TSTP Solution File: SET648+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET648+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:07:20 EST 2010
% Result : Theorem 0.46s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 111 ( 15 unt; 0 def)
% Number of atoms : 550 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 722 ( 283 ~; 325 |; 70 &)
% ( 7 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 244 ( 4 sgn 128 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmphXA5HS/sel_SET648+3.p_1',p24) ).
fof(3,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmphXA5HS/sel_SET648+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/tmphXA5HS/sel_SET648+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/tmphXA5HS/sel_SET648+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/tmphXA5HS/sel_SET648+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/tmphXA5HS/sel_SET648+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/tmphXA5HS/sel_SET648+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)
=> ( subset(X1,X2)
=> ( subset(cross_product(X1,X3),cross_product(X2,X3))
& subset(cross_product(X3,X1),cross_product(X3,X2)) ) ) ) ) ),
file('/tmp/tmphXA5HS/sel_SET648+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/tmphXA5HS/sel_SET648+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/tmphXA5HS/sel_SET648+3.p_1',p4) ).
fof(27,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(range_of(X2),X1)
=> ilf_type(X2,relation_type(domain_of(X2),X1)) ) ) ),
file('/tmp/tmphXA5HS/sel_SET648+3.p_1',prove_relset_1_10) ).
fof(28,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(range_of(X2),X1)
=> ilf_type(X2,relation_type(domain_of(X2),X1)) ) ) ),
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)
| ~ subset(X1,X2)
| ( subset(cross_product(X1,X3),cross_product(X2,X3))
& subset(cross_product(X3,X1),cross_product(X3,X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(128,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ subset(X4,X5)
| ( subset(cross_product(X4,X6),cross_product(X5,X6))
& subset(cross_product(X6,X4),cross_product(X6,X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[127]) ).
fof(129,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,set_type)
| ~ subset(X4,X5)
| ( subset(cross_product(X4,X6),cross_product(X5,X6))
& subset(cross_product(X6,X4),cross_product(X6,X5)) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[128]) ).
fof(130,plain,
! [X4,X5,X6] :
( ( subset(cross_product(X4,X6),cross_product(X5,X6))
| ~ subset(X4,X5)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( subset(cross_product(X6,X4),cross_product(X6,X5))
| ~ subset(X4,X5)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[129]) ).
cnf(131,plain,
( subset(cross_product(X3,X1),cross_product(X3,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(133,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(134,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)],[133]) ).
fof(135,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)],[134]) ).
cnf(136,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)],[135]) ).
fof(148,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(149,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)],[148]) ).
fof(150,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)],[149]) ).
fof(151,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)],[150]) ).
cnf(152,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)],[151]) ).
fof(170,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,binary_relation_type)
& subset(range_of(X2),X1)
& ~ ilf_type(X2,relation_type(domain_of(X2),X1)) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(171,negated_conjecture,
? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,binary_relation_type)
& subset(range_of(X4),X3)
& ~ ilf_type(X4,relation_type(domain_of(X4),X3)) ) ),
inference(variable_rename,[status(thm)],[170]) ).
fof(172,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,binary_relation_type)
& subset(range_of(esk14_0),esk13_0)
& ~ ilf_type(esk14_0,relation_type(domain_of(esk14_0),esk13_0)) ),
inference(skolemize,[status(esa)],[171]) ).
cnf(173,negated_conjecture,
~ ilf_type(esk14_0,relation_type(domain_of(esk14_0),esk13_0)),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(174,negated_conjecture,
subset(range_of(esk14_0),esk13_0),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(175,negated_conjecture,
ilf_type(esk14_0,binary_relation_type),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(197,negated_conjecture,
subset(esk14_0,cross_product(domain_of(esk14_0),range_of(esk14_0))),
inference(spm,[status(thm)],[126,175,theory(equality)]) ).
cnf(226,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[43,45,theory(equality)]) ).
cnf(227,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[226,45,theory(equality)]) ).
cnf(228,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[227,theory(equality)]) ).
cnf(231,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(232,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[231,45,theory(equality)]) ).
cnf(233,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[232,theory(equality)]) ).
cnf(234,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[233,228]) ).
cnf(247,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)],[136,45,theory(equality)]) ).
cnf(248,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[247,45,theory(equality)]) ).
