift_quantors,[status(thm)],[179]) ).

fof(181,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(ordered_pair(esk10_2(X5,X6),X11),X5)
        | ~ in(esk10_2(X5,X6),X6)
        | equal(X6,relation_dom(X5))
        | ~ relation(X5) )
      & ( in(esk10_2(X5,X6),X6)
        | in(ordered_pair(esk10_2(X5,X6),esk11_2(X5,X6)),X5)
        | equal(X6,relation_dom(X5))
        | ~ relation(X5) )
      & ( ~ in(ordered_pair(X7,X9),X5)
        | in(X7,X6)
        | ~ equal(X6,relation_dom(X5))
        | ~ relation(X5) )
      & ( ~ in(X7,X6)
        | in(ordered_pair(X7,esk9_3(X5,X6,X7)),X5)
        | ~ equal(X6,relation_dom(X5))
        | ~ relation(X5) ) ),
    inference(distribute,[status(thm)],[180]) ).

cnf(184,plain,
    ( X2 = relation_dom(X1)
    | in(ordered_pair(esk10_2(X1,X2),esk11_2(X1,X2)),X1)
    | in(esk10_2(X1,X2),X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[181]) ).

fof(194,plain,
    ! [X1] :
      ( empty(X1)
      | ~ relation(X1)
      | ~ empty(relation_rng(X1)) ),
    inference(fof_nnf,[status(thm)],[58]) ).

fof(195,plain,
    ! [X2] :
      ( empty(X2)
      | ~ relation(X2)
      | ~ empty(relation_rng(X2)) ),
    inference(variable_rename,[status(thm)],[194]) ).

cnf(196,plain,
    ( empty(X1)
    | ~ empty(relation_rng(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[195]) ).

fof(197,plain,
    ! [X1,X2] :
      ( ( ~ element(X1,powerset(X2))
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | element(X1,powerset(X2)) ) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(198,plain,
    ! [X3,X4] :
      ( ( ~ element(X3,powerset(X4))
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | element(X3,powerset(X4)) ) ),
    inference(variable_rename,[status(thm)],[197]) ).

cnf(199,plain,
    ( element(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[198]) ).

fof(204,plain,
    ! [X1,X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ~ transfinite_sequence(X2)
      | ( ( ~ transfinite_sequence_of(X2,X1)
          | subset(relation_rng(X2),X1) )
        & ( ~ subset(relation_rng(X2),X1)
          | transfinite_sequence_of(X2,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[36]) ).

fof(205,plain,
    ! [X3,X4] :
      ( ~ relation(X4)
      | ~ function(X4)
      | ~ transfinite_sequence(X4)
      | ( ( ~ transfinite_sequence_of(X4,X3)
          | subset(relation_rng(X4),X3) )
        & ( ~ subset(relation_rng(X4),X3)
          | transfinite_sequence_of(X4,X3) ) ) ),
    inference(variable_rename,[status(thm)],[204]) ).

fof(206,plain,
    ! [X3,X4] :
      ( ( ~ transfinite_sequence_of(X4,X3)
        | subset(relation_rng(X4),X3)
        | ~ relation(X4)
        | ~ function(X4)
        | ~ transfinite_sequence(X4) )
      & ( ~ subset(relation_rng(X4),X3)
        | transfinite_sequence_of(X4,X3)
        | ~ relation(X4)
        | ~ function(X4)
        | ~ transfinite_sequence(X4) ) ),
    inference(distribute,[status(thm)],[205]) ).

cnf(207,plain,
    ( transfinite_sequence_of(X1,X2)
    | ~ transfinite_sequence(X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ subset(relation_rng(X1),X2) ),
    inference(split_conjunct,[status(thm)],[206]) ).

cnf(208,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence(X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[206]) ).

fof(212,plain,
    ! [X3,X4] : equal(ordered_pair(X3,X4),unordered_pair(unordered_pair(X3,X4),singleton(X3))),
    inference(variable_rename,[status(thm)],[38]) ).

cnf(213,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[212]) ).

fof(214,plain,
    ! [X1] :
      ( ~ empty(X1)
      | equal(X1,empty_set) ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(215,plain,
    ! [X2] :
      ( ~ empty(X2)
      | equal(X2,empty_set) ),
    inference(variable_rename,[status(thm)],[214]) ).

cnf(216,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[215]) ).

fof(233,negated_conjecture,
    ? [X1] : ~ transfinite_sequence_of(empty_set,X1),
    inference(fof_nnf,[status(thm)],[52]) ).

fof(234,negated_conjecture,
    ? [X2] : ~ transfinite_sequence_of(empty_set,X2),
    inference(variable_rename,[status(thm)],[233]) ).

