TSTP Solution File: SET666+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET666+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:09:04 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 99 ( 12 unt; 0 def)
% Number of atoms : 476 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 624 ( 247 ~; 280 |; 62 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 208 ( 4 sgn 109 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
file('/tmp/tmpBExxDK/sel_SET666+3.p_1',prove_relset_1_29) ).
fof(2,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpBExxDK/sel_SET666+3.p_1',p24) ).
fof(6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpBExxDK/sel_SET666+3.p_1',p22) ).
fof(9,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/tmpBExxDK/sel_SET666+3.p_1',p12) ).
fof(11,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/tmpBExxDK/sel_SET666+3.p_1',p14) ).
fof(13,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/tmpBExxDK/sel_SET666+3.p_1',p16) ).
fof(15,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/tmpBExxDK/sel_SET666+3.p_1',p18) ).
fof(18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(identity_relation_of(X1),cross_product(X1,X1)) ),
file('/tmp/tmpBExxDK/sel_SET666+3.p_1',p3) ).
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/tmpBExxDK/sel_SET666+3.p_1',p1) ).
fof(20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/tmp/tmpBExxDK/sel_SET666+3.p_1',p6) ).
fof(26,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(27,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(29,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)],[15,theory(equality)]) ).
fof(31,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ~ ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(32,negated_conjecture,
? [X2] :
( ilf_type(X2,set_type)
& ~ ilf_type(identity_relation_of(X2),identity_relation_of_type(X2)) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ~ ilf_type(identity_relation_of(esk1_0),identity_relation_of_type(esk1_0)) ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
~ ilf_type(identity_relation_of(esk1_0),identity_relation_of_type(esk1_0)),
inference(split_conjunct,[status(thm)],[33]) ).
fof(36,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[2]) ).
cnf(37,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[36]) ).
fof(56,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)],[27]) ).
fof(57,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)],[56]) ).
fof(58,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)],[57]) ).
fof(59,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)],[58]) ).
fof(60,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)],[59]) ).
cnf(63,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(73,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)],[9]) ).
fof(74,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)],[73]) ).
fof(75,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)],[74]) ).
fof(76,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)],[75]) ).
cnf(77,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)],[76]) ).
fof(83,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)],[11]) ).
fof(84,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)],[83]) ).
fof(85,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(esk8_2(X4,X5),set_type)
& member(esk8_2(X4,X5),X4)
& ~ member(esk8_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[84]) ).
fof(86,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk8_2(X4,X5),set_type)
& member(esk8_2(X4,X5),X4)
& ~ member(esk8_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[85]) ).
fof(87,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(esk8_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk8_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk8_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[86]) ).
cnf(91,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)],[87]) ).
fof(95,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)],[13]) ).
fof(96,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)],[95]) ).
fof(97,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(esk9_2(X4,X5),set_type)
& member(esk9_2(X4,X5),X4)
& ~ member(esk9_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[96]) ).
fof(98,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk9_2(X4,X5),set_type)
& member(esk9_2(X4,X5),X4)
& ~ member(esk9_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[97]) ).
fof(99,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(esk9_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk9_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk9_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[98]) ).
cnf(100,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk9_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[99]) ).
cnf(101,plain,
( member(X1,power_set(X2))
| member(esk9_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[99]) ).
fof(109,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)],[29]) ).
fof(110,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)],[109]) ).
fof(111,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)],[110]) ).
fof(112,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)],[111]) ).
cnf(113,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)],[112]) ).
fof(124,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| subset(identity_relation_of(X1),cross_product(X1,X1)) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(125,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| subset(identity_relation_of(X2),cross_product(X2,X2)) ),
inference(variable_rename,[status(thm)],[124]) ).
cnf(126,plain,
( subset(identity_relation_of(X1),cross_product(X1,X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[125]) ).
fof(127,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(128,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)],[127]) ).
fof(129,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)],[128]) ).
fof(130,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)],[129]) ).
cnf(131,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)],[130]) ).
fof(133,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,identity_relation_of_type(X1))
| ilf_type(X2,relation_type(X1,X1)) )
& ( ~ ilf_type(X2,relation_type(X1,X1))
| ilf_type(X2,identity_relation_of_type(X1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(134,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3)) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3)) ) ) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3)) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[134]) ).