cnf(249,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[248,45,theory(equality)]) ).
cnf(250,plain,
( subset(X1,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[249,theory(equality)]) ).
cnf(275,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(276,plain,
( ilf_type(X2,subset_type(X1))
| $false
| $false
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(rw,[status(thm)],[275,45,theory(equality)]) ).
cnf(277,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(cn,[status(thm)],[276,theory(equality)]) ).
cnf(288,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)],[152,45,theory(equality)]) ).
cnf(289,plain,
( ilf_type(X3,relation_type(X1,X2))
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[288,45,theory(equality)]) ).
cnf(290,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(300,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(301,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[300,45,theory(equality)]) ).
cnf(302,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[301,45,theory(equality)]) ).
cnf(303,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[302,theory(equality)]) ).
cnf(306,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(307,plain,
( member(X1,power_set(X2))
| member(esk2_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[306,45,theory(equality)]) ).
cnf(308,plain,
( member(X1,power_set(X2))
| member(esk2_2(X1,X2),X1) ),
inference(cn,[status(thm)],[307,theory(equality)]) ).
cnf(311,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(312,plain,
( member(X1,power_set(X2))
| $false
| $false
| ~ member(esk2_2(X1,X2),X2) ),
inference(rw,[status(thm)],[311,45,theory(equality)]) ).
cnf(313,plain,
( member(X1,power_set(X2))
| ~ member(esk2_2(X1,X2),X2) ),
inference(cn,[status(thm)],[312,theory(equality)]) ).
cnf(315,plain,
( subset(cross_product(X3,X1),cross_product(X3,X2))
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[131,45,theory(equality)]) ).
cnf(316,plain,
( subset(cross_product(X3,X1),cross_product(X3,X2))
| ~ subset(X1,X2)
| $false
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[315,45,theory(equality)]) ).
cnf(317,plain,
( subset(cross_product(X3,X1),cross_product(X3,X2))
| ~ subset(X1,X2)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[316,45,theory(equality)]) ).
cnf(318,plain,
( subset(cross_product(X3,X1),cross_product(X3,X2))
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[317,theory(equality)]) ).
cnf(319,negated_conjecture,
subset(cross_product(X1,range_of(esk14_0)),cross_product(X1,esk13_0)),
inference(spm,[status(thm)],[318,174,theory(equality)]) ).
cnf(409,negated_conjecture,
( subset(X1,cross_product(X2,esk13_0))
| ~ subset(X1,cross_product(X2,range_of(esk14_0))) ),
inference(spm,[status(thm)],[250,319,theory(equality)]) ).
cnf(1000,negated_conjecture,
subset(esk14_0,cross_product(domain_of(esk14_0),esk13_0)),
inference(spm,[status(thm)],[409,197,theory(equality)]) ).
cnf(1030,negated_conjecture,
( member(X1,cross_product(domain_of(esk14_0),esk13_0))
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[303,1000,theory(equality)]) ).
cnf(2415,negated_conjecture,
( member(esk2_2(esk14_0,X1),cross_product(domain_of(esk14_0),esk13_0))
| member(esk14_0,power_set(X1)) ),
inference(spm,[status(thm)],[1030,308,theory(equality)]) ).
cnf(3666,negated_conjecture,
member(esk14_0,power_set(cross_product(domain_of(esk14_0),esk13_0))),
inference(spm,[status(thm)],[313,2415,theory(equality)]) ).
cnf(3671,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(domain_of(esk14_0),esk13_0)))),
inference(spm,[status(thm)],[234,3666,theory(equality)]) ).
cnf(3675,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(domain_of(esk14_0),esk13_0))),
inference(spm,[status(thm)],[277,3671,theory(equality)]) ).
cnf(3691,negated_conjecture,
ilf_type(esk14_0,relation_type(domain_of(esk14_0),esk13_0)),
inference(spm,[status(thm)],[290,3675,theory(equality)]) ).
cnf(3694,negated_conjecture,
$false,
inference(sr,[status(thm)],[3691,173,theory(equality)]) ).
cnf(3695,negated_conjecture,
$false,
3694,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET648+3.p
% --creating new selector for []
% -running prover on /tmp/tmphXA5HS/sel_SET648+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET648+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET648+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET648+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
%
%------------------------------------------------------------------------------