TSTP Solution File: SET655+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET655+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:07:54 EST 2010
% Result : Theorem 0.65s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 148 ( 20 unt; 0 def)
% Number of atoms : 706 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 909 ( 351 ~; 421 |; 85 &)
% ( 7 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 331 ( 6 sgn 137 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,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)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/tmp/tmptRtIog/sel_SET655+3.p_1',p2) ).
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)))
=> 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/tmptRtIog/sel_SET655+3.p_1',p3) ).
fof(3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/tmp/tmptRtIog/sel_SET655+3.p_1',p1) ).
fof(5,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/tmptRtIog/sel_SET655+3.p_1',p7) ).
fof(7,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/tmptRtIog/sel_SET655+3.p_1',p5) ).
fof(10,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/tmptRtIog/sel_SET655+3.p_1',p10) ).
fof(11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmptRtIog/sel_SET655+3.p_1',p11) ).
fof(12,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/tmptRtIog/sel_SET655+3.p_1',p12) ).
fof(14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmptRtIog/sel_SET655+3.p_1',p14) ).
fof(19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmptRtIog/sel_SET655+3.p_1',p19) ).
fof(20,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X3))
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
file('/tmp/tmptRtIog/sel_SET655+3.p_1',prove_relset_1_17) ).
fof(21,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X3))
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[20]) ).
fof(22,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(23,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)],[12,theory(equality)]) ).
fof(25,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(26,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)
| ~ subset(X1,X2)
| ~ subset(X3,X4)
| subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(27,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)
| ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cross_product(X5,X7),cross_product(X6,X8)) ) ) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cross_product(X5,X7),cross_product(X6,X8))
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[27]) ).
cnf(29,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,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)],[2]) ).
fof(31,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)],[30]) ).
fof(32,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)],[31]) ).
fof(33,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)],[32]) ).
cnf(34,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,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)],[33]) ).
fof(36,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3)
| subset(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(37,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,set_type)
| ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[37]) ).
cnf(39,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(44,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,subset_type(X1))
| ilf_type(X2,member_type(power_set(X1))) )
& ( ~ ilf_type(X2,member_type(power_set(X1)))
| ilf_type(X2,subset_type(X1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(45,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3))) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3)) ) ) ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3))) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[45]) ).
fof(47,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3)))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(48,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)],[47]) ).
cnf(49,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(55,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)],[7]) ).
fof(56,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)],[55]) ).
fof(57,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(esk2_2(X4,X5),set_type)
& member(esk2_2(X4,X5),X4)
& ~ member(esk2_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[56]) ).
fof(58,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk2_2(X4,X5),set_type)
& member(esk2_2(X4,X5),X4)
& ~ member(esk2_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[57]) ).
fof(59,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(esk2_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk2_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk2_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[58]) ).
cnf(60,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(61,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(63,plain,
( member(X3,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(71,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)],[10]) ).
fof(72,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)],[71]) ).
fof(73,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)],[72]) ).
fof(74,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)],[73]) ).
fof(75,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)],[74]) ).
cnf(76,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)],[75]) ).
cnf(77,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)],[75]) ).
cnf(79,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)],[75]) ).
fof(80,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(81,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,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)],[81]) ).
cnf(84,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(85,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)],[23]) ).
fof(86,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)],[85]) ).
fof(87,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)],[86]) ).
fof(88,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)],[87]) ).
cnf(89,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)],[88]) ).
cnf(90,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)],[88]) ).
fof(95,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)],[25]) ).
fof(96,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)],[95]) ).
fof(97,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk6_1(X3),set_type)
& member(esk6_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[96]) ).
fof(98,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk6_1(X3),set_type)
& member(esk6_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[97]) ).
fof(99,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk6_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk6_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[98]) ).
cnf(102,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[99]) ).
fof(125,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[19]) ).
cnf(126,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[125]) ).
