%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET659+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:08:20 EST 2010
% Result : Theorem 20.28s
% Output : CNFRefutation 20.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 24
% Syntax : Number of formulae : 297 ( 24 unt; 0 def)
% Number of atoms : 1294 ( 129 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 1652 ( 655 ~; 768 |; 149 &)
% ( 18 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-3 aty)
% Number of variables : 560 ( 41 sgn 251 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X4,X5),X3) ) ) )
<=> domain(X2,X1,X3) = X2 ) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',prove_relset_1_22) ).
fof(3,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/tmpxl0riV/sel_SET659+3.p_1',p24) ).
fof(4,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/tmpxl0riV/sel_SET659+3.p_1',p27) ).
fof(7,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/tmpxl0riV/sel_SET659+3.p_1',p20) ).
fof(8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p23) ).
fof(9,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/tmpxl0riV/sel_SET659+3.p_1',p22) ).
fof(11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p28) ).
fof(12,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/tmpxl0riV/sel_SET659+3.p_1',p33) ).
fof(13,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/tmpxl0riV/sel_SET659+3.p_1',p32) ).
fof(19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p15) ).
fof(21,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/tmpxl0riV/sel_SET659+3.p_1',p17) ).
fof(22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ? [X2] : ilf_type(X2,subset_type(X1)) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p18) ).
fof(23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
<=> member(X3,X2) ) ) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p19) ).
fof(24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> domain(X1,X2,X3) = domain_of(X3) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p30) ).
fof(25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p31) ).
fof(26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p34) ).
fof(28,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),X3)
=> ( member(X1,domain_of(X3))
& member(X2,range_of(X3)) ) ) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p3) ).
fof(29,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/tmpxl0riV/sel_SET659+3.p_1',p1) ).
fof(31,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/tmpxl0riV/sel_SET659+3.p_1',p7) ).
fof(35,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ) ) ),
file('/tmp/tmpxl0riV/sel_SET659+3.p_1',p9) ).
fof(36,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X4,X5),X3) ) ) )
<=> domain(X2,X1,X3) = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
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)],[3,theory(equality)]) ).
fof(39,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(40,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(41,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X2,X1))
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(X4,X2)
& ! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(ordered_pair(X4,X5),X3) ) )
| domain(X2,X1,X3) != X2 )
& ( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X2)
| ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X4,X5),X3) ) )
| domain(X2,X1,X3) = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(42,negated_conjecture,
? [X6] :
( ilf_type(X6,set_type)
& ? [X7] :
( ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,relation_type(X7,X6))
& ( ? [X9] :
( ilf_type(X9,set_type)
& member(X9,X7)
& ! [X10] :
( ~ ilf_type(X10,set_type)
| ~ member(ordered_pair(X9,X10),X8) ) )
| domain(X7,X6,X8) != X7 )
& ( ! [X11] :
( ~ ilf_type(X11,set_type)
| ~ member(X11,X7)
| ? [X12] :
( ilf_type(X12,set_type)
& member(ordered_pair(X11,X12),X8) ) )
| domain(X7,X6,X8) = X7 ) ) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
& ( ( ilf_type(esk4_0,set_type)
& member(esk4_0,esk2_0)
& ! [X10] :
( ~ ilf_type(X10,set_type)
| ~ member(ordered_pair(esk4_0,X10),esk3_0) ) )
| domain(esk2_0,esk1_0,esk3_0) != esk2_0 )
& ( ! [X11] :
( ~ ilf_type(X11,set_type)
| ~ member(X11,esk2_0)
| ( ilf_type(esk5_1(X11),set_type)
& member(ordered_pair(X11,esk5_1(X11)),esk3_0) ) )
| domain(esk2_0,esk1_0,esk3_0) = esk2_0 ) ),
inference(skolemize,[status(esa)],[42]) ).
fof(44,negated_conjecture,
! [X10,X11] :
( ( ~ ilf_type(X11,set_type)
| ~ member(X11,esk2_0)
| ( ilf_type(esk5_1(X11),set_type)
& member(ordered_pair(X11,esk5_1(X11)),esk3_0) )
| domain(esk2_0,esk1_0,esk3_0) = esk2_0 )
& ( ( ( ~ ilf_type(X10,set_type)
| ~ member(ordered_pair(esk4_0,X10),esk3_0) )
& member(esk4_0,esk2_0)
& ilf_type(esk4_0,set_type) )
| domain(esk2_0,esk1_0,esk3_0) != esk2_0 )
& ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
& ilf_type(esk2_0,set_type)
& ilf_type(esk1_0,set_type) ),
inference(shift_quantors,[status(thm)],[43]) ).