fof(235,negated_conjecture,
    ~ transfinite_sequence_of(empty_set,esk15_0),
    inference(skolemize,[status(esa)],[234]) ).

cnf(236,negated_conjecture,
    ~ transfinite_sequence_of(empty_set,esk15_0),
    inference(split_conjunct,[status(thm)],[235]) ).

fof(262,plain,
    ! [X2] : subset(empty_set,X2),
    inference(variable_rename,[status(thm)],[51]) ).

cnf(263,plain,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[262]) ).

cnf(264,plain,
    ( relation_dom(X1) = X2
    | in(esk10_2(X1,X2),X2)
    | in(unordered_pair(unordered_pair(esk10_2(X1,X2),esk11_2(X1,X2)),singleton(esk10_2(X1,X2))),X1)
    | ~ relation(X1) ),
    inference(rw,[status(thm)],[184,213,theory(equality)]),
    [unfolding] ).

cnf(279,plain,
    relation(esk8_1(X1)),
    inference(spm,[status(thm)],[105,147,theory(equality)]) ).

cnf(280,plain,
    function(esk8_1(X1)),
    inference(spm,[status(thm)],[104,147,theory(equality)]) ).

cnf(281,plain,
    transfinite_sequence(esk8_1(X1)),
    inference(spm,[status(thm)],[103,147,theory(equality)]) ).

cnf(334,plain,
    ( ~ empty(X2)
    | ~ in(X3,X1)
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[75,199,theory(equality)]) ).

cnf(340,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence_of(X1,X2)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[208,103]) ).

cnf(341,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence_of(X1,X2)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[340,104]) ).

cnf(342,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(csr,[status(thm)],[341,105]) ).

cnf(361,plain,
    ( relation_dom(X1) = X2
    | in(esk10_2(X1,X2),X2)
    | in(unordered_pair(singleton(esk10_2(X1,X2)),unordered_pair(esk10_2(X1,X2),esk11_2(X1,X2))),X1)
    | ~ relation(X1) ),
    inference(rw,[status(thm)],[264,144,theory(equality)]) ).

cnf(366,plain,
    ( ~ empty(X1)
    | ~ in(X2,empty_set) ),
    inference(spm,[status(thm)],[334,263,theory(equality)]) ).

cnf(368,plain,
    ( ~ empty(X2)
    | ~ in(X3,relation_rng(X1))
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(spm,[status(thm)],[334,342,theory(equality)]) ).

fof(369,plain,
    ( ~ epred1_0
  <=> ! [X1] : ~ empty(X1) ),
    introduced(definition),
    [split] ).

cnf(370,plain,
    ( epred1_0
    | ~ empty(X1) ),
    inference(split_equiv,[status(thm)],[369]) ).

fof(371,plain,
    ( ~ epred2_0
  <=> ! [X2] : ~ in(X2,empty_set) ),
    introduced(definition),
    [split] ).

cnf(372,plain,
    ( epred2_0
    | ~ in(X2,empty_set) ),
    inference(split_equiv,[status(thm)],[371]) ).

cnf(373,plain,
    ( ~ epred2_0
    | ~ epred1_0 ),
    inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[366,369,theory(equality)]),371,theory(equality)]),
    [split] ).

cnf(400,plain,
    epred1_0,
    inference(spm,[status(thm)],[370,112,theory(equality)]) ).

cnf(404,plain,
    ( ~ epred2_0
    | $false ),
    inference(rw,[status(thm)],[373,400,theory(equality)]) ).

cnf(405,plain,
    ~ epred2_0,
    inference(cn,[status(thm)],[404,theory(equality)]) ).

cnf(406,plain,
    ~ in(X2,empty_set),
    inference(sr,[status(thm)],[372,405,theory(equality)]) ).

cnf(408,plain,
    ( relation_dom(empty_set) = X1
    | in(esk10_2(empty_set,X1),X1)
    | ~ relation(empty_set) ),
    inference(spm,[status(thm)],[406,361,theory(equality)]) ).

cnf(411,plain,
    ( relation_dom(empty_set) = X1
    | in(esk10_2(empty_set,X1),X1)
    | $false ),
    inference(rw,[status(thm)],[408,116,theory(equality)]) ).

cnf(412,plain,
    ( relation_dom(empty_set) = X1
    | in(esk10_2(empty_set,X1),X1) ),
    inference(cn,[status(thm)],[411,theory(equality)]) ).

cnf(425,plain,
    relation_dom(empty_set) = empty_set,
    inference(spm,[status(thm)],[406,412,theory(equality)]) ).

