%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET671+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 03:09:35 EST 2010
% Result : Theorem 10.98s
% Output : CNFRefutation 10.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 212 ( 23 unt; 0 def)
% Number of atoms : 1131 ( 60 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 1514 ( 595 ~; 698 |; 148 &)
% ( 12 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 6 con; 0-4 aty)
% Number of variables : 528 ( 28 sgn 238 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> restrict4(X1,X2,X3,X4) = restrict(X3,X4) ) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p25) ).
fof(3,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p27) ).
fof(5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( relation_like(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
=> ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X2 = ordered_pair(X3,X4) ) ) ) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p21) ).
fof(7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p23) ).
fof(8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p22) ).
fof(9,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X1))
=> ( subset(X2,X3)
=> restrict4(X2,X1,X4,X3) = X4 ) ) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',prove_relset_1_34) ).
fof(10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p10) ).
fof(12,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('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p12) ).
fof(17,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('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p17) ).
fof(18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p18) ).
fof(19,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('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p19) ).
fof(20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,binary_relation_type)
=> ( member(ordered_pair(X2,X3),restrict(X4,X1))
<=> ( member(X2,X1)
& member(ordered_pair(X2,X3),X4) ) ) ) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p2) ).
fof(21,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p3) ).
fof(22,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( X1 = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( member(ordered_pair(X3,X4),X1)
<=> member(ordered_pair(X3,X4),X2) ) ) ) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p1) ).
fof(23,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('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p6) ).
fof(25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p4) ).
fof(28,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(restrict(X1,X2),binary_relation_type) ) ),
file('/tmp/tmpmlkqRX/sel_SET671+3.p_1',p9) ).
fof(29,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X1))
=> ( subset(X2,X3)
=> restrict4(X2,X1,X4,X3) = X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(31,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(32,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[18,theory(equality)]) ).
fof(33,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)],[19,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| restrict4(X1,X2,X3,X4) = restrict(X3,X4) ) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(35,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,relation_type(X5,X6))
| ! [X8] :
( ~ ilf_type(X8,set_type)
| restrict4(X5,X6,X7,X8) = restrict(X7,X8) ) ) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| restrict4(X5,X6,X7,X8) = restrict(X7,X8)
| ~ ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[35]) ).
cnf(37,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(41,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[3]) ).
cnf(42,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[41]) ).
fof(47,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ relation_like(X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X2 = ordered_pair(X3,X4) ) ) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X1)
& ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| X2 != ordered_pair(X3,X4) ) ) )
| relation_like(X1) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(48,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ relation_like(X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X5)
| ? [X7] :
( ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,set_type)
& X6 = ordered_pair(X7,X8) ) ) ) )
& ( ? [X9] :
( ilf_type(X9,set_type)
& member(X9,X5)
& ! [X10] :
( ~ ilf_type(X10,set_type)
| ! [X11] :
( ~ ilf_type(X11,set_type)
| X9 != ordered_pair(X10,X11) ) ) )
| relation_like(X5) ) ) ),
inference(variable_rename,[status(thm)],[47]) ).
fof(49,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ relation_like(X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X5)
| ( ilf_type(esk1_2(X5,X6),set_type)
& ilf_type(esk2_2(X5,X6),set_type)
& X6 = ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)) ) ) )
& ( ( ilf_type(esk3_1(X5),set_type)
& member(esk3_1(X5),X5)
& ! [X10] :
( ~ ilf_type(X10,set_type)
| ! [X11] :
( ~ ilf_type(X11,set_type)
| esk3_1(X5) != ordered_pair(X10,X11) ) ) )
| relation_like(X5) ) ) ),
inference(skolemize,[status(esa)],[48]) ).
fof(50,plain,
! [X5,X6,X10,X11] :
( ( ( ( ( ~ ilf_type(X11,set_type)
| esk3_1(X5) != ordered_pair(X10,X11)
| ~ ilf_type(X10,set_type) )
& member(esk3_1(X5),X5)
& ilf_type(esk3_1(X5),set_type) )
| relation_like(X5) )
& ( ~ ilf_type(X6,set_type)
| ~ member(X6,X5)
| ( ilf_type(esk1_2(X5,X6),set_type)
& ilf_type(esk2_2(X5,X6),set_type)
& X6 = ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)) )
| ~ relation_like(X5) ) )
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[49]) ).
