%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET665+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:08:52 EST 2010
% Result : Theorem 5.05s
% Output : CNFRefutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 136 ( 13 unt; 0 def)
% Number of atoms : 698 ( 17 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 935 ( 373 ~; 436 |; 83 &)
% ( 10 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 315 ( 21 sgn 136 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> subset(identity_relation_of(X1),cross_product(X1,X1)) ),
file('/tmp/tmp0FBQVm/sel_SET665+3.p_1',prove_relset_1_28) ).
fof(2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmp0FBQVm/sel_SET665+3.p_1',p25) ).
fof(4,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmp0FBQVm/sel_SET665+3.p_1',p27) ).
fof(6,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/tmp0FBQVm/sel_SET665+3.p_1',p21) ).
fof(7,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/tmp0FBQVm/sel_SET665+3.p_1',p20) ).
fof(8,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/tmp0FBQVm/sel_SET665+3.p_1',p23) ).
fof(11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmp0FBQVm/sel_SET665+3.p_1',p11) ).
fof(17,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/tmp0FBQVm/sel_SET665+3.p_1',p17) ).
fof(20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X2,X3),identity_relation_of(X1))
<=> ( member(X2,X1)
& X2 = X3 ) ) ) ) ),
file('/tmp/tmp0FBQVm/sel_SET665+3.p_1',p2) ).
fof(21,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/tmp0FBQVm/sel_SET665+3.p_1',p3) ).
fof(22,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( member(ordered_pair(X3,X4),X1)
=> member(ordered_pair(X3,X4),X2) ) ) ) ) ) ),
file('/tmp/tmp0FBQVm/sel_SET665+3.p_1',p1) ).
fof(27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),binary_relation_type) ),
file('/tmp/tmp0FBQVm/sel_SET665+3.p_1',p8) ).
fof(29,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> subset(identity_relation_of(X1),cross_product(X1,X1)) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(30,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[2,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)],[8,theory(equality)]) ).
fof(34,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ~ subset(identity_relation_of(X1),cross_product(X1,X1)) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(35,negated_conjecture,
? [X2] :
( ilf_type(X2,set_type)
& ~ subset(identity_relation_of(X2),cross_product(X2,X2)) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ~ subset(identity_relation_of(esk1_0),cross_product(esk1_0,esk1_0)) ),
inference(skolemize,[status(esa)],[35]) ).
cnf(37,negated_conjecture,
~ subset(identity_relation_of(esk1_0),cross_product(esk1_0,esk1_0)),
inference(split_conjunct,[status(thm)],[36]) ).
fof(39,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)],[30]) ).
fof(40,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)],[39]) ).
fof(41,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk2_1(X3),set_type)
& member(esk2_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk2_1(X3),set_type)
& member(esk2_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk2_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk2_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(46,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(51,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[4]) ).
cnf(52,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[51]) ).
fof(56,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)],[6]) ).
fof(57,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)],[56]) ).
fof(58,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(esk4_2(X4,X5),set_type)
& member(esk4_2(X4,X5),X4)
& ~ member(esk4_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[57]) ).
fof(59,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk4_2(X4,X5),set_type)
& member(esk4_2(X4,X5),X4)
& ~ member(esk4_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[58]) ).
fof(60,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(esk4_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk4_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk4_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[59]) ).
cnf(61,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
cnf(62,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(65,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)],[7]) ).
fof(66,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)],[65]) ).
fof(67,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)],[66]) ).
cnf(68,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)],[67]) ).
fof(69,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(70,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)],[69]) ).
fof(71,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)],[70]) ).
fof(72,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)],[71]) ).
cnf(73,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)],[72]) ).
fof(84,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)],[11]) ).
fof(85,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)],[84]) ).
fof(86,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)],[85]) ).
cnf(87,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)],[86]) ).
fof(110,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)],[17]) ).
fof(111,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)],[110]) ).
fof(112,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)],[111]) ).
fof(113,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)],[112]) ).
cnf(114,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(split_conjunct,[status(thm)],[113]) ).
fof(131,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(ordered_pair(X2,X3),identity_relation_of(X1))
| ( member(X2,X1)
& X2 = X3 ) )
& ( ~ member(X2,X1)
| X2 != X3
| member(ordered_pair(X2,X3),identity_relation_of(X1)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(132,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(ordered_pair(X5,X6),identity_relation_of(X4))
| ( member(X5,X4)
& X5 = X6 ) )
& ( ~ member(X5,X4)
| X5 != X6
| member(ordered_pair(X5,X6),identity_relation_of(X4)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[131]) ).
