TSTP Solution File: SET649+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET649+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 03:07:22 EST 2010
% Result : Theorem 2.28s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 113 ( 16 unt; 0 def)
% Number of atoms : 573 ( 0 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 753 ( 293 ~; 339 |; 74 &)
% ( 7 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 258 ( 4 sgn 131 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpCO-jdn/sel_SET649+3.p_1',p24) ).
fof(3,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpCO-jdn/sel_SET649+3.p_1',p26) ).
fof(5,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/tmpCO-jdn/sel_SET649+3.p_1',p20) ).
fof(7,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/tmpCO-jdn/sel_SET649+3.p_1',p22) ).
fof(10,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/tmpCO-jdn/sel_SET649+3.p_1',p12) ).
fof(13,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/tmpCO-jdn/sel_SET649+3.p_1',p15) ).
fof(18,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
file('/tmp/tmpCO-jdn/sel_SET649+3.p_1',p2) ).
fof(19,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/tmpCO-jdn/sel_SET649+3.p_1',p3) ).
fof(20,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/tmpCO-jdn/sel_SET649+3.p_1',p1) ).
fof(23,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/tmpCO-jdn/sel_SET649+3.p_1',p4) ).
fof(27,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) )
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/tmp/tmpCO-jdn/sel_SET649+3.p_1',prove_relset_1_11) ).
fof(28,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) )
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[27]) ).
fof(29,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)],[7,theory(equality)]) ).
fof(36,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)],[29]) ).
fof(37,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)],[36]) ).
fof(38,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk1_1(X3),set_type)
& member(esk1_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[37]) ).
fof(39,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk1_1(X3),set_type)
& member(esk1_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[38]) ).
fof(40,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk1_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk1_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[39]) ).
cnf(43,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(44,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[3]) ).
cnf(45,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[44]) ).
fof(51,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)],[5]) ).
fof(52,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)],[51]) ).
fof(53,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(esk2_2(X4,X5),set_type)
& member(esk2_2(X4,X5),X4)
& ~ member(esk2_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[52]) ).
fof(54,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk2_2(X4,X5),set_type)
& member(esk2_2(X4,X5),X4)
& ~ member(esk2_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[53]) ).
fof(55,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(esk2_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk2_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk2_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[54]) ).
cnf(56,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(57,plain,
( member(X1,power_set(X2))
| member(esk2_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(64,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(65,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)],[64]) ).
fof(66,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)],[65]) ).
fof(67,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)],[66]) ).
cnf(68,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)],[67]) ).
fof(79,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)],[10]) ).
fof(80,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)],[79]) ).
fof(81,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(esk5_2(X4,X5),set_type)
& member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[80]) ).
fof(82,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk5_2(X4,X5),set_type)
& member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[81]) ).
fof(83,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(esk5_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk5_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk5_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[82]) ).
cnf(87,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)],[83]) ).
fof(96,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)],[13]) ).
fof(97,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)],[96]) ).
fof(98,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)],[97]) ).
fof(99,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)],[98]) ).
cnf(100,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)],[99]) ).
fof(124,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(125,plain,
! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| subset(X2,cross_product(domain_of(X2),range_of(X2))) ),
inference(variable_rename,[status(thm)],[124]) ).
cnf(126,plain,
( subset(X1,cross_product(domain_of(X1),range_of(X1)))
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[125]) ).
fof(127,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)],[19]) ).
fof(128,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)],[127]) ).
fof(129,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)],[128]) ).
cnf(130,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)],[129]) ).
fof(131,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)],[20]) ).
fof(132,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)],[131]) ).
fof(133,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)],[132]) ).
cnf(134,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)],[133]) ).
fof(146,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)],[23]) ).
fof(147,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)],[146]) ).
fof(148,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)],[147]) ).
fof(149,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)],[148]) ).
cnf(150,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)],[149]) ).
fof(168,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,binary_relation_type)
& subset(domain_of(X3),X1)
& subset(range_of(X3),X2)
& ~ ilf_type(X3,relation_type(X1,X2)) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(169,negated_conjecture,
? [X4] :
( ilf_type(X4,set_type)
& ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,binary_relation_type)
& subset(domain_of(X6),X4)
& subset(range_of(X6),X5)
& ~ ilf_type(X6,relation_type(X4,X5)) ) ) ),
inference(variable_rename,[status(thm)],[168]) ).
fof(170,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,binary_relation_type)
& subset(domain_of(esk15_0),esk13_0)
& subset(range_of(esk15_0),esk14_0)
& ~ ilf_type(esk15_0,relation_type(esk13_0,esk14_0)) ),
inference(skolemize,[status(esa)],[169]) ).
cnf(171,negated_conjecture,
~ ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(172,negated_conjecture,
subset(range_of(esk15_0),esk14_0),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(173,negated_conjecture,
subset(domain_of(esk15_0),esk13_0),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(174,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(201,negated_conjecture,
subset(esk15_0,cross_product(domain_of(esk15_0),range_of(esk15_0))),
inference(spm,[status(thm)],[126,174,theory(equality)]) ).