fof(51,plain,
! [X5,X6,X10,X11] :
( ( ~ ilf_type(X11,set_type)
| esk3_1(X5) != ordered_pair(X10,X11)
| ~ ilf_type(X10,set_type)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( member(esk3_1(X5),X5)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk3_1(X5),set_type)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk1_2(X5,X6),set_type)
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk2_2(X5,X6),set_type)
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( X6 = ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6))
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[50]) ).
cnf(52,plain,
( X2 = ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(62,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ empty(X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X1) )
| empty(X1) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(63,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ? [X5] :
( ilf_type(X5,set_type)
& member(X5,X3) )
| empty(X3) ) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk5_1(X3),set_type)
& member(esk5_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk5_1(X3),set_type)
& member(esk5_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[64]) ).
fof(66,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk5_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk5_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[65]) ).
cnf(69,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(70,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| relation_like(X3) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(71,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6) ) ) ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[71]) ).
cnf(73,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(74,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,relation_type(X2,X1))
& subset(X2,X3)
& restrict4(X2,X1,X4,X3) != X4 ) ) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(75,negated_conjecture,
? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,set_type)
& ? [X7] :
( ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,relation_type(X6,X5))
& subset(X6,X7)
& restrict4(X6,X5,X8,X7) != X8 ) ) ) ),
inference(variable_rename,[status(thm)],[74]) ).
fof(76,negated_conjecture,
( ilf_type(esk6_0,set_type)
& ilf_type(esk7_0,set_type)
& ilf_type(esk8_0,set_type)
& ilf_type(esk9_0,relation_type(esk7_0,esk6_0))
& subset(esk7_0,esk8_0)
& restrict4(esk7_0,esk6_0,esk9_0,esk8_0) != esk9_0 ),
inference(skolemize,[status(esa)],[75]) ).
cnf(77,negated_conjecture,
restrict4(esk7_0,esk6_0,esk9_0,esk8_0) != esk9_0,
inference(split_conjunct,[status(thm)],[76]) ).
cnf(78,negated_conjecture,
subset(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(79,negated_conjecture,
ilf_type(esk9_0,relation_type(esk7_0,esk6_0)),
inference(split_conjunct,[status(thm)],[76]) ).
fof(83,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,binary_relation_type)
| ( relation_like(X1)
& ilf_type(X1,set_type) ) )
& ( ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,binary_relation_type) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(84,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,binary_relation_type)
| ( relation_like(X2)
& ilf_type(X2,set_type) ) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type) ) ) ),
inference(variable_rename,[status(thm)],[83]) ).
fof(85,plain,
! [X2] :
( ( relation_like(X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ilf_type(X2,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[84]) ).
cnf(86,plain,
( ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1) ),
inference(split_conjunct,[status(thm)],[85]) ).
fof(92,plain,
! [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))) )
& ( ~ ilf_type(X2,member_type(power_set(X1)))
| ilf_type(X2,subset_type(X1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(93,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3))) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3)) ) ) ) ),
inference(variable_rename,[status(thm)],[92]) ).
fof(94,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3))) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[93]) ).
fof(95,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3)))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[94]) ).
cnf(96,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(97,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[95]) ).
fof(112,plain,
! [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) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ~ member(X3,X2) )
| member(X1,power_set(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(113,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(X4,power_set(X5))
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& member(X7,X4)
& ~ member(X7,X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(X4,power_set(X5))
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( ilf_type(esk12_2(X4,X5),set_type)
& member(esk12_2(X4,X5),X4)
& ~ member(esk12_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[113]) ).
fof(115,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk12_2(X4,X5),set_type)
& member(esk12_2(X4,X5),X4)
& ~ member(esk12_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[114]) ).
