TSTP Solution File: SET646+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET646+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:07:16 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 100 ( 9 unt; 0 def)
% Number of atoms : 596 ( 50 equ)
% Maximal formula atoms : 31 ( 5 avg)
% Number of connectives : 809 ( 313 ~; 362 |; 89 &)
% ( 9 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 257 ( 8 sgn 128 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpg5mXFL/sel_SET646+3.p_1',p25) ).
fof(3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpg5mXFL/sel_SET646+3.p_1',p21) ).
fof(7,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ( member(X3,X1)
& member(X4,X2) )
=> ilf_type(singleton(ordered_pair(X3,X4)),relation_type(X1,X2)) ) ) ) ) ),
file('/tmp/tmpg5mXFL/sel_SET646+3.p_1',prove_relset_1_8) ).
fof(10,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/tmpg5mXFL/sel_SET646+3.p_1',p12) ).
fof(15,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/tmpg5mXFL/sel_SET646+3.p_1',p17) ).
fof(17,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/tmpg5mXFL/sel_SET646+3.p_1',p19) ).
fof(18,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)
=> ( member(ordered_pair(X1,X2),cross_product(X3,X4))
<=> ( member(X1,X3)
& member(X2,X4) ) ) ) ) ) ),
file('/tmp/tmpg5mXFL/sel_SET646+3.p_1',p2) ).
fof(19,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/tmpg5mXFL/sel_SET646+3.p_1',p3) ).
fof(24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( X3 = singleton(X2)
<=> ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X3)
<=> X4 = X2 ) ) ) ) ) ),
file('/tmp/tmpg5mXFL/sel_SET646+3.p_1',p5) ).
fof(27,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ( member(X3,X1)
& member(X4,X2) )
=> ilf_type(singleton(ordered_pair(X3,X4)),relation_type(X1,X2)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(28,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(31,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)],[17,theory(equality)]) ).
fof(32,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[1]) ).
cnf(33,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[32]) ).
fof(38,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)],[28]) ).
fof(39,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)],[38]) ).
fof(40,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk1_1(X3),set_type)
& member(esk1_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[39]) ).
fof(41,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk1_1(X3),set_type)
& member(esk1_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[40]) ).
fof(42,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk1_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk1_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[41]) ).
cnf(45,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(64,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& member(X3,X1)
& member(X4,X2)
& ~ ilf_type(singleton(ordered_pair(X3,X4)),relation_type(X1,X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(65,negated_conjecture,
? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,set_type)
& ? [X7] :
( ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,set_type)
& member(X7,X5)
& member(X8,X6)
& ~ ilf_type(singleton(ordered_pair(X7,X8)),relation_type(X5,X6)) ) ) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,negated_conjecture,
( ilf_type(esk6_0,set_type)
& ilf_type(esk7_0,set_type)
& ilf_type(esk8_0,set_type)
& ilf_type(esk9_0,set_type)
& member(esk8_0,esk6_0)
& member(esk9_0,esk7_0)
& ~ ilf_type(singleton(ordered_pair(esk8_0,esk9_0)),relation_type(esk6_0,esk7_0)) ),
inference(skolemize,[status(esa)],[65]) ).
cnf(67,negated_conjecture,
~ ilf_type(singleton(ordered_pair(esk8_0,esk9_0)),relation_type(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(68,negated_conjecture,
member(esk9_0,esk7_0),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(69,negated_conjecture,
member(esk8_0,esk6_0),
inference(split_conjunct,[status(thm)],[66]) ).
fof(82,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)],[10]) ).
fof(83,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)],[82]) ).
fof(84,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)],[83]) ).
fof(85,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)],[84]) ).
cnf(86,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)],[85]) ).
fof(114,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)],[15]) ).
fof(115,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)],[114]) ).
fof(116,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(esk13_2(X4,X5),set_type)
& member(esk13_2(X4,X5),X4)
& ~ member(esk13_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[115]) ).
fof(117,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk13_2(X4,X5),set_type)
& member(esk13_2(X4,X5),X4)
& ~ member(esk13_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[116]) ).
fof(118,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(esk13_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk13_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk13_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[117]) ).
cnf(119,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[118]) ).
cnf(120,plain,
( member(X1,power_set(X2))
| member(esk13_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[118]) ).
fof(128,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)],[31]) ).
