TSTP Solution File: SET650+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET650+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 03:07:25 EST 2010
% Result : Theorem 0.55s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 100 ( 12 unt; 0 def)
% Number of atoms : 506 ( 0 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 676 ( 270 ~; 309 |; 65 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 261 ( 22 sgn 121 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmptpgocm/sel_SET650+3.p_1',p26) ).
fof(6,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/tmptpgocm/sel_SET650+3.p_1',p23) ).
fof(8,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/tmptpgocm/sel_SET650+3.p_1',p10) ).
fof(11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmptpgocm/sel_SET650+3.p_1',p13) ).
fof(18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,range_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2) ) ) ) ),
file('/tmp/tmptpgocm/sel_SET650+3.p_1',p2) ).
fof(19,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/tmptpgocm/sel_SET650+3.p_1',p3) ).
fof(23,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,domain_of(X1))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X2,X3),X1) ) ) ) ),
file('/tmp/tmptpgocm/sel_SET650+3.p_1',p4) ).
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/tmptpgocm/sel_SET650+3.p_1',p8) ).
fof(27,conjecture,
! [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/tmptpgocm/sel_SET650+3.p_1',prove_relset_1_12) ).
fof(28,negated_conjecture,
~ ! [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(assume_negation,[status(cth)],[27]) ).
fof(44,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[3]) ).
cnf(45,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[44]) ).
fof(56,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)],[6]) ).
fof(57,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)],[56]) ).
fof(58,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)],[57]) ).
cnf(59,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)],[58]) ).
fof(71,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)],[8]) ).
fof(72,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)],[71]) ).
fof(73,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(esk6_2(X4,X5),set_type)
& member(esk6_2(X4,X5),X4)
& ~ member(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[72]) ).
fof(74,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk6_2(X4,X5),set_type)
& member(esk6_2(X4,X5),X4)
& ~ member(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[73]) ).
fof(75,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(esk6_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk6_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk6_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[74]) ).
cnf(76,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(77,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(88,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)],[11]) ).
fof(89,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)],[88]) ).
fof(90,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)],[89]) ).
cnf(91,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)],[90]) ).
fof(124,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ( ( ~ member(X1,range_of(X2))
| ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2) ) )
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2) )
| member(X1,range_of(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(125,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ( ( ~ member(X4,range_of(X5))
| ? [X6] :
( ilf_type(X6,set_type)
& member(ordered_pair(X6,X4),X5) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5) )
| member(X4,range_of(X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[124]) ).
fof(126,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ( ( ~ member(X4,range_of(X5))
| ( ilf_type(esk10_2(X4,X5),set_type)
& member(ordered_pair(esk10_2(X4,X5),X4),X5) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5) )
| member(X4,range_of(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[125]) ).
fof(127,plain,
! [X4,X5,X7] :
( ( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5)
| member(X4,range_of(X5)) )
& ( ~ member(X4,range_of(X5))
| ( ilf_type(esk10_2(X4,X5),set_type)
& member(ordered_pair(esk10_2(X4,X5),X4),X5) ) ) )
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[126]) ).
fof(128,plain,
! [X4,X5,X7] :
( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5)
| member(X4,range_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk10_2(X4,X5),set_type)
| ~ member(X4,range_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) )
& ( member(ordered_pair(esk10_2(X4,X5),X4),X5)
| ~ member(X4,range_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[127]) ).
cnf(129,plain,
( member(ordered_pair(esk10_2(X1,X2),X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2)) ),
inference(split_conjunct,[status(thm)],[128]) ).
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,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)],[19]) ).
fof(133,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)],[132]) ).
fof(134,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)],[133]) ).
fof(135,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)],[134]) ).
cnf(136,plain,
( member(X4,X2)
| ~ 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)],[135]) ).
cnf(137,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)],[135]) ).
fof(157,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ member(X2,domain_of(X1))
| ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X2,X3),X1) ) )
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X2,X3),X1) )
| member(X2,domain_of(X1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(158,plain,
! [X4] :
( ~ ilf_type(X4,binary_relation_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(X5,domain_of(X4))
| ? [X6] :
( ilf_type(X6,set_type)
& member(ordered_pair(X5,X6),X4) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X5,X7),X4) )
| member(X5,domain_of(X4)) ) ) ) ),
inference(variable_rename,[status(thm)],[157]) ).