fof(116,plain,
! [X4,X5,X6] :
( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk12_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk12_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk12_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(117,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(118,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(120,plain,
( member(X3,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X2))
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(121,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(122,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[121]) ).
fof(123,plain,
! [X2] :
( ( ~ empty(power_set(X2))
| ~ ilf_type(X2,set_type) )
& ( ilf_type(power_set(X2),set_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[122]) ).
cnf(125,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[123]) ).
fof(126,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( empty(X2)
| ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X1,member_type(X2))
| member(X1,X2) )
& ( ~ member(X1,X2)
| ilf_type(X1,member_type(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(127,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( empty(X4)
| ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4)) ) ) ) ),
inference(variable_rename,[status(thm)],[126]) ).
fof(128,plain,
! [X3,X4] :
( empty(X4)
| ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[127]) ).
fof(129,plain,
! [X3,X4] :
( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4)
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4))
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[128]) ).
cnf(130,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[129]) ).
cnf(131,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[129]) ).
fof(132,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,binary_relation_type)
| ( ( ~ member(ordered_pair(X2,X3),restrict(X4,X1))
| ( member(X2,X1)
& member(ordered_pair(X2,X3),X4) ) )
& ( ~ member(X2,X1)
| ~ member(ordered_pair(X2,X3),X4)
| member(ordered_pair(X2,X3),restrict(X4,X1)) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(133,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,binary_relation_type)
| ( ( ~ member(ordered_pair(X6,X7),restrict(X8,X5))
| ( member(X6,X5)
& member(ordered_pair(X6,X7),X8) ) )
& ( ~ member(X6,X5)
| ~ member(ordered_pair(X6,X7),X8)
| member(ordered_pair(X6,X7),restrict(X8,X5)) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[132]) ).
fof(134,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,binary_relation_type)
| ( ( ~ member(ordered_pair(X6,X7),restrict(X8,X5))
| ( member(X6,X5)
& member(ordered_pair(X6,X7),X8) ) )
& ( ~ member(X6,X5)
| ~ member(ordered_pair(X6,X7),X8)
| member(ordered_pair(X6,X7),restrict(X8,X5)) ) )
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[133]) ).
fof(135,plain,
! [X5,X6,X7,X8] :
( ( member(X6,X5)
| ~ member(ordered_pair(X6,X7),restrict(X8,X5))
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(ordered_pair(X6,X7),X8)
| ~ member(ordered_pair(X6,X7),restrict(X8,X5))
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ member(X6,X5)
| ~ member(ordered_pair(X6,X7),X8)
| member(ordered_pair(X6,X7),restrict(X8,X5))
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[134]) ).
cnf(136,plain,
( member(ordered_pair(X2,X3),restrict(X4,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X2,X3),X4)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(137,plain,
( member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X2,X3),restrict(X4,X1)) ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(139,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5)
| ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(140,plain,
! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ! [X9] :
( ~ ilf_type(X9,set_type)
| ! [X10] :
( ~ ilf_type(X10,relation_type(X6,X7))
| ~ member(ordered_pair(X8,X9),X10)
| ( member(X8,X6)
& member(X9,X7) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,plain,
! [X6,X7,X8,X9,X10] :
( ~ ilf_type(X10,relation_type(X6,X7))
| ~ member(ordered_pair(X8,X9),X10)
| ( member(X8,X6)
& member(X9,X7) )
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ),
inference(shift_quantors,[status(thm)],[140]) ).
fof(142,plain,
! [X6,X7,X8,X9,X10] :
( ( member(X8,X6)
| ~ member(ordered_pair(X8,X9),X10)
| ~ ilf_type(X10,relation_type(X6,X7))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( member(X9,X7)
| ~ member(ordered_pair(X8,X9),X10)
| ~ ilf_type(X10,relation_type(X6,X7))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ) ),
inference(distribute,[status(thm)],[141]) ).
cnf(144,plain,
( member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[142]) ).