fof(127,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& ? [X5] :
( ilf_type(X5,relation_type(X1,X3))
& subset(X1,X2)
& subset(X3,X4)
& ~ ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(128,negated_conjecture,
? [X6] :
( ilf_type(X6,set_type)
& ? [X7] :
( ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,set_type)
& ? [X9] :
( ilf_type(X9,set_type)
& ? [X10] :
( ilf_type(X10,relation_type(X6,X8))
& subset(X6,X7)
& subset(X8,X9)
& ~ ilf_type(X10,relation_type(X7,X9)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[127]) ).
fof(129,negated_conjecture,
( ilf_type(esk10_0,set_type)
& ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,relation_type(esk10_0,esk12_0))
& subset(esk10_0,esk11_0)
& subset(esk12_0,esk13_0)
& ~ ilf_type(esk14_0,relation_type(esk11_0,esk13_0)) ),
inference(skolemize,[status(esa)],[128]) ).
cnf(130,negated_conjecture,
~ ilf_type(esk14_0,relation_type(esk11_0,esk13_0)),
inference(split_conjunct,[status(thm)],[129]) ).
cnf(131,negated_conjecture,
subset(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[129]) ).
cnf(132,negated_conjecture,
subset(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[129]) ).
cnf(133,negated_conjecture,
ilf_type(esk14_0,relation_type(esk10_0,esk12_0)),
inference(split_conjunct,[status(thm)],[129]) ).
cnf(149,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[84,126,theory(equality)]) ).
cnf(150,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[149,theory(equality)]) ).
cnf(173,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[102,126,theory(equality)]) ).
cnf(174,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[173,126,theory(equality)]) ).
cnf(175,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[174,theory(equality)]) ).
cnf(185,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[61,126,theory(equality)]) ).
cnf(186,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[185,126,theory(equality)]) ).
cnf(187,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(cn,[status(thm)],[186,theory(equality)]) ).
cnf(189,plain,
( subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk2_2(X1,X2),X2) ),
inference(rw,[status(thm)],[60,126,theory(equality)]) ).
cnf(190,plain,
( subset(X1,X2)
| $false
| $false
| ~ member(esk2_2(X1,X2),X2) ),
inference(rw,[status(thm)],[189,126,theory(equality)]) ).
cnf(191,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(cn,[status(thm)],[190,theory(equality)]) ).
cnf(194,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[89,126,theory(equality)]) ).
cnf(195,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[194,126,theory(equality)]) ).
cnf(196,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[195,theory(equality)]) ).
cnf(197,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[196,175]) ).
cnf(201,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[39,126,theory(equality)]) ).
cnf(202,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[201,126,theory(equality)]) ).
cnf(203,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[202,126,theory(equality)]) ).
cnf(204,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[203,theory(equality)]) ).
cnf(212,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[49,126,theory(equality)]) ).
cnf(213,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[212,126,theory(equality)]) ).
cnf(214,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[213,theory(equality)]) ).
cnf(216,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)],[48,126,theory(equality)]) ).
cnf(217,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[216,126,theory(equality)]) ).
cnf(218,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[217,theory(equality)]) ).
cnf(225,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[90,126,theory(equality)]) ).
cnf(226,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[225,126,theory(equality)]) ).
cnf(227,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[226,theory(equality)]) ).
cnf(233,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[77,126,theory(equality)]) ).
cnf(234,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[233,126,theory(equality)]) ).
cnf(235,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(242,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)],[35,126,theory(equality)]) ).
cnf(243,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[242,126,theory(equality)]) ).
cnf(244,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[243,theory(equality)]) ).
cnf(245,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk10_0,esk12_0))),
inference(spm,[status(thm)],[244,133,theory(equality)]) ).
cnf(247,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[34,126,theory(equality)]) ).
cnf(248,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[247,126,theory(equality)]) ).
cnf(249,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[248,theory(equality)]) ).
cnf(255,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[63,126,theory(equality)]) ).
cnf(256,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[255,126,theory(equality)]) ).
cnf(257,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[256,126,theory(equality)]) ).
cnf(258,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(cn,[status(thm)],[257,theory(equality)]) ).
cnf(262,plain,
( member(X1,power_set(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk4_2(X1,X2),X2) ),
inference(rw,[status(thm)],[76,126,theory(equality)]) ).
cnf(263,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk4_2(X1,X2),X2) ),
inference(rw,[status(thm)],[262,126,theory(equality)]) ).
