TSTP Solution File: SET669+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET669+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:09:22 EST 2010
% Result : Theorem 1.00s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 125 ( 16 unt; 0 def)
% Number of atoms : 573 ( 26 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 746 ( 298 ~; 340 |; 65 &)
% ( 5 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 273 ( 6 sgn 123 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpEtqMXT/sel_SET669+3.p_1',p21) ).
fof(6,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/tmpEtqMXT/sel_SET669+3.p_1',p20) ).
fof(8,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/tmpEtqMXT/sel_SET669+3.p_1',p22) ).
fof(11,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpEtqMXT/sel_SET669+3.p_1',p32) ).
fof(12,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,domain(X1,X2,X3))
& X2 = range(X1,X2,X3) ) ) ) ) ),
file('/tmp/tmpEtqMXT/sel_SET669+3.p_1',prove_relset_1_32) ).
fof(19,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/tmpEtqMXT/sel_SET669+3.p_1',p16) ).
fof(23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/tmp/tmpEtqMXT/sel_SET669+3.p_1',p30) ).
fof(24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
file('/tmp/tmpEtqMXT/sel_SET669+3.p_1',p31) ).
fof(25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ( subset(identity_relation_of(X3),X4)
=> ( subset(X3,domain(X1,X2,X4))
& subset(X3,range(X1,X2,X4)) ) ) ) ) ) ),
file('/tmp/tmpEtqMXT/sel_SET669+3.p_1',p2) ).
fof(27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X1) )
=> X1 = X2 ) ) ),
file('/tmp/tmpEtqMXT/sel_SET669+3.p_1',p1) ).
fof(29,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/tmpEtqMXT/sel_SET669+3.p_1',p7) ).
fof(34,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,domain(X1,X2,X3))
& X2 = range(X1,X2,X3) ) ) ) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(36,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(38,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)],[8,theory(equality)]) ).
fof(65,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(66,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X2] :
( ( ~ empty(power_set(X2))
| ~ ilf_type(X2,set_type) )
& ( ilf_type(power_set(X2),set_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[66]) ).
cnf(69,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(70,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)],[6]) ).
fof(71,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)],[70]) ).
fof(72,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(esk5_2(X4,X5),set_type)
& member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[71]) ).
fof(73,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk5_2(X4,X5),set_type)
& member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[72]) ).
fof(74,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(esk5_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk5_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk5_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[73]) ).
cnf(78,plain,
( member(X3,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X2))
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(83,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)],[38]) ).
fof(84,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)],[83]) ).
fof(85,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)],[84]) ).
fof(86,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)],[85]) ).
cnf(88,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[86]) ).
fof(97,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[11]) ).
cnf(98,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[97]) ).
fof(99,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X1,X2))
& subset(identity_relation_of(X2),X3)
& ( ~ subset(X2,domain(X1,X2,X3))
| X2 != range(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(100,negated_conjecture,
? [X4] :
( ilf_type(X4,set_type)
& ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,relation_type(X4,X5))
& subset(identity_relation_of(X5),X6)
& ( ~ subset(X5,domain(X4,X5,X6))
| X5 != range(X4,X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,negated_conjecture,
( ilf_type(esk7_0,set_type)
& ilf_type(esk8_0,set_type)
& ilf_type(esk9_0,relation_type(esk7_0,esk8_0))
& subset(identity_relation_of(esk8_0),esk9_0)
& ( ~ subset(esk8_0,domain(esk7_0,esk8_0,esk9_0))
| esk8_0 != range(esk7_0,esk8_0,esk9_0) ) ),
inference(skolemize,[status(esa)],[100]) ).
cnf(102,negated_conjecture,
( esk8_0 != range(esk7_0,esk8_0,esk9_0)
| ~ subset(esk8_0,domain(esk7_0,esk8_0,esk9_0)) ),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(103,negated_conjecture,
subset(identity_relation_of(esk8_0),esk9_0),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(104,negated_conjecture,
ilf_type(esk9_0,relation_type(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[101]) ).
fof(130,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)],[19]) ).
fof(131,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)],[130]) ).
fof(132,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)],[131]) ).
fof(133,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)],[132]) ).
cnf(135,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[133]) ).
fof(146,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| range(X1,X2,X3) = range_of(X3) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(147,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| range(X4,X5,X6) = range_of(X6) ) ) ),
inference(variable_rename,[status(thm)],[146]) ).
fof(148,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| range(X4,X5,X6) = range_of(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[147]) ).
cnf(149,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[148]) ).
fof(150,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(151,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(range(X4,X5,X6),subset_type(X5)) ) ) ),
inference(variable_rename,[status(thm)],[150]) ).
