TSTP Solution File: SEU238+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU238+3 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 06:14:59 EST 2010
% Result : Theorem 1.64s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 92 ( 14 unt; 0 def)
% Number of atoms : 392 ( 43 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 523 ( 223 ~; 198 |; 79 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 74 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',t21_ordinal1) ).
fof(7,axiom,
! [X1] : in(X1,succ(X1)),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',t10_ordinal1) ).
fof(9,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',t33_ordinal1) ).
fof(25,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',antisymmetry_r2_hidden) ).
fof(29,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',redefinition_r1_ordinal1) ).
fof(30,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',d1_ordinal1) ).
fof(31,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',fc3_ordinal1) ).
fof(35,axiom,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',t41_ordinal1) ).
fof(37,conjecture,
! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',t42_ordinal1) ).
fof(39,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/tmp/tmpptBHyv/sel_SEU238+3.p_1',d8_xboole_0) ).
fof(55,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
inference(assume_negation,[status(cth)],[37]) ).
fof(61,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(62,plain,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(64,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
inference(fof_simplification,[status(thm)],[55,theory(equality)]) ).
fof(80,plain,
! [X1] :
( ~ epsilon_transitive(X1)
| ! [X2] :
( ~ ordinal(X2)
| ~ proper_subset(X1,X2)
| in(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(81,plain,
! [X3] :
( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ ordinal(X4)
| ~ proper_subset(X3,X4)
| in(X3,X4) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
! [X3,X4] :
( ~ ordinal(X4)
| ~ proper_subset(X3,X4)
| in(X3,X4)
| ~ epsilon_transitive(X3) ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(83,plain,
( in(X1,X2)
| ~ epsilon_transitive(X1)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(90,plain,
! [X2] : in(X2,succ(X2)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(91,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[90]) ).
fof(95,plain,
! [X1] :
( ~ ordinal(X1)
| ! [X2] :
( ~ ordinal(X2)
| ( ( ~ in(X1,X2)
| ordinal_subset(succ(X1),X2) )
& ( ~ ordinal_subset(succ(X1),X2)
| in(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(96,plain,
! [X3] :
( ~ ordinal(X3)
| ! [X4] :
( ~ ordinal(X4)
| ( ( ~ in(X3,X4)
| ordinal_subset(succ(X3),X4) )
& ( ~ ordinal_subset(succ(X3),X4)
| in(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[95]) ).
fof(97,plain,
! [X3,X4] :
( ~ ordinal(X4)
| ( ( ~ in(X3,X4)
| ordinal_subset(succ(X3),X4) )
& ( ~ ordinal_subset(succ(X3),X4)
| in(X3,X4) ) )
| ~ ordinal(X3) ),
inference(shift_quantors,[status(thm)],[96]) ).
fof(98,plain,
! [X3,X4] :
( ( ~ in(X3,X4)
| ordinal_subset(succ(X3),X4)
| ~ ordinal(X4)
| ~ ordinal(X3) )
& ( ~ ordinal_subset(succ(X3),X4)
| in(X3,X4)
| ~ ordinal(X4)
| ~ ordinal(X3) ) ),
inference(distribute,[status(thm)],[97]) ).
cnf(100,plain,
( ordinal_subset(succ(X1),X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[98]) ).
fof(158,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(fof_nnf,[status(thm)],[61]) ).
fof(159,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[158]) ).
cnf(160,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[159]) ).
fof(171,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)],[29]) ).
fof(172,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)],[171]) ).
fof(173,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)],[172]) ).
cnf(175,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[173]) ).
fof(176,plain,
! [X2] : succ(X2) = set_union2(X2,singleton(X2)),
inference(variable_rename,[status(thm)],[30]) ).
cnf(177,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[176]) ).
fof(178,plain,
! [X1] :
( ~ ordinal(X1)
| ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_nnf,[status(thm)],[62]) ).