fof(45,negated_conjecture,
! [X10,X11] :
( ( ilf_type(esk5_1(X11),set_type)
| ~ member(X11,esk2_0)
| ~ ilf_type(X11,set_type)
| domain(esk2_0,esk1_0,esk3_0) = esk2_0 )
& ( member(ordered_pair(X11,esk5_1(X11)),esk3_0)
| ~ member(X11,esk2_0)
| ~ ilf_type(X11,set_type)
| domain(esk2_0,esk1_0,esk3_0) = esk2_0 )
& ( ~ ilf_type(X10,set_type)
| ~ member(ordered_pair(esk4_0,X10),esk3_0)
| domain(esk2_0,esk1_0,esk3_0) != esk2_0 )
& ( member(esk4_0,esk2_0)
| domain(esk2_0,esk1_0,esk3_0) != esk2_0 )
& ( ilf_type(esk4_0,set_type)
| domain(esk2_0,esk1_0,esk3_0) != esk2_0 )
& ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
& ilf_type(esk2_0,set_type)
& ilf_type(esk1_0,set_type) ),
inference(distribute,[status(thm)],[44]) ).
cnf(48,negated_conjecture,
ilf_type(esk3_0,relation_type(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(50,negated_conjecture,
( member(esk4_0,esk2_0)
| domain(esk2_0,esk1_0,esk3_0) != esk2_0 ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(51,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(52,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| member(ordered_pair(X1,esk5_1(X1)),esk3_0)
| ~ ilf_type(X1,set_type)
| ~ member(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(58,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(59,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)],[58]) ).
fof(60,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)],[59]) ).
fof(61,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)],[60]) ).
cnf(63,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)],[61]) ).
fof(64,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)],[4]) ).
fof(65,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)],[64]) ).
fof(66,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)],[65]) ).
cnf(67,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)],[66]) ).
fof(82,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)],[7]) ).
fof(83,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)],[82]) ).
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) ) )
& ( ( ilf_type(esk10_2(X4,X5),set_type)
& member(esk10_2(X4,X5),X4)
& ~ member(esk10_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[83]) ).
fof(85,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk10_2(X4,X5),set_type)
& member(esk10_2(X4,X5),X4)
& ~ member(esk10_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[84]) ).
fof(86,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(esk10_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk10_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk10_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[85]) ).
cnf(87,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk10_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[86]) ).
cnf(88,plain,
( subset(X1,X2)
| member(esk10_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[86]) ).
fof(91,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(92,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[91]) ).
fof(93,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)],[92]) ).
cnf(95,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(96,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)],[9]) ).
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) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& member(X7,X4)
& ~ member(X7,X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[96]) ).
fof(98,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(esk11_2(X4,X5),set_type)
& member(esk11_2(X4,X5),X4)
& ~ member(esk11_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[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(esk11_2(X4,X5),set_type)
& member(esk11_2(X4,X5),X4)
& ~ member(esk11_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[98]) ).
fof(100,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(esk11_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk11_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk11_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[99]) ).
cnf(104,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)],[100]) ).
fof(108,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)],[40]) ).
fof(109,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)],[108]) ).
fof(110,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk12_1(X3),set_type)
& member(esk12_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[109]) ).
fof(111,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk12_1(X3),set_type)
& member(esk12_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[110]) ).
fof(112,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk12_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk12_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[111]) ).
cnf(113,plain,
( empty(X1)
| member(esk12_1(X1),X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[112]) ).
cnf(115,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[112]) ).
fof(116,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)],[12]) ).
fof(117,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)],[116]) ).
fof(118,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)],[117]) ).
cnf(119,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)],[118]) ).
fof(120,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)],[13]) ).
fof(121,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)],[120]) ).
fof(122,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)],[121]) ).
cnf(123,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)],[122]) ).
fof(142,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)],[19]) ).
fof(143,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)],[142]) ).
fof(144,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)],[143]) ).
cnf(145,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)],[144]) ).
fof(151,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)],[21]) ).
fof(152,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)],[151]) ).
fof(153,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)],[152]) ).
fof(154,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)],[153]) ).
cnf(156,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)],[154]) ).
fof(157,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ? [X2] : ilf_type(X2,subset_type(X1)) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(158,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ? [X4] : ilf_type(X4,subset_type(X3)) ),
inference(variable_rename,[status(thm)],[157]) ).
fof(159,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ilf_type(esk14_1(X3),subset_type(X3)) ),
inference(skolemize,[status(esa)],[158]) ).
cnf(160,plain,
( ilf_type(esk14_1(X1),subset_type(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[159]) ).
fof(161,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( X1 != X2
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(X3,X1)
| member(X3,X2) )
& ( ~ member(X3,X2)
| member(X3,X1) ) ) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& ( ~ member(X3,X1)
| ~ member(X3,X2) )
& ( member(X3,X1)
| member(X3,X2) ) )
| X1 = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(162,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( X4 != X5
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& ( ~ member(X7,X4)
| ~ member(X7,X5) )
& ( member(X7,X4)
| member(X7,X5) ) )
| X4 = X5 ) ) ) ),
inference(variable_rename,[status(thm)],[161]) ).
