TSTP Solution File: NUM401+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM401+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n117.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 : 33
% Number of leaves : 14
% Syntax : Number of formulae : 122 ( 13 unt; 0 def)
% Number of atoms : 479 ( 20 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 585 ( 228 ~; 257 |; 76 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 199 ( 9 sgn 124 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',cc1_ordinal1) ).
fof(4,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',t5_subset) ).
fof(11,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',reflexivity_r1_tarski) ).
fof(14,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',t4_subset) ).
fof(21,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',d2_ordinal1) ).
fof(23,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',antisymmetry_r2_hidden) ).
fof(27,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',redefinition_r1_ordinal1) ).
fof(28,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',t34_ordinal1) ).
fof(29,axiom,
! [X1] : equal(succ(X1),set_union2(X1,singleton(X1))),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',d1_ordinal1) ).
fof(31,axiom,
! [X1,X2,X3] :
( equal(X3,set_union2(X1,X2))
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',d2_xboole_0) ).
fof(33,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& ~ equal(X1,X2)
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',t24_ordinal1) ).
fof(34,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',t2_subset) ).
fof(37,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',t3_subset) ).
fof(49,axiom,
! [X1,X2] :
( equal(X2,singleton(X1))
<=> ! [X3] :
( in(X3,X2)
<=> equal(X3,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1',d1_tarski) ).
fof(55,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[28]) ).
fof(61,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[23,theory(equality)]) ).
fof(63,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& ~ equal(X1,X2)
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).
fof(73,plain,
! [X1] :
( ~ ordinal(X1)
| ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(74,plain,
! [X2] :
( ~ ordinal(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[74]) ).
cnf(77,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(78,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(79,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[78]) ).
cnf(80,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(103,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[11]) ).
cnf(104,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[103]) ).
fof(114,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(115,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[114]) ).
cnf(116,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(136,plain,
! [X1] :
( ( ~ epsilon_transitive(X1)
| ! [X2] :
( ~ in(X2,X1)
| subset(X2,X1) ) )
& ( ? [X2] :
( in(X2,X1)
& ~ subset(X2,X1) )
| epsilon_transitive(X1) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(137,plain,
! [X3] :
( ( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ in(X4,X3)
| subset(X4,X3) ) )
& ( ? [X5] :
( in(X5,X3)
& ~ subset(X5,X3) )
| epsilon_transitive(X3) ) ),
inference(variable_rename,[status(thm)],[136]) ).
fof(138,plain,
! [X3] :
( ( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ in(X4,X3)
| subset(X4,X3) ) )
& ( ( in(esk6_1(X3),X3)
& ~ subset(esk6_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(skolemize,[status(esa)],[137]) ).
fof(139,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( ( in(esk6_1(X3),X3)
& ~ subset(esk6_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(shift_quantors,[status(thm)],[138]) ).
fof(140,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( in(esk6_1(X3),X3)
| epsilon_transitive(X3) )
& ( ~ subset(esk6_1(X3),X3)
| epsilon_transitive(X3) ) ),
inference(distribute,[status(thm)],[139]) ).
cnf(143,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[140]) ).
fof(151,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(fof_nnf,[status(thm)],[61]) ).
fof(152,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[151]) ).
cnf(153,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[152]) ).
fof(165,plain,
! [X1,X2] :
( ~ ordinal(X1)
| ~ ordinal(X2)
| ( ( ~ ordinal_subset(X1,X2)
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| ordinal_subset(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(166,plain,
! [X3,X4] :
( ~ ordinal(X3)
| ~ ordinal(X4)
| ( ( ~ ordinal_subset(X3,X4)
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| ordinal_subset(X3,X4) ) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,plain,
! [X3,X4] :
( ( ~ ordinal_subset(X3,X4)
| subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) )
& ( ~ subset(X3,X4)
| ordinal_subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) ) ),
inference(distribute,[status(thm)],[166]) ).
cnf(168,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[167]) ).
cnf(169,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[167]) ).
