TSTP Solution File: SEU147+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU147+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 04:52:25 EST 2010
% Result : Theorem 21.09s
% Output : CNFRefutation 21.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 135 ( 50 unt; 0 def)
% Number of atoms : 391 ( 163 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 420 ( 164 ~; 173 |; 70 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 269 ( 12 sgn 146 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t1_boole) ).
fof(9,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t69_enumset1) ).
fof(12,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t83_xboole_1) ).
fof(14,axiom,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t40_xboole_1) ).
fof(17,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t3_boole) ).
fof(18,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t3_xboole_1) ).
fof(19,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t3_xboole_0) ).
fof(24,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',d1_zfmisc_1) ).
fof(26,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',commutativity_k2_xboole_0) ).
fof(28,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t37_xboole_1) ).
fof(32,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t7_xboole_1) ).
fof(41,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t48_xboole_1) ).
fof(43,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t1_zfmisc_1) ).
fof(45,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',symmetry_r1_xboole_0) ).
fof(46,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',d1_xboole_0) ).
fof(49,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',commutativity_k3_xboole_0) ).
fof(58,axiom,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',t39_xboole_1) ).
fof(63,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',l2_zfmisc_1) ).
fof(65,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',d1_tarski) ).
fof(66,axiom,
! [X1] : singleton(X1) != empty_set,
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',l1_zfmisc_1) ).
fof(68,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpxVJoJh/sel_SEU147+2.p_1',d3_tarski) ).
fof(71,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(assume_negation,[status(cth)],[43]) ).
fof(75,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).
fof(79,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(fof_simplification,[status(thm)],[71,theory(equality)]) ).
fof(80,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[46,theory(equality)]) ).
fof(86,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(87,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[86]) ).
fof(105,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[9]) ).
cnf(106,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[105]) ).
fof(115,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_difference(X1,X2) = X1 )
& ( set_difference(X1,X2) != X1
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(116,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X3,X4) != X3
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[115]) ).
cnf(118,plain,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(122,plain,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[14]) ).
cnf(123,plain,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[122]) ).
fof(128,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[17]) ).
cnf(129,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[128]) ).
fof(130,plain,
! [X1] :
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(131,plain,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[130]) ).
cnf(132,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[131]) ).
fof(133,plain,
! [X1,X2] :
( ( disjoint(X1,X2)
| ? [X3] :
( in(X3,X1)
& in(X3,X2) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X2) )
| ~ disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[75]) ).
fof(134,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| ? [X6] :
( in(X6,X4)
& in(X6,X5) ) )
& ( ! [X7] :
( ~ in(X7,X4)
| ~ in(X7,X5) )
| ~ disjoint(X4,X5) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| ( in(esk2_2(X4,X5),X4)
& in(esk2_2(X4,X5),X5) ) )
& ( ! [X7] :
( ~ in(X7,X4)
| ~ in(X7,X5) )
| ~ disjoint(X4,X5) ) ),
inference(skolemize,[status(esa)],[134]) ).
fof(136,plain,
! [X4,X5,X7] :
( ( ~ in(X7,X4)
| ~ in(X7,X5)
| ~ disjoint(X4,X5) )
& ( disjoint(X4,X5)
| ( in(esk2_2(X4,X5),X4)
& in(esk2_2(X4,X5),X5) ) ) ),
inference(shift_quantors,[status(thm)],[135]) ).
fof(137,plain,
! [X4,X5,X7] :
( ( ~ in(X7,X4)
| ~ in(X7,X5)
| ~ disjoint(X4,X5) )
& ( in(esk2_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk2_2(X4,X5),X5)
| disjoint(X4,X5) ) ),
inference(distribute,[status(thm)],[136]) ).
cnf(138,plain,
( disjoint(X1,X2)
| in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(139,plain,
( disjoint(X1,X2)
| in(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(154,plain,
! [X1,X2] :
( ( X2 != powerset(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| subset(X3,X1) )
& ( ~ subset(X3,X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ subset(X3,X1) )
& ( in(X3,X2)
| subset(X3,X1) ) )
| X2 = powerset(X1) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(155,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ subset(X7,X4) )
& ( in(X7,X5)
| subset(X7,X4) ) )
| X5 = powerset(X4) ) ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| ~ subset(esk4_2(X4,X5),X4) )
& ( in(esk4_2(X4,X5),X5)
| subset(esk4_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(skolemize,[status(esa)],[155]) ).
fof(157,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) )
| X5 != powerset(X4) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| ~ subset(esk4_2(X4,X5),X4) )
& ( in(esk4_2(X4,X5),X5)
| subset(esk4_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(shift_quantors,[status(thm)],[156]) ).
fof(158,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| ~ subset(esk4_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk4_2(X4,X5),X5)
| subset(esk4_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
inference(distribute,[status(thm)],[157]) ).
cnf(161,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(162,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[158]) ).
fof(165,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[26]) ).
cnf(166,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[165]) ).