fof(129,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)],[128]) ).
fof(130,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)],[129]) ).
fof(131,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)],[130]) ).
cnf(132,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)],[131]) ).
fof(134,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)
| ( ( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| ( member(X1,X3)
& member(X2,X4) ) )
& ( ~ member(X1,X3)
| ~ member(X2,X4)
| member(ordered_pair(X1,X2),cross_product(X3,X4)) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(135,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ( member(X5,X7)
& member(X6,X8) ) )
& ( ~ member(X5,X7)
| ~ member(X6,X8)
| member(ordered_pair(X5,X6),cross_product(X7,X8)) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ( member(X5,X7)
& member(X6,X8) ) )
& ( ~ member(X5,X7)
| ~ member(X6,X8)
| member(ordered_pair(X5,X6),cross_product(X7,X8)) ) )
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[135]) ).
fof(137,plain,
! [X5,X6,X7,X8] :
( ( member(X5,X7)
| ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(X6,X8)
| ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ member(X5,X7)
| ~ member(X6,X8)
| member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[136]) ).
cnf(138,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(141,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)],[19]) ).
fof(142,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)],[141]) ).
fof(143,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)],[142]) ).
fof(144,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)],[143]) ).
cnf(145,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[144]) ).
fof(167,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( X3 != singleton(X2)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ member(X4,X3)
| X4 = X2 )
& ( X4 != X2
| member(X4,X3) ) ) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& ( ~ member(X4,X3)
| X4 != X2 )
& ( member(X4,X3)
| X4 = X2 ) )
| X3 = singleton(X2) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(168,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ( ( X7 != singleton(X6)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(X8,X7)
| X8 = X6 )
& ( X8 != X6
| member(X8,X7) ) ) ) )
& ( ? [X9] :
( ilf_type(X9,set_type)
& ( ~ member(X9,X7)
| X9 != X6 )
& ( member(X9,X7)
| X9 = X6 ) )
| X7 = singleton(X6) ) ) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ( ( X7 != singleton(X6)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(X8,X7)
| X8 = X6 )
& ( X8 != X6
| member(X8,X7) ) ) ) )
& ( ( ilf_type(esk15_3(X5,X6,X7),set_type)
& ( ~ member(esk15_3(X5,X6,X7),X7)
| esk15_3(X5,X6,X7) != X6 )
& ( member(esk15_3(X5,X6,X7),X7)
| esk15_3(X5,X6,X7) = X6 ) )
| X7 = singleton(X6) ) ) ) ) ),
inference(skolemize,[status(esa)],[168]) ).
fof(170,plain,
! [X5,X6,X7,X8] :
( ( ( ~ ilf_type(X8,set_type)
| ( ( ~ member(X8,X7)
| X8 = X6 )
& ( X8 != X6
| member(X8,X7) ) )
| X7 != singleton(X6) )
& ( ( ilf_type(esk15_3(X5,X6,X7),set_type)
& ( ~ member(esk15_3(X5,X6,X7),X7)
| esk15_3(X5,X6,X7) != X6 )
& ( member(esk15_3(X5,X6,X7),X7)
| esk15_3(X5,X6,X7) = X6 ) )
| X7 = singleton(X6) ) )
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[169]) ).
fof(171,plain,
! [X5,X6,X7,X8] :
( ( ~ member(X8,X7)
| X8 = X6
| ~ ilf_type(X8,set_type)
| X7 != singleton(X6)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( X8 != X6
| member(X8,X7)
| ~ ilf_type(X8,set_type)
| X7 != singleton(X6)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk15_3(X5,X6,X7),set_type)
| X7 = singleton(X6)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ member(esk15_3(X5,X6,X7),X7)
| esk15_3(X5,X6,X7) != X6
| X7 = singleton(X6)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(esk15_3(X5,X6,X7),X7)
| esk15_3(X5,X6,X7) = X6
| X7 = singleton(X6)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[170]) ).
cnf(176,plain,
( X4 = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| X3 != singleton(X2)
| ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(208,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[45,33,theory(equality)]) ).
cnf(209,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[208,33,theory(equality)]) ).
cnf(210,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[209,theory(equality)]) ).
cnf(263,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)],[86,33,theory(equality)]) ).
cnf(264,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[263,33,theory(equality)]) ).
cnf(265,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[264,theory(equality)]) ).