fof(163,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( X4 != X5
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) ) )
& ( ( ilf_type(esk15_2(X4,X5),set_type)
& ( ~ member(esk15_2(X4,X5),X4)
| ~ member(esk15_2(X4,X5),X5) )
& ( member(esk15_2(X4,X5),X4)
| member(esk15_2(X4,X5),X5) ) )
| X4 = X5 ) ) ) ),
inference(skolemize,[status(esa)],[162]) ).
fof(164,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ilf_type(esk15_2(X4,X5),set_type)
& ( ~ member(esk15_2(X4,X5),X4)
| ~ member(esk15_2(X4,X5),X5) )
& ( member(esk15_2(X4,X5),X4)
| member(esk15_2(X4,X5),X5) ) )
| X4 = X5 ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[163]) ).
fof(165,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(X6,X5)
| member(X6,X4)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk15_2(X4,X5),set_type)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk15_2(X4,X5),X4)
| ~ member(esk15_2(X4,X5),X5)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk15_2(X4,X5),X4)
| member(esk15_2(X4,X5),X5)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[164]) ).
cnf(166,plain,
( X1 = X2
| member(esk15_2(X1,X2),X2)
| member(esk15_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[165]) ).
fof(171,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| domain(X1,X2,X3) = domain_of(X3) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(172,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| domain(X4,X5,X6) = domain_of(X6) ) ) ),
inference(variable_rename,[status(thm)],[171]) ).
fof(173,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| domain(X4,X5,X6) = domain_of(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[172]) ).
cnf(174,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[173]) ).
fof(175,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(176,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(domain(X4,X5,X6),subset_type(X4)) ) ) ),
inference(variable_rename,[status(thm)],[175]) ).
fof(177,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(domain(X4,X5,X6),subset_type(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[176]) ).
cnf(178,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[177]) ).
fof(179,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[26]) ).
cnf(180,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[179]) ).
fof(184,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3)
| ( member(X1,domain_of(X3))
& member(X2,range_of(X3)) ) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(185,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,binary_relation_type)
| ~ member(ordered_pair(X4,X5),X6)
| ( member(X4,domain_of(X6))
& member(X5,range_of(X6)) ) ) ) ),
inference(variable_rename,[status(thm)],[184]) ).
fof(186,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,binary_relation_type)
| ~ member(ordered_pair(X4,X5),X6)
| ( member(X4,domain_of(X6))
& member(X5,range_of(X6)) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[185]) ).
fof(187,plain,
! [X4,X5,X6] :
( ( member(X4,domain_of(X6))
| ~ member(ordered_pair(X4,X5),X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(X5,range_of(X6))
| ~ member(ordered_pair(X4,X5),X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[186]) ).
cnf(188,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[187]) ).
fof(190,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)],[29]) ).
fof(191,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)],[190]) ).
fof(192,plain,
! [X4] :
( ~ ilf_type(X4,binary_relation_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(X5,domain_of(X4))
| ( ilf_type(esk16_2(X4,X5),set_type)
& member(ordered_pair(X5,esk16_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)],[191]) ).
fof(193,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(esk16_2(X4,X5),set_type)
& member(ordered_pair(X5,esk16_2(X4,X5)),X4) ) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) ),
inference(shift_quantors,[status(thm)],[192]) ).
fof(194,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(esk16_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,esk16_2(X4,X5)),X4)
| ~ member(X5,domain_of(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) ) ),
inference(distribute,[status(thm)],[193]) ).
cnf(195,plain,
( member(ordered_pair(X2,esk16_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)],[194]) ).
cnf(197,plain,
( member(X2,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X3),X1)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[194]) ).
fof(202,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)],[31]) ).
fof(203,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)],[202]) ).
fof(204,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)],[203]) ).
fof(205,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)],[204]) ).
cnf(207,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)],[205]) ).
fof(227,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(228,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ) ) ),
inference(variable_rename,[status(thm)],[227]) ).
fof(229,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[228]) ).
fof(230,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( subset(X4,X3)
| X3 != X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[229]) ).
cnf(231,plain,
( X1 = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[230]) ).
cnf(237,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[95,180,theory(equality)]) ).
cnf(238,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[237,theory(equality)]) ).
cnf(251,plain,
( ilf_type(esk14_1(X1),subset_type(X1))
| $false ),
inference(rw,[status(thm)],[160,180,theory(equality)]) ).
cnf(252,plain,
ilf_type(esk14_1(X1),subset_type(X1)),
inference(cn,[status(thm)],[251,theory(equality)]) ).
cnf(253,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[145,180,theory(equality)]) ).
cnf(254,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[253,theory(equality)]) ).
cnf(264,plain,
( empty(X1)
| member(esk12_1(X1),X1)
| $false ),
inference(rw,[status(thm)],[113,180,theory(equality)]) ).