fof(169,plain,
! [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(170,plain,
! [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[169]) ).
cnf(171,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[170]) ).
fof(183,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[32]) ).
cnf(184,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[183]) ).
fof(222,plain,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[41]) ).
cnf(223,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[222]) ).
cnf(227,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(split_conjunct,[status(thm)],[79]) ).
fof(230,plain,
! [X1,X2] :
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(231,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[230]) ).
cnf(232,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[231]) ).
fof(233,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[80]) ).
fof(234,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[233]) ).
fof(235,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk8_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[234]) ).
fof(236,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk8_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[235]) ).
cnf(238,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[236]) ).
fof(248,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[49]) ).
cnf(249,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[248]) ).
fof(268,plain,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[58]) ).
cnf(269,plain,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[268]) ).
fof(283,plain,
! [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| in(X1,X2) )
& ( ~ in(X1,X2)
| subset(singleton(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[63]) ).
fof(284,plain,
! [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(variable_rename,[status(thm)],[283]) ).
cnf(285,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[284]) ).
fof(289,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[65]) ).
fof(290,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[289]) ).
fof(291,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) != X4 )
& ( in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[290]) ).
fof(292,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) != X4 )
& ( in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[291]) ).
fof(293,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[292]) ).
cnf(294,plain,
( X1 = singleton(X2)
| esk10_2(X2,X1) = X2
| in(esk10_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[293]) ).
cnf(295,plain,
( X1 = singleton(X2)
| esk10_2(X2,X1) != X2
| ~ in(esk10_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[293]) ).
cnf(297,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[293]) ).
fof(298,plain,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[66]) ).
cnf(299,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[298]) ).
fof(311,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[68]) ).
fof(312,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[311]) ).
fof(313,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk12_2(X4,X5),X4)
& ~ in(esk12_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[312]) ).
fof(314,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk12_2(X4,X5),X4)
& ~ in(esk12_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[313]) ).
fof(315,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk12_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk12_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[314]) ).
cnf(317,plain,
( subset(X1,X2)
| in(esk12_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[315]) ).
cnf(332,plain,
( unordered_pair(X2,X2) = X1
| esk10_2(X2,X1) = X2
| in(esk10_2(X2,X1),X1) ),
inference(rw,[status(thm)],[294,106,theory(equality)]),
[unfolding] ).
cnf(336,plain,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[285,106,theory(equality)]),
[unfolding] ).
cnf(339,plain,
( X2 = X3
| unordered_pair(X2,X2) != X1
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[297,106,theory(equality)]),
[unfolding] ).
cnf(341,plain,
( unordered_pair(X2,X2) = X1
| esk10_2(X2,X1) != X2
| ~ in(esk10_2(X2,X1),X1) ),
inference(rw,[status(thm)],[295,106,theory(equality)]),
[unfolding] ).
cnf(342,plain,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[299,106,theory(equality)]),
[unfolding] ).
cnf(343,negated_conjecture,
powerset(empty_set) != unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[227,106,theory(equality)]),
[unfolding] ).
cnf(346,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[249,223,theory(equality)]),223,theory(equality)]),
[unfolding] ).
cnf(399,plain,
set_difference(X1,set_union2(X1,X2)) = empty_set,
inference(spm,[status(thm)],[171,184,theory(equality)]) ).
cnf(422,plain,
set_difference(set_union2(X1,X2),set_difference(X2,X1)) = set_difference(X1,set_difference(X2,X1)),
inference(spm,[status(thm)],[123,269,theory(equality)]) ).
cnf(423,plain,
set_difference(set_union2(X2,X1),X2) = set_difference(X1,X2),
inference(spm,[status(thm)],[123,166,theory(equality)]) ).
cnf(443,plain,
( X1 = X2
| ~ in(X2,unordered_pair(X1,X1)) ),
inference(er,[status(thm)],[339,theory(equality)]) ).
cnf(467,plain,
( subset(X1,X2)
| empty_set != X1 ),
inference(spm,[status(thm)],[238,317,theory(equality)]) ).
cnf(484,plain,
( set_difference(unordered_pair(X1,X1),X2) = empty_set
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[171,336,theory(equality)]) ).
cnf(531,plain,
( subset(esk2_2(X1,X2),X3)
| disjoint(X1,X2)
| powerset(X3) != X2 ),
inference(spm,[status(thm)],[162,138,theory(equality)]) ).
cnf(534,plain,
( in(X1,X2)
| powerset(set_union2(X1,X3)) != X2 ),
inference(spm,[status(thm)],[161,184,theory(equality)]) ).
cnf(673,negated_conjecture,
( esk10_2(X1,powerset(empty_set)) = X1
| in(esk10_2(X1,powerset(empty_set)),powerset(empty_set))
| unordered_pair(X1,X1) != unordered_pair(empty_set,empty_set) ),
inference(spm,[status(thm)],[343,332,theory(equality)]) ).