fof(145,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ( ( X1 != X2
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ member(ordered_pair(X3,X4),X1)
| member(ordered_pair(X3,X4),X2) )
& ( ~ member(ordered_pair(X3,X4),X2)
| member(ordered_pair(X3,X4),X1) ) ) ) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& ( ~ member(ordered_pair(X3,X4),X1)
| ~ member(ordered_pair(X3,X4),X2) )
& ( member(ordered_pair(X3,X4),X1)
| member(ordered_pair(X3,X4),X2) ) ) )
| X1 = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(146,plain,
! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ! [X6] :
( ~ ilf_type(X6,binary_relation_type)
| ( ( X5 != X6
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6) )
& ( ~ member(ordered_pair(X7,X8),X6)
| member(ordered_pair(X7,X8),X5) ) ) ) ) )
& ( ? [X9] :
( ilf_type(X9,set_type)
& ? [X10] :
( ilf_type(X10,set_type)
& ( ~ member(ordered_pair(X9,X10),X5)
| ~ member(ordered_pair(X9,X10),X6) )
& ( member(ordered_pair(X9,X10),X5)
| member(ordered_pair(X9,X10),X6) ) ) )
| X5 = X6 ) ) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ! [X6] :
( ~ ilf_type(X6,binary_relation_type)
| ( ( X5 != X6
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6) )
& ( ~ member(ordered_pair(X7,X8),X6)
| member(ordered_pair(X7,X8),X5) ) ) ) ) )
& ( ( ilf_type(esk13_2(X5,X6),set_type)
& ilf_type(esk14_2(X5,X6),set_type)
& ( ~ member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X5)
| ~ member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X6) )
& ( member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X5)
| member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X6) ) )
| X5 = X6 ) ) ) ),
inference(skolemize,[status(esa)],[146]) ).
fof(148,plain,
! [X5,X6,X7,X8] :
( ( ( ~ ilf_type(X8,set_type)
| ( ( ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6) )
& ( ~ member(ordered_pair(X7,X8),X6)
| member(ordered_pair(X7,X8),X5) ) )
| ~ ilf_type(X7,set_type)
| X5 != X6 )
& ( ( ilf_type(esk13_2(X5,X6),set_type)
& ilf_type(esk14_2(X5,X6),set_type)
& ( ~ member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X5)
| ~ member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X6) )
& ( member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X5)
| member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X6) ) )
| X5 = X6 ) )
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) ),
inference(shift_quantors,[status(thm)],[147]) ).
fof(149,plain,
! [X5,X6,X7,X8] :
( ( ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| X5 != X6
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ~ member(ordered_pair(X7,X8),X6)
| member(ordered_pair(X7,X8),X5)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| X5 != X6
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ilf_type(esk13_2(X5,X6),set_type)
| X5 = X6
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ilf_type(esk14_2(X5,X6),set_type)
| X5 = X6
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ~ member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X5)
| ~ member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X6)
| X5 = X6
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X5)
| member(ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)),X6)
| X5 = X6
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) ) ),
inference(distribute,[status(thm)],[148]) ).
cnf(150,plain,
( X1 = X2
| member(ordered_pair(esk13_2(X1,X2),esk14_2(X1,X2)),X2)
| member(ordered_pair(esk13_2(X1,X2),esk14_2(X1,X2)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[149]) ).
cnf(151,plain,
( X1 = X2
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(esk13_2(X1,X2),esk14_2(X1,X2)),X2)
| ~ member(ordered_pair(esk13_2(X1,X2),esk14_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[149]) ).
fof(156,plain,
! [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) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(157,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ subset(X4,X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[156]) ).
fof(158,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ subset(X4,X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( ilf_type(esk15_2(X4,X5),set_type)
& member(esk15_2(X4,X5),X4)
& ~ member(esk15_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[157]) ).
fof(159,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk15_2(X4,X5),set_type)
& member(esk15_2(X4,X5),X4)
& ~ member(esk15_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[158]) ).
fof(160,plain,
! [X4,X5,X6] :
( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk15_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk15_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk15_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[159]) ).
cnf(164,plain,
( member(X3,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[160]) ).