fof(152,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(range(X4,X5,X6),subset_type(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[151]) ).
cnf(153,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[152]) ).
fof(154,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X4)
| ( subset(X3,domain(X1,X2,X4))
& subset(X3,range(X1,X2,X4)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(155,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,relation_type(X5,X6))
| ~ subset(identity_relation_of(X7),X8)
| ( subset(X7,domain(X5,X6,X8))
& subset(X7,range(X5,X6,X8)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,relation_type(X5,X6))
| ~ subset(identity_relation_of(X7),X8)
| ( subset(X7,domain(X5,X6,X8))
& subset(X7,range(X5,X6,X8)) )
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[155]) ).
fof(157,plain,
! [X5,X6,X7,X8] :
( ( subset(X7,domain(X5,X6,X8))
| ~ subset(identity_relation_of(X7),X8)
| ~ ilf_type(X8,relation_type(X5,X6))
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( subset(X7,range(X5,X6,X8))
| ~ subset(identity_relation_of(X7),X8)
| ~ ilf_type(X8,relation_type(X5,X6))
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[156]) ).
cnf(158,plain,
( subset(X3,range(X1,X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X4) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,plain,
( subset(X3,domain(X1,X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X4) ),
inference(split_conjunct,[status(thm)],[157]) ).
fof(167,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(168,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[168]) ).
cnf(170,plain,
( X1 = X2
| ~ ilf_type(X1,set_type)
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[169]) ).
fof(176,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)],[29]) ).
fof(177,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)],[176]) ).
fof(178,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(esk13_2(X4,X5),set_type)
& member(esk13_2(X4,X5),X4)
& ~ member(esk13_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[177]) ).
fof(179,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk13_2(X4,X5),set_type)
& member(esk13_2(X4,X5),X4)
& ~ member(esk13_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[178]) ).
fof(180,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(esk13_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk13_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk13_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[179]) ).
cnf(181,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[180]) ).
cnf(182,plain,
( subset(X1,X2)
| member(esk13_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[180]) ).
cnf(215,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[69,98,theory(equality)]) ).
cnf(216,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[215,theory(equality)]) ).
cnf(278,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[170,98,theory(equality)]) ).
cnf(279,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[278,98,theory(equality)]) ).
cnf(280,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[279,theory(equality)]) ).
cnf(285,plain,
( subset(X1,X2)
| member(esk13_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[182,98,theory(equality)]) ).
cnf(286,plain,
( subset(X1,X2)
| member(esk13_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[285,98,theory(equality)]) ).
cnf(287,plain,
( subset(X1,X2)
| member(esk13_2(X1,X2),X1) ),
inference(cn,[status(thm)],[286,theory(equality)]) ).
cnf(289,plain,
( subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk13_2(X1,X2),X2) ),
inference(rw,[status(thm)],[181,98,theory(equality)]) ).
cnf(290,plain,
( subset(X1,X2)
| $false
| $false
| ~ member(esk13_2(X1,X2),X2) ),
inference(rw,[status(thm)],[289,98,theory(equality)]) ).
cnf(291,plain,
( subset(X1,X2)
| ~ member(esk13_2(X1,X2),X2) ),
inference(cn,[status(thm)],[290,theory(equality)]) ).
cnf(302,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[135,98,theory(equality)]) ).
cnf(303,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[302,98,theory(equality)]) ).
cnf(304,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[303,theory(equality)]) ).
cnf(318,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[88,98,theory(equality)]) ).
cnf(319,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[318,98,theory(equality)]) ).
cnf(320,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[319,theory(equality)]) ).
cnf(322,plain,
( empty(power_set(X1))
| member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(spm,[status(thm)],[320,304,theory(equality)]) ).
cnf(323,plain,
( member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(sr,[status(thm)],[322,216,theory(equality)]) ).
cnf(341,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[149,98,theory(equality)]) ).
cnf(342,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[341,98,theory(equality)]) ).
cnf(343,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[342,theory(equality)]) ).
cnf(376,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[78,98,theory(equality)]) ).
cnf(377,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[376,98,theory(equality)]) ).
cnf(378,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[377,98,theory(equality)]) ).
cnf(379,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[378,theory(equality)]) ).
cnf(391,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[153,98,theory(equality)]) ).
cnf(392,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[391,98,theory(equality)]) ).
cnf(393,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[392,theory(equality)]) ).
cnf(395,plain,
( ilf_type(range_of(X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[393,343,theory(equality)]) ).
cnf(419,plain,
( subset(X3,domain(X1,X2,X4))
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[159,98,theory(equality)]) ).
cnf(420,plain,
( subset(X3,domain(X1,X2,X4))
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[419,98,theory(equality)]) ).
