TSTP Solution File: SET656+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET656+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 03:08:02 EST 2010
% Result : Theorem 81.79s
% Output : CNFRefutation 81.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 135 ( 12 unt; 0 def)
% Number of atoms : 703 ( 36 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 926 ( 358 ~; 421 |; 98 &)
% ( 10 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 296 ( 13 sgn 146 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',p26) ).
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/tmpnebYKB/sel_SET656+3.p_2',p21) ).
fof(6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',p20) ).
fof(7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
<=> member(X3,X2) ) ) ) ) ),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',p23) ).
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/tmpnebYKB/sel_SET656+3.p_2',p13) ).
fof(18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',p17) ).
fof(20,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/tmpnebYKB/sel_SET656+3.p_2',p19) ).
fof(21,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',p30) ).
fof(22,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> intersection(X3,cross_product(X1,X2)) = X3 ) ) ),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',prove_relset_1_18) ).
fof(25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
=> intersection(X1,X2) = X1 ) ) ),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',p1) ).
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/tmpnebYKB/sel_SET656+3.p_2',p6) ).
fof(28,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ) ) ) ),
file('/tmp/tmpnebYKB/sel_SET656+3.p_2',p4) ).
fof(32,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> intersection(X3,cross_product(X1,X2)) = X3 ) ) ),
inference(assume_negation,[status(cth)],[22]) ).
fof(33,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(35,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(55,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)],[33]) ).
fof(56,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)],[55]) ).
fof(57,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk4_1(X3),set_type)
& member(esk4_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[56]) ).
fof(58,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk4_1(X3),set_type)
& member(esk4_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[57]) ).
fof(59,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk4_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk4_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[58]) ).
cnf(62,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(63,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( empty(X2)
| ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X1,member_type(X2))
| member(X1,X2) )
& ( ~ member(X1,X2)
| ilf_type(X1,member_type(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(64,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)],[63]) ).
fof(65,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)],[64]) ).
fof(66,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)],[65]) ).
cnf(67,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)],[66]) ).
cnf(68,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)],[66]) ).
fof(69,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(70,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,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)],[70]) ).
cnf(73,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(74,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( X1 != X2
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(X3,X1)
| member(X3,X2) )
& ( ~ member(X3,X2)
| member(X3,X1) ) ) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& ( ~ member(X3,X1)
| ~ member(X3,X2) )
& ( member(X3,X1)
| member(X3,X2) ) )
| X1 = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(75,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( X4 != X5
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& ( ~ member(X7,X4)
| ~ member(X7,X5) )
& ( member(X7,X4)
| member(X7,X5) ) )
| X4 = X5 ) ) ) ),
inference(variable_rename,[status(thm)],[74]) ).
fof(76,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( X4 != X5
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) ) )
& ( ( ilf_type(esk5_2(X4,X5),set_type)
& ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5) )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5) ) )
| X4 = X5 ) ) ) ),
inference(skolemize,[status(esa)],[75]) ).
fof(77,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ilf_type(esk5_2(X4,X5),set_type)
& ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5) )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5) ) )
| X4 = X5 ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[76]) ).
fof(78,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(X6,X5)
| member(X6,X4)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk5_2(X4,X5),set_type)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[77]) ).
cnf(79,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(109,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(110,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)],[109]) ).
fof(111,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)],[110]) ).
fof(112,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)],[111]) ).
cnf(114,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)],[112]) ).
fof(126,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ subset(X1,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) )
| subset(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(127,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ subset(X4,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) )
| subset(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[126]) ).
fof(128,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ subset(X4,X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( ilf_type(esk9_2(X4,X5),set_type)
& member(esk9_2(X4,X5),X4)
& ~ member(esk9_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[127]) ).
fof(129,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk9_2(X4,X5),set_type)
& member(esk9_2(X4,X5),X4)
& ~ member(esk9_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[128]) ).
fof(130,plain,
! [X4,X5,X6] :
( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk9_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk9_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk9_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[129]) ).
cnf(131,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk9_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(132,plain,
( subset(X1,X2)
| member(esk9_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(138,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)],[20]) ).
fof(139,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)],[138]) ).
fof(140,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(esk10_2(X4,X5),set_type)
& member(esk10_2(X4,X5),X4)
& ~ member(esk10_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[139]) ).
fof(141,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk10_2(X4,X5),set_type)
& member(esk10_2(X4,X5),X4)
& ~ member(esk10_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[140]) ).
fof(142,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(esk10_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk10_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk10_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[141]) ).