fof(169,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ! [X3] :
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(170,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ! [X7] :
( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6)) )
& ! [X8] :
( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6))) ) ) ) ),
inference(variable_rename,[status(thm)],[169]) ).
fof(171,plain,
! [X5,X6,X7,X8] :
( ( ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6))) )
& ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6)) ) )
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[170]) ).
fof(172,plain,
! [X5,X6,X7,X8] :
( ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6)))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[171]) ).
cnf(174,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[172]) ).
fof(184,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ilf_type(restrict(X1,X2),binary_relation_type) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(185,plain,
! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ilf_type(restrict(X3,X4),binary_relation_type) ) ),
inference(variable_rename,[status(thm)],[184]) ).
fof(186,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ilf_type(restrict(X3,X4),binary_relation_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(shift_quantors,[status(thm)],[185]) ).
cnf(187,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[186]) ).
cnf(195,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[125,42,theory(equality)]) ).
cnf(196,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[195,theory(equality)]) ).
cnf(206,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[86,42,theory(equality)]) ).
cnf(207,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[206,theory(equality)]) ).
cnf(227,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| $false
| ~ ilf_type(X1,binary_relation_type) ),
inference(rw,[status(thm)],[187,42,theory(equality)]) ).
cnf(228,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[227,theory(equality)]) ).
cnf(234,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[69,42,theory(equality)]) ).
cnf(235,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[234,42,theory(equality)]) ).
cnf(236,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[235,theory(equality)]) ).
cnf(253,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[73,42,theory(equality)]) ).
cnf(254,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[253,42,theory(equality)]) ).
cnf(255,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[254,theory(equality)]) ).
cnf(257,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[118,42,theory(equality)]) ).
cnf(258,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[257,42,theory(equality)]) ).
cnf(259,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1) ),
inference(cn,[status(thm)],[258,theory(equality)]) ).
cnf(261,plain,
( member(X1,power_set(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk12_2(X1,X2),X2) ),
inference(rw,[status(thm)],[117,42,theory(equality)]) ).
cnf(262,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk12_2(X1,X2),X2) ),
inference(rw,[status(thm)],[261,42,theory(equality)]) ).
cnf(263,plain,
( member(X1,power_set(X2))
| ~ member(esk12_2(X1,X2),X2) ),
inference(cn,[status(thm)],[262,theory(equality)]) ).
cnf(264,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[263,259,theory(equality)]) ).
cnf(265,plain,
( ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[52,42,theory(equality)]) ).
cnf(266,plain,
( ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[265,42,theory(equality)]) ).
cnf(267,plain,
( ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[266,theory(equality)]) ).
cnf(272,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[130,42,theory(equality)]) ).
cnf(273,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[272,42,theory(equality)]) ).
cnf(274,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[273,theory(equality)]) ).
cnf(275,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[274,236]) ).
cnf(280,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[131,42,theory(equality)]) ).
cnf(281,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[280,42,theory(equality)]) ).
cnf(282,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[281,theory(equality)]) ).
cnf(288,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[97,42,theory(equality)]) ).
cnf(289,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[288,42,theory(equality)]) ).
cnf(290,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(292,plain,
( ilf_type(X2,subset_type(X1))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[96,42,theory(equality)]) ).
cnf(293,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[292,42,theory(equality)]) ).
cnf(294,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[293,theory(equality)]) ).
cnf(311,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[164,42,theory(equality)]) ).
cnf(312,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[311,42,theory(equality)]) ).
cnf(313,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[312,42,theory(equality)]) ).
cnf(314,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[313,theory(equality)]) ).
cnf(315,negated_conjecture,
( member(X1,esk8_0)
| ~ member(X1,esk7_0) ),
inference(spm,[status(thm)],[314,78,theory(equality)]) ).
cnf(317,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[174,42,theory(equality)]) ).
cnf(318,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[317,42,theory(equality)]) ).
cnf(319,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[318,theory(equality)]) ).
cnf(320,negated_conjecture,
ilf_type(esk9_0,subset_type(cross_product(esk7_0,esk6_0))),
inference(spm,[status(thm)],[319,79,theory(equality)]) ).