cnf(268,plain,
( member(X1,power_set(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk13_2(X1,X2),X2) ),
inference(rw,[status(thm)],[119,33,theory(equality)]) ).
cnf(269,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk13_2(X1,X2),X2) ),
inference(rw,[status(thm)],[268,33,theory(equality)]) ).
cnf(270,plain,
( member(X1,power_set(X2))
| ~ member(esk13_2(X1,X2),X2) ),
inference(cn,[status(thm)],[269,theory(equality)]) ).
cnf(303,plain,
( member(X1,power_set(X2))
| member(esk13_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[120,33,theory(equality)]) ).
cnf(304,plain,
( member(X1,power_set(X2))
| member(esk13_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[303,33,theory(equality)]) ).
cnf(305,plain,
( member(X1,power_set(X2))
| member(esk13_2(X1,X2),X1) ),
inference(cn,[status(thm)],[304,theory(equality)]) ).
cnf(308,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[132,33,theory(equality)]) ).
cnf(309,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[308,33,theory(equality)]) ).
cnf(310,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[309,theory(equality)]) ).
cnf(311,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[310,210]) ).
cnf(312,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[265,311,theory(equality)]) ).
cnf(314,plain,
( X2 = X4
| singleton(X2) != X3
| ~ member(X4,X3)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[176,33,theory(equality)]) ).
cnf(315,plain,
( X2 = X4
| singleton(X2) != X3
| ~ member(X4,X3)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[314,33,theory(equality)]) ).
cnf(316,plain,
( X2 = X4
| singleton(X2) != X3
| ~ member(X4,X3)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[315,33,theory(equality)]) ).
cnf(317,plain,
( X2 = X4
| singleton(X2) != X3
| ~ member(X4,X3)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[316,33,theory(equality)]) ).
cnf(318,plain,
( X2 = X4
| singleton(X2) != X3
| ~ member(X4,X3) ),
inference(cn,[status(thm)],[317,theory(equality)]) ).
cnf(324,plain,
( X1 = esk13_2(X2,X3)
| member(X2,power_set(X3))
| singleton(X1) != X2 ),
inference(spm,[status(thm)],[318,305,theory(equality)]) ).
cnf(346,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[145,33,theory(equality)]) ).
cnf(347,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[346,33,theory(equality)]) ).
cnf(348,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[347,theory(equality)]) ).
cnf(423,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[138,33,theory(equality)]) ).
cnf(424,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[423,33,theory(equality)]) ).
cnf(425,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[424,33,theory(equality)]) ).
cnf(426,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[425,33,theory(equality)]) ).
cnf(427,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[426,theory(equality)]) ).
cnf(644,plain,
( X1 = esk13_2(singleton(X1),X2)
| member(singleton(X1),power_set(X2)) ),
inference(er,[status(thm)],[324,theory(equality)]) ).
cnf(647,plain,
( member(singleton(X1),power_set(X2))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[270,644,theory(equality)]) ).
cnf(653,plain,
( ilf_type(singleton(X1),subset_type(X2))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[312,647,theory(equality)]) ).
cnf(656,plain,
( ilf_type(singleton(X1),relation_type(X2,X3))
| ~ member(X1,cross_product(X2,X3)) ),
inference(spm,[status(thm)],[348,653,theory(equality)]) ).
cnf(669,negated_conjecture,
~ member(ordered_pair(esk8_0,esk9_0),cross_product(esk6_0,esk7_0)),
inference(spm,[status(thm)],[67,656,theory(equality)]) ).
cnf(671,negated_conjecture,
( ~ member(esk9_0,esk7_0)
| ~ member(esk8_0,esk6_0) ),
inference(spm,[status(thm)],[669,427,theory(equality)]) ).
cnf(672,negated_conjecture,
( $false
| ~ member(esk8_0,esk6_0) ),
inference(rw,[status(thm)],[671,68,theory(equality)]) ).
cnf(673,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[672,69,theory(equality)]) ).
cnf(674,negated_conjecture,
$false,
inference(cn,[status(thm)],[673,theory(equality)]) ).
cnf(675,negated_conjecture,
$false,
674,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET646+3.p
% --creating new selector for []
% -running prover on /tmp/tmpg5mXFL/sel_SET646+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET646+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET646+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET646+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
%
%------------------------------------------------------------------------------