cnf(227,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[43,45,theory(equality)]) ).
cnf(228,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[227,45,theory(equality)]) ).
cnf(229,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[228,theory(equality)]) ).
cnf(241,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)],[134,45,theory(equality)]) ).
cnf(242,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[241,45,theory(equality)]) ).
cnf(243,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[242,45,theory(equality)]) ).
cnf(244,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[243,theory(equality)]) ).
cnf(258,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[68,45,theory(equality)]) ).
cnf(259,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[258,45,theory(equality)]) ).
cnf(260,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[259,theory(equality)]) ).
cnf(261,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[260,229]) ).
cnf(273,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)],[100,45,theory(equality)]) ).
cnf(274,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[273,45,theory(equality)]) ).
cnf(275,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[274,theory(equality)]) ).
cnf(286,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)],[150,45,theory(equality)]) ).
cnf(287,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[286,45,theory(equality)]) ).
cnf(288,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[287,theory(equality)]) ).
cnf(298,plain,
( member(X1,power_set(X2))
| member(esk2_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[57,45,theory(equality)]) ).
cnf(299,plain,
( member(X1,power_set(X2))
| member(esk2_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[298,45,theory(equality)]) ).
cnf(300,plain,
( member(X1,power_set(X2))
| member(esk2_2(X1,X2),X1) ),
inference(cn,[status(thm)],[299,theory(equality)]) ).
cnf(307,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[87,45,theory(equality)]) ).
cnf(308,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[307,45,theory(equality)]) ).
cnf(309,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[308,45,theory(equality)]) ).
cnf(310,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[309,theory(equality)]) ).
cnf(314,plain,
( member(X1,power_set(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk2_2(X1,X2),X2) ),
inference(rw,[status(thm)],[56,45,theory(equality)]) ).
cnf(315,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk2_2(X1,X2),X2) ),
inference(rw,[status(thm)],[314,45,theory(equality)]) ).
cnf(316,plain,
( member(X1,power_set(X2))
| ~ member(esk2_2(X1,X2),X2) ),
inference(cn,[status(thm)],[315,theory(equality)]) ).
cnf(336,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)],[130,45,theory(equality)]) ).
cnf(337,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)],[336,45,theory(equality)]) ).
cnf(338,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)],[337,45,theory(equality)]) ).
cnf(339,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[338,45,theory(equality)]) ).
cnf(340,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ subset(X3,X4)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[339,theory(equality)]) ).
cnf(342,negated_conjecture,
( subset(cross_product(X1,range_of(esk15_0)),cross_product(X2,esk14_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[340,172,theory(equality)]) ).
cnf(754,negated_conjecture,
subset(cross_product(domain_of(esk15_0),range_of(esk15_0)),cross_product(esk13_0,esk14_0)),
inference(spm,[status(thm)],[342,173,theory(equality)]) ).
cnf(796,negated_conjecture,
( subset(X1,cross_product(esk13_0,esk14_0))
| ~ subset(X1,cross_product(domain_of(esk15_0),range_of(esk15_0))) ),
inference(spm,[status(thm)],[244,754,theory(equality)]) ).
cnf(1684,negated_conjecture,
subset(esk15_0,cross_product(esk13_0,esk14_0)),
inference(spm,[status(thm)],[796,201,theory(equality)]) ).
cnf(1704,negated_conjecture,
( member(X1,cross_product(esk13_0,esk14_0))
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[310,1684,theory(equality)]) ).
cnf(2060,negated_conjecture,
( member(esk2_2(esk15_0,X1),cross_product(esk13_0,esk14_0))
| member(esk15_0,power_set(X1)) ),
inference(spm,[status(thm)],[1704,300,theory(equality)]) ).
cnf(38924,negated_conjecture,
member(esk15_0,power_set(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[316,2060,theory(equality)]) ).
cnf(38929,negated_conjecture,
ilf_type(esk15_0,member_type(power_set(cross_product(esk13_0,esk14_0)))),
inference(spm,[status(thm)],[261,38924,theory(equality)]) ).
cnf(38977,negated_conjecture,
ilf_type(esk15_0,subset_type(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[275,38929,theory(equality)]) ).
cnf(38981,negated_conjecture,
ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
inference(spm,[status(thm)],[288,38977,theory(equality)]) ).
cnf(38984,negated_conjecture,
$false,
inference(sr,[status(thm)],[38981,171,theory(equality)]) ).
cnf(38985,negated_conjecture,
$false,
38984,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET649+3.p
% --creating new selector for []
% -running prover on /tmp/tmpCO-jdn/sel_SET649+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET649+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET649+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET649+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
%
%------------------------------------------------------------------------------