cnf(421,plain,
( subset(X3,domain(X1,X2,X4))
| $false
| $false
| $false
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[420,98,theory(equality)]) ).
cnf(422,plain,
( subset(X3,domain(X1,X2,X4))
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[421,theory(equality)]) ).
cnf(423,negated_conjecture,
( subset(esk8_0,domain(X1,X2,esk9_0))
| ~ ilf_type(esk9_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[422,103,theory(equality)]) ).
cnf(425,plain,
( subset(X3,range(X1,X2,X4))
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[158,98,theory(equality)]) ).
cnf(426,plain,
( subset(X3,range(X1,X2,X4))
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[425,98,theory(equality)]) ).
cnf(427,plain,
( subset(X3,range(X1,X2,X4))
| $false
| $false
| $false
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[426,98,theory(equality)]) ).
cnf(428,plain,
( subset(X3,range(X1,X2,X4))
| ~ subset(identity_relation_of(X3),X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[427,theory(equality)]) ).
cnf(429,negated_conjecture,
( subset(esk8_0,range(X1,X2,esk9_0))
| ~ ilf_type(esk9_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[428,103,theory(equality)]) ).
cnf(860,negated_conjecture,
ilf_type(range_of(esk9_0),subset_type(esk8_0)),
inference(spm,[status(thm)],[395,104,theory(equality)]) ).
cnf(869,negated_conjecture,
member(range_of(esk9_0),power_set(esk8_0)),
inference(spm,[status(thm)],[323,860,theory(equality)]) ).
cnf(873,negated_conjecture,
( member(X1,esk8_0)
| ~ member(X1,range_of(esk9_0)) ),
inference(spm,[status(thm)],[379,869,theory(equality)]) ).
cnf(978,negated_conjecture,
( member(esk13_2(range_of(esk9_0),X1),esk8_0)
| subset(range_of(esk9_0),X1) ),
inference(spm,[status(thm)],[873,287,theory(equality)]) ).
cnf(1080,negated_conjecture,
subset(range_of(esk9_0),esk8_0),
inference(spm,[status(thm)],[291,978,theory(equality)]) ).
cnf(1084,negated_conjecture,
( esk8_0 = range_of(esk9_0)
| ~ subset(esk8_0,range_of(esk9_0)) ),
inference(spm,[status(thm)],[280,1080,theory(equality)]) ).
cnf(1406,negated_conjecture,
( subset(esk8_0,range_of(esk9_0))
| ~ ilf_type(esk9_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[429,343,theory(equality)]) ).
cnf(11294,negated_conjecture,
subset(esk8_0,range_of(esk9_0)),
inference(spm,[status(thm)],[1406,104,theory(equality)]) ).
cnf(11305,negated_conjecture,
( range_of(esk9_0) = esk8_0
| $false ),
inference(rw,[status(thm)],[1084,11294,theory(equality)]) ).
cnf(11306,negated_conjecture,
range_of(esk9_0) = esk8_0,
inference(cn,[status(thm)],[11305,theory(equality)]) ).
cnf(11311,negated_conjecture,
( range(X1,X2,esk9_0) = esk8_0
| ~ ilf_type(esk9_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[343,11306,theory(equality)]) ).
cnf(12684,negated_conjecture,
( ~ subset(esk8_0,domain(esk7_0,esk8_0,esk9_0))
| ~ ilf_type(esk9_0,relation_type(esk7_0,esk8_0)) ),
inference(spm,[status(thm)],[102,11311,theory(equality)]) ).
cnf(12701,negated_conjecture,
( ~ subset(esk8_0,domain(esk7_0,esk8_0,esk9_0))
| $false ),
inference(rw,[status(thm)],[12684,104,theory(equality)]) ).
cnf(12702,negated_conjecture,
~ subset(esk8_0,domain(esk7_0,esk8_0,esk9_0)),
inference(cn,[status(thm)],[12701,theory(equality)]) ).
cnf(12711,negated_conjecture,
~ ilf_type(esk9_0,relation_type(esk7_0,esk8_0)),
inference(spm,[status(thm)],[12702,423,theory(equality)]) ).
cnf(12718,negated_conjecture,
$false,
inference(rw,[status(thm)],[12711,104,theory(equality)]) ).
cnf(12719,negated_conjecture,
$false,
inference(cn,[status(thm)],[12718,theory(equality)]) ).
cnf(12720,negated_conjecture,
$false,
12719,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET669+3.p
% --creating new selector for []
% -running prover on /tmp/tmpEtqMXT/sel_SET669+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET669+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET669+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET669+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
%
%------------------------------------------------------------------------------