fof(170,negated_conjecture,
? [X1] :
( ordinal(X1)
& ? [X2] :
( ordinal(X2)
& ( ~ in(X1,succ(X2))
| ~ ordinal_subset(X1,X2) )
& ( in(X1,succ(X2))
| ordinal_subset(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(171,negated_conjecture,
? [X3] :
( ordinal(X3)
& ? [X4] :
( ordinal(X4)
& ( ~ in(X3,succ(X4))
| ~ ordinal_subset(X3,X4) )
& ( in(X3,succ(X4))
| ordinal_subset(X3,X4) ) ) ),
inference(variable_rename,[status(thm)],[170]) ).
fof(172,negated_conjecture,
( ordinal(esk7_0)
& ordinal(esk8_0)
& ( ~ in(esk7_0,succ(esk8_0))
| ~ ordinal_subset(esk7_0,esk8_0) )
& ( in(esk7_0,succ(esk8_0))
| ordinal_subset(esk7_0,esk8_0) ) ),
inference(skolemize,[status(esa)],[171]) ).
cnf(173,negated_conjecture,
( ordinal_subset(esk7_0,esk8_0)
| in(esk7_0,succ(esk8_0)) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(174,negated_conjecture,
( ~ ordinal_subset(esk7_0,esk8_0)
| ~ in(esk7_0,succ(esk8_0)) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(175,negated_conjecture,
ordinal(esk8_0),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(176,negated_conjecture,
ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[172]) ).
fof(177,plain,
! [X2] : equal(succ(X2),set_union2(X2,singleton(X2))),
inference(variable_rename,[status(thm)],[29]) ).
cnf(178,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[177]) ).
fof(181,plain,
! [X1,X2,X3] :
( ( ~ equal(X3,set_union2(X1,X2))
| ! [X4] :
( ( ~ in(X4,X3)
| in(X4,X1)
| in(X4,X2) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X2) )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) )
& ( in(X4,X3)
| in(X4,X1)
| in(X4,X2) ) )
| equal(X3,set_union2(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(182,plain,
! [X5,X6,X7] :
( ( ~ equal(X7,set_union2(X5,X6))
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( ~ in(X9,X5)
& ~ in(X9,X6) ) )
& ( in(X9,X7)
| in(X9,X5)
| in(X9,X6) ) )
| equal(X7,set_union2(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[181]) ).
fof(183,plain,
! [X5,X6,X7] :
( ( ~ equal(X7,set_union2(X5,X6))
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk9_3(X5,X6,X7),X7)
| ( ~ in(esk9_3(X5,X6,X7),X5)
& ~ in(esk9_3(X5,X6,X7),X6) ) )
& ( in(esk9_3(X5,X6,X7),X7)
| in(esk9_3(X5,X6,X7),X5)
| in(esk9_3(X5,X6,X7),X6) ) )
| equal(X7,set_union2(X5,X6)) ) ),
inference(skolemize,[status(esa)],[182]) ).
fof(184,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) )
| ~ equal(X7,set_union2(X5,X6)) )
& ( ( ( ~ in(esk9_3(X5,X6,X7),X7)
| ( ~ in(esk9_3(X5,X6,X7),X5)
& ~ in(esk9_3(X5,X6,X7),X6) ) )
& ( in(esk9_3(X5,X6,X7),X7)
| in(esk9_3(X5,X6,X7),X5)
| in(esk9_3(X5,X6,X7),X6) ) )
| equal(X7,set_union2(X5,X6)) ) ),
inference(shift_quantors,[status(thm)],[183]) ).
fof(185,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| ~ equal(X7,set_union2(X5,X6)) )
& ( ~ in(X8,X5)
| in(X8,X7)
| ~ equal(X7,set_union2(X5,X6)) )
& ( ~ in(X8,X6)
| in(X8,X7)
| ~ equal(X7,set_union2(X5,X6)) )
& ( ~ in(esk9_3(X5,X6,X7),X5)
| ~ in(esk9_3(X5,X6,X7),X7)
| equal(X7,set_union2(X5,X6)) )
& ( ~ in(esk9_3(X5,X6,X7),X6)
| ~ in(esk9_3(X5,X6,X7),X7)
| equal(X7,set_union2(X5,X6)) )
& ( in(esk9_3(X5,X6,X7),X7)
| in(esk9_3(X5,X6,X7),X5)
| in(esk9_3(X5,X6,X7),X6)
| equal(X7,set_union2(X5,X6)) ) ),
inference(distribute,[status(thm)],[184]) ).