fof(136,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[135]) ).
cnf(137,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(198,plain,
( subset(identity_relation_of(X1),cross_product(X1,X1))
| $false ),
inference(rw,[status(thm)],[126,37,theory(equality)]) ).
cnf(199,plain,
subset(identity_relation_of(X1),cross_product(X1,X1)),
inference(cn,[status(thm)],[198,theory(equality)]) ).
cnf(204,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[63,37,theory(equality)]) ).
cnf(205,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[204,37,theory(equality)]) ).
cnf(206,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[205,theory(equality)]) ).
cnf(213,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(rw,[status(thm)],[137,37,theory(equality)]) ).
cnf(214,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| $false
| $false
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(rw,[status(thm)],[213,37,theory(equality)]) ).
cnf(215,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(cn,[status(thm)],[214,theory(equality)]) ).
cnf(224,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[113,37,theory(equality)]) ).
cnf(225,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[224,37,theory(equality)]) ).
cnf(226,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[225,theory(equality)]) ).
cnf(227,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[226,206]) ).
cnf(235,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)],[77,37,theory(equality)]) ).
cnf(236,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[235,37,theory(equality)]) ).
cnf(237,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[236,theory(equality)]) ).
cnf(239,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[237,227,theory(equality)]) ).
cnf(282,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)],[131,37,theory(equality)]) ).
cnf(283,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[282,37,theory(equality)]) ).
cnf(284,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[283,theory(equality)]) ).
cnf(287,plain,
( member(X1,power_set(X2))
| member(esk9_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[101,37,theory(equality)]) ).
cnf(288,plain,
( member(X1,power_set(X2))
| member(esk9_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[287,37,theory(equality)]) ).
cnf(289,plain,
( member(X1,power_set(X2))
| member(esk9_2(X1,X2),X1) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(291,plain,
( member(X1,power_set(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk9_2(X1,X2),X2) ),
inference(rw,[status(thm)],[100,37,theory(equality)]) ).
cnf(292,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk9_2(X1,X2),X2) ),
inference(rw,[status(thm)],[291,37,theory(equality)]) ).
cnf(293,plain,
( member(X1,power_set(X2))
| ~ member(esk9_2(X1,X2),X2) ),
inference(cn,[status(thm)],[292,theory(equality)]) ).
cnf(299,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)],[91,37,theory(equality)]) ).
cnf(300,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[299,37,theory(equality)]) ).
cnf(301,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[300,37,theory(equality)]) ).
cnf(302,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[301,theory(equality)]) ).
cnf(304,plain,
( member(X1,cross_product(X2,X2))
| ~ member(X1,identity_relation_of(X2)) ),
inference(spm,[status(thm)],[302,199,theory(equality)]) ).
cnf(384,plain,
( member(X1,power_set(cross_product(X2,X2)))
| ~ member(esk9_2(X1,cross_product(X2,X2)),identity_relation_of(X2)) ),
inference(spm,[status(thm)],[293,304,theory(equality)]) ).
cnf(670,plain,
member(identity_relation_of(X1),power_set(cross_product(X1,X1))),
inference(spm,[status(thm)],[384,289,theory(equality)]) ).
cnf(687,plain,
ilf_type(identity_relation_of(X1),subset_type(cross_product(X1,X1))),
inference(spm,[status(thm)],[239,670,theory(equality)]) ).
cnf(702,plain,
ilf_type(identity_relation_of(X1),relation_type(X1,X1)),
inference(spm,[status(thm)],[284,687,theory(equality)]) ).
cnf(705,plain,
ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)),
inference(spm,[status(thm)],[215,702,theory(equality)]) ).
cnf(709,negated_conjecture,
$false,
inference(rw,[status(thm)],[34,705,theory(equality)]) ).
cnf(710,negated_conjecture,
$false,
inference(cn,[status(thm)],[709,theory(equality)]) ).
cnf(711,negated_conjecture,
$false,
710,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET666+3.p
% --creating new selector for []
% -running prover on /tmp/tmpBExxDK/sel_SET666+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET666+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET666+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET666+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
%
%------------------------------------------------------------------------------