TSTP Solution File: SET685+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET685+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:11:07 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of formulae : 164 ( 11 unt; 0 def)
% Number of atoms : 826 ( 9 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 1114 ( 452 ~; 489 |; 120 &)
% ( 9 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 344 ( 20 sgn 148 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> image4(X1,X2,X3,X4) = image(X3,X4) ) ) ) ),
file('/tmp/tmpA75A7w/sel_SET685+3.p_1',p25) ).
fof(2,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/tmpA75A7w/sel_SET685+3.p_1',p24) ).
fof(3,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpA75A7w/sel_SET685+3.p_1',p27) ).
fof(9,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(X3,X1))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,image4(X3,X1,X4,X2))
<=> ? [X6] :
( ilf_type(X6,member_type(X3))
& member(ordered_pair(X6,X5),X4)
& member(X6,X2) ) ) ) ) ) ) ),
file('/tmp/tmpA75A7w/sel_SET685+3.p_1',prove_relset_1_52) ).
fof(15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpA75A7w/sel_SET685+3.p_1',p15) ).
fof(20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/tmp/tmpA75A7w/sel_SET685+3.p_1',p2) ).
fof(22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,image(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X2),X3)
& member(X4,X1) ) ) ) ) ),
file('/tmp/tmpA75A7w/sel_SET685+3.p_1',p1) ).
fof(24,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/tmpA75A7w/sel_SET685+3.p_1',p7) ).
fof(26,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/tmpA75A7w/sel_SET685+3.p_1',p5) ).
fof(28,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpA75A7w/sel_SET685+3.p_1',p9) ).
fof(29,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(X3,X1))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,image4(X3,X1,X4,X2))
<=> ? [X6] :
( ilf_type(X6,member_type(X3))
& member(ordered_pair(X6,X5),X4)
& member(X6,X2) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[9]) ).
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(X3,X1))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,image4(X3,X1,X4,X2))
<=> ? [X6] :
( ilf_type(X6,member_type(X3))
& member(ordered_pair(X6,X5),X4)
& member(X6,X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[29,theory(equality)]) ).
fof(32,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)],[24,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[28,theory(equality)]) ).
fof(35,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| image4(X1,X2,X3,X4) = image(X3,X4) ) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(36,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,relation_type(X5,X6))
| ! [X8] :
( ~ ilf_type(X8,set_type)
| image4(X5,X6,X7,X8) = image(X7,X8) ) ) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| image4(X5,X6,X7,X8) = image(X7,X8)
| ~ ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[36]) ).
cnf(38,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,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)],[2]) ).
fof(40,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)],[39]) ).
fof(41,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)],[40]) ).
cnf(42,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)],[41]) ).
fof(43,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[3]) ).
cnf(44,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[43]) ).
fof(77,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(X3,X1))
& ? [X5] :
( ilf_type(X5,member_type(X1))
& ( ~ member(X5,image4(X3,X1,X4,X2))
| ! [X6] :
( ~ ilf_type(X6,member_type(X3))
| ~ member(ordered_pair(X6,X5),X4)
| ~ member(X6,X2) ) )
& ( member(X5,image4(X3,X1,X4,X2))
| ? [X6] :
( ilf_type(X6,member_type(X3))
& member(ordered_pair(X6,X5),X4)
& member(X6,X2) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(78,negated_conjecture,
? [X7] :
( ~ empty(X7)
& ilf_type(X7,set_type)
& ? [X8] :
( ~ empty(X8)
& ilf_type(X8,set_type)
& ? [X9] :
( ~ empty(X9)
& ilf_type(X9,set_type)
& ? [X10] :
( ilf_type(X10,relation_type(X9,X7))
& ? [X11] :
( ilf_type(X11,member_type(X7))
& ( ~ member(X11,image4(X9,X7,X10,X8))
| ! [X12] :
( ~ ilf_type(X12,member_type(X9))
| ~ member(ordered_pair(X12,X11),X10)
| ~ member(X12,X8) ) )
& ( member(X11,image4(X9,X7,X10,X8))
| ? [X13] :
( ilf_type(X13,member_type(X9))
& member(ordered_pair(X13,X11),X10)
& member(X13,X8) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,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(esk7_0,esk5_0))
& ilf_type(esk9_0,member_type(esk5_0))
& ( ~ member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0))
| ! [X12] :
( ~ ilf_type(X12,member_type(esk7_0))
| ~ member(ordered_pair(X12,esk9_0),esk8_0)
| ~ member(X12,esk6_0) ) )
& ( member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0))
| ( ilf_type(esk10_0,member_type(esk7_0))
& member(ordered_pair(esk10_0,esk9_0),esk8_0)
& member(esk10_0,esk6_0) ) ) ),
inference(skolemize,[status(esa)],[78]) ).