cnf(265,plain,
( empty(X1)
| member(esk12_1(X1),X1) ),
inference(cn,[status(thm)],[264,theory(equality)]) ).
cnf(270,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) != esk2_0
| $false
| ~ member(ordered_pair(esk4_0,X1),esk3_0) ),
inference(rw,[status(thm)],[51,180,theory(equality)]) ).
cnf(271,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0) ),
inference(cn,[status(thm)],[270,theory(equality)]) ).
cnf(294,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[115,180,theory(equality)]) ).
cnf(295,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[294,180,theory(equality)]) ).
cnf(296,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[295,theory(equality)]) ).
cnf(316,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| member(ordered_pair(X1,esk5_1(X1)),esk3_0)
| $false
| ~ member(X1,esk2_0) ),
inference(rw,[status(thm)],[52,180,theory(equality)]) ).
cnf(317,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| member(ordered_pair(X1,esk5_1(X1)),esk3_0)
| ~ member(X1,esk2_0) ),
inference(cn,[status(thm)],[316,theory(equality)]) ).
cnf(323,plain,
( subset(X1,X2)
| member(esk10_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[88,180,theory(equality)]) ).
cnf(324,plain,
( subset(X1,X2)
| member(esk10_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[323,180,theory(equality)]) ).
cnf(325,plain,
( subset(X1,X2)
| member(esk10_2(X1,X2),X1) ),
inference(cn,[status(thm)],[324,theory(equality)]) ).
cnf(331,plain,
( subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk10_2(X1,X2),X2) ),
inference(rw,[status(thm)],[87,180,theory(equality)]) ).
cnf(332,plain,
( subset(X1,X2)
| $false
| $false
| ~ member(esk10_2(X1,X2),X2) ),
inference(rw,[status(thm)],[331,180,theory(equality)]) ).
cnf(333,plain,
( subset(X1,X2)
| ~ member(esk10_2(X1,X2),X2) ),
inference(cn,[status(thm)],[332,theory(equality)]) ).
cnf(336,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[67,180,theory(equality)]) ).
cnf(337,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[336,180,theory(equality)]) ).
cnf(338,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[337,theory(equality)]) ).
cnf(340,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)],[156,180,theory(equality)]) ).
cnf(341,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[340,180,theory(equality)]) ).
cnf(342,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[341,theory(equality)]) ).
cnf(352,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[231,180,theory(equality)]) ).
cnf(353,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[352,180,theory(equality)]) ).
cnf(354,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[353,theory(equality)]) ).
cnf(372,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[63,180,theory(equality)]) ).
cnf(373,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[372,180,theory(equality)]) ).
cnf(374,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[373,theory(equality)]) ).
cnf(376,plain,
( empty(power_set(X1))
| member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(spm,[status(thm)],[374,342,theory(equality)]) ).
cnf(377,plain,
( member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(sr,[status(thm)],[376,238,theory(equality)]) ).
cnf(390,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)],[123,180,theory(equality)]) ).
cnf(391,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[390,180,theory(equality)]) ).
cnf(392,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[391,theory(equality)]) ).
cnf(393,plain,
( member(ordered_pair(X2,esk16_2(X1,X2)),X1)
| $false
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[195,180,theory(equality)]) ).
cnf(394,plain,
( member(ordered_pair(X2,esk16_2(X1,X2)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,domain_of(X1)) ),
inference(cn,[status(thm)],[393,theory(equality)]) ).
cnf(397,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)],[207,180,theory(equality)]) ).
cnf(398,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[397,180,theory(equality)]) ).
cnf(399,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[398,theory(equality)]) ).
cnf(400,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[338,399,theory(equality)]) ).
cnf(406,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[174,180,theory(equality)]) ).
cnf(407,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[406,180,theory(equality)]) ).
cnf(408,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[407,theory(equality)]) ).
cnf(409,plain,
( domain(X1,X2,X3) = domain(X4,X5,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X4,X5)) ),
inference(spm,[status(thm)],[408,408,theory(equality)]) ).
cnf(415,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[178,180,theory(equality)]) ).
cnf(416,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[415,180,theory(equality)]) ).
cnf(417,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[416,theory(equality)]) ).
cnf(419,plain,
( ilf_type(domain_of(X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[417,408,theory(equality)]) ).
cnf(421,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(rw,[status(thm)],[188,180,theory(equality)]) ).
cnf(422,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X1,X2),X3) ),
inference(rw,[status(thm)],[421,180,theory(equality)]) ).
cnf(423,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(cn,[status(thm)],[422,theory(equality)]) ).
cnf(424,negated_conjecture,
( member(esk5_1(X1),range_of(esk3_0))
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ ilf_type(esk3_0,binary_relation_type)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[423,317,theory(equality)]) ).
