TSTP Solution File: SET684+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET684+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:11:03 EST 2010
% Result : Theorem 0.35s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 169 ( 14 unt; 0 def)
% Number of atoms : 910 ( 9 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 1238 ( 497 ~; 550 |; 130 &)
% ( 9 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-5 aty)
% Number of variables : 393 ( 18 sgn 164 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,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))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> compose5(X1,X2,X3,X4,X5) = compose(X4,X5) ) ) ) ) ),
file('/tmp/tmpyH0E3M/sel_SET684+3.p_1',p27) ).
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/tmpyH0E3M/sel_SET684+3.p_1',p26) ).
fof(9,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpyH0E3M/sel_SET684+3.p_1',p29) ).
fof(11,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ( ~ empty(X3)
& ilf_type(X3,set_type) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( ilf_type(X8,member_type(X2))
& member(ordered_pair(X6,X8),X4)
& member(ordered_pair(X8,X7),X5) ) ) ) ) ) ) ) ) ),
file('/tmp/tmpyH0E3M/sel_SET684+3.p_1',prove_relset_1_51) ).
fof(17,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpyH0E3M/sel_SET684+3.p_1',p15) ).
fof(22,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/tmpyH0E3M/sel_SET684+3.p_1',p2) ).
fof(24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ! [X4] :
( ilf_type(X4,binary_relation_type)
=> ( member(ordered_pair(X1,X2),compose(X3,X4))
<=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X1,X5),X3)
& member(ordered_pair(X5,X2),X4) ) ) ) ) ) ),
file('/tmp/tmpyH0E3M/sel_SET684+3.p_1',p1) ).
fof(26,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/tmpyH0E3M/sel_SET684+3.p_1',p7) ).
fof(28,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/tmpyH0E3M/sel_SET684+3.p_1',p5) ).
fof(30,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpyH0E3M/sel_SET684+3.p_1',p9) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ( ~ empty(X3)
& ilf_type(X3,set_type) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( ilf_type(X8,member_type(X2))
& member(ordered_pair(X6,X8),X4)
& member(ordered_pair(X8,X7),X5) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ( ~ empty(X3)
& ilf_type(X3,set_type) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( ilf_type(X8,member_type(X2))
& member(ordered_pair(X6,X8),X4)
& member(ordered_pair(X8,X7),X5) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(34,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)],[26,theory(equality)]) ).
fof(36,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).
fof(51,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))
| ! [X5] :
( ~ ilf_type(X5,relation_type(X2,X3))
| compose5(X1,X2,X3,X4,X5) = compose(X4,X5) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(52,plain,
! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ! [X9] :
( ~ ilf_type(X9,relation_type(X6,X7))
| ! [X10] :
( ~ ilf_type(X10,relation_type(X7,X8))
| compose5(X6,X7,X8,X9,X10) = compose(X9,X10) ) ) ) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X6,X7,X8,X9,X10] :
( ~ ilf_type(X10,relation_type(X7,X8))
| compose5(X6,X7,X8,X9,X10) = compose(X9,X10)
| ~ ilf_type(X9,relation_type(X6,X7))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ),
inference(shift_quantors,[status(thm)],[52]) ).
cnf(54,plain,
( compose5(X1,X2,X3,X4,X5) = compose(X4,X5)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X5,relation_type(X2,X3)) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(55,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(56,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)],[55]) ).
fof(57,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)],[56]) ).
cnf(58,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)],[57]) ).
fof(80,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[9]) ).
cnf(81,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[80]) ).