fof(80,negated_conjecture,
! [X12] :
( ( ~ ilf_type(X12,member_type(esk7_0))
| ~ member(ordered_pair(X12,esk9_0),esk8_0)
| ~ member(X12,esk6_0)
| ~ member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0)) )
& ( member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0))
| ( ilf_type(esk10_0,member_type(esk7_0))
& member(ordered_pair(esk10_0,esk9_0),esk8_0)
& member(esk10_0,esk6_0) ) )
& ilf_type(esk9_0,member_type(esk5_0))
& ilf_type(esk8_0,relation_type(esk7_0,esk5_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)],[79]) ).
fof(81,negated_conjecture,
! [X12] :
( ( ~ ilf_type(X12,member_type(esk7_0))
| ~ member(ordered_pair(X12,esk9_0),esk8_0)
| ~ member(X12,esk6_0)
| ~ member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0)) )
& ( ilf_type(esk10_0,member_type(esk7_0))
| member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0)) )
& ( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0)) )
& ( member(esk10_0,esk6_0)
| member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0)) )
& ilf_type(esk9_0,member_type(esk5_0))
& ilf_type(esk8_0,relation_type(esk7_0,esk5_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)],[80]) ).
cnf(88,negated_conjecture,
ilf_type(esk8_0,relation_type(esk7_0,esk5_0)),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(90,negated_conjecture,
( member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0))
| member(esk10_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(91,negated_conjecture,
( member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0))
| member(ordered_pair(esk10_0,esk9_0),esk8_0) ),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(92,negated_conjecture,
( member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0))
| ilf_type(esk10_0,member_type(esk7_0)) ),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(93,negated_conjecture,
( ~ member(esk9_0,image4(esk7_0,esk5_0,esk8_0,esk6_0))
| ~ member(X1,esk6_0)
| ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ ilf_type(X1,member_type(esk7_0)) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(113,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)],[15]) ).
fof(114,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)],[113]) ).
fof(115,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)],[114]) ).
cnf(116,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)],[115]) ).
fof(142,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)],[20]) ).
fof(143,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)],[142]) ).
fof(144,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)],[143]) ).
fof(145,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)],[144]) ).
cnf(147,plain,
( member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(154,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(X2,image(X3,X1))
| ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X2),X3)
& member(X4,X1) ) )
& ( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,X2),X3)
| ~ member(X4,X1) )
| member(X2,image(X3,X1)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(155,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,binary_relation_type)
| ( ( ~ member(X6,image(X7,X5))
| ? [X8] :
( ilf_type(X8,set_type)
& member(ordered_pair(X8,X6),X7)
& member(X8,X5) ) )
& ( ! [X9] :
( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5) )
| member(X6,image(X7,X5)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,binary_relation_type)
| ( ( ~ member(X6,image(X7,X5))
| ( ilf_type(esk14_3(X5,X6,X7),set_type)
& member(ordered_pair(esk14_3(X5,X6,X7),X6),X7)
& member(esk14_3(X5,X6,X7),X5) ) )
& ( ! [X9] :
( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5) )
| member(X6,image(X7,X5)) ) ) ) ) ),
inference(skolemize,[status(esa)],[155]) ).
fof(157,plain,
! [X5,X6,X7,X9] :
( ( ( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5)
| member(X6,image(X7,X5)) )
& ( ~ member(X6,image(X7,X5))
| ( ilf_type(esk14_3(X5,X6,X7),set_type)
& member(ordered_pair(esk14_3(X5,X6,X7),X6),X7)
& member(esk14_3(X5,X6,X7),X5) ) ) )
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[156]) ).
fof(158,plain,
! [X5,X6,X7,X9] :
( ( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5)
| member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk14_3(X5,X6,X7),set_type)
| ~ member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(ordered_pair(esk14_3(X5,X6,X7),X6),X7)
| ~ member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(esk14_3(X5,X6,X7),X5)
| ~ member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[157]) ).
cnf(159,plain,
( member(esk14_3(X1,X2,X3),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1)) ),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(160,plain,
( member(ordered_pair(esk14_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1)) ),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(162,plain,
( member(X2,image(X3,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X4,X1)
| ~ member(ordered_pair(X4,X2),X3)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[158]) ).