cnf(425,plain,
( member(esk16_2(X1,X2),range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,domain_of(X1)) ),
inference(spm,[status(thm)],[423,394,theory(equality)]) ).
cnf(426,plain,
( member(X2,domain_of(X1))
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X2,X3),X1) ),
inference(rw,[status(thm)],[197,180,theory(equality)]) ).
cnf(427,plain,
( member(X2,domain_of(X1))
| $false
| $false
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X2,X3),X1) ),
inference(rw,[status(thm)],[426,180,theory(equality)]) ).
cnf(428,plain,
( member(X2,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X2,X3),X1) ),
inference(cn,[status(thm)],[427,theory(equality)]) ).
cnf(429,negated_conjecture,
( member(X1,domain_of(esk3_0))
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ ilf_type(esk3_0,binary_relation_type)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[428,317,theory(equality)]) ).
cnf(434,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)],[119,180,theory(equality)]) ).
cnf(435,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[434,180,theory(equality)]) ).
cnf(436,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[435,theory(equality)]) ).
cnf(438,plain,
( ilf_type(range_of(X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[436,392,theory(equality)]) ).
cnf(446,plain,
( X1 = X2
| member(esk15_2(X1,X2),X2)
| member(esk15_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[166,180,theory(equality)]) ).
cnf(447,plain,
( X1 = X2
| member(esk15_2(X1,X2),X2)
| member(esk15_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[446,180,theory(equality)]) ).
cnf(448,plain,
( X1 = X2
| member(esk15_2(X1,X2),X2)
| member(esk15_2(X1,X2),X1) ),
inference(cn,[status(thm)],[447,theory(equality)]) ).
cnf(451,plain,
( X1 = X2
| member(esk15_2(X1,X2),X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[296,448,theory(equality)]) ).
cnf(464,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)],[104,180,theory(equality)]) ).
cnf(465,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[464,180,theory(equality)]) ).
cnf(466,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[465,180,theory(equality)]) ).
cnf(467,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[466,theory(equality)]) ).
cnf(618,plain,
member(esk14_1(X1),power_set(X1)),
inference(spm,[status(thm)],[377,252,theory(equality)]) ).
cnf(629,plain,
( member(X1,X2)
| ~ member(X1,esk14_1(X2)) ),
inference(spm,[status(thm)],[467,618,theory(equality)]) ).
cnf(661,plain,
( member(esk12_1(esk14_1(X1)),X1)
| empty(esk14_1(X1)) ),
inference(spm,[status(thm)],[629,265,theory(equality)]) ).
cnf(663,plain,
( member(esk10_2(esk14_1(X1),X2),X1)
| subset(esk14_1(X1),X2) ),
inference(spm,[status(thm)],[629,325,theory(equality)]) ).
cnf(726,negated_conjecture,
relation_like(esk3_0),
inference(spm,[status(thm)],[400,48,theory(equality)]) ).
cnf(736,negated_conjecture,
ilf_type(esk3_0,binary_relation_type),
inference(spm,[status(thm)],[254,726,theory(equality)]) ).
cnf(745,negated_conjecture,
( member(esk4_0,esk2_0)
| domain(X1,X2,esk3_0) != esk2_0
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[50,409,theory(equality)]) ).
cnf(747,negated_conjecture,
( domain(X2,X3,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0)
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
| ~ ilf_type(esk3_0,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[271,409,theory(equality)]) ).
cnf(748,negated_conjecture,
( domain(X2,X3,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0)
| ~ ilf_type(esk3_0,relation_type(X2,X3))
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[271,409,theory(equality)]) ).
cnf(761,negated_conjecture,
( member(esk4_0,esk2_0)
| domain(X1,X2,esk3_0) != esk2_0
| $false
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[745,48,theory(equality)]) ).
cnf(762,negated_conjecture,
( member(esk4_0,esk2_0)
| domain(X1,X2,esk3_0) != esk2_0
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[761,theory(equality)]) ).
cnf(765,negated_conjecture,
( domain(X2,X3,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0)
| $false
| ~ ilf_type(esk3_0,relation_type(X2,X3)) ),
inference(rw,[status(thm)],[747,48,theory(equality)]) ).
cnf(766,negated_conjecture,
( domain(X2,X3,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0)
| ~ ilf_type(esk3_0,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[765,theory(equality)]) ).
cnf(767,negated_conjecture,
( domain(X2,X3,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0)
| ~ ilf_type(esk3_0,relation_type(X2,X3))
| $false ),
inference(rw,[status(thm)],[748,48,theory(equality)]) ).
cnf(768,negated_conjecture,
( domain(X2,X3,esk3_0) != esk2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0)
| ~ ilf_type(esk3_0,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[767,theory(equality)]) ).
cnf(821,plain,
subset(esk14_1(X1),X1),
inference(spm,[status(thm)],[333,663,theory(equality)]) ).