fof(86,negated_conjecture,
? [X1] :
( ~ empty(X1)
& ilf_type(X1,set_type)
& ? [X2] :
( ~ empty(X2)
& ilf_type(X2,set_type)
& ? [X3] :
( ~ empty(X3)
& ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,relation_type(X2,X3))
& ? [X6] :
( ilf_type(X6,member_type(X1))
& ? [X7] :
( ilf_type(X7,member_type(X3))
& ( ~ member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
| ! [X8] :
( ~ ilf_type(X8,member_type(X2))
| ~ member(ordered_pair(X6,X8),X4)
| ~ member(ordered_pair(X8,X7),X5) ) )
& ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
| ? [X8] :
( ilf_type(X8,member_type(X2))
& member(ordered_pair(X6,X8),X4)
& member(ordered_pair(X8,X7),X5) ) ) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(87,negated_conjecture,
? [X9] :
( ~ empty(X9)
& ilf_type(X9,set_type)
& ? [X10] :
( ~ empty(X10)
& ilf_type(X10,set_type)
& ? [X11] :
( ~ empty(X11)
& ilf_type(X11,set_type)
& ? [X12] :
( ilf_type(X12,relation_type(X9,X10))
& ? [X13] :
( ilf_type(X13,relation_type(X10,X11))
& ? [X14] :
( ilf_type(X14,member_type(X9))
& ? [X15] :
( ilf_type(X15,member_type(X11))
& ( ~ member(ordered_pair(X14,X15),compose5(X9,X10,X11,X12,X13))
| ! [X16] :
( ~ ilf_type(X16,member_type(X10))
| ~ member(ordered_pair(X14,X16),X12)
| ~ member(ordered_pair(X16,X15),X13) ) )
& ( member(ordered_pair(X14,X15),compose5(X9,X10,X11,X12,X13))
| ? [X17] :
( ilf_type(X17,member_type(X10))
& member(ordered_pair(X14,X17),X12)
& member(ordered_pair(X17,X15),X13) ) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[86]) ).
fof(88,negated_conjecture,
( ~ empty(esk5_0)
& ilf_type(esk5_0,set_type)
& ~ empty(esk6_0)
& ilf_type(esk6_0,set_type)
& ~ empty(esk7_0)
& ilf_type(esk7_0,set_type)
& ilf_type(esk8_0,relation_type(esk5_0,esk6_0))
& ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
& ilf_type(esk10_0,member_type(esk5_0))
& ilf_type(esk11_0,member_type(esk7_0))
& ( ~ member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0))
| ! [X16] :
( ~ ilf_type(X16,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,X16),esk8_0)
| ~ member(ordered_pair(X16,esk11_0),esk9_0) ) )
& ( member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0))
| ( ilf_type(esk12_0,member_type(esk6_0))
& member(ordered_pair(esk10_0,esk12_0),esk8_0)
& member(ordered_pair(esk12_0,esk11_0),esk9_0) ) ) ),
inference(skolemize,[status(esa)],[87]) ).
fof(89,negated_conjecture,
! [X16] :
( ( ~ ilf_type(X16,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,X16),esk8_0)
| ~ member(ordered_pair(X16,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0)) )
& ( member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0))
| ( ilf_type(esk12_0,member_type(esk6_0))
& member(ordered_pair(esk10_0,esk12_0),esk8_0)
& member(ordered_pair(esk12_0,esk11_0),esk9_0) ) )
& ilf_type(esk11_0,member_type(esk7_0))
& ilf_type(esk10_0,member_type(esk5_0))
& ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
& ilf_type(esk8_0,relation_type(esk5_0,esk6_0))
& ~ empty(esk7_0)
& ilf_type(esk7_0,set_type)
& ~ empty(esk6_0)
& ilf_type(esk6_0,set_type)
& ~ empty(esk5_0)
& ilf_type(esk5_0,set_type) ),
inference(shift_quantors,[status(thm)],[88]) ).
fof(90,negated_conjecture,
! [X16] :
( ( ~ ilf_type(X16,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,X16),esk8_0)
| ~ member(ordered_pair(X16,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0)) )
& ( ilf_type(esk12_0,member_type(esk6_0))
| member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0)) )
& ( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0)) )
& ( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0)) )
& ilf_type(esk11_0,member_type(esk7_0))
& ilf_type(esk10_0,member_type(esk5_0))
& ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
& ilf_type(esk8_0,relation_type(esk5_0,esk6_0))
& ~ empty(esk7_0)
& ilf_type(esk7_0,set_type)
& ~ empty(esk6_0)
& ilf_type(esk6_0,set_type)
& ~ empty(esk5_0)
& ilf_type(esk5_0,set_type) ),
inference(distribute,[status(thm)],[89]) ).