cnf(146,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)],[142]) ).
fof(147,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[21]) ).
cnf(148,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[147]) ).
fof(149,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X1,X2))
& intersection(X3,cross_product(X1,X2)) != X3 ) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(150,negated_conjecture,
? [X4] :
( ilf_type(X4,set_type)
& ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,relation_type(X4,X5))
& intersection(X6,cross_product(X4,X5)) != X6 ) ) ),
inference(variable_rename,[status(thm)],[149]) ).
fof(151,negated_conjecture,
( ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,relation_type(esk11_0,esk12_0))
& intersection(esk13_0,cross_product(esk11_0,esk12_0)) != esk13_0 ),
inference(skolemize,[status(esa)],[150]) ).
cnf(152,negated_conjecture,
intersection(esk13_0,cross_product(esk11_0,esk12_0)) != esk13_0,
inference(split_conjunct,[status(thm)],[151]) ).
cnf(153,negated_conjecture,
ilf_type(esk13_0,relation_type(esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[151]) ).
fof(171,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| intersection(X1,X2) = X1 ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(172,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ subset(X3,X4)
| intersection(X3,X4) = X3 ) ),
inference(variable_rename,[status(thm)],[171]) ).
fof(173,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ~ subset(X3,X4)
| intersection(X3,X4) = X3
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[172]) ).
cnf(174,plain,
( intersection(X1,X2) = X1
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[173]) ).
fof(175,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(176,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)],[175]) ).
fof(177,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)],[176]) ).
fof(178,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)],[177]) ).
cnf(180,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)],[178]) ).
fof(186,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(X3,intersection(X1,X2))
| ( member(X3,X1)
& member(X3,X2) ) )
& ( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(187,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,intersection(X4,X5))
| ( member(X6,X4)
& member(X6,X5) ) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[186]) ).
fof(188,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,intersection(X4,X5))
| ( member(X6,X4)
& member(X6,X5) ) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[187]) ).
fof(189,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[188]) ).
cnf(192,plain,
( member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X3,intersection(X1,X2)) ),
inference(split_conjunct,[status(thm)],[189]) ).
cnf(216,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[73,148,theory(equality)]) ).
cnf(217,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[216,theory(equality)]) ).
cnf(257,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[62,148,theory(equality)]) ).
cnf(258,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[257,148,theory(equality)]) ).
cnf(259,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[258,theory(equality)]) ).
cnf(269,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[174,148,theory(equality)]) ).
cnf(270,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[269,148,theory(equality)]) ).
cnf(271,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[270,theory(equality)]) ).
cnf(283,plain,
( subset(X1,X2)
| member(esk9_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[132,148,theory(equality)]) ).
cnf(284,plain,
( subset(X1,X2)
| member(esk9_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[283,148,theory(equality)]) ).
cnf(285,plain,
( subset(X1,X2)
| member(esk9_2(X1,X2),X1) ),
inference(cn,[status(thm)],[284,theory(equality)]) ).
cnf(291,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[67,148,theory(equality)]) ).
cnf(292,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[291,148,theory(equality)]) ).
cnf(293,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[292,theory(equality)]) ).
cnf(294,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[293,259]) ).
cnf(298,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)],[114,148,theory(equality)]) ).
cnf(299,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[298,148,theory(equality)]) ).
cnf(300,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[299,theory(equality)]) ).
cnf(307,plain,
( subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk9_2(X1,X2),X2) ),
inference(rw,[status(thm)],[131,148,theory(equality)]) ).
cnf(308,plain,
( subset(X1,X2)
| $false
| $false
| ~ member(esk9_2(X1,X2),X2) ),
inference(rw,[status(thm)],[307,148,theory(equality)]) ).
cnf(309,plain,
( subset(X1,X2)
| ~ member(esk9_2(X1,X2),X2) ),
inference(cn,[status(thm)],[308,theory(equality)]) ).
cnf(312,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[68,148,theory(equality)]) ).
cnf(313,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[312,148,theory(equality)]) ).
cnf(314,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[313,theory(equality)]) ).
cnf(316,plain,
( empty(power_set(X1))
| member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(spm,[status(thm)],[314,300,theory(equality)]) ).
cnf(317,plain,
( member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(sr,[status(thm)],[316,217,theory(equality)]) ).
cnf(354,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)],[180,148,theory(equality)]) ).
cnf(355,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[354,148,theory(equality)]) ).
cnf(356,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[355,theory(equality)]) ).
cnf(363,plain,
( member(X3,X1)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X3,intersection(X1,X2)) ),
inference(rw,[status(thm)],[192,148,theory(equality)]) ).