cnf(829,plain,
( X1 = esk14_1(X1)
| ~ subset(X1,esk14_1(X1)) ),
inference(spm,[status(thm)],[354,821,theory(equality)]) ).
cnf(878,negated_conjecture,
ilf_type(domain_of(esk3_0),subset_type(esk2_0)),
inference(spm,[status(thm)],[419,48,theory(equality)]) ).
cnf(885,negated_conjecture,
member(domain_of(esk3_0),power_set(esk2_0)),
inference(spm,[status(thm)],[377,878,theory(equality)]) ).
cnf(889,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,domain_of(esk3_0)) ),
inference(spm,[status(thm)],[467,885,theory(equality)]) ).
cnf(909,negated_conjecture,
( member(esk10_2(domain_of(esk3_0),X1),esk2_0)
| subset(domain_of(esk3_0),X1) ),
inference(spm,[status(thm)],[889,325,theory(equality)]) ).
cnf(913,negated_conjecture,
( member(esk15_2(domain_of(esk3_0),X1),esk2_0)
| domain_of(esk3_0) = X1
| member(esk15_2(domain_of(esk3_0),X1),X1) ),
inference(spm,[status(thm)],[889,448,theory(equality)]) ).
cnf(954,negated_conjecture,
( member(esk5_1(X1),range_of(esk3_0))
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| $false
| ~ member(X1,esk2_0) ),
inference(rw,[status(thm)],[424,736,theory(equality)]) ).
cnf(955,negated_conjecture,
( member(esk5_1(X1),range_of(esk3_0))
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ member(X1,esk2_0) ),
inference(cn,[status(thm)],[954,theory(equality)]) ).
cnf(1027,negated_conjecture,
( member(X1,domain_of(esk3_0))
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| $false
| ~ member(X1,esk2_0) ),
inference(rw,[status(thm)],[429,736,theory(equality)]) ).
cnf(1028,negated_conjecture,
( member(X1,domain_of(esk3_0))
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ member(X1,esk2_0) ),
inference(cn,[status(thm)],[1027,theory(equality)]) ).
cnf(1030,negated_conjecture,
( subset(X1,domain_of(esk3_0))
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ member(esk10_2(X1,domain_of(esk3_0)),esk2_0) ),
inference(spm,[status(thm)],[333,1028,theory(equality)]) ).
cnf(1046,negated_conjecture,
subset(domain_of(esk3_0),esk2_0),
inference(spm,[status(thm)],[333,909,theory(equality)]) ).
cnf(1101,negated_conjecture,
ilf_type(range_of(esk3_0),subset_type(esk1_0)),
inference(spm,[status(thm)],[438,48,theory(equality)]) ).
cnf(1108,negated_conjecture,
member(range_of(esk3_0),power_set(esk1_0)),
inference(spm,[status(thm)],[377,1101,theory(equality)]) ).
cnf(1111,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,range_of(esk3_0)) ),
inference(spm,[status(thm)],[467,1108,theory(equality)]) ).
cnf(1146,negated_conjecture,
( member(esk5_1(X1),esk1_0)
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[1111,955,theory(equality)]) ).
cnf(1147,negated_conjecture,
( member(esk16_2(esk3_0,X1),esk1_0)
| ~ member(X1,domain_of(esk3_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(spm,[status(thm)],[1111,425,theory(equality)]) ).
cnf(1148,negated_conjecture,
( member(esk16_2(esk3_0,X1),esk1_0)
| ~ member(X1,domain_of(esk3_0))
| $false ),
inference(rw,[status(thm)],[1147,736,theory(equality)]) ).
cnf(1149,negated_conjecture,
( member(esk16_2(esk3_0,X1),esk1_0)
| ~ member(X1,domain_of(esk3_0)) ),
inference(cn,[status(thm)],[1148,theory(equality)]) ).
cnf(1478,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ empty(esk1_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[296,1146,theory(equality)]) ).
cnf(1496,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| empty(esk2_0)
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1478,265,theory(equality)]) ).
cnf(1524,negated_conjecture,
( member(esk4_0,esk2_0)
| empty(esk2_0)
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[50,1496,theory(equality)]) ).
cnf(1573,negated_conjecture,
( ~ empty(esk1_0)
| ~ member(X1,domain_of(esk3_0)) ),
inference(spm,[status(thm)],[296,1149,theory(equality)]) ).
cnf(1578,negated_conjecture,
( subset(domain_of(esk3_0),X1)
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1573,325,theory(equality)]) ).
cnf(1587,negated_conjecture,
( empty(esk14_1(domain_of(esk3_0)))
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1573,661,theory(equality)]) ).
cnf(1593,negated_conjecture,
( X1 = domain_of(esk3_0)
| ~ empty(esk1_0)
| ~ empty(X1) ),
inference(spm,[status(thm)],[1573,451,theory(equality)]) ).