cnf(97,negated_conjecture,
ilf_type(esk8_0,relation_type(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(98,negated_conjecture,
ilf_type(esk9_0,relation_type(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(101,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0))
| member(ordered_pair(esk12_0,esk11_0),esk9_0) ),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(102,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0))
| member(ordered_pair(esk10_0,esk12_0),esk8_0) ),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(103,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0))
| ilf_type(esk12_0,member_type(esk6_0)) ),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(104,negated_conjecture,
( ~ member(ordered_pair(esk10_0,esk11_0),compose5(esk5_0,esk6_0,esk7_0,esk8_0,esk9_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0)) ),
inference(split_conjunct,[status(thm)],[90]) ).
fof(124,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)],[17]) ).
fof(125,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)],[124]) ).
fof(126,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)],[125]) ).
cnf(127,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)],[126]) ).
fof(153,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)],[22]) ).
fof(154,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)],[153]) ).
fof(155,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)],[154]) ).
fof(156,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)],[155]) ).
cnf(157,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)],[156]) ).
fof(165,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ! [X4] :
( ~ ilf_type(X4,binary_relation_type)
| ( ( ~ member(ordered_pair(X1,X2),compose(X3,X4))
| ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X1,X5),X3)
& member(ordered_pair(X5,X2),X4) ) )
& ( ! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(ordered_pair(X1,X5),X3)
| ~ member(ordered_pair(X5,X2),X4) )
| member(ordered_pair(X1,X2),compose(X3,X4)) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(166,plain,
! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,binary_relation_type)
| ! [X9] :
( ~ ilf_type(X9,binary_relation_type)
| ( ( ~ member(ordered_pair(X6,X7),compose(X8,X9))
| ? [X10] :
( ilf_type(X10,set_type)
& member(ordered_pair(X6,X10),X8)
& member(ordered_pair(X10,X7),X9) ) )
& ( ! [X11] :
( ~ ilf_type(X11,set_type)
| ~ member(ordered_pair(X6,X11),X8)
| ~ member(ordered_pair(X11,X7),X9) )
| member(ordered_pair(X6,X7),compose(X8,X9)) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,plain,
! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,binary_relation_type)
| ! [X9] :
( ~ ilf_type(X9,binary_relation_type)
| ( ( ~ member(ordered_pair(X6,X7),compose(X8,X9))
| ( ilf_type(esk16_4(X6,X7,X8,X9),set_type)
& member(ordered_pair(X6,esk16_4(X6,X7,X8,X9)),X8)
& member(ordered_pair(esk16_4(X6,X7,X8,X9),X7),X9) ) )
& ( ! [X11] :
( ~ ilf_type(X11,set_type)
| ~ member(ordered_pair(X6,X11),X8)
| ~ member(ordered_pair(X11,X7),X9) )
| member(ordered_pair(X6,X7),compose(X8,X9)) ) ) ) ) ) ),
inference(skolemize,[status(esa)],[166]) ).
fof(168,plain,
! [X6,X7,X8,X9,X11] :
( ( ( ~ ilf_type(X11,set_type)
| ~ member(ordered_pair(X6,X11),X8)
| ~ member(ordered_pair(X11,X7),X9)
| member(ordered_pair(X6,X7),compose(X8,X9)) )
& ( ~ member(ordered_pair(X6,X7),compose(X8,X9))
| ( ilf_type(esk16_4(X6,X7,X8,X9),set_type)
& member(ordered_pair(X6,esk16_4(X6,X7,X8,X9)),X8)
& member(ordered_pair(esk16_4(X6,X7,X8,X9),X7),X9) ) ) )
| ~ ilf_type(X9,binary_relation_type)
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ),
inference(shift_quantors,[status(thm)],[167]) ).