cnf(189,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[185]) ).
cnf(190,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[185]) ).
cnf(191,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[185]) ).
fof(198,plain,
! [X1] :
( ~ ordinal(X1)
| ! [X2] :
( ~ ordinal(X2)
| in(X1,X2)
| equal(X1,X2)
| in(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[63]) ).
fof(199,plain,
! [X3] :
( ~ ordinal(X3)
| ! [X4] :
( ~ ordinal(X4)
| in(X3,X4)
| equal(X3,X4)
| in(X4,X3) ) ),
inference(variable_rename,[status(thm)],[198]) ).
fof(200,plain,
! [X3,X4] :
( ~ ordinal(X4)
| in(X3,X4)
| equal(X3,X4)
| in(X4,X3)
| ~ ordinal(X3) ),
inference(shift_quantors,[status(thm)],[199]) ).
cnf(201,plain,
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[200]) ).
fof(202,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(203,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[202]) ).
cnf(204,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[203]) ).
fof(210,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(211,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[210]) ).
cnf(212,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[211]) ).
fof(255,plain,
! [X1,X2] :
( ( ~ equal(X2,singleton(X1))
| ! [X3] :
( ( ~ in(X3,X2)
| equal(X3,X1) )
& ( ~ equal(X3,X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ equal(X3,X1) )
& ( in(X3,X2)
| equal(X3,X1) ) )
| equal(X2,singleton(X1)) ) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(256,plain,
! [X4,X5] :
( ( ~ equal(X5,singleton(X4))
| ! [X6] :
( ( ~ in(X6,X5)
| equal(X6,X4) )
& ( ~ equal(X6,X4)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ equal(X7,X4) )
& ( in(X7,X5)
| equal(X7,X4) ) )
| equal(X5,singleton(X4)) ) ),
inference(variable_rename,[status(thm)],[255]) ).
fof(257,plain,
! [X4,X5] :
( ( ~ equal(X5,singleton(X4))
| ! [X6] :
( ( ~ in(X6,X5)
| equal(X6,X4) )
& ( ~ equal(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk14_2(X4,X5),X5)
| ~ equal(esk14_2(X4,X5),X4) )
& ( in(esk14_2(X4,X5),X5)
| equal(esk14_2(X4,X5),X4) ) )
| equal(X5,singleton(X4)) ) ),
inference(skolemize,[status(esa)],[256]) ).
fof(258,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| equal(X6,X4) )
& ( ~ equal(X6,X4)
| in(X6,X5) ) )
| ~ equal(X5,singleton(X4)) )
& ( ( ( ~ in(esk14_2(X4,X5),X5)
| ~ equal(esk14_2(X4,X5),X4) )
& ( in(esk14_2(X4,X5),X5)
| equal(esk14_2(X4,X5),X4) ) )
| equal(X5,singleton(X4)) ) ),
inference(shift_quantors,[status(thm)],[257]) ).
fof(259,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| equal(X6,X4)
| ~ equal(X5,singleton(X4)) )
& ( ~ equal(X6,X4)
| in(X6,X5)
| ~ equal(X5,singleton(X4)) )
& ( ~ in(esk14_2(X4,X5),X5)
| ~ equal(esk14_2(X4,X5),X4)
| equal(X5,singleton(X4)) )
& ( in(esk14_2(X4,X5),X5)
| equal(esk14_2(X4,X5),X4)
| equal(X5,singleton(X4)) ) ),
inference(distribute,[status(thm)],[258]) ).
cnf(262,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[259]) ).
cnf(263,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[259]) ).
cnf(287,negated_conjecture,
( ordinal_subset(esk7_0,esk8_0)
| in(esk7_0,set_union2(esk8_0,singleton(esk8_0))) ),
inference(rw,[status(thm)],[173,178,theory(equality)]),
[unfolding] ).
cnf(294,negated_conjecture,
( ~ ordinal_subset(esk7_0,esk8_0)
| ~ in(esk7_0,set_union2(esk8_0,singleton(esk8_0))) ),
inference(rw,[status(thm)],[174,178,theory(equality)]),
[unfolding] ).
cnf(359,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[262,theory(equality)]) ).
cnf(374,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[189,theory(equality)]) ).
cnf(384,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[190,theory(equality)]) ).