fof(168,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)],[32]) ).
fof(169,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)],[168]) ).
fof(170,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)],[169]) ).
fof(171,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)],[170]) ).
cnf(172,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)],[171]) ).
fof(178,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)],[26]) ).
fof(179,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)],[178]) ).
fof(180,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)],[179]) ).
fof(181,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)],[180]) ).
cnf(183,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)],[181]) ).
fof(188,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)],[34]) ).
fof(189,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)],[188]) ).
fof(190,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk17_1(X3),set_type)
& member(esk17_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[189]) ).
fof(191,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk17_1(X3),set_type)
& member(esk17_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[190]) ).
fof(192,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk17_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk17_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[191]) ).
cnf(195,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[192]) ).
cnf(209,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0)) ),
inference(spm,[status(thm)],[93,90,theory(equality)]) ).
cnf(210,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0)) ),
inference(spm,[status(thm)],[93,92,theory(equality)]) ).
cnf(211,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0)) ),
inference(spm,[status(thm)],[93,91,theory(equality)]) ).
cnf(212,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[195,44,theory(equality)]) ).
cnf(213,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[212,44,theory(equality)]) ).
cnf(214,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[213,theory(equality)]) ).
cnf(227,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[116,44,theory(equality)]) ).
cnf(228,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[227,theory(equality)]) ).
cnf(261,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[172,44,theory(equality)]) ).
cnf(262,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[261,44,theory(equality)]) ).
cnf(263,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[262,theory(equality)]) ).
cnf(264,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[263,214]) ).
cnf(285,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[42,44,theory(equality)]) ).
cnf(286,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[285,44,theory(equality)]) ).
cnf(287,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[286,theory(equality)]) ).
cnf(328,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)],[183,44,theory(equality)]) ).
cnf(329,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[328,44,theory(equality)]) ).
cnf(330,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[329,theory(equality)]) ).
cnf(331,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[287,330,theory(equality)]) ).
cnf(343,plain,
( member(X3,X1)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[147,44,theory(equality)]) ).
cnf(344,plain,
( member(X3,X1)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[343,44,theory(equality)]) ).
cnf(345,plain,
( member(X3,X1)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[344,44,theory(equality)]) ).
cnf(346,plain,
( member(X3,X1)
| $false
| $false
| $false
| $false
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[345,44,theory(equality)]) ).
cnf(347,plain,
( member(X3,X1)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(cn,[status(thm)],[346,theory(equality)]) ).
cnf(348,negated_conjecture,
( member(X1,esk7_0)
| ~ member(ordered_pair(X1,X2),esk8_0) ),
inference(spm,[status(thm)],[347,88,theory(equality)]) ).
cnf(384,plain,
( member(esk14_3(X1,X2,X3),X1)
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X2,image(X3,X1)) ),
inference(rw,[status(thm)],[159,44,theory(equality)]) ).
cnf(385,plain,
( member(esk14_3(X1,X2,X3),X1)
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(X2,image(X3,X1)) ),
inference(rw,[status(thm)],[384,44,theory(equality)]) ).
cnf(386,plain,
( member(esk14_3(X1,X2,X3),X1)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1)) ),
inference(cn,[status(thm)],[385,theory(equality)]) ).
cnf(389,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[38,44,theory(equality)]) ).
cnf(390,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[389,44,theory(equality)]) ).
cnf(391,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| $false
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[390,44,theory(equality)]) ).
cnf(392,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[391,theory(equality)]) ).
cnf(393,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| member(esk10_0,esk6_0)
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk5_0)) ),
inference(spm,[status(thm)],[90,392,theory(equality)]) ).
cnf(394,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| ilf_type(esk10_0,member_type(esk7_0))
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk5_0)) ),
inference(spm,[status(thm)],[92,392,theory(equality)]) ).
cnf(395,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk5_0)) ),
inference(spm,[status(thm)],[91,392,theory(equality)]) ).
cnf(396,negated_conjecture,
( ~ member(esk9_0,image(esk8_0,esk6_0))
| ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0))
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk5_0)) ),
inference(spm,[status(thm)],[93,392,theory(equality)]) ).
cnf(398,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| member(esk10_0,esk6_0)
| $false ),
inference(rw,[status(thm)],[393,88,theory(equality)]) ).
cnf(399,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| member(esk10_0,esk6_0) ),
inference(cn,[status(thm)],[398,theory(equality)]) ).