fof(169,plain,
! [X6,X7,X8,X9,X11] :
( ( ~ ilf_type(X11,set_type)
| ~ member(ordered_pair(X6,X11),X8)
| ~ member(ordered_pair(X11,X7),X9)
| member(ordered_pair(X6,X7),compose(X8,X9))
| ~ ilf_type(X9,binary_relation_type)
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( ilf_type(esk16_4(X6,X7,X8,X9),set_type)
| ~ member(ordered_pair(X6,X7),compose(X8,X9))
| ~ ilf_type(X9,binary_relation_type)
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( member(ordered_pair(X6,esk16_4(X6,X7,X8,X9)),X8)
| ~ member(ordered_pair(X6,X7),compose(X8,X9))
| ~ ilf_type(X9,binary_relation_type)
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( member(ordered_pair(esk16_4(X6,X7,X8,X9),X7),X9)
| ~ member(ordered_pair(X6,X7),compose(X8,X9))
| ~ ilf_type(X9,binary_relation_type)
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ) ),
inference(distribute,[status(thm)],[168]) ).
cnf(170,plain,
( member(ordered_pair(esk16_4(X1,X2,X3,X4),X2),X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(171,plain,
( member(ordered_pair(X1,esk16_4(X1,X2,X3,X4)),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(173,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X5,X2),X4)
| ~ member(ordered_pair(X1,X5),X3)
| ~ ilf_type(X5,set_type) ),
inference(split_conjunct,[status(thm)],[169]) ).
fof(179,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)],[34]) ).
fof(180,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)],[179]) ).
fof(181,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)],[180]) ).
fof(182,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)],[181]) ).
cnf(183,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[182]) ).
fof(189,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)],[28]) ).
fof(190,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)],[189]) ).
fof(191,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)],[190]) ).
fof(192,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)],[191]) ).
cnf(194,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)],[192]) ).
fof(199,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)],[36]) ).
fof(200,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)],[199]) ).
fof(201,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk19_1(X3),set_type)
& member(esk19_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[200]) ).
fof(202,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk19_1(X3),set_type)
& member(esk19_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[201]) ).
fof(203,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk19_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk19_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[202]) ).
cnf(206,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[203]) ).
cnf(220,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0)) ),
inference(spm,[status(thm)],[104,103,theory(equality)]) ).
cnf(221,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0)) ),
inference(spm,[status(thm)],[104,102,theory(equality)]) ).
cnf(222,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0)) ),
inference(spm,[status(thm)],[104,101,theory(equality)]) ).
cnf(223,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[206,81,theory(equality)]) ).
cnf(224,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[223,81,theory(equality)]) ).
cnf(225,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[224,theory(equality)]) ).
cnf(240,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[127,81,theory(equality)]) ).
cnf(241,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[240,theory(equality)]) ).
cnf(271,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[183,81,theory(equality)]) ).
cnf(272,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[271,81,theory(equality)]) ).
cnf(273,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[272,theory(equality)]) ).
cnf(274,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[273,225]) ).
cnf(306,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[58,81,theory(equality)]) ).
cnf(307,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[306,81,theory(equality)]) ).
cnf(308,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[307,theory(equality)]) ).
cnf(338,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)],[194,81,theory(equality)]) ).
cnf(339,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[338,81,theory(equality)]) ).
cnf(340,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[339,theory(equality)]) ).
cnf(341,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[308,340,theory(equality)]) ).
cnf(346,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)],[157,81,theory(equality)]) ).
cnf(347,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)],[346,81,theory(equality)]) ).
cnf(348,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)],[347,81,theory(equality)]) ).
cnf(349,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)],[348,81,theory(equality)]) ).
cnf(350,plain,
( member(X4,X2)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(cn,[status(thm)],[349,theory(equality)]) ).