cnf(1635,negated_conjecture,
( esk14_1(domain_of(esk3_0)) = domain_of(esk3_0)
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[829,1578,theory(equality)]) ).
cnf(1808,negated_conjecture,
( esk2_0 = domain_of(esk3_0)
| member(esk4_0,esk2_0)
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1593,1524,theory(equality)]) ).
cnf(1946,negated_conjecture,
( empty(esk14_1(esk2_0))
| member(esk4_0,esk2_0)
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1587,1808,theory(equality)]) ).
cnf(2075,negated_conjecture,
( esk14_1(esk2_0) = domain_of(esk3_0)
| member(esk4_0,esk2_0)
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1593,1946,theory(equality)]) ).
cnf(5934,negated_conjecture,
( member(esk4_0,esk2_0)
| domain_of(esk3_0) != esk2_0
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[762,408,theory(equality)]) ).
fof(5974,plain,
( ~ epred1_0
<=> ! [X3,X2] :
( ~ ilf_type(esk3_0,relation_type(X2,X3))
| domain(X2,X3,esk3_0) != esk2_0 ) ),
introduced(definition),
[split] ).
cnf(5975,plain,
( epred1_0
| ~ ilf_type(esk3_0,relation_type(X2,X3))
| domain(X2,X3,esk3_0) != esk2_0 ),
inference(split_equiv,[status(thm)],[5974]) ).
fof(5976,plain,
( ~ epred2_0
<=> ! [X1] : ~ member(ordered_pair(esk4_0,X1),esk3_0) ),
introduced(definition),
[split] ).
cnf(5977,plain,
( epred2_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0) ),
inference(split_equiv,[status(thm)],[5976]) ).
cnf(5978,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[766,5974,theory(equality)]),5976,theory(equality)]),
[split] ).
cnf(5979,negated_conjecture,
( epred2_0
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ member(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[5977,317,theory(equality)]) ).
cnf(5980,negated_conjecture,
( epred2_0
| ~ member(esk4_0,domain_of(esk3_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(spm,[status(thm)],[5977,394,theory(equality)]) ).
cnf(5982,negated_conjecture,
( epred2_0
| ~ member(esk4_0,domain_of(esk3_0))
| $false ),
inference(rw,[status(thm)],[5980,736,theory(equality)]) ).
cnf(5983,negated_conjecture,
( epred2_0
| ~ member(esk4_0,domain_of(esk3_0)) ),
inference(cn,[status(thm)],[5982,theory(equality)]) ).
cnf(5984,negated_conjecture,
( epred2_0
| ~ member(esk4_0,domain(X1,X2,esk3_0))
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[5983,408,theory(equality)]) ).
fof(6029,plain,
( ~ epred3_0
<=> ! [X3,X2] :
( ~ ilf_type(esk3_0,relation_type(X2,X3))
| domain(X2,X3,esk3_0) != esk2_0 ) ),
introduced(definition),
[split] ).
cnf(6030,plain,
( epred3_0
| ~ ilf_type(esk3_0,relation_type(X2,X3))
| domain(X2,X3,esk3_0) != esk2_0 ),
inference(split_equiv,[status(thm)],[6029]) ).
fof(6031,plain,
( ~ epred4_0
<=> ! [X1] : ~ member(ordered_pair(esk4_0,X1),esk3_0) ),
introduced(definition),
[split] ).
cnf(6032,plain,
( epred4_0
| ~ member(ordered_pair(esk4_0,X1),esk3_0) ),
inference(split_equiv,[status(thm)],[6031]) ).
cnf(6033,negated_conjecture,
( ~ epred4_0
| ~ epred3_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[768,6029,theory(equality)]),6031,theory(equality)]),
[split] ).
cnf(6034,negated_conjecture,
( epred4_0
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ member(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[6032,317,theory(equality)]) ).
cnf(10977,negated_conjecture,
( domain_of(esk3_0) = esk2_0
| member(esk15_2(domain_of(esk3_0),esk2_0),esk2_0) ),
inference(ef,[status(thm)],[913,theory(equality)]) ).
cnf(11025,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| domain_of(esk3_0) = esk2_0
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1478,10977,theory(equality)]) ).
cnf(11624,negated_conjecture,
( esk14_1(esk2_0) = esk2_0
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[1635,11025,theory(equality)]) ).
cnf(11931,negated_conjecture,
( esk2_0 = domain_of(esk3_0)
| member(esk4_0,esk2_0)
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ empty(esk1_0) ),
inference(spm,[status(thm)],[2075,11624,theory(equality)]) ).
cnf(15025,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| subset(esk2_0,domain_of(esk3_0)) ),
inference(spm,[status(thm)],[1030,325,theory(equality)]) ).
cnf(15042,negated_conjecture,
( domain_of(esk3_0) = esk2_0
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ subset(domain_of(esk3_0),esk2_0) ),
inference(spm,[status(thm)],[354,15025,theory(equality)]) ).