cnf(392,negated_conjecture,
( X1 = esk7_0
| in(X1,esk7_0)
| in(esk7_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[201,176,theory(equality)]) ).
cnf(414,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[191,theory(equality)]) ).
cnf(423,plain,
( ~ empty(X2)
| ~ in(X3,X1)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[80,212,theory(equality)]) ).
cnf(426,plain,
( element(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(spm,[status(thm)],[116,212,theory(equality)]) ).
cnf(733,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[359,theory(equality)]) ).
cnf(830,negated_conjecture,
( ~ ordinal_subset(esk7_0,esk8_0)
| ~ in(esk7_0,singleton(esk8_0)) ),
inference(spm,[status(thm)],[294,374,theory(equality)]) ).
cnf(834,negated_conjecture,
( ~ in(esk7_0,singleton(esk8_0))
| ~ subset(esk7_0,esk8_0)
| ~ ordinal(esk7_0)
| ~ ordinal(esk8_0) ),
inference(spm,[status(thm)],[830,168,theory(equality)]) ).
cnf(836,negated_conjecture,
( ~ in(esk7_0,singleton(esk8_0))
| ~ subset(esk7_0,esk8_0)
| $false
| ~ ordinal(esk8_0) ),
inference(rw,[status(thm)],[834,176,theory(equality)]) ).
cnf(837,negated_conjecture,
( ~ in(esk7_0,singleton(esk8_0))
| ~ subset(esk7_0,esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[836,175,theory(equality)]) ).
cnf(838,negated_conjecture,
( ~ in(esk7_0,singleton(esk8_0))
| ~ subset(esk7_0,esk8_0) ),
inference(cn,[status(thm)],[837,theory(equality)]) ).
cnf(909,negated_conjecture,
( ~ ordinal_subset(esk7_0,esk8_0)
| ~ in(esk7_0,esk8_0) ),
inference(spm,[status(thm)],[294,384,theory(equality)]) ).
cnf(914,negated_conjecture,
( ~ in(esk7_0,esk8_0)
| ~ subset(esk7_0,esk8_0)
| ~ ordinal(esk7_0)
| ~ ordinal(esk8_0) ),
inference(spm,[status(thm)],[909,168,theory(equality)]) ).
cnf(916,negated_conjecture,
( ~ in(esk7_0,esk8_0)
| ~ subset(esk7_0,esk8_0)
| $false
| ~ ordinal(esk8_0) ),
inference(rw,[status(thm)],[914,176,theory(equality)]) ).
cnf(917,negated_conjecture,
( ~ in(esk7_0,esk8_0)
| ~ subset(esk7_0,esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[916,175,theory(equality)]) ).
cnf(918,negated_conjecture,
( ~ in(esk7_0,esk8_0)
| ~ subset(esk7_0,esk8_0) ),
inference(cn,[status(thm)],[917,theory(equality)]) ).
cnf(931,negated_conjecture,
( ~ in(esk7_0,esk8_0)
| ~ epsilon_transitive(esk8_0) ),
inference(spm,[status(thm)],[918,143,theory(equality)]) ).
cnf(933,negated_conjecture,
( esk8_0 = esk7_0
| in(esk7_0,esk8_0)
| in(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[392,175,theory(equality)]) ).
cnf(941,negated_conjecture,
( ~ in(esk7_0,esk8_0)
| ~ ordinal(esk8_0) ),
inference(spm,[status(thm)],[931,77,theory(equality)]) ).
cnf(943,negated_conjecture,
( ~ in(esk7_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[941,175,theory(equality)]) ).
cnf(944,negated_conjecture,
~ in(esk7_0,esk8_0),
inference(cn,[status(thm)],[943,theory(equality)]) ).
cnf(948,negated_conjecture,
( esk7_0 = esk8_0
| in(esk8_0,esk7_0) ),
inference(sr,[status(thm)],[933,944,theory(equality)]) ).
cnf(1193,negated_conjecture,
( in(esk7_0,singleton(esk8_0))
| in(esk7_0,esk8_0)
| ordinal_subset(esk7_0,esk8_0) ),
inference(spm,[status(thm)],[414,287,theory(equality)]) ).
