%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET644+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 03:06:59 EST 2010
% Result : Theorem 0.47s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 116 ( 11 unt; 0 def)
% Number of atoms : 649 ( 28 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 890 ( 357 ~; 392 |; 99 &)
% ( 6 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 316 ( 26 sgn 137 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmptwbeDm/sel_SET644+3.p_1',p24) ).
fof(3,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmptwbeDm/sel_SET644+3.p_1',p27) ).
fof(5,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/tmptwbeDm/sel_SET644+3.p_1',p21) ).
fof(6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmptwbeDm/sel_SET644+3.p_1',p20) ).
fof(7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( relation_like(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
=> ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X2 = ordered_pair(X3,X4) ) ) ) ) ) ),
file('/tmp/tmptwbeDm/sel_SET644+3.p_1',p23) ).
fof(9,conjecture,
! [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))
=> ( member(X3,X4)
=> ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,set_type)
& X3 = ordered_pair(X5,X6)
& member(X5,X1)
& member(X6,X2) ) ) ) ) ) ) ),
file('/tmp/tmptwbeDm/sel_SET644+3.p_1',prove_relset_1_6) ).
fof(14,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/tmptwbeDm/sel_SET644+3.p_1',p14) ).
fof(19,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/tmptwbeDm/sel_SET644+3.p_1',p19) ).
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)
=> ( member(ordered_pair(X1,X2),cross_product(X3,X4))
<=> ( member(X1,X3)
& member(X2,X4) ) ) ) ) ) ),
file('/tmp/tmptwbeDm/sel_SET644+3.p_1',p2) ).
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/tmptwbeDm/sel_SET644+3.p_1',p5) ).
fof(29,negated_conjecture,
~ ! [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))
=> ( member(X3,X4)
=> ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,set_type)
& X3 = ordered_pair(X5,X6)
& member(X5,X1)
& member(X6,X2) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(31,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)],[5,theory(equality)]) ).
fof(32,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(42,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(43,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)],[42]) ).
fof(44,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)],[43]) ).
cnf(45,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)],[44]) ).
fof(46,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[3]) ).
cnf(47,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[46]) ).
fof(51,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)],[31]) ).
fof(52,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)],[51]) ).
fof(53,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)],[52]) ).
fof(54,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)],[53]) ).
cnf(56,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)],[54]) ).
fof(57,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(58,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,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)],[58]) ).
cnf(61,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(62,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ relation_like(X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X2 = ordered_pair(X3,X4) ) ) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X1)
& ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| X2 != ordered_pair(X3,X4) ) ) )
| relation_like(X1) ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(63,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ relation_like(X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X5)
| ? [X7] :
( ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,set_type)
& X6 = ordered_pair(X7,X8) ) ) ) )
& ( ? [X9] :
( ilf_type(X9,set_type)
& member(X9,X5)
& ! [X10] :
( ~ ilf_type(X10,set_type)
| ! [X11] :
( ~ ilf_type(X11,set_type)
| X9 != ordered_pair(X10,X11) ) ) )
| relation_like(X5) ) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ relation_like(X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X5)
| ( ilf_type(esk2_2(X5,X6),set_type)
& ilf_type(esk3_2(X5,X6),set_type)
& X6 = ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)) ) ) )
& ( ( ilf_type(esk4_1(X5),set_type)
& member(esk4_1(X5),X5)
& ! [X10] :
( ~ ilf_type(X10,set_type)
| ! [X11] :
( ~ ilf_type(X11,set_type)
| esk4_1(X5) != ordered_pair(X10,X11) ) ) )
| relation_like(X5) ) ) ),
inference(skolemize,[status(esa)],[63]) ).
fof(65,plain,
! [X5,X6,X10,X11] :
( ( ( ( ( ~ ilf_type(X11,set_type)
| esk4_1(X5) != ordered_pair(X10,X11)
| ~ ilf_type(X10,set_type) )
& member(esk4_1(X5),X5)
& ilf_type(esk4_1(X5),set_type) )
| relation_like(X5) )
& ( ~ ilf_type(X6,set_type)
| ~ member(X6,X5)
| ( ilf_type(esk2_2(X5,X6),set_type)
& ilf_type(esk3_2(X5,X6),set_type)
& X6 = ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)) )
| ~ relation_like(X5) ) )
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[64]) ).
fof(66,plain,
! [X5,X6,X10,X11] :
( ( ~ ilf_type(X11,set_type)
| esk4_1(X5) != ordered_pair(X10,X11)
| ~ ilf_type(X10,set_type)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( member(esk4_1(X5),X5)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk4_1(X5),set_type)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk2_2(X5,X6),set_type)
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk3_2(X5,X6),set_type)
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( X6 = ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6))
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[65]) ).