cnf(364,plain,
( member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X3,intersection(X1,X2)) ),
inference(rw,[status(thm)],[363,148,theory(equality)]) ).
cnf(365,plain,
( member(X3,X1)
| $false
| $false
| $false
| ~ member(X3,intersection(X1,X2)) ),
inference(rw,[status(thm)],[364,148,theory(equality)]) ).
cnf(366,plain,
( member(X3,X1)
| ~ member(X3,intersection(X1,X2)) ),
inference(cn,[status(thm)],[365,theory(equality)]) ).
cnf(373,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[79,148,theory(equality)]) ).
cnf(374,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[373,148,theory(equality)]) ).
cnf(375,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(cn,[status(thm)],[374,theory(equality)]) ).
cnf(384,plain,
( member(esk5_2(intersection(X1,X2),X3),X1)
| intersection(X1,X2) = X3
| member(esk5_2(intersection(X1,X2),X3),X3) ),
inference(spm,[status(thm)],[366,375,theory(equality)]) ).
cnf(404,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)],[146,148,theory(equality)]) ).
cnf(405,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[404,148,theory(equality)]) ).
cnf(406,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[405,148,theory(equality)]) ).
cnf(407,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[406,theory(equality)]) ).
cnf(540,plain,
( member(X1,power_set(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[317,356,theory(equality)]) ).
cnf(1294,plain,
( intersection(X4,X5) = X4
| member(esk5_2(intersection(X4,X5),X4),X4) ),
inference(ef,[status(thm)],[384,theory(equality)]) ).
cnf(4472,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[407,540,theory(equality)]) ).
cnf(1270804,negated_conjecture,
( member(X1,cross_product(esk11_0,esk12_0))
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[4472,153,theory(equality)]) ).
cnf(1270878,negated_conjecture,
( ~ empty(cross_product(esk11_0,esk12_0))
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[259,1270804,theory(equality)]) ).
cnf(1270879,negated_conjecture,
( ilf_type(X1,member_type(cross_product(esk11_0,esk12_0)))
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[294,1270804,theory(equality)]) ).
cnf(1271005,negated_conjecture,
( ilf_type(esk9_2(esk13_0,X1),member_type(cross_product(esk11_0,esk12_0)))
| subset(esk13_0,X1) ),
inference(spm,[status(thm)],[1270879,285,theory(equality)]) ).
cnf(1271967,negated_conjecture,
( empty(cross_product(esk11_0,esk12_0))
| member(esk9_2(esk13_0,X1),cross_product(esk11_0,esk12_0))
| subset(esk13_0,X1) ),
inference(spm,[status(thm)],[314,1271005,theory(equality)]) ).
cnf(1289054,negated_conjecture,
( subset(esk13_0,cross_product(esk11_0,esk12_0))
| empty(cross_product(esk11_0,esk12_0)) ),
inference(spm,[status(thm)],[309,1271967,theory(equality)]) ).
cnf(1289072,negated_conjecture,
( intersection(esk13_0,cross_product(esk11_0,esk12_0)) = esk13_0
| empty(cross_product(esk11_0,esk12_0)) ),
inference(spm,[status(thm)],[271,1289054,theory(equality)]) ).
cnf(1289074,negated_conjecture,
empty(cross_product(esk11_0,esk12_0)),
inference(sr,[status(thm)],[1289072,152,theory(equality)]) ).
cnf(1289247,negated_conjecture,
( $false
| ~ member(X1,esk13_0) ),
inference(rw,[status(thm)],[1270878,1289074,theory(equality)]) ).
cnf(1289248,negated_conjecture,
~ member(X1,esk13_0),
inference(cn,[status(thm)],[1289247,theory(equality)]) ).
cnf(1289402,negated_conjecture,
intersection(esk13_0,X1) = esk13_0,
inference(spm,[status(thm)],[1289248,1294,theory(equality)]) ).
cnf(1297579,negated_conjecture,
$false,
inference(rw,[status(thm)],[152,1289402,theory(equality)]) ).
cnf(1297580,negated_conjecture,
$false,
inference(cn,[status(thm)],[1297579,theory(equality)]) ).
cnf(1297581,negated_conjecture,
$false,
1297580,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET656+3.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpnebYKB/sel_SET656+3.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpnebYKB/sel_SET656+3.p_2 with time limit 80
% -prover status Theorem
% Problem SET656+3.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET656+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET656+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
%
%------------------------------------------------------------------------------