cnf(351,negated_conjecture,
( member(X1,esk6_0)
| ~ member(ordered_pair(X2,X1),esk8_0) ),
inference(spm,[status(thm)],[350,97,theory(equality)]) ).
cnf(407,plain,
( compose5(X1,X2,X3,X4,X5) = compose(X4,X5)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X2,X3))
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[54,81,theory(equality)]) ).
cnf(408,plain,
( compose5(X1,X2,X3,X4,X5) = compose(X4,X5)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X2,X3))
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[407,81,theory(equality)]) ).
cnf(409,plain,
( compose5(X1,X2,X3,X4,X5) = compose(X4,X5)
| $false
| $false
| $false
| ~ ilf_type(X5,relation_type(X2,X3))
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[408,81,theory(equality)]) ).
cnf(410,plain,
( compose5(X1,X2,X3,X4,X5) = compose(X4,X5)
| ~ ilf_type(X5,relation_type(X2,X3))
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[409,theory(equality)]) ).
cnf(411,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ilf_type(esk12_0,member_type(esk6_0))
| ~ ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[103,410,theory(equality)]) ).
cnf(412,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[102,410,theory(equality)]) ).
cnf(413,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[101,410,theory(equality)]) ).
cnf(414,negated_conjecture,
( ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0))
| ~ ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[104,410,theory(equality)]) ).
cnf(416,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ilf_type(esk12_0,member_type(esk6_0))
| $false
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[411,98,theory(equality)]) ).
cnf(417,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ilf_type(esk12_0,member_type(esk6_0))
| $false
| $false ),
inference(rw,[status(thm)],[416,97,theory(equality)]) ).
cnf(418,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ilf_type(esk12_0,member_type(esk6_0)) ),
inference(cn,[status(thm)],[417,theory(equality)]) ).
cnf(419,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk10_0,esk12_0),esk8_0)
| $false
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[412,98,theory(equality)]) ).
cnf(420,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk10_0,esk12_0),esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[419,97,theory(equality)]) ).
cnf(421,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk10_0,esk12_0),esk8_0) ),
inference(cn,[status(thm)],[420,theory(equality)]) ).
cnf(422,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk12_0,esk11_0),esk9_0)
| $false
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[413,98,theory(equality)]) ).
cnf(423,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk12_0,esk11_0),esk9_0)
| $false
| $false ),
inference(rw,[status(thm)],[422,97,theory(equality)]) ).
cnf(424,negated_conjecture,
( member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| member(ordered_pair(esk12_0,esk11_0),esk9_0) ),
inference(cn,[status(thm)],[423,theory(equality)]) ).
cnf(425,negated_conjecture,
( ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0))
| $false
| ~ ilf_type(esk8_0,relation_type(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[414,98,theory(equality)]) ).
cnf(426,negated_conjecture,
( ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0))
| $false
| $false ),
inference(rw,[status(thm)],[425,97,theory(equality)]) ).
cnf(427,negated_conjecture,
( ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0)) ),
inference(cn,[status(thm)],[426,theory(equality)]) ).
cnf(428,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| $false
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X5,X2),X4)
| ~ member(ordered_pair(X1,X5),X3) ),
inference(rw,[status(thm)],[173,81,theory(equality)]) ).
cnf(429,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| $false
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X5,X2),X4)
| ~ member(ordered_pair(X1,X5),X3) ),
inference(rw,[status(thm)],[428,81,theory(equality)]) ).
cnf(430,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| $false
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X5,X2),X4)
| ~ member(ordered_pair(X1,X5),X3) ),
inference(rw,[status(thm)],[429,81,theory(equality)]) ).
cnf(431,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X5,X2),X4)
| ~ member(ordered_pair(X1,X5),X3) ),
inference(cn,[status(thm)],[430,theory(equality)]) ).
cnf(436,plain,
( member(ordered_pair(X1,esk16_4(X1,X2,X3,X4)),X3)
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(rw,[status(thm)],[171,81,theory(equality)]) ).