cnf(264,plain,
( member(X1,power_set(X2))
| ~ member(esk4_2(X1,X2),X2) ),
inference(cn,[status(thm)],[263,theory(equality)]) ).
cnf(266,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)],[79,126,theory(equality)]) ).
cnf(267,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[266,126,theory(equality)]) ).
cnf(268,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[267,126,theory(equality)]) ).
cnf(269,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[268,theory(equality)]) ).
cnf(282,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[29,126,theory(equality)]) ).
cnf(283,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[282,126,theory(equality)]) ).
cnf(284,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[283,126,theory(equality)]) ).
cnf(285,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[284,126,theory(equality)]) ).
cnf(286,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[285,theory(equality)]) ).
cnf(288,negated_conjecture,
( subset(cross_product(X1,esk12_0),cross_product(X2,esk13_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[286,131,theory(equality)]) ).
cnf(303,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk10_0,esk12_0)))),
inference(spm,[status(thm)],[214,245,theory(equality)]) ).
cnf(326,negated_conjecture,
( empty(power_set(cross_product(esk10_0,esk12_0)))
| member(esk14_0,power_set(cross_product(esk10_0,esk12_0))) ),
inference(spm,[status(thm)],[227,303,theory(equality)]) ).
cnf(328,negated_conjecture,
member(esk14_0,power_set(cross_product(esk10_0,esk12_0))),
inference(sr,[status(thm)],[326,150,theory(equality)]) ).
cnf(331,negated_conjecture,
( member(X1,cross_product(esk10_0,esk12_0))
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[269,328,theory(equality)]) ).
cnf(596,negated_conjecture,
subset(cross_product(esk10_0,esk12_0),cross_product(esk11_0,esk13_0)),
inference(spm,[status(thm)],[288,132,theory(equality)]) ).
cnf(685,negated_conjecture,
( subset(X1,cross_product(esk11_0,esk13_0))
| ~ subset(X1,cross_product(esk10_0,esk12_0)) ),
inference(spm,[status(thm)],[204,596,theory(equality)]) ).
cnf(812,negated_conjecture,
( member(esk2_2(esk14_0,X1),cross_product(esk10_0,esk12_0))
| subset(esk14_0,X1) ),
inference(spm,[status(thm)],[331,187,theory(equality)]) ).
cnf(1107,negated_conjecture,
subset(esk14_0,cross_product(esk10_0,esk12_0)),
inference(spm,[status(thm)],[191,812,theory(equality)]) ).
cnf(1660,negated_conjecture,
subset(esk14_0,cross_product(esk11_0,esk13_0)),
inference(spm,[status(thm)],[685,1107,theory(equality)]) ).
cnf(1677,negated_conjecture,
( member(X1,cross_product(esk11_0,esk13_0))
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[258,1660,theory(equality)]) ).
cnf(4294,negated_conjecture,
( member(esk4_2(esk14_0,X1),cross_product(esk11_0,esk13_0))
| member(esk14_0,power_set(X1)) ),
inference(spm,[status(thm)],[1677,235,theory(equality)]) ).
cnf(7867,negated_conjecture,
member(esk14_0,power_set(cross_product(esk11_0,esk13_0))),
inference(spm,[status(thm)],[264,4294,theory(equality)]) ).
cnf(7872,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk11_0,esk13_0)))),
inference(spm,[status(thm)],[197,7867,theory(equality)]) ).
cnf(7875,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk11_0,esk13_0))),
inference(spm,[status(thm)],[218,7872,theory(equality)]) ).
cnf(7880,negated_conjecture,
ilf_type(esk14_0,relation_type(esk11_0,esk13_0)),
inference(spm,[status(thm)],[249,7875,theory(equality)]) ).
cnf(7883,negated_conjecture,
$false,
inference(sr,[status(thm)],[7880,130,theory(equality)]) ).
cnf(7884,negated_conjecture,
$false,
7883,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET655+3.p
% --creating new selector for []
% -running prover on /tmp/tmptRtIog/sel_SET655+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET655+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET655+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET655+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
%
%------------------------------------------------------------------------------