cnf(326,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[37,42,theory(equality)]) ).
cnf(327,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[326,42,theory(equality)]) ).
cnf(328,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| $false
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[327,42,theory(equality)]) ).
cnf(329,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[328,theory(equality)]) ).
cnf(330,negated_conjecture,
restrict4(esk7_0,esk6_0,esk9_0,X1) = restrict(esk9_0,X1),
inference(spm,[status(thm)],[329,79,theory(equality)]) ).
cnf(338,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[120,42,theory(equality)]) ).
cnf(339,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[338,42,theory(equality)]) ).
cnf(340,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[339,42,theory(equality)]) ).
cnf(341,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[340,theory(equality)]) ).
cnf(352,plain,
( member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,binary_relation_type)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),restrict(X4,X1)) ),
inference(rw,[status(thm)],[137,42,theory(equality)]) ).
cnf(353,plain,
( member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,binary_relation_type)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),restrict(X4,X1)) ),
inference(rw,[status(thm)],[352,42,theory(equality)]) ).
cnf(354,plain,
( member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,binary_relation_type)
| $false
| $false
| $false
| ~ member(ordered_pair(X2,X3),restrict(X4,X1)) ),
inference(rw,[status(thm)],[353,42,theory(equality)]) ).
cnf(355,plain,
( member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X2,X3),restrict(X4,X1)) ),
inference(cn,[status(thm)],[354,theory(equality)]) ).
cnf(364,plain,
( member(X3,X1)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[144,42,theory(equality)]) ).
cnf(365,plain,
( member(X3,X1)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[364,42,theory(equality)]) ).
cnf(366,plain,
( member(X3,X1)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[365,42,theory(equality)]) ).
cnf(367,plain,
( member(X3,X1)
| $false
| $false
| $false
| $false
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[366,42,theory(equality)]) ).
cnf(368,plain,
( member(X3,X1)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(cn,[status(thm)],[367,theory(equality)]) ).
cnf(369,negated_conjecture,
( member(X1,esk7_0)
| ~ member(ordered_pair(X1,X2),esk9_0) ),
inference(spm,[status(thm)],[368,79,theory(equality)]) ).
cnf(371,plain,
( member(ordered_pair(X2,X3),restrict(X4,X1))
| ~ member(X2,X1)
| ~ ilf_type(X4,binary_relation_type)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(rw,[status(thm)],[136,42,theory(equality)]) ).
cnf(372,plain,
( member(ordered_pair(X2,X3),restrict(X4,X1))
| ~ member(X2,X1)
| ~ ilf_type(X4,binary_relation_type)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(rw,[status(thm)],[371,42,theory(equality)]) ).
cnf(373,plain,
( member(ordered_pair(X2,X3),restrict(X4,X1))
| ~ member(X2,X1)
| ~ ilf_type(X4,binary_relation_type)
| $false
| $false
| $false
| ~ member(ordered_pair(X2,X3),X4) ),
inference(rw,[status(thm)],[372,42,theory(equality)]) ).
cnf(374,plain,
( member(ordered_pair(X2,X3),restrict(X4,X1))
| ~ member(X2,X1)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(cn,[status(thm)],[373,theory(equality)]) ).
cnf(380,negated_conjecture,
restrict(esk9_0,esk8_0) != esk9_0,
inference(rw,[status(thm)],[77,330,theory(equality)]) ).
cnf(397,plain,
ilf_type(X1,member_type(power_set(X1))),
inference(spm,[status(thm)],[275,264,theory(equality)]) ).
cnf(407,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[294,397,theory(equality)]) ).
cnf(409,plain,
relation_like(cross_product(X1,X2)),
inference(spm,[status(thm)],[255,407,theory(equality)]) ).
cnf(427,negated_conjecture,
relation_like(esk9_0),
inference(spm,[status(thm)],[255,320,theory(equality)]) ).
cnf(428,negated_conjecture,
ilf_type(esk9_0,member_type(power_set(cross_product(esk7_0,esk6_0)))),
inference(spm,[status(thm)],[290,320,theory(equality)]) ).