cnf(15052,negated_conjecture,
( domain_of(esk3_0) = esk2_0
| domain(esk2_0,esk1_0,esk3_0) = esk2_0
| $false ),
inference(rw,[status(thm)],[15042,1046,theory(equality)]) ).
cnf(15053,negated_conjecture,
( domain_of(esk3_0) = esk2_0
| domain(esk2_0,esk1_0,esk3_0) = esk2_0 ),
inference(cn,[status(thm)],[15052,theory(equality)]) ).
cnf(22215,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| domain_of(esk3_0) = esk2_0
| member(esk4_0,esk2_0) ),
inference(csr,[status(thm)],[11931,15053]) ).
cnf(22216,negated_conjecture,
( domain_of(esk3_0) = esk2_0
| member(esk4_0,esk2_0) ),
inference(csr,[status(thm)],[22215,50]) ).
cnf(293878,negated_conjecture,
( member(esk4_0,esk2_0)
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(csr,[status(thm)],[5934,22216]) ).
cnf(293879,negated_conjecture,
member(esk4_0,esk2_0),
inference(spm,[status(thm)],[293878,48,theory(equality)]) ).
cnf(293890,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| epred4_0
| $false ),
inference(rw,[status(thm)],[6034,293879,theory(equality)]) ).
cnf(293891,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| epred4_0 ),
inference(cn,[status(thm)],[293890,theory(equality)]) ).
cnf(293892,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| epred2_0
| $false ),
inference(rw,[status(thm)],[5979,293879,theory(equality)]) ).
cnf(293893,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| epred2_0 ),
inference(cn,[status(thm)],[293892,theory(equality)]) ).
cnf(294633,negated_conjecture,
( epred1_0
| epred4_0
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[5975,293891,theory(equality)]) ).
cnf(294637,negated_conjecture,
( epred1_0
| epred4_0
| $false ),
inference(rw,[status(thm)],[294633,48,theory(equality)]) ).
cnf(294638,negated_conjecture,
( epred1_0
| epred4_0 ),
inference(cn,[status(thm)],[294637,theory(equality)]) ).
cnf(294641,negated_conjecture,
( epred4_0
| ~ epred2_0 ),
inference(spm,[status(thm)],[5978,294638,theory(equality)]) ).
cnf(294726,negated_conjecture,
( epred2_0
| ~ member(esk4_0,esk2_0)
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[5984,293893,theory(equality)]) ).
cnf(294734,negated_conjecture,
( epred2_0
| $false
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
inference(rw,[status(thm)],[294726,293879,theory(equality)]) ).
cnf(294735,negated_conjecture,
( epred2_0
| $false
| $false ),
inference(rw,[status(thm)],[294734,48,theory(equality)]) ).
cnf(294736,negated_conjecture,
epred2_0,
inference(cn,[status(thm)],[294735,theory(equality)]) ).
cnf(294741,negated_conjecture,
( epred4_0
| $false ),
inference(rw,[status(thm)],[294641,294736,theory(equality)]) ).
cnf(294742,negated_conjecture,
epred4_0,
inference(cn,[status(thm)],[294741,theory(equality)]) ).
cnf(294759,negated_conjecture,
( $false
| ~ epred3_0 ),
inference(rw,[status(thm)],[6033,294742,theory(equality)]) ).
cnf(294760,negated_conjecture,
~ epred3_0,
inference(cn,[status(thm)],[294759,theory(equality)]) ).
cnf(295447,negated_conjecture,
( ~ ilf_type(esk3_0,relation_type(X2,X3))
| domain(X2,X3,esk3_0) != esk2_0 ),
inference(sr,[status(thm)],[6030,294760,theory(equality)]) ).
cnf(295448,negated_conjecture,
( domain_of(esk3_0) != esk2_0
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[295447,408,theory(equality)]) ).
cnf(295461,negated_conjecture,
( domain(esk2_0,esk1_0,esk3_0) = esk2_0
| ~ ilf_type(esk3_0,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[295448,15053,theory(equality)]) ).
cnf(295490,negated_conjecture,
domain(esk2_0,esk1_0,esk3_0) = esk2_0,
inference(spm,[status(thm)],[295461,48,theory(equality)]) ).
cnf(295586,negated_conjecture,
~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)),
inference(spm,[status(thm)],[295447,295490,theory(equality)]) ).
cnf(295948,negated_conjecture,
$false,
inference(rw,[status(thm)],[295586,48,theory(equality)]) ).
cnf(295949,negated_conjecture,
$false,
inference(cn,[status(thm)],[295948,theory(equality)]) ).
cnf(295950,negated_conjecture,
$false,
295949,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET659+3.p
% --creating new selector for []
% -running prover on /tmp/tmpxl0riV/sel_SET659+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET659+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET659+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET659+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
%
%------------------------------------------------------------------------------