fof(133,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(ordered_pair(X5,X6),identity_relation_of(X4))
| ( member(X5,X4)
& X5 = X6 ) )
& ( ~ member(X5,X4)
| X5 != X6
| member(ordered_pair(X5,X6),identity_relation_of(X4)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[132]) ).
fof(134,plain,
! [X4,X5,X6] :
( ( member(X5,X4)
| ~ member(ordered_pair(X5,X6),identity_relation_of(X4))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( X5 = X6
| ~ member(ordered_pair(X5,X6),identity_relation_of(X4))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(X5,X4)
| X5 != X6
| member(ordered_pair(X5,X6),identity_relation_of(X4))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[133]) ).
cnf(136,plain,
( X2 = X3
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(split_conjunct,[status(thm)],[134]) ).
cnf(137,plain,
( member(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(split_conjunct,[status(thm)],[134]) ).
fof(138,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)],[21]) ).
fof(139,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)],[138]) ).
fof(140,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)],[139]) ).
fof(141,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)],[140]) ).
cnf(142,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[141]) ).
fof(145,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ( ( ~ subset(X1,X2)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X3,X4),X1)
| member(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X3,X4),X1)
& ~ member(ordered_pair(X3,X4),X2) ) )
| subset(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(146,plain,
! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ! [X6] :
( ~ ilf_type(X6,binary_relation_type)
| ( ( ~ subset(X5,X6)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6) ) ) )
& ( ? [X9] :
( ilf_type(X9,set_type)
& ? [X10] :
( ilf_type(X10,set_type)
& member(ordered_pair(X9,X10),X5)
& ~ member(ordered_pair(X9,X10),X6) ) )
| subset(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ! [X6] :
( ~ ilf_type(X6,binary_relation_type)
| ( ( ~ subset(X5,X6)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6) ) ) )
& ( ( ilf_type(esk11_2(X5,X6),set_type)
& ilf_type(esk12_2(X5,X6),set_type)
& member(ordered_pair(esk11_2(X5,X6),esk12_2(X5,X6)),X5)
& ~ member(ordered_pair(esk11_2(X5,X6),esk12_2(X5,X6)),X6) )
| subset(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[146]) ).
fof(148,plain,
! [X5,X6,X7,X8] :
( ( ( ~ ilf_type(X8,set_type)
| ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6)
| ~ ilf_type(X7,set_type)
| ~ subset(X5,X6) )
& ( ( ilf_type(esk11_2(X5,X6),set_type)
& ilf_type(esk12_2(X5,X6),set_type)
& member(ordered_pair(esk11_2(X5,X6),esk12_2(X5,X6)),X5)
& ~ member(ordered_pair(esk11_2(X5,X6),esk12_2(X5,X6)),X6) )
| subset(X5,X6) ) )
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) ),
inference(shift_quantors,[status(thm)],[147]) ).
fof(149,plain,
! [X5,X6,X7,X8] :
( ( ~ ilf_type(X8,set_type)
| ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6)
| ~ ilf_type(X7,set_type)
| ~ subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ilf_type(esk11_2(X5,X6),set_type)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ilf_type(esk12_2(X5,X6),set_type)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( member(ordered_pair(esk11_2(X5,X6),esk12_2(X5,X6)),X5)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ~ member(ordered_pair(esk11_2(X5,X6),esk12_2(X5,X6)),X6)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) ) ),
inference(distribute,[status(thm)],[148]) ).
cnf(150,plain,
( subset(X1,X2)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(esk11_2(X1,X2),esk12_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[149]) ).
cnf(151,plain,
( subset(X1,X2)
| member(ordered_pair(esk11_2(X1,X2),esk12_2(X1,X2)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[149]) ).
fof(181,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ilf_type(identity_relation_of(X1),binary_relation_type) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(182,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ilf_type(identity_relation_of(X2),binary_relation_type) ),
inference(variable_rename,[status(thm)],[181]) ).
cnf(183,plain,
( ilf_type(identity_relation_of(X1),binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(197,plain,
( ilf_type(identity_relation_of(X1),binary_relation_type)
| $false ),
inference(rw,[status(thm)],[183,52,theory(equality)]) ).