cnf(437,plain,
( member(ordered_pair(X1,esk16_4(X1,X2,X3,X4)),X3)
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(rw,[status(thm)],[436,81,theory(equality)]) ).
cnf(438,plain,
( member(ordered_pair(X1,esk16_4(X1,X2,X3,X4)),X3)
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(cn,[status(thm)],[437,theory(equality)]) ).
cnf(442,plain,
( member(ordered_pair(esk16_4(X1,X2,X3,X4),X2),X4)
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(rw,[status(thm)],[170,81,theory(equality)]) ).
cnf(443,plain,
( member(ordered_pair(esk16_4(X1,X2,X3,X4),X2),X4)
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(rw,[status(thm)],[442,81,theory(equality)]) ).
cnf(444,plain,
( member(ordered_pair(esk16_4(X1,X2,X3,X4),X2),X4)
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(cn,[status(thm)],[443,theory(equality)]) ).
cnf(454,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[220,274,theory(equality)]) ).
cnf(475,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[221,274,theory(equality)]) ).
cnf(490,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[222,274,theory(equality)]) ).
cnf(507,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0) ),
inference(csr,[status(thm)],[454,351]) ).
cnf(508,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ ilf_type(esk9_0,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[507,444,theory(equality)]) ).
cnf(509,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0) ),
inference(csr,[status(thm)],[475,351]) ).
cnf(510,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ ilf_type(esk9_0,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[509,444,theory(equality)]) ).
cnf(511,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0) ),
inference(csr,[status(thm)],[490,351]) ).
cnf(512,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ ilf_type(esk9_0,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[511,444,theory(equality)]) ).
cnf(520,negated_conjecture,
relation_like(esk8_0),
inference(spm,[status(thm)],[341,97,theory(equality)]) ).
cnf(521,negated_conjecture,
relation_like(esk9_0),
inference(spm,[status(thm)],[341,98,theory(equality)]) ).
cnf(524,negated_conjecture,
ilf_type(esk8_0,binary_relation_type),
inference(spm,[status(thm)],[241,520,theory(equality)]) ).
cnf(525,negated_conjecture,
ilf_type(esk9_0,binary_relation_type),
inference(spm,[status(thm)],[241,521,theory(equality)]) ).
cnf(2387,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| $false
| ~ ilf_type(X2,binary_relation_type) ),
inference(rw,[status(thm)],[508,525,theory(equality)]) ).
cnf(2388,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[2387,theory(equality)]) ).
cnf(2389,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ~ ilf_type(esk8_0,binary_relation_type)
| ~ ilf_type(esk9_0,binary_relation_type) ),
inference(spm,[status(thm)],[2388,438,theory(equality)]) ).
cnf(2390,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| $false
| ~ ilf_type(esk9_0,binary_relation_type) ),
inference(rw,[status(thm)],[2389,524,theory(equality)]) ).
cnf(2391,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| $false
| $false ),
inference(rw,[status(thm)],[2390,525,theory(equality)]) ).
cnf(2392,negated_conjecture,
( ilf_type(esk12_0,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0)) ),
inference(cn,[status(thm)],[2391,theory(equality)]) ).
cnf(2393,negated_conjecture,
ilf_type(esk12_0,member_type(esk6_0)),
inference(csr,[status(thm)],[2392,418]) ).
cnf(2432,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| $false
| ~ ilf_type(X2,binary_relation_type) ),
inference(rw,[status(thm)],[510,525,theory(equality)]) ).
cnf(2433,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[2432,theory(equality)]) ).
cnf(2434,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ~ ilf_type(esk8_0,binary_relation_type)
| ~ ilf_type(esk9_0,binary_relation_type) ),
inference(spm,[status(thm)],[2433,438,theory(equality)]) ).
cnf(2435,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| $false
| ~ ilf_type(esk9_0,binary_relation_type) ),
inference(rw,[status(thm)],[2434,524,theory(equality)]) ).