cnf(1275,plain,
( set_difference(X1,X2) = empty_set
| empty_set != X1 ),
inference(spm,[status(thm)],[171,467,theory(equality)]) ).
cnf(1349,plain,
( set_union2(X1,empty_set) = set_union2(X1,X2)
| empty_set != X2 ),
inference(spm,[status(thm)],[269,1275,theory(equality)]) ).
cnf(1382,plain,
( X1 = set_union2(X1,X2)
| empty_set != X2 ),
inference(rw,[status(thm)],[1349,87,theory(equality)]) ).
cnf(1405,plain,
( X1 = set_union2(X2,X1)
| empty_set != X2 ),
inference(spm,[status(thm)],[166,1382,theory(equality)]) ).
cnf(2272,plain,
set_difference(set_union2(X1,X2),set_difference(X2,X1)) = set_difference(X1,set_difference(X1,set_union2(X1,X2))),
inference(spm,[status(thm)],[346,423,theory(equality)]) ).
cnf(2313,plain,
set_difference(X1,set_difference(X2,X1)) = set_difference(X1,set_difference(X1,set_union2(X1,X2))),
inference(rw,[status(thm)],[2272,422,theory(equality)]) ).
cnf(2314,plain,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2313,399,theory(equality)]),129,theory(equality)]) ).
cnf(2615,plain,
( X1 = esk2_2(unordered_pair(X1,X1),X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[443,139,theory(equality)]) ).
cnf(3982,plain,
( empty_set = unordered_pair(X1,X1)
| ~ in(X1,set_difference(X2,unordered_pair(X1,X1))) ),
inference(spm,[status(thm)],[2314,484,theory(equality)]) ).
cnf(4042,plain,
~ in(X1,set_difference(X2,unordered_pair(X1,X1))),
inference(sr,[status(thm)],[3982,342,theory(equality)]) ).
cnf(4989,plain,
( empty_set = esk2_2(X1,X2)
| disjoint(X1,X2)
| powerset(empty_set) != X2 ),
inference(spm,[status(thm)],[132,531,theory(equality)]) ).
cnf(5010,plain,
in(X1,powerset(set_union2(X1,X2))),
inference(er,[status(thm)],[534,theory(equality)]) ).
cnf(5072,plain,
( in(X1,powerset(X2))
| empty_set != X1 ),
inference(spm,[status(thm)],[5010,1405,theory(equality)]) ).
cnf(13605,negated_conjecture,
( esk10_2(empty_set,powerset(empty_set)) = empty_set
| in(esk10_2(empty_set,powerset(empty_set)),powerset(empty_set)) ),
inference(er,[status(thm)],[673,theory(equality)]) ).
cnf(13635,negated_conjecture,
in(esk10_2(empty_set,powerset(empty_set)),powerset(empty_set)),
inference(csr,[status(thm)],[13605,5072]) ).
cnf(13642,negated_conjecture,
( unordered_pair(empty_set,empty_set) = powerset(empty_set)
| esk10_2(empty_set,powerset(empty_set)) != empty_set ),
inference(spm,[status(thm)],[341,13635,theory(equality)]) ).
cnf(13648,negated_conjecture,
esk10_2(empty_set,powerset(empty_set)) != empty_set,
inference(sr,[status(thm)],[13642,343,theory(equality)]) ).
cnf(374547,plain,
( empty_set = X1
| disjoint(unordered_pair(X1,X1),X2)
| powerset(empty_set) != X2 ),
inference(spm,[status(thm)],[2615,4989,theory(equality)]) ).
cnf(375040,plain,
( disjoint(X1,unordered_pair(X2,X2))
| empty_set = X2
| powerset(empty_set) != X1 ),
inference(spm,[status(thm)],[232,374547,theory(equality)]) ).
cnf(375547,plain,
( set_difference(X1,unordered_pair(X2,X2)) = X1
| empty_set = X2
| powerset(empty_set) != X1 ),
inference(spm,[status(thm)],[118,375040,theory(equality)]) ).
cnf(375626,plain,
( set_difference(powerset(empty_set),unordered_pair(X1,X1)) = powerset(empty_set)
| empty_set = X1 ),
inference(er,[status(thm)],[375547,theory(equality)]) ).
cnf(376180,plain,
( empty_set = X1
| ~ in(X1,powerset(empty_set)) ),
inference(spm,[status(thm)],[4042,375626,theory(equality)]) ).
cnf(377033,negated_conjecture,
empty_set = esk10_2(empty_set,powerset(empty_set)),
inference(spm,[status(thm)],[376180,13635,theory(equality)]) ).
cnf(377293,negated_conjecture,
$false,
inference(sr,[status(thm)],[377033,13648,theory(equality)]) ).
cnf(377294,negated_conjecture,
$false,
377293,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU147+2.p
% --creating new selector for []
% -running prover on /tmp/tmpxVJoJh/sel_SEU147+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU147+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU147+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU147+2.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
%
%------------------------------------------------------------------------------