cnf(198,plain,
ilf_type(identity_relation_of(X1),binary_relation_type),
inference(cn,[status(thm)],[197,theory(equality)]) ).
cnf(208,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[87,52,theory(equality)]) ).
cnf(209,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[208,theory(equality)]) ).
cnf(233,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[46,52,theory(equality)]) ).
cnf(234,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[233,52,theory(equality)]) ).
cnf(235,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(250,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[73,52,theory(equality)]) ).
cnf(251,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[250,52,theory(equality)]) ).
cnf(252,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[251,theory(equality)]) ).
cnf(253,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[252,235]) ).
cnf(263,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[68,52,theory(equality)]) ).
cnf(264,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[263,52,theory(equality)]) ).
cnf(265,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[264,theory(equality)]) ).
cnf(270,plain,
( ilf_type(X2,subset_type(X1))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[114,52,theory(equality)]) ).
cnf(271,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[270,52,theory(equality)]) ).
cnf(272,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[271,theory(equality)]) ).
cnf(274,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[272,253,theory(equality)]) ).
cnf(301,plain,
( X2 = X3
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(rw,[status(thm)],[136,52,theory(equality)]) ).
cnf(302,plain,
( X2 = X3
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(rw,[status(thm)],[301,52,theory(equality)]) ).
cnf(303,plain,
( X2 = X3
| $false
| $false
| $false
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(rw,[status(thm)],[302,52,theory(equality)]) ).
cnf(304,plain,
( X2 = X3
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(cn,[status(thm)],[303,theory(equality)]) ).
cnf(327,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[62,52,theory(equality)]) ).
cnf(328,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[327,52,theory(equality)]) ).
cnf(329,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1) ),
inference(cn,[status(thm)],[328,theory(equality)]) ).
cnf(331,plain,
( member(X1,power_set(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk4_2(X1,X2),X2) ),
inference(rw,[status(thm)],[61,52,theory(equality)]) ).
cnf(332,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk4_2(X1,X2),X2) ),
inference(rw,[status(thm)],[331,52,theory(equality)]) ).
cnf(333,plain,
( member(X1,power_set(X2))
| ~ member(esk4_2(X1,X2),X2) ),
inference(cn,[status(thm)],[332,theory(equality)]) ).
cnf(334,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[333,329,theory(equality)]) ).
cnf(335,plain,
( member(X2,X1)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(rw,[status(thm)],[137,52,theory(equality)]) ).
cnf(336,plain,
( member(X2,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(rw,[status(thm)],[335,52,theory(equality)]) ).
cnf(337,plain,
( member(X2,X1)
| $false
| $false
| $false
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(rw,[status(thm)],[336,52,theory(equality)]) ).
cnf(338,plain,
( member(X2,X1)
| ~ member(ordered_pair(X2,X3),identity_relation_of(X1)) ),
inference(cn,[status(thm)],[337,theory(equality)]) ).
cnf(369,plain,
( esk11_2(identity_relation_of(X1),X2) = esk12_2(identity_relation_of(X1),X2)
| subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(identity_relation_of(X1),binary_relation_type) ),
inference(spm,[status(thm)],[304,151,theory(equality)]) ).
cnf(370,plain,
( member(esk11_2(identity_relation_of(X1),X2),X1)
| subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(identity_relation_of(X1),binary_relation_type) ),
inference(spm,[status(thm)],[338,151,theory(equality)]) ).
cnf(371,plain,
( esk11_2(identity_relation_of(X1),X2) = esk12_2(identity_relation_of(X1),X2)
| subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| $false ),
inference(rw,[status(thm)],[369,198,theory(equality)]) ).
cnf(372,plain,
( esk11_2(identity_relation_of(X1),X2) = esk12_2(identity_relation_of(X1),X2)
| subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[371,theory(equality)]) ).
cnf(373,plain,
( member(esk11_2(identity_relation_of(X1),X2),X1)
| subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| $false ),
inference(rw,[status(thm)],[370,198,theory(equality)]) ).
cnf(374,plain,
( member(esk11_2(identity_relation_of(X1),X2),X1)
| subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[373,theory(equality)]) ).
cnf(409,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[142,52,theory(equality)]) ).
cnf(410,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[409,52,theory(equality)]) ).
cnf(411,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[410,52,theory(equality)]) ).
cnf(412,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[411,52,theory(equality)]) ).