fof(179,plain,
! [X2] :
( ~ ordinal(X2)
| ( ~ empty(succ(X2))
& epsilon_transitive(succ(X2))
& epsilon_connected(succ(X2))
& ordinal(succ(X2)) ) ),
inference(variable_rename,[status(thm)],[178]) ).
fof(180,plain,
! [X2] :
( ( ~ empty(succ(X2))
| ~ ordinal(X2) )
& ( epsilon_transitive(succ(X2))
| ~ ordinal(X2) )
& ( epsilon_connected(succ(X2))
| ~ ordinal(X2) )
& ( ordinal(succ(X2))
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[179]) ).
cnf(181,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[180]) ).
cnf(183,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[180]) ).
fof(197,plain,
! [X1] :
( ~ ordinal(X1)
| ( ( ~ being_limit_ordinal(X1)
| ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X1)
| in(succ(X2),X1) ) )
& ( ? [X2] :
( ordinal(X2)
& in(X2,X1)
& ~ in(succ(X2),X1) )
| being_limit_ordinal(X1) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(198,plain,
! [X3] :
( ~ ordinal(X3)
| ( ( ~ being_limit_ordinal(X3)
| ! [X4] :
( ~ ordinal(X4)
| ~ in(X4,X3)
| in(succ(X4),X3) ) )
& ( ? [X5] :
( ordinal(X5)
& in(X5,X3)
& ~ in(succ(X5),X3) )
| being_limit_ordinal(X3) ) ) ),
inference(variable_rename,[status(thm)],[197]) ).
fof(199,plain,
! [X3] :
( ~ ordinal(X3)
| ( ( ~ being_limit_ordinal(X3)
| ! [X4] :
( ~ ordinal(X4)
| ~ in(X4,X3)
| in(succ(X4),X3) ) )
& ( ( ordinal(esk7_1(X3))
& in(esk7_1(X3),X3)
& ~ in(succ(esk7_1(X3)),X3) )
| being_limit_ordinal(X3) ) ) ),
inference(skolemize,[status(esa)],[198]) ).
fof(200,plain,
! [X3,X4] :
( ( ( ~ ordinal(X4)
| ~ in(X4,X3)
| in(succ(X4),X3)
| ~ being_limit_ordinal(X3) )
& ( ( ordinal(esk7_1(X3))
& in(esk7_1(X3),X3)
& ~ in(succ(esk7_1(X3)),X3) )
| being_limit_ordinal(X3) ) )
| ~ ordinal(X3) ),
inference(shift_quantors,[status(thm)],[199]) ).
fof(201,plain,
! [X3,X4] :
( ( ~ ordinal(X4)
| ~ in(X4,X3)
| in(succ(X4),X3)
| ~ being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( ordinal(esk7_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( in(esk7_1(X3),X3)
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( ~ in(succ(esk7_1(X3)),X3)
| being_limit_ordinal(X3)
| ~ ordinal(X3) ) ),
inference(distribute,[status(thm)],[200]) ).
cnf(202,plain,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(succ(esk7_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(203,plain,
( being_limit_ordinal(X1)
| in(esk7_1(X1),X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(204,plain,
( being_limit_ordinal(X1)
| ordinal(esk7_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(205,plain,
( in(succ(X2),X1)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(X2,X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[201]) ).
fof(208,negated_conjecture,
? [X1] :
( ordinal(X1)
& ( ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ~ ordinal(X2)
| X1 != succ(X2) ) )
| ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
inference(fof_nnf,[status(thm)],[64]) ).
fof(209,negated_conjecture,
? [X3] :
( ordinal(X3)
& ( ( ~ being_limit_ordinal(X3)
& ! [X4] :
( ~ ordinal(X4)
| X3 != succ(X4) ) )
| ( ? [X5] :
( ordinal(X5)
& X3 = succ(X5) )
& being_limit_ordinal(X3) ) ) ),
inference(variable_rename,[status(thm)],[208]) ).