cnf(67,plain,
( X2 = ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(77,negated_conjecture,
? [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))
& member(X3,X4)
& ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| X3 != ordered_pair(X5,X6)
| ~ member(X5,X1)
| ~ member(X6,X2) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(78,negated_conjecture,
? [X7] :
( ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,set_type)
& ? [X9] :
( ilf_type(X9,set_type)
& ? [X10] :
( ilf_type(X10,relation_type(X7,X8))
& member(X9,X10)
& ! [X11] :
( ~ ilf_type(X11,set_type)
| ! [X12] :
( ~ ilf_type(X12,set_type)
| X9 != ordered_pair(X11,X12)
| ~ member(X11,X7)
| ~ member(X12,X8) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,negated_conjecture,
( ilf_type(esk6_0,set_type)
& ilf_type(esk7_0,set_type)
& ilf_type(esk8_0,set_type)
& ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
& member(esk8_0,esk9_0)
& ! [X11] :
( ~ ilf_type(X11,set_type)
| ! [X12] :
( ~ ilf_type(X12,set_type)
| esk8_0 != ordered_pair(X11,X12)
| ~ member(X11,esk6_0)
| ~ member(X12,esk7_0) ) ) ),
inference(skolemize,[status(esa)],[78]) ).
fof(80,negated_conjecture,
! [X11,X12] :
( ( ~ ilf_type(X12,set_type)
| esk8_0 != ordered_pair(X11,X12)
| ~ member(X11,esk6_0)
| ~ member(X12,esk7_0)
| ~ ilf_type(X11,set_type) )
& member(esk8_0,esk9_0)
& ilf_type(esk9_0,relation_type(esk6_0,esk7_0))
& ilf_type(esk8_0,set_type)
& ilf_type(esk7_0,set_type)
& ilf_type(esk6_0,set_type) ),
inference(shift_quantors,[status(thm)],[79]) ).
cnf(84,negated_conjecture,
ilf_type(esk9_0,relation_type(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(85,negated_conjecture,
member(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(86,negated_conjecture,
( ~ ilf_type(X1,set_type)
| ~ member(X2,esk7_0)
| ~ member(X1,esk6_0)
| esk8_0 != ordered_pair(X1,X2)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(104,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)],[14]) ).
fof(105,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)],[104]) ).
fof(106,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)],[105]) ).
fof(107,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)],[106]) ).
cnf(109,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)],[107]) ).
fof(136,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)],[19]) ).
fof(137,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)],[136]) ).
fof(138,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(esk14_2(X4,X5),set_type)
& member(esk14_2(X4,X5),X4)
& ~ member(esk14_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[137]) ).
fof(139,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk14_2(X4,X5),set_type)
& member(esk14_2(X4,X5),X4)
& ~ member(esk14_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[138]) ).
fof(140,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(esk14_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk14_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk14_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[139]) ).
cnf(144,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)],[140]) ).
fof(145,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)],[20]) ).
fof(146,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)],[145]) ).
fof(147,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)],[146]) ).
fof(148,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)],[147]) ).
cnf(150,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)],[148]) ).
cnf(151,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)],[148]) ).
fof(182,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(183,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)],[182]) ).
fof(184,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)],[183]) ).
fof(185,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)],[184]) ).
cnf(187,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)],[185]) ).
cnf(208,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[61,47,theory(equality)]) ).
cnf(209,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[208,theory(equality)]) ).
cnf(293,negated_conjecture,
( ordered_pair(X1,X2) != esk8_0
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X2,esk7_0)
| ~ member(X1,esk6_0) ),
inference(rw,[status(thm)],[86,47,theory(equality)]) ).
cnf(294,negated_conjecture,
( ordered_pair(X1,X2) != esk8_0
| $false
| $false
| ~ member(X2,esk7_0)
| ~ member(X1,esk6_0) ),
inference(rw,[status(thm)],[293,47,theory(equality)]) ).
cnf(295,negated_conjecture,
( ordered_pair(X1,X2) != esk8_0
| ~ member(X2,esk7_0)
| ~ member(X1,esk6_0) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(308,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[56,47,theory(equality)]) ).
cnf(309,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[308,47,theory(equality)]) ).
cnf(310,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[309,theory(equality)]) ).
cnf(321,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[45,47,theory(equality)]) ).
cnf(322,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[321,47,theory(equality)]) ).
cnf(323,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[322,theory(equality)]) ).
cnf(329,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)],[109,47,theory(equality)]) ).
cnf(330,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[329,47,theory(equality)]) ).
cnf(331,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[330,theory(equality)]) ).
