TSTP Solution File: SET645+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET645+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:07:09 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 87 ( 15 unt; 0 def)
% Number of atoms : 443 ( 0 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 579 ( 223 ~; 255 |; 64 &)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 205 ( 17 sgn 97 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpPmCvCa/sel_SET645+3.p_1',p21) ).
fof(3,conjecture,
! [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/tmpPmCvCa/sel_SET645+3.p_1',prove_relset_1_7) ).
fof(4,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/tmpPmCvCa/sel_SET645+3.p_1',p10) ).
fof(7,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/tmpPmCvCa/sel_SET645+3.p_1',p13) ).
fof(8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpPmCvCa/sel_SET645+3.p_1',p14) ).
fof(9,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/tmpPmCvCa/sel_SET645+3.p_1',p15) ).
fof(16,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)
=> ( member(ordered_pair(X1,X2),cross_product(X3,X4))
<=> ( member(X1,X3)
& member(X2,X4) ) ) ) ) ) ),
file('/tmp/tmpPmCvCa/sel_SET645+3.p_1',p1) ).
fof(19,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/tmpPmCvCa/sel_SET645+3.p_1',p4) ).
fof(23,negated_conjecture,
~ ! [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(assume_negation,[status(cth)],[3]) ).
fof(24,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(25,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)],[9,theory(equality)]) ).
fof(28,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[1]) ).
cnf(29,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[28]) ).
fof(34,negated_conjecture,
? [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)],[23]) ).
fof(35,negated_conjecture,
? [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)],[34]) ).
fof(36,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,set_type)
& ilf_type(esk4_0,set_type)
& ilf_type(esk5_0,relation_type(esk1_0,esk2_0))
& member(ordered_pair(esk3_0,esk4_0),esk5_0)
& ( ~ member(esk3_0,esk1_0)
| ~ member(esk4_0,esk2_0) ) ),
inference(skolemize,[status(esa)],[35]) ).
cnf(37,negated_conjecture,
( ~ member(esk4_0,esk2_0)
| ~ member(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
member(ordered_pair(esk3_0,esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(39,negated_conjecture,
ilf_type(esk5_0,relation_type(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[36]) ).
fof(44,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)],[4]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
fof(47,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)],[46]) ).
cnf(49,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)],[47]) ).
fof(64,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)],[7]) ).
fof(65,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)],[64]) ).
fof(66,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(esk8_2(X4,X5),set_type)
& member(esk8_2(X4,X5),X4)
& ~ member(esk8_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[65]) ).
fof(67,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk8_2(X4,X5),set_type)
& member(esk8_2(X4,X5),X4)
& ~ member(esk8_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[66]) ).
fof(68,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(esk8_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk8_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk8_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[67]) ).
cnf(72,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)],[68]) ).
fof(73,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(74,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,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)],[74]) ).
cnf(77,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(78,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)],[25]) ).
fof(79,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)],[78]) ).
fof(80,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)],[79]) ).
fof(81,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)],[80]) ).
cnf(83,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)],[81]) ).
fof(120,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)
| ( ( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| ( member(X1,X3)
& member(X2,X4) ) )
& ( ~ member(X1,X3)
| ~ member(X2,X4)
| member(ordered_pair(X1,X2),cross_product(X3,X4)) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(121,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ( member(X5,X7)
& member(X6,X8) ) )
& ( ~ member(X5,X7)
| ~ member(X6,X8)
| member(ordered_pair(X5,X6),cross_product(X7,X8)) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[120]) ).
fof(122,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| ( ( ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ( member(X5,X7)
& member(X6,X8) ) )
& ( ~ member(X5,X7)
| ~ member(X6,X8)
| member(ordered_pair(X5,X6),cross_product(X7,X8)) ) )
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[121]) ).
fof(123,plain,
! [X5,X6,X7,X8] :
( ( member(X5,X7)
| ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(X6,X8)
| ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ member(X5,X7)
| ~ member(X6,X8)
| member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[122]) ).
cnf(125,plain,
( member(X2,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[123]) ).