cnf(431,negated_conjecture,
ilf_type(esk9_0,binary_relation_type),
inference(spm,[status(thm)],[207,427,theory(equality)]) ).
cnf(433,negated_conjecture,
ilf_type(restrict(esk9_0,X1),binary_relation_type),
inference(spm,[status(thm)],[228,431,theory(equality)]) ).
cnf(434,negated_conjecture,
( X1 = esk9_0
| member(ordered_pair(esk13_2(X1,esk9_0),esk14_2(X1,esk9_0)),X1)
| member(ordered_pair(esk13_2(X1,esk9_0),esk14_2(X1,esk9_0)),esk9_0)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[150,431,theory(equality)]) ).
cnf(435,negated_conjecture,
( X1 = esk9_0
| ~ member(ordered_pair(esk13_2(X1,esk9_0),esk14_2(X1,esk9_0)),esk9_0)
| ~ member(ordered_pair(esk13_2(X1,esk9_0),esk14_2(X1,esk9_0)),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[151,431,theory(equality)]) ).
cnf(437,negated_conjecture,
( member(ordered_pair(X1,X2),esk9_0)
| ~ member(ordered_pair(X1,X2),restrict(esk9_0,X3)) ),
inference(spm,[status(thm)],[355,431,theory(equality)]) ).
cnf(438,negated_conjecture,
( member(ordered_pair(X1,X2),restrict(esk9_0,X3))
| ~ member(ordered_pair(X1,X2),esk9_0)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[374,431,theory(equality)]) ).
cnf(489,negated_conjecture,
( member(esk9_0,power_set(cross_product(esk7_0,esk6_0)))
| empty(power_set(cross_product(esk7_0,esk6_0))) ),
inference(spm,[status(thm)],[282,428,theory(equality)]) ).
cnf(491,negated_conjecture,
member(esk9_0,power_set(cross_product(esk7_0,esk6_0))),
inference(sr,[status(thm)],[489,196,theory(equality)]) ).
cnf(506,negated_conjecture,
( member(X1,cross_product(esk7_0,esk6_0))
| ~ member(X1,esk9_0) ),
inference(spm,[status(thm)],[341,491,theory(equality)]) ).
cnf(1111,negated_conjecture,
( member(esk12_2(esk9_0,X1),cross_product(esk7_0,esk6_0))
| member(esk9_0,power_set(X1)) ),
inference(spm,[status(thm)],[506,259,theory(equality)]) ).
cnf(1187,negated_conjecture,
( ordered_pair(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),esk2_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1))) = esk12_2(esk9_0,X1)
| member(esk9_0,power_set(X1))
| ~ relation_like(cross_product(esk7_0,esk6_0)) ),
inference(spm,[status(thm)],[267,1111,theory(equality)]) ).
cnf(1190,negated_conjecture,
( ordered_pair(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),esk2_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1))) = esk12_2(esk9_0,X1)
| member(esk9_0,power_set(X1))
| $false ),
inference(rw,[status(thm)],[1187,409,theory(equality)]) ).
cnf(1191,negated_conjecture,
( ordered_pair(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),esk2_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1))) = esk12_2(esk9_0,X1)
| member(esk9_0,power_set(X1)) ),
inference(cn,[status(thm)],[1190,theory(equality)]) ).
cnf(1575,negated_conjecture,
( restrict(esk9_0,X1) = esk9_0
| member(ordered_pair(esk13_2(restrict(esk9_0,X1),esk9_0),esk14_2(restrict(esk9_0,X1),esk9_0)),esk9_0)
| member(ordered_pair(esk13_2(restrict(esk9_0,X1),esk9_0),esk14_2(restrict(esk9_0,X1),esk9_0)),restrict(esk9_0,X1)) ),
inference(spm,[status(thm)],[434,433,theory(equality)]) ).