cnf(332,plain,
( member(X1,power_set(X2))
| empty(power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(spm,[status(thm)],[310,331,theory(equality)]) ).
cnf(333,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[332,209,theory(equality)]) ).
cnf(346,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)],[144,47,theory(equality)]) ).
cnf(347,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[346,47,theory(equality)]) ).
cnf(348,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[347,47,theory(equality)]) ).
cnf(349,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[348,theory(equality)]) ).
cnf(355,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)],[187,47,theory(equality)]) ).
cnf(356,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[355,47,theory(equality)]) ).
cnf(357,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[356,theory(equality)]) ).
cnf(358,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[323,357,theory(equality)]) ).
cnf(364,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)],[150,47,theory(equality)]) ).
cnf(365,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)],[364,47,theory(equality)]) ).
cnf(366,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)],[365,47,theory(equality)]) ).
cnf(367,plain,
( member(X2,X4)
| $false
| $false
| $false
| $false
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[366,47,theory(equality)]) ).
cnf(368,plain,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(cn,[status(thm)],[367,theory(equality)]) ).
cnf(387,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)],[151,47,theory(equality)]) ).
cnf(388,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)],[387,47,theory(equality)]) ).
cnf(389,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)],[388,47,theory(equality)]) ).
cnf(390,plain,
( member(X1,X3)
| $false
| $false
| $false
| $false
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[389,47,theory(equality)]) ).
cnf(391,plain,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(cn,[status(thm)],[390,theory(equality)]) ).
cnf(393,plain,
( ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[67,47,theory(equality)]) ).
cnf(394,plain,
( ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[393,47,theory(equality)]) ).
cnf(395,plain,
( ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[394,theory(equality)]) ).
cnf(396,negated_conjecture,
( X2 != esk8_0
| ~ member(esk3_2(X1,X2),esk7_0)
| ~ member(esk2_2(X1,X2),esk6_0)
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[295,395,theory(equality)]) ).
cnf(398,plain,
( member(esk3_2(X1,X2),X3)
| ~ member(X2,cross_product(X4,X3))
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[368,395,theory(equality)]) ).
cnf(399,plain,
( member(esk2_2(X1,X2),X3)
| ~ member(X2,cross_product(X3,X4))
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[391,395,theory(equality)]) ).
cnf(451,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[349,333,theory(equality)]) ).
cnf(480,negated_conjecture,
relation_like(esk9_0),
inference(spm,[status(thm)],[358,84,theory(equality)]) ).
cnf(541,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[451,357,theory(equality)]) ).
cnf(1224,negated_conjecture,
( member(X1,cross_product(esk6_0,esk7_0))
| ~ member(X1,esk9_0) ),
inference(spm,[status(thm)],[541,84,theory(equality)]) ).
cnf(1242,negated_conjecture,
( member(esk3_2(X1,X2),esk7_0)
| ~ relation_like(X1)
| ~ member(X2,X1)
| ~ member(X2,esk9_0) ),
inference(spm,[status(thm)],[398,1224,theory(equality)]) ).
cnf(1243,negated_conjecture,
( member(esk2_2(X1,X2),esk6_0)
| ~ relation_like(X1)
| ~ member(X2,X1)
| ~ member(X2,esk9_0) ),
inference(spm,[status(thm)],[399,1224,theory(equality)]) ).
cnf(1316,negated_conjecture,
( X1 != esk8_0
| ~ relation_like(X2)
| ~ member(esk2_2(X2,X1),esk6_0)
| ~ member(X1,X2)
| ~ member(X1,esk9_0) ),
inference(spm,[status(thm)],[396,1242,theory(equality)]) ).
cnf(3769,negated_conjecture,
( X1 != esk8_0
| ~ relation_like(X2)
| ~ member(X1,esk9_0)
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[1316,1243]) ).
cnf(3770,negated_conjecture,
( ~ relation_like(X1)
| ~ member(esk8_0,X1) ),
inference(spm,[status(thm)],[3769,85,theory(equality)]) ).
cnf(3842,negated_conjecture,
~ member(esk8_0,esk9_0),
inference(spm,[status(thm)],[3770,480,theory(equality)]) ).
cnf(3855,negated_conjecture,
$false,
inference(rw,[status(thm)],[3842,85,theory(equality)]) ).
cnf(3856,negated_conjecture,
$false,
inference(cn,[status(thm)],[3855,theory(equality)]) ).
cnf(3857,negated_conjecture,
$false,
3856,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET644+3.p
% --creating new selector for []
% -running prover on /tmp/tmptwbeDm/sel_SET644+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET644+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET644+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET644+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
%
%------------------------------------------------------------------------------