fof(210,negated_conjecture,
( ordinal(esk8_0)
& ( ( ~ being_limit_ordinal(esk8_0)
& ! [X4] :
( ~ ordinal(X4)
| esk8_0 != succ(X4) ) )
| ( ordinal(esk9_0)
& esk8_0 = succ(esk9_0)
& being_limit_ordinal(esk8_0) ) ) ),
inference(skolemize,[status(esa)],[209]) ).
fof(211,negated_conjecture,
! [X4] :
( ( ( ( ~ ordinal(X4)
| esk8_0 != succ(X4) )
& ~ being_limit_ordinal(esk8_0) )
| ( ordinal(esk9_0)
& esk8_0 = succ(esk9_0)
& being_limit_ordinal(esk8_0) ) )
& ordinal(esk8_0) ),
inference(shift_quantors,[status(thm)],[210]) ).
fof(212,negated_conjecture,
! [X4] :
( ( ordinal(esk9_0)
| ~ ordinal(X4)
| esk8_0 != succ(X4) )
& ( esk8_0 = succ(esk9_0)
| ~ ordinal(X4)
| esk8_0 != succ(X4) )
& ( being_limit_ordinal(esk8_0)
| ~ ordinal(X4)
| esk8_0 != succ(X4) )
& ( ordinal(esk9_0)
| ~ being_limit_ordinal(esk8_0) )
& ( esk8_0 = succ(esk9_0)
| ~ being_limit_ordinal(esk8_0) )
& ( being_limit_ordinal(esk8_0)
| ~ being_limit_ordinal(esk8_0) )
& ordinal(esk8_0) ),
inference(distribute,[status(thm)],[211]) ).
cnf(213,negated_conjecture,
ordinal(esk8_0),
inference(split_conjunct,[status(thm)],[212]) ).
cnf(215,negated_conjecture,
( esk8_0 = succ(esk9_0)
| ~ being_limit_ordinal(esk8_0) ),
inference(split_conjunct,[status(thm)],[212]) ).
cnf(216,negated_conjecture,
( ordinal(esk9_0)
| ~ being_limit_ordinal(esk8_0) ),
inference(split_conjunct,[status(thm)],[212]) ).
cnf(217,negated_conjecture,
( being_limit_ordinal(esk8_0)
| esk8_0 != succ(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[212]) ).
fof(224,plain,
! [X1,X2] :
( ( ~ proper_subset(X1,X2)
| ( subset(X1,X2)
& X1 != X2 ) )
& ( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(225,plain,
! [X3,X4] :
( ( ~ proper_subset(X3,X4)
| ( subset(X3,X4)
& X3 != X4 ) )
& ( ~ subset(X3,X4)
| X3 = X4
| proper_subset(X3,X4) ) ),
inference(variable_rename,[status(thm)],[224]) ).
fof(226,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ proper_subset(X3,X4) )
& ( X3 != X4
| ~ proper_subset(X3,X4) )
& ( ~ subset(X3,X4)
| X3 = X4
| proper_subset(X3,X4) ) ),
inference(distribute,[status(thm)],[225]) ).
cnf(227,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[226]) ).
cnf(283,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[91,177,theory(equality)]),
[unfolding] ).
cnf(284,negated_conjecture,
( set_union2(esk9_0,singleton(esk9_0)) = esk8_0
| ~ being_limit_ordinal(esk8_0) ),
inference(rw,[status(thm)],[215,177,theory(equality)]),
[unfolding] ).
cnf(285,plain,
( epsilon_transitive(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[183,177,theory(equality)]),
[unfolding] ).
cnf(287,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[181,177,theory(equality)]),
[unfolding] ).
cnf(290,negated_conjecture,
( being_limit_ordinal(esk8_0)
| set_union2(X1,singleton(X1)) != esk8_0
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[217,177,theory(equality)]),
[unfolding] ).
cnf(291,plain,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(set_union2(esk7_1(X1),singleton(esk7_1(X1))),X1) ),
inference(rw,[status(thm)],[202,177,theory(equality)]),
[unfolding] ).
cnf(293,plain,
( ordinal_subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[100,177,theory(equality)]),
[unfolding] ).