cnf(413,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[412,theory(equality)]) ).
cnf(415,plain,
( subset(X1,cross_product(X2,X3))
| ~ ilf_type(cross_product(X2,X3),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(esk12_2(X1,cross_product(X2,X3)),X3)
| ~ member(esk11_2(X1,cross_product(X2,X3)),X2) ),
inference(spm,[status(thm)],[150,413,theory(equality)]) ).
cnf(451,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[274,334,theory(equality)]) ).
cnf(460,plain,
relation_like(cross_product(X1,X2)),
inference(spm,[status(thm)],[265,451,theory(equality)]) ).
cnf(463,plain,
ilf_type(cross_product(X1,X2),binary_relation_type),
inference(spm,[status(thm)],[209,460,theory(equality)]) ).
cnf(1112,plain,
( subset(X1,cross_product(X2,X3))
| $false
| ~ ilf_type(X1,binary_relation_type)
| ~ member(esk12_2(X1,cross_product(X2,X3)),X3)
| ~ member(esk11_2(X1,cross_product(X2,X3)),X2) ),
inference(rw,[status(thm)],[415,463,theory(equality)]) ).
cnf(1113,plain,
( subset(X1,cross_product(X2,X3))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(esk12_2(X1,cross_product(X2,X3)),X3)
| ~ member(esk11_2(X1,cross_product(X2,X3)),X2) ),
inference(cn,[status(thm)],[1112,theory(equality)]) ).
cnf(1116,plain,
( subset(identity_relation_of(X1),cross_product(X2,X3))
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X3)
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X2)
| ~ ilf_type(identity_relation_of(X1),binary_relation_type)
| ~ ilf_type(cross_product(X2,X3),binary_relation_type) ),
inference(spm,[status(thm)],[1113,372,theory(equality)]) ).
cnf(1118,plain,
( subset(identity_relation_of(X1),cross_product(X2,X3))
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X3)
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X2)
| $false
| ~ ilf_type(cross_product(X2,X3),binary_relation_type) ),
inference(rw,[status(thm)],[1116,198,theory(equality)]) ).
cnf(1119,plain,
( subset(identity_relation_of(X1),cross_product(X2,X3))
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X3)
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X2)
| $false
| $false ),
inference(rw,[status(thm)],[1118,463,theory(equality)]) ).
cnf(1120,plain,
( subset(identity_relation_of(X1),cross_product(X2,X3))
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X3)
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X3)),X2) ),
inference(cn,[status(thm)],[1119,theory(equality)]) ).
cnf(38611,plain,
( subset(identity_relation_of(X1),cross_product(X2,X1))
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X1)),X2)
| ~ ilf_type(cross_product(X2,X1),binary_relation_type) ),
inference(spm,[status(thm)],[1120,374,theory(equality)]) ).
cnf(38621,plain,
( subset(identity_relation_of(X1),cross_product(X2,X1))
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X1)),X2)
| $false ),
inference(rw,[status(thm)],[38611,463,theory(equality)]) ).
cnf(38622,plain,
( subset(identity_relation_of(X1),cross_product(X2,X1))
| ~ member(esk11_2(identity_relation_of(X1),cross_product(X2,X1)),X2) ),
inference(cn,[status(thm)],[38621,theory(equality)]) ).
cnf(58781,plain,
( subset(identity_relation_of(X1),cross_product(X1,X1))
| ~ ilf_type(cross_product(X1,X1),binary_relation_type) ),
inference(spm,[status(thm)],[38622,374,theory(equality)]) ).
cnf(58792,plain,
( subset(identity_relation_of(X1),cross_product(X1,X1))
| $false ),
inference(rw,[status(thm)],[58781,463,theory(equality)]) ).
cnf(58793,plain,
subset(identity_relation_of(X1),cross_product(X1,X1)),
inference(cn,[status(thm)],[58792,theory(equality)]) ).
cnf(58815,negated_conjecture,
$false,
inference(rw,[status(thm)],[37,58793,theory(equality)]) ).
cnf(58816,negated_conjecture,
$false,
inference(cn,[status(thm)],[58815,theory(equality)]) ).
cnf(58817,negated_conjecture,
$false,
58816,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET665+3.p
% --creating new selector for []
% -running prover on /tmp/tmp0FBQVm/sel_SET665+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET665+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET665+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET665+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
%
%------------------------------------------------------------------------------