TSTP Solution File: SET652+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET652+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:07:36 EST 2010
% Result : Theorem 72.76s
% Output : CNFRefutation 72.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 144 ( 19 unt; 0 def)
% Number of atoms : 699 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 913 ( 358 ~; 414 |; 84 &)
% ( 8 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 332 ( 12 sgn 164 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,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(X3,X1))
=> ( subset(range_of(X4),X2)
=> ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',prove_relset_1_14) ).
fof(3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',p24) ).
fof(4,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',p26) ).
fof(6,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/tmplIH5Ic/sel_SET652+3.p_2',p20) ).
fof(7,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/tmplIH5Ic/sel_SET652+3.p_2',p23) ).
fof(12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',p13) ).
fof(14,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/tmplIH5Ic/sel_SET652+3.p_2',p15) ).
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/tmplIH5Ic/sel_SET652+3.p_2',p18) ).
fof(19,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',p2) ).
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,set_type)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',p3) ).
fof(21,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',p1) ).
fof(22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/tmp/tmplIH5Ic/sel_SET652+3.p_2',p6) ).
fof(24,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/tmplIH5Ic/sel_SET652+3.p_2',p4) ).
fof(27,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/tmplIH5Ic/sel_SET652+3.p_2',p9) ).
fof(28,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(X3,X1))
=> ( subset(range_of(X4),X2)
=> ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(29,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)],[6,theory(equality)]) ).
fof(33,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(X3,X1))
& subset(range_of(X4),X2)
& ~ ilf_type(X4,relation_type(X3,X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(34,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(X7,X5))
& subset(range_of(X8),X6)
& ~ ilf_type(X8,relation_type(X7,X6)) ) ) ) ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,set_type)
& ilf_type(esk4_0,relation_type(esk3_0,esk1_0))
& subset(range_of(esk4_0),esk2_0)
& ~ ilf_type(esk4_0,relation_type(esk3_0,esk2_0)) ),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
~ ilf_type(esk4_0,relation_type(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
subset(range_of(esk4_0),esk2_0),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,negated_conjecture,
ilf_type(esk4_0,relation_type(esk3_0,esk1_0)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(45,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)],[29]) ).
fof(46,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)],[45]) ).
fof(47,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)],[46]) ).
fof(48,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)],[47]) ).
fof(49,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)],[48]) ).
cnf(52,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(53,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[4]) ).
cnf(54,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[53]) ).
fof(59,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(60,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)],[59]) ).
fof(61,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)],[60]) ).
fof(62,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)],[61]) ).
cnf(63,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)],[62]) ).
fof(65,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)],[7]) ).
fof(66,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)],[65]) ).
fof(67,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)],[66]) ).
cnf(68,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)],[67]) ).
fof(91,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)],[12]) ).
fof(92,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)],[91]) ).
fof(93,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)],[92]) ).
cnf(94,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)],[93]) ).
fof(100,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)],[14]) ).
fof(101,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)],[100]) ).
fof(102,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)],[101]) ).
fof(103,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)],[102]) ).
cnf(104,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)],[103]) ).
fof(113,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(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) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& member(X7,X4)
& ~ member(X7,X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[113]) ).
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) ) )
& ( ( 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)],[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(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)],[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(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)],[116]) ).
cnf(118,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)],[117]) ).
cnf(119,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)],[117]) ).
fof(127,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(128,plain,
! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| subset(X2,cross_product(domain_of(X2),range_of(X2))) ),
inference(variable_rename,[status(thm)],[127]) ).
cnf(129,plain,
( subset(X1,cross_product(domain_of(X1),range_of(X1)))
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[128]) ).
fof(130,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)
| ~ subset(X1,X2)
| ~ subset(X3,X4)
| subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(131,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)
| ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cross_product(X5,X7),cross_product(X6,X8)) ) ) ) ),
inference(variable_rename,[status(thm)],[130]) ).
fof(132,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cross_product(X5,X7),cross_product(X6,X8))
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[131]) ).
cnf(133,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(134,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3)
| subset(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(135,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,set_type)
| ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[135]) ).
cnf(137,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(138,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(139,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ( subset(domain_of(X6),X4)
& subset(range_of(X6),X5) ) ) ) ),
inference(variable_rename,[status(thm)],[138]) ).
fof(140,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ( subset(domain_of(X6),X4)
& subset(range_of(X6),X5) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[139]) ).
fof(141,plain,
! [X4,X5,X6] :
( ( subset(domain_of(X6),X4)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( subset(range_of(X6),X5)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[140]) ).
cnf(143,plain,
( subset(domain_of(X3),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[141]) ).
fof(152,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)],[24]) ).
fof(153,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)],[152]) ).
fof(154,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)],[153]) ).
fof(155,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)],[154]) ).
cnf(156,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)],[155]) ).
cnf(157,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)],[155]) ).
fof(166,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)],[27]) ).
fof(167,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)],[166]) ).
fof(168,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)],[167]) ).
fof(169,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)],[168]) ).
fof(170,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)],[169]) ).
cnf(174,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)],[170]) ).
cnf(189,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[94,54,theory(equality)]) ).
cnf(190,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[189,theory(equality)]) ).
cnf(225,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[52,54,theory(equality)]) ).
cnf(226,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[225,54,theory(equality)]) ).
cnf(227,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[226,theory(equality)]) ).
cnf(234,plain,
( subset(domain_of(X3),X1)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[143,54,theory(equality)]) ).
cnf(235,plain,
( subset(domain_of(X3),X1)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[234,54,theory(equality)]) ).
cnf(236,plain,
( subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[235,theory(equality)]) ).