fof(159,plain,
! [X4] :
( ~ ilf_type(X4,binary_relation_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(X5,domain_of(X4))
| ( ilf_type(esk13_2(X4,X5),set_type)
& member(ordered_pair(X5,esk13_2(X4,X5)),X4) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X5,X7),X4) )
| member(X5,domain_of(X4)) ) ) ) ),
inference(skolemize,[status(esa)],[158]) ).
fof(160,plain,
! [X4,X5,X7] :
( ( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X5,X7),X4)
| member(X5,domain_of(X4)) )
& ( ~ member(X5,domain_of(X4))
| ( ilf_type(esk13_2(X4,X5),set_type)
& member(ordered_pair(X5,esk13_2(X4,X5)),X4) ) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) ),
inference(shift_quantors,[status(thm)],[159]) ).
fof(161,plain,
! [X4,X5,X7] :
( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X5,X7),X4)
| member(X5,domain_of(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) )
& ( ilf_type(esk13_2(X4,X5),set_type)
| ~ member(X5,domain_of(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) )
& ( member(ordered_pair(X5,esk13_2(X4,X5)),X4)
| ~ member(X5,domain_of(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) ) ),
inference(distribute,[status(thm)],[160]) ).
cnf(162,plain,
( member(ordered_pair(X2,esk13_2(X1,X2)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,domain_of(X1)) ),
inference(split_conjunct,[status(thm)],[161]) ).
fof(168,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(169,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)],[168]) ).
fof(170,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)],[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(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)],[170]) ).
cnf(173,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)],[171]) ).
fof(179,negated_conjecture,
? [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)],[28]) ).
fof(180,negated_conjecture,
? [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)],[179]) ).
fof(181,negated_conjecture,
( ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,set_type)
& ilf_type(esk17_0,relation_type(esk15_0,esk16_0))
& ( ~ subset(domain_of(esk17_0),esk15_0)
| ~ subset(range_of(esk17_0),esk16_0) ) ),
inference(skolemize,[status(esa)],[180]) ).
cnf(182,negated_conjecture,
( ~ subset(range_of(esk17_0),esk16_0)
| ~ subset(domain_of(esk17_0),esk15_0) ),
inference(split_conjunct,[status(thm)],[181]) ).
cnf(183,negated_conjecture,
ilf_type(esk17_0,relation_type(esk15_0,esk16_0)),
inference(split_conjunct,[status(thm)],[181]) ).
cnf(201,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[91,45,theory(equality)]) ).
cnf(202,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[201,theory(equality)]) ).
cnf(233,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[77,45,theory(equality)]) ).
cnf(234,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[233,45,theory(equality)]) ).
cnf(235,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(249,plain,
( subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk6_2(X1,X2),X2) ),
inference(rw,[status(thm)],[76,45,theory(equality)]) ).
cnf(250,plain,
( subset(X1,X2)
| $false
| $false
| ~ member(esk6_2(X1,X2),X2) ),
inference(rw,[status(thm)],[249,45,theory(equality)]) ).
cnf(251,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(254,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[59,45,theory(equality)]) ).
cnf(255,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[254,45,theory(equality)]) ).
cnf(256,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[255,theory(equality)]) ).
cnf(291,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)],[173,45,theory(equality)]) ).
cnf(292,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[291,45,theory(equality)]) ).
cnf(293,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[292,theory(equality)]) ).
cnf(294,negated_conjecture,
ilf_type(esk17_0,subset_type(cross_product(esk15_0,esk16_0))),
inference(spm,[status(thm)],[293,183,theory(equality)]) ).
cnf(336,plain,
( member(ordered_pair(X2,esk13_2(X1,X2)),X1)
| $false
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[162,45,theory(equality)]) ).
cnf(337,plain,
( member(ordered_pair(X2,esk13_2(X1,X2)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,domain_of(X1)) ),
inference(cn,[status(thm)],[336,theory(equality)]) ).
cnf(342,plain,
( member(ordered_pair(esk10_2(X1,X2),X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| $false
| ~ member(X1,range_of(X2)) ),
inference(rw,[status(thm)],[129,45,theory(equality)]) ).
cnf(343,plain,
( member(ordered_pair(esk10_2(X1,X2),X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2)) ),
inference(cn,[status(thm)],[342,theory(equality)]) ).