cnf(294,plain,
( in(set_union2(X2,singleton(X2)),X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[205,177,theory(equality)]),
[unfolding] ).
cnf(362,plain,
~ in(set_union2(X1,singleton(X1)),X1),
inference(spm,[status(thm)],[160,283,theory(equality)]) ).
cnf(404,plain,
( in(X1,X2)
| X1 = X2
| ~ ordinal(X2)
| ~ epsilon_transitive(X1)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[83,227,theory(equality)]) ).
cnf(409,plain,
( subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X2)
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[175,293,theory(equality)]) ).
cnf(502,plain,
( ~ being_limit_ordinal(X1)
| ~ in(X1,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[362,294,theory(equality)]) ).
cnf(510,plain,
( ~ being_limit_ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(set_union2(X1,singleton(X1)))
| ~ in(X1,set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[502,294,theory(equality)]) ).
cnf(511,plain,
( ~ being_limit_ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(set_union2(X1,singleton(X1)))
| $false
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[510,283,theory(equality)]) ).
cnf(512,plain,
( ~ being_limit_ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(cn,[status(thm)],[511,theory(equality)]) ).
cnf(555,plain,
( ~ being_limit_ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[512,287]) ).
cnf(557,negated_conjecture,
( ~ being_limit_ordinal(esk8_0)
| ~ ordinal(esk9_0) ),
inference(spm,[status(thm)],[555,284,theory(equality)]) ).
cnf(562,negated_conjecture,
~ being_limit_ordinal(esk8_0),
inference(csr,[status(thm)],[557,216]) ).
cnf(908,plain,
( subset(set_union2(X1,singleton(X1)),X2)
| ~ in(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[409,287]) ).
cnf(915,plain,
( set_union2(X1,singleton(X1)) = X2
| in(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(set_union2(X1,singleton(X1)))
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[404,908,theory(equality)]) ).
cnf(2791,plain,
( set_union2(X1,singleton(X1)) = X2
| in(set_union2(X1,singleton(X1)),X2)
| ~ in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(csr,[status(thm)],[915,285]) ).
cnf(2798,plain,
( being_limit_ordinal(X1)
| set_union2(esk7_1(X1),singleton(esk7_1(X1))) = X1
| ~ ordinal(X1)
| ~ in(esk7_1(X1),X1)
| ~ ordinal(esk7_1(X1)) ),
inference(spm,[status(thm)],[291,2791,theory(equality)]) ).
cnf(21050,plain,
( set_union2(esk7_1(X1),singleton(esk7_1(X1))) = X1
| being_limit_ordinal(X1)
| ~ in(esk7_1(X1),X1)
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[2798,204]) ).
cnf(21051,plain,
( set_union2(esk7_1(X1),singleton(esk7_1(X1))) = X1
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[21050,203]) ).
cnf(21057,negated_conjecture,
( being_limit_ordinal(esk8_0)
| being_limit_ordinal(X1)
| X1 != esk8_0
| ~ ordinal(esk7_1(X1))
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[290,21051,theory(equality)]) ).
cnf(21134,negated_conjecture,
( being_limit_ordinal(X1)
| X1 != esk8_0
| ~ ordinal(esk7_1(X1))
| ~ ordinal(X1) ),
inference(sr,[status(thm)],[21057,562,theory(equality)]) ).
cnf(21149,negated_conjecture,
( being_limit_ordinal(X1)
| X1 != esk8_0
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[21134,204]) ).
cnf(21150,negated_conjecture,
~ ordinal(esk8_0),
inference(spm,[status(thm)],[562,21149,theory(equality)]) ).
cnf(21176,negated_conjecture,
$false,
inference(rw,[status(thm)],[21150,213,theory(equality)]) ).
cnf(21177,negated_conjecture,
$false,
inference(cn,[status(thm)],[21176,theory(equality)]) ).
cnf(21178,negated_conjecture,
$false,
21177,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU238+3.p
% --creating new selector for []
% -running prover on /tmp/tmpptBHyv/sel_SEU238+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU238+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU238+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU238+3.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------