cnf(1616,negated_conjecture,
( restrict(esk9_0,X1) = esk9_0
| ~ member(ordered_pair(esk13_2(restrict(esk9_0,X1),esk9_0),esk14_2(restrict(esk9_0,X1),esk9_0)),esk9_0)
| ~ member(ordered_pair(esk13_2(restrict(esk9_0,X1),esk9_0),esk14_2(restrict(esk9_0,X1),esk9_0)),restrict(esk9_0,X1)) ),
inference(spm,[status(thm)],[435,433,theory(equality)]) ).
cnf(1669,negated_conjecture,
( member(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),esk7_0)
| member(esk9_0,power_set(X1))
| ~ member(esk12_2(esk9_0,X1),esk9_0) ),
inference(spm,[status(thm)],[369,1191,theory(equality)]) ).
cnf(1753,negated_conjecture,
( member(esk12_2(esk9_0,X1),restrict(esk9_0,X2))
| member(esk9_0,power_set(X1))
| ~ member(esk12_2(esk9_0,X1),esk9_0)
| ~ member(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),X2) ),
inference(spm,[status(thm)],[438,1191,theory(equality)]) ).
cnf(64565,negated_conjecture,
( restrict(esk9_0,X1) = esk9_0
| member(ordered_pair(esk13_2(restrict(esk9_0,X1),esk9_0),esk14_2(restrict(esk9_0,X1),esk9_0)),esk9_0) ),
inference(csr,[status(thm)],[1575,437]) ).
cnf(65453,negated_conjecture,
( restrict(esk9_0,X1) = esk9_0
| ~ member(ordered_pair(esk13_2(restrict(esk9_0,X1),esk9_0),esk14_2(restrict(esk9_0,X1),esk9_0)),restrict(esk9_0,X1)) ),
inference(csr,[status(thm)],[1616,64565]) ).
cnf(67180,negated_conjecture,
( member(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),esk7_0)
| member(esk9_0,power_set(X1)) ),
inference(csr,[status(thm)],[1669,259]) ).
cnf(67184,negated_conjecture,
( member(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),esk8_0)
| member(esk9_0,power_set(X1)) ),
inference(spm,[status(thm)],[315,67180,theory(equality)]) ).
cnf(70852,negated_conjecture,
( member(esk12_2(esk9_0,X1),restrict(esk9_0,X2))
| member(esk9_0,power_set(X1))
| ~ member(esk1_2(cross_product(esk7_0,esk6_0),esk12_2(esk9_0,X1)),X2) ),
inference(csr,[status(thm)],[1753,259]) ).
cnf(70856,negated_conjecture,
( member(esk12_2(esk9_0,X1),restrict(esk9_0,esk8_0))
| member(esk9_0,power_set(X1)) ),
inference(spm,[status(thm)],[70852,67184,theory(equality)]) ).
cnf(71389,negated_conjecture,
member(esk9_0,power_set(restrict(esk9_0,esk8_0))),
inference(spm,[status(thm)],[263,70856,theory(equality)]) ).
cnf(71405,negated_conjecture,
( member(X1,restrict(esk9_0,esk8_0))
| ~ member(X1,esk9_0) ),
inference(spm,[status(thm)],[341,71389,theory(equality)]) ).
cnf(71623,negated_conjecture,
( member(ordered_pair(esk13_2(restrict(esk9_0,X1),esk9_0),esk14_2(restrict(esk9_0,X1),esk9_0)),restrict(esk9_0,esk8_0))
| restrict(esk9_0,X1) = esk9_0 ),
inference(spm,[status(thm)],[71405,64565,theory(equality)]) ).
cnf(72738,negated_conjecture,
restrict(esk9_0,esk8_0) = esk9_0,
inference(spm,[status(thm)],[65453,71623,theory(equality)]) ).
cnf(72743,negated_conjecture,
$false,
inference(sr,[status(thm)],[72738,380,theory(equality)]) ).
cnf(72744,negated_conjecture,
$false,
72743,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET671+3.p
% --creating new selector for []
% -running prover on /tmp/tmpmlkqRX/sel_SET671+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET671+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET671+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET671+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
%
%------------------------------------------------------------------------------