cnf(400,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| ilf_type(esk10_0,member_type(esk7_0))
| $false ),
inference(rw,[status(thm)],[394,88,theory(equality)]) ).
cnf(401,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| ilf_type(esk10_0,member_type(esk7_0)) ),
inference(cn,[status(thm)],[400,theory(equality)]) ).
cnf(402,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| member(ordered_pair(esk10_0,esk9_0),esk8_0)
| $false ),
inference(rw,[status(thm)],[395,88,theory(equality)]) ).
cnf(403,negated_conjecture,
( member(esk9_0,image(esk8_0,esk6_0))
| member(ordered_pair(esk10_0,esk9_0),esk8_0) ),
inference(cn,[status(thm)],[402,theory(equality)]) ).
cnf(404,negated_conjecture,
( ~ member(esk9_0,image(esk8_0,esk6_0))
| ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0))
| $false ),
inference(rw,[status(thm)],[396,88,theory(equality)]) ).
cnf(405,negated_conjecture,
( ~ member(esk9_0,image(esk8_0,esk6_0))
| ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0)) ),
inference(cn,[status(thm)],[404,theory(equality)]) ).
cnf(406,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X4,X2),X3) ),
inference(rw,[status(thm)],[162,44,theory(equality)]) ).
cnf(407,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X4,X2),X3) ),
inference(rw,[status(thm)],[406,44,theory(equality)]) ).
cnf(408,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X4,X2),X3) ),
inference(rw,[status(thm)],[407,44,theory(equality)]) ).
cnf(409,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X4,X2),X3) ),
inference(cn,[status(thm)],[408,theory(equality)]) ).
cnf(422,plain,
( member(ordered_pair(esk14_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X2,image(X3,X1)) ),
inference(rw,[status(thm)],[160,44,theory(equality)]) ).
cnf(423,plain,
( member(ordered_pair(esk14_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(X2,image(X3,X1)) ),
inference(rw,[status(thm)],[422,44,theory(equality)]) ).
cnf(424,plain,
( member(ordered_pair(esk14_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1)) ),
inference(cn,[status(thm)],[423,theory(equality)]) ).
cnf(439,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[209,424,theory(equality)]) ).
cnf(448,negated_conjecture,
( member(esk14_3(X1,X2,esk8_0),esk7_0)
| ~ member(X2,image(esk8_0,X1))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[348,424,theory(equality)]) ).
cnf(452,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[210,424,theory(equality)]) ).
cnf(453,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[211,424,theory(equality)]) ).
cnf(460,negated_conjecture,
relation_like(esk8_0),
inference(spm,[status(thm)],[331,88,theory(equality)]) ).
cnf(462,negated_conjecture,
ilf_type(esk8_0,binary_relation_type),
inference(spm,[status(thm)],[228,460,theory(equality)]) ).
cnf(621,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1))
| $false ),
inference(rw,[status(thm)],[439,462,theory(equality)]) ).
cnf(622,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1)) ),
inference(cn,[status(thm)],[621,theory(equality)]) ).
cnf(623,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ member(esk9_0,image(esk8_0,X1))
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk7_0) ),
inference(spm,[status(thm)],[622,264,theory(equality)]) ).
cnf(624,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[623,386,theory(equality)]) ).
cnf(625,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0))
| $false ),
inference(rw,[status(thm)],[624,462,theory(equality)]) ).
cnf(626,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0)) ),
inference(cn,[status(thm)],[625,theory(equality)]) ).
cnf(627,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0) ),
inference(csr,[status(thm)],[626,399]) ).
cnf(628,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1))
| $false ),
inference(rw,[status(thm)],[452,462,theory(equality)]) ).
cnf(629,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1)) ),
inference(cn,[status(thm)],[628,theory(equality)]) ).
cnf(630,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ member(esk9_0,image(esk8_0,X1))
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk7_0) ),
inference(spm,[status(thm)],[629,264,theory(equality)]) ).
cnf(631,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[630,386,theory(equality)]) ).
cnf(632,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0))
| $false ),
inference(rw,[status(thm)],[631,462,theory(equality)]) ).
cnf(633,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0)) ),
inference(cn,[status(thm)],[632,theory(equality)]) ).
cnf(634,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0) ),
inference(csr,[status(thm)],[633,401]) ).
cnf(635,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1))
| $false ),
inference(rw,[status(thm)],[453,462,theory(equality)]) ).