cnf(126,plain,
( member(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[123]) ).
fof(134,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)],[19]) ).
fof(135,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)],[134]) ).
fof(136,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)],[135]) ).
fof(137,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)],[136]) ).
cnf(139,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)],[137]) ).
cnf(165,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[77,29,theory(equality)]) ).
cnf(166,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[165,theory(equality)]) ).
cnf(233,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[83,29,theory(equality)]) ).
cnf(234,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[233,29,theory(equality)]) ).
cnf(235,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(245,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)],[72,29,theory(equality)]) ).
cnf(246,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[245,29,theory(equality)]) ).
cnf(247,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[246,29,theory(equality)]) ).
cnf(248,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[247,theory(equality)]) ).
cnf(253,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)],[49,29,theory(equality)]) ).
cnf(254,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[253,29,theory(equality)]) ).
cnf(255,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[254,theory(equality)]) ).
cnf(266,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)],[139,29,theory(equality)]) ).
cnf(267,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[266,29,theory(equality)]) ).
cnf(268,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[267,theory(equality)]) ).
cnf(269,negated_conjecture,
ilf_type(esk5_0,subset_type(cross_product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[268,39,theory(equality)]) ).
cnf(286,plain,
( member(X2,X4)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[125,29,theory(equality)]) ).
cnf(287,plain,
( member(X2,X4)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[286,29,theory(equality)]) ).
cnf(288,plain,
( member(X2,X4)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[287,29,theory(equality)]) ).
cnf(289,plain,
( member(X2,X4)
| $false
| $false
| $false
| $false
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[288,29,theory(equality)]) ).
cnf(290,plain,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(291,plain,
( member(X1,X3)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[126,29,theory(equality)]) ).
cnf(292,plain,
( member(X1,X3)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[291,29,theory(equality)]) ).
cnf(293,plain,
( member(X1,X3)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[292,29,theory(equality)]) ).
cnf(294,plain,
( member(X1,X3)
| $false
| $false
| $false
| $false
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[293,29,theory(equality)]) ).
cnf(295,plain,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(346,negated_conjecture,
ilf_type(esk5_0,member_type(power_set(cross_product(esk1_0,esk2_0)))),
inference(spm,[status(thm)],[255,269,theory(equality)]) ).
cnf(364,negated_conjecture,
( empty(power_set(cross_product(esk1_0,esk2_0)))
| member(esk5_0,power_set(cross_product(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[235,346,theory(equality)]) ).
cnf(366,negated_conjecture,
member(esk5_0,power_set(cross_product(esk1_0,esk2_0))),
inference(sr,[status(thm)],[364,166,theory(equality)]) ).
cnf(370,negated_conjecture,
( member(X1,cross_product(esk1_0,esk2_0))
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[248,366,theory(equality)]) ).
cnf(385,negated_conjecture,
member(ordered_pair(esk3_0,esk4_0),cross_product(esk1_0,esk2_0)),
inference(spm,[status(thm)],[370,38,theory(equality)]) ).
cnf(397,negated_conjecture,
member(esk4_0,esk2_0),
inference(spm,[status(thm)],[290,385,theory(equality)]) ).
cnf(398,negated_conjecture,
member(esk3_0,esk1_0),
inference(spm,[status(thm)],[295,385,theory(equality)]) ).
cnf(407,negated_conjecture,
( ~ member(esk3_0,esk1_0)
| $false ),
inference(rw,[status(thm)],[37,397,theory(equality)]) ).
cnf(408,negated_conjecture,
~ member(esk3_0,esk1_0),
inference(cn,[status(thm)],[407,theory(equality)]) ).
cnf(421,negated_conjecture,
$false,
inference(sr,[status(thm)],[398,408,theory(equality)]) ).
cnf(422,negated_conjecture,
$false,
421,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET645+3.p
% --creating new selector for []
% -running prover on /tmp/tmpPmCvCa/sel_SET645+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET645+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET645+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET645+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
%
%------------------------------------------------------------------------------