cnf(237,negated_conjecture,
subset(domain_of(esk4_0),esk3_0),
inference(spm,[status(thm)],[236,38,theory(equality)]) ).
cnf(243,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[137,54,theory(equality)]) ).
cnf(244,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[243,54,theory(equality)]) ).
cnf(245,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[244,54,theory(equality)]) ).
cnf(246,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[245,theory(equality)]) ).
cnf(257,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[68,54,theory(equality)]) ).
cnf(258,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[257,54,theory(equality)]) ).
cnf(259,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[258,theory(equality)]) ).
cnf(261,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[63,54,theory(equality)]) ).
cnf(262,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[261,54,theory(equality)]) ).
cnf(263,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[262,theory(equality)]) ).
cnf(264,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[263,227]) ).
cnf(272,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)],[104,54,theory(equality)]) ).
cnf(273,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[272,54,theory(equality)]) ).
cnf(274,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[273,theory(equality)]) ).
cnf(285,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)],[157,54,theory(equality)]) ).
cnf(286,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[285,54,theory(equality)]) ).
cnf(287,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[286,theory(equality)]) ).
cnf(288,negated_conjecture,
ilf_type(esk4_0,subset_type(cross_product(esk3_0,esk1_0))),
inference(spm,[status(thm)],[287,38,theory(equality)]) ).
cnf(290,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)],[156,54,theory(equality)]) ).
cnf(291,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[290,54,theory(equality)]) ).
cnf(292,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[291,theory(equality)]) ).
cnf(298,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[119,54,theory(equality)]) ).
cnf(299,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[298,54,theory(equality)]) ).
cnf(300,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1) ),
inference(cn,[status(thm)],[299,theory(equality)]) ).
cnf(311,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[174,54,theory(equality)]) ).
cnf(312,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[311,54,theory(equality)]) ).
cnf(313,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[312,54,theory(equality)]) ).
cnf(314,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(cn,[status(thm)],[313,theory(equality)]) ).
cnf(317,plain,
( member(X1,power_set(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk12_2(X1,X2),X2) ),
inference(rw,[status(thm)],[118,54,theory(equality)]) ).
cnf(318,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk12_2(X1,X2),X2) ),
inference(rw,[status(thm)],[317,54,theory(equality)]) ).
cnf(319,plain,
( member(X1,power_set(X2))
| ~ member(esk12_2(X1,X2),X2) ),
inference(cn,[status(thm)],[318,theory(equality)]) ).
cnf(328,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[133,54,theory(equality)]) ).
cnf(329,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[328,54,theory(equality)]) ).
cnf(330,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[329,54,theory(equality)]) ).
cnf(331,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[330,54,theory(equality)]) ).
cnf(332,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[331,theory(equality)]) ).
cnf(333,negated_conjecture,
( subset(cross_product(X1,range_of(esk4_0)),cross_product(X2,esk2_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[332,37,theory(equality)]) ).
cnf(442,negated_conjecture,
relation_like(esk4_0),
inference(spm,[status(thm)],[259,288,theory(equality)]) ).
cnf(446,negated_conjecture,
ilf_type(esk4_0,binary_relation_type),
inference(spm,[status(thm)],[190,442,theory(equality)]) ).
cnf(448,negated_conjecture,
subset(esk4_0,cross_product(domain_of(esk4_0),range_of(esk4_0))),
inference(spm,[status(thm)],[129,446,theory(equality)]) ).
cnf(650,negated_conjecture,
subset(cross_product(domain_of(esk4_0),range_of(esk4_0)),cross_product(esk3_0,esk2_0)),
inference(spm,[status(thm)],[333,237,theory(equality)]) ).
cnf(878,negated_conjecture,
( subset(X1,cross_product(esk3_0,esk2_0))
| ~ subset(X1,cross_product(domain_of(esk4_0),range_of(esk4_0))) ),
inference(spm,[status(thm)],[246,650,theory(equality)]) ).
cnf(73195,negated_conjecture,
subset(esk4_0,cross_product(esk3_0,esk2_0)),
inference(spm,[status(thm)],[878,448,theory(equality)]) ).
cnf(73717,negated_conjecture,
( member(X1,cross_product(esk3_0,esk2_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[314,73195,theory(equality)]) ).
cnf(154697,negated_conjecture,
( member(esk12_2(esk4_0,X1),cross_product(esk3_0,esk2_0))
| member(esk4_0,power_set(X1)) ),
inference(spm,[status(thm)],[73717,300,theory(equality)]) ).
cnf(692070,negated_conjecture,
member(esk4_0,power_set(cross_product(esk3_0,esk2_0))),
inference(spm,[status(thm)],[319,154697,theory(equality)]) ).
cnf(692079,negated_conjecture,
ilf_type(esk4_0,member_type(power_set(cross_product(esk3_0,esk2_0)))),
inference(spm,[status(thm)],[264,692070,theory(equality)]) ).
cnf(692082,negated_conjecture,
ilf_type(esk4_0,subset_type(cross_product(esk3_0,esk2_0))),
inference(spm,[status(thm)],[274,692079,theory(equality)]) ).
cnf(692210,negated_conjecture,
ilf_type(esk4_0,relation_type(esk3_0,esk2_0)),
inference(spm,[status(thm)],[292,692082,theory(equality)]) ).
cnf(692213,negated_conjecture,
$false,
inference(sr,[status(thm)],[692210,36,theory(equality)]) ).
cnf(692214,negated_conjecture,
$false,
692213,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET652+3.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmplIH5Ic/sel_SET652+3.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmplIH5Ic/sel_SET652+3.p_2 with time limit 81
% -prover status Theorem
% Problem SET652+3.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET652+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET652+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
%
%------------------------------------------------------------------------------