cnf(636,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,X1)) ),
inference(cn,[status(thm)],[635,theory(equality)]) ).
cnf(637,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
| ~ member(esk9_0,image(esk8_0,X1))
| ~ member(esk14_3(X1,esk9_0,esk8_0),esk7_0) ),
inference(spm,[status(thm)],[636,264,theory(equality)]) ).
cnf(638,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[637,386,theory(equality)]) ).
cnf(639,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0))
| $false ),
inference(rw,[status(thm)],[638,462,theory(equality)]) ).
cnf(640,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
| ~ member(esk9_0,image(esk8_0,esk6_0)) ),
inference(cn,[status(thm)],[639,theory(equality)]) ).
cnf(641,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0) ),
inference(csr,[status(thm)],[640,403]) ).
cnf(710,negated_conjecture,
( member(esk14_3(X1,X2,esk8_0),esk7_0)
| ~ member(X2,image(esk8_0,X1))
| $false ),
inference(rw,[status(thm)],[448,462,theory(equality)]) ).
cnf(711,negated_conjecture,
( member(esk14_3(X1,X2,esk8_0),esk7_0)
| ~ member(X2,image(esk8_0,X1)) ),
inference(cn,[status(thm)],[710,theory(equality)]) ).
cnf(713,negated_conjecture,
( member(esk10_0,esk6_0)
| ~ member(esk9_0,image(esk8_0,esk6_0)) ),
inference(spm,[status(thm)],[627,711,theory(equality)]) ).
cnf(714,negated_conjecture,
( ilf_type(esk10_0,member_type(esk7_0))
| ~ member(esk9_0,image(esk8_0,esk6_0)) ),
inference(spm,[status(thm)],[634,711,theory(equality)]) ).
cnf(715,negated_conjecture,
( member(ordered_pair(esk10_0,esk9_0),esk8_0)
| ~ member(esk9_0,image(esk8_0,esk6_0)) ),
inference(spm,[status(thm)],[641,711,theory(equality)]) ).
cnf(716,negated_conjecture,
member(esk10_0,esk6_0),
inference(csr,[status(thm)],[713,399]) ).
cnf(727,negated_conjecture,
ilf_type(esk10_0,member_type(esk7_0)),
inference(csr,[status(thm)],[714,401]) ).
cnf(741,negated_conjecture,
member(ordered_pair(esk10_0,esk9_0),esk8_0),
inference(csr,[status(thm)],[715,403]) ).
cnf(743,negated_conjecture,
( member(esk9_0,image(esk8_0,X1))
| ~ member(esk10_0,X1)
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[409,741,theory(equality)]) ).
cnf(754,negated_conjecture,
( member(esk9_0,image(esk8_0,X1))
| ~ member(esk10_0,X1)
| $false ),
inference(rw,[status(thm)],[743,462,theory(equality)]) ).
cnf(755,negated_conjecture,
( member(esk9_0,image(esk8_0,X1))
| ~ member(esk10_0,X1) ),
inference(cn,[status(thm)],[754,theory(equality)]) ).
cnf(769,negated_conjecture,
( ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0))
| ~ member(esk10_0,esk6_0) ),
inference(spm,[status(thm)],[405,755,theory(equality)]) ).
cnf(773,negated_conjecture,
( ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0))
| $false ),
inference(rw,[status(thm)],[769,716,theory(equality)]) ).
cnf(774,negated_conjecture,
( ~ member(ordered_pair(X1,esk9_0),esk8_0)
| ~ member(X1,esk6_0)
| ~ ilf_type(X1,member_type(esk7_0)) ),
inference(cn,[status(thm)],[773,theory(equality)]) ).
cnf(782,negated_conjecture,
( ~ member(esk10_0,esk6_0)
| ~ ilf_type(esk10_0,member_type(esk7_0)) ),
inference(spm,[status(thm)],[774,741,theory(equality)]) ).
cnf(784,negated_conjecture,
( $false
| ~ ilf_type(esk10_0,member_type(esk7_0)) ),
inference(rw,[status(thm)],[782,716,theory(equality)]) ).
cnf(785,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[784,727,theory(equality)]) ).
cnf(786,negated_conjecture,
$false,
inference(cn,[status(thm)],[785,theory(equality)]) ).
cnf(787,negated_conjecture,
$false,
786,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET685+3.p
% --creating new selector for []
% -running prover on /tmp/tmpA75A7w/sel_SET685+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET685+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET685+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET685+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
%
%------------------------------------------------------------------------------