cnf(2436,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| $false
| $false ),
inference(rw,[status(thm)],[2435,525,theory(equality)]) ).
cnf(2437,negated_conjecture,
( member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0)) ),
inference(cn,[status(thm)],[2436,theory(equality)]) ).
cnf(2438,negated_conjecture,
member(ordered_pair(esk10_0,esk12_0),esk8_0),
inference(csr,[status(thm)],[2437,421]) ).
cnf(2496,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| $false
| ~ ilf_type(X2,binary_relation_type) ),
inference(rw,[status(thm)],[512,525,theory(equality)]) ).
cnf(2497,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk16_4(X1,esk11_0,X2,esk9_0)),esk8_0)
| ~ member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[2496,theory(equality)]) ).
cnf(2498,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| ~ ilf_type(esk8_0,binary_relation_type)
| ~ ilf_type(esk9_0,binary_relation_type) ),
inference(spm,[status(thm)],[2497,438,theory(equality)]) ).
cnf(2499,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| $false
| ~ ilf_type(esk9_0,binary_relation_type) ),
inference(rw,[status(thm)],[2498,524,theory(equality)]) ).
cnf(2500,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0))
| $false
| $false ),
inference(rw,[status(thm)],[2499,525,theory(equality)]) ).
cnf(2501,negated_conjecture,
( member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk11_0),compose(esk8_0,esk9_0)) ),
inference(cn,[status(thm)],[2500,theory(equality)]) ).
cnf(2502,negated_conjecture,
member(ordered_pair(esk12_0,esk11_0),esk9_0),
inference(csr,[status(thm)],[2501,424]) ).
cnf(2504,negated_conjecture,
( member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ member(ordered_pair(X1,esk12_0),X2)
| ~ ilf_type(esk9_0,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[431,2502,theory(equality)]) ).
cnf(2519,negated_conjecture,
( member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ member(ordered_pair(X1,esk12_0),X2)
| $false
| ~ ilf_type(X2,binary_relation_type) ),
inference(rw,[status(thm)],[2504,525,theory(equality)]) ).
cnf(2520,negated_conjecture,
( member(ordered_pair(X1,esk11_0),compose(X2,esk9_0))
| ~ member(ordered_pair(X1,esk12_0),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[2519,theory(equality)]) ).
cnf(2897,negated_conjecture,
( ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0))
| ~ member(ordered_pair(esk10_0,esk12_0),esk8_0)
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[427,2520,theory(equality)]) ).
cnf(2906,negated_conjecture,
( ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0))
| $false
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(rw,[status(thm)],[2897,2438,theory(equality)]) ).
cnf(2907,negated_conjecture,
( ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0))
| $false
| $false ),
inference(rw,[status(thm)],[2906,524,theory(equality)]) ).
cnf(2908,negated_conjecture,
( ~ member(ordered_pair(X1,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,X1),esk8_0)
| ~ ilf_type(X1,member_type(esk6_0)) ),
inference(cn,[status(thm)],[2907,theory(equality)]) ).
cnf(2918,negated_conjecture,
( ~ member(ordered_pair(esk12_0,esk11_0),esk9_0)
| ~ member(ordered_pair(esk10_0,esk12_0),esk8_0) ),
inference(spm,[status(thm)],[2908,2393,theory(equality)]) ).
cnf(2921,negated_conjecture,
( $false
| ~ member(ordered_pair(esk10_0,esk12_0),esk8_0) ),
inference(rw,[status(thm)],[2918,2502,theory(equality)]) ).
cnf(2922,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[2921,2438,theory(equality)]) ).
cnf(2923,negated_conjecture,
$false,
inference(cn,[status(thm)],[2922,theory(equality)]) ).
cnf(2924,negated_conjecture,
$false,
2923,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET684+3.p
% --creating new selector for []
% -running prover on /tmp/tmpyH0E3M/sel_SET684+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET684+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET684+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET684+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
%
%------------------------------------------------------------------------------