cnf(364,plain,
( member(X4,X2)
| $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)],[136,45,theory(equality)]) ).
cnf(365,plain,
( member(X4,X2)
| $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)],[364,45,theory(equality)]) ).
cnf(366,plain,
( member(X4,X2)
| $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)],[365,45,theory(equality)]) ).
cnf(367,plain,
( member(X4,X2)
| $false
| $false
| $false
| $false
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[366,45,theory(equality)]) ).
cnf(368,plain,
( member(X4,X2)
| ~ 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,esk16_0)
| ~ member(ordered_pair(X2,X1),esk17_0) ),
inference(spm,[status(thm)],[368,183,theory(equality)]) ).
cnf(371,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)],[137,45,theory(equality)]) ).
cnf(372,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)],[371,45,theory(equality)]) ).
cnf(373,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)],[372,45,theory(equality)]) ).
cnf(374,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)],[373,45,theory(equality)]) ).
cnf(375,plain,
( member(X3,X1)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(cn,[status(thm)],[374,theory(equality)]) ).
cnf(376,negated_conjecture,
( member(X1,esk15_0)
| ~ member(ordered_pair(X1,X2),esk17_0) ),
inference(spm,[status(thm)],[375,183,theory(equality)]) ).
cnf(382,negated_conjecture,
relation_like(esk17_0),
inference(spm,[status(thm)],[256,294,theory(equality)]) ).
cnf(386,negated_conjecture,
ilf_type(esk17_0,binary_relation_type),
inference(spm,[status(thm)],[202,382,theory(equality)]) ).
cnf(390,negated_conjecture,
( member(ordered_pair(X1,esk13_2(esk17_0,X1)),esk17_0)
| ~ member(X1,domain_of(esk17_0)) ),
inference(spm,[status(thm)],[337,386,theory(equality)]) ).
cnf(392,negated_conjecture,
( member(ordered_pair(esk10_2(X1,esk17_0),X1),esk17_0)
| ~ member(X1,range_of(esk17_0)) ),
inference(spm,[status(thm)],[343,386,theory(equality)]) ).
cnf(940,negated_conjecture,
( member(ordered_pair(esk6_2(domain_of(esk17_0),X1),esk13_2(esk17_0,esk6_2(domain_of(esk17_0),X1))),esk17_0)
| subset(domain_of(esk17_0),X1) ),
inference(spm,[status(thm)],[390,235,theory(equality)]) ).
cnf(1044,negated_conjecture,
( member(ordered_pair(esk10_2(esk6_2(range_of(esk17_0),X1),esk17_0),esk6_2(range_of(esk17_0),X1)),esk17_0)
| subset(range_of(esk17_0),X1) ),
inference(spm,[status(thm)],[392,235,theory(equality)]) ).
cnf(2474,negated_conjecture,
( member(esk6_2(domain_of(esk17_0),X1),esk15_0)
| subset(domain_of(esk17_0),X1) ),
inference(spm,[status(thm)],[376,940,theory(equality)]) ).
cnf(2481,negated_conjecture,
subset(domain_of(esk17_0),esk15_0),
inference(spm,[status(thm)],[251,2474,theory(equality)]) ).
cnf(2513,negated_conjecture,
( ~ subset(range_of(esk17_0),esk16_0)
| $false ),
inference(rw,[status(thm)],[182,2481,theory(equality)]) ).
cnf(2514,negated_conjecture,
~ subset(range_of(esk17_0),esk16_0),
inference(cn,[status(thm)],[2513,theory(equality)]) ).
cnf(4906,negated_conjecture,
( member(esk6_2(range_of(esk17_0),X1),esk16_0)
| subset(range_of(esk17_0),X1) ),
inference(spm,[status(thm)],[369,1044,theory(equality)]) ).
cnf(4914,negated_conjecture,
subset(range_of(esk17_0),esk16_0),
inference(spm,[status(thm)],[251,4906,theory(equality)]) ).
cnf(4916,negated_conjecture,
$false,
inference(sr,[status(thm)],[4914,2514,theory(equality)]) ).
cnf(4917,negated_conjecture,
$false,
4916,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET650+3.p
% --creating new selector for []
% -running prover on /tmp/tmptpgocm/sel_SET650+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET650+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET650+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET650+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
%
%------------------------------------------------------------------------------