cnf(434,plain,
    ( empty_set = X1
    | in(esk10_2(empty_set,X1),X1) ),
    inference(rw,[status(thm)],[412,425,theory(equality)]) ).

cnf(677,plain,
    ( empty_set = relation_rng(X1)
    | ~ transfinite_sequence_of(X1,X2)
    | ~ empty(X2) ),
    inference(spm,[status(thm)],[368,434,theory(equality)]) ).

cnf(681,plain,
    ( relation_rng(esk8_1(X1)) = empty_set
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[677,147,theory(equality)]) ).

cnf(685,plain,
    ( empty(esk8_1(X1))
    | ~ relation(esk8_1(X1))
    | ~ empty(empty_set)
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[196,681,theory(equality)]) ).

cnf(688,plain,
    ( transfinite_sequence_of(esk8_1(X1),X2)
    | ~ subset(empty_set,X2)
    | ~ transfinite_sequence(esk8_1(X1))
    | ~ function(esk8_1(X1))
    | ~ relation(esk8_1(X1))
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[207,681,theory(equality)]) ).

cnf(698,plain,
    ( empty(esk8_1(X1))
    | $false
    | ~ empty(empty_set)
    | ~ empty(X1) ),
    inference(rw,[status(thm)],[685,279,theory(equality)]) ).

cnf(699,plain,
    ( empty(esk8_1(X1))
    | $false
    | $false
    | ~ empty(X1) ),
    inference(rw,[status(thm)],[698,112,theory(equality)]) ).

cnf(700,plain,
    ( empty(esk8_1(X1))
    | ~ empty(X1) ),
    inference(cn,[status(thm)],[699,theory(equality)]) ).

cnf(705,plain,
    ( transfinite_sequence_of(esk8_1(X1),X2)
    | $false
    | ~ transfinite_sequence(esk8_1(X1))
    | ~ function(esk8_1(X1))
    | ~ relation(esk8_1(X1))
    | ~ empty(X1) ),
    inference(rw,[status(thm)],[688,263,theory(equality)]) ).

cnf(706,plain,
    ( transfinite_sequence_of(esk8_1(X1),X2)
    | $false
    | $false
    | ~ function(esk8_1(X1))
    | ~ relation(esk8_1(X1))
    | ~ empty(X1) ),
    inference(rw,[status(thm)],[705,281,theory(equality)]) ).

cnf(707,plain,
    ( transfinite_sequence_of(esk8_1(X1),X2)
    | $false
    | $false
    | $false
    | ~ relation(esk8_1(X1))
    | ~ empty(X1) ),
    inference(rw,[status(thm)],[706,280,theory(equality)]) ).

cnf(708,plain,
    ( transfinite_sequence_of(esk8_1(X1),X2)
    | $false
    | $false
    | $false
    | $false
    | ~ empty(X1) ),
    inference(rw,[status(thm)],[707,279,theory(equality)]) ).

cnf(709,plain,
    ( transfinite_sequence_of(esk8_1(X1),X2)
    | ~ empty(X1) ),
    inference(cn,[status(thm)],[708,theory(equality)]) ).

cnf(719,plain,
    ( empty_set = esk8_1(X1)
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[216,700,theory(equality)]) ).

cnf(729,plain,
    ( transfinite_sequence_of(empty_set,X2)
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[709,719,theory(equality)]) ).

cnf(749,plain,
    transfinite_sequence_of(empty_set,X1),
    inference(spm,[status(thm)],[729,112,theory(equality)]) ).

cnf(759,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[236,749,theory(equality)]) ).

cnf(760,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[759,theory(equality)]) ).

cnf(761,negated_conjecture,
    $false,
    760,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM409+1 : TPTP v7.0.0. Released v3.2.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.03/0.23  % Computer : n042.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.625MB
% 0.03/0.23  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Fri Jan  5 02:47:30 CST 2018
% 0.03/0.23  % CPUTime  : 
% 0.03/0.28  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.28  --creating new selector for []
% 0.07/0.36  -running prover on /export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1 with time limit 29
% 0.07/0.36  -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1']
% 0.07/0.36  -prover status Theorem
% 0.07/0.36  Problem theBenchmark.p solved in phase 0.
% 0.07/0.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36  Solved 1 out of 1.
% 0.07/0.36  # Problem is unsatisfiable (or provable), constructing proof object
% 0.07/0.36  # SZS status Theorem
% 0.07/0.36  # SZS output start CNFRefutation.
% See solution above
% 0.07/0.36  # SZS output end CNFRefutation
%------------------------------------------------------------------------------