cnf(1208,negated_conjecture,
( in(esk7_0,singleton(esk8_0))
| ordinal_subset(esk7_0,esk8_0) ),
inference(sr,[status(thm)],[1193,944,theory(equality)]) ).
cnf(1209,negated_conjecture,
( subset(esk7_0,esk8_0)
| in(esk7_0,singleton(esk8_0))
| ~ ordinal(esk7_0)
| ~ ordinal(esk8_0) ),
inference(spm,[status(thm)],[169,1208,theory(equality)]) ).
cnf(1212,negated_conjecture,
( subset(esk7_0,esk8_0)
| in(esk7_0,singleton(esk8_0))
| $false
| ~ ordinal(esk8_0) ),
inference(rw,[status(thm)],[1209,176,theory(equality)]) ).
cnf(1213,negated_conjecture,
( subset(esk7_0,esk8_0)
| in(esk7_0,singleton(esk8_0))
| $false
| $false ),
inference(rw,[status(thm)],[1212,175,theory(equality)]) ).
cnf(1214,negated_conjecture,
( subset(esk7_0,esk8_0)
| in(esk7_0,singleton(esk8_0)) ),
inference(cn,[status(thm)],[1213,theory(equality)]) ).
cnf(1216,negated_conjecture,
( in(esk7_0,singleton(esk8_0))
| ~ empty(esk8_0)
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[423,1214,theory(equality)]) ).
cnf(1390,negated_conjecture,
( element(X1,esk8_0)
| in(esk7_0,singleton(esk8_0))
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[426,1214,theory(equality)]) ).
cnf(1720,negated_conjecture,
( empty(esk8_0)
| in(X1,esk8_0)
| in(esk7_0,singleton(esk8_0))
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[204,1390,theory(equality)]) ).
cnf(2806,negated_conjecture,
( in(esk7_0,singleton(esk8_0))
| in(X1,esk8_0)
| ~ in(X1,esk7_0) ),
inference(csr,[status(thm)],[1720,1216]) ).
cnf(2819,negated_conjecture,
( in(esk7_0,singleton(esk8_0))
| in(esk8_0,esk8_0)
| esk7_0 = esk8_0 ),
inference(spm,[status(thm)],[2806,948,theory(equality)]) ).
cnf(2840,negated_conjecture,
( X1 = esk7_0
| esk7_0 = esk8_0
| in(esk8_0,esk8_0)
| singleton(X1) != singleton(esk8_0) ),
inference(spm,[status(thm)],[263,2819,theory(equality)]) ).
cnf(2952,negated_conjecture,
( esk7_0 = esk8_0
| in(esk8_0,esk8_0) ),
inference(er,[status(thm)],[2840,theory(equality)]) ).
cnf(2953,negated_conjecture,
( esk7_0 = esk8_0
| ~ in(esk8_0,esk8_0) ),
inference(spm,[status(thm)],[153,2952,theory(equality)]) ).
cnf(2982,negated_conjecture,
esk7_0 = esk8_0,
inference(csr,[status(thm)],[2953,2952]) ).
cnf(3162,negated_conjecture,
( $false
| ~ in(esk7_0,singleton(esk8_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[838,2982,theory(equality)]),104,theory(equality)]) ).
cnf(3163,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3162,2982,theory(equality)]),733,theory(equality)]) ).
cnf(3164,negated_conjecture,
$false,
inference(cn,[status(thm)],[3163,theory(equality)]) ).
cnf(3165,negated_conjecture,
$false,
3164,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM401+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 : n117.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 02:40:45 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 []
% 0.07/0.46 -running prover on /export/starexec/sandbox2/tmp/tmpjSus_y/sel_theBenchmark.p_1 with time limit 29
% 0.07/0.46 -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/tmpjSus_y/sel_theBenchmark.p_1']
% 0.07/0.46 -prover status Theorem
% 0.07/0.46 Problem theBenchmark.p solved in phase 0.
% 0.07/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.46 % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.46 Solved 1 out of 1.
% 0.07/0.46 # Problem is unsatisfiable (or provable), constructing proof object
% 0.07/0.46 # SZS status Theorem
% 0.07/0.46 # SZS output start CNFRefutation.
% See solution above
% 0.07/0.46 # SZS output end CNFRefutation
%------------------------------------------------------------------------------