TSTP Solution File: SET678+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET678+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 03:10:31 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 169 ( 19 unt; 0 def)
% Number of atoms : 707 ( 50 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 903 ( 365 ~; 414 |; 69 &)
% ( 7 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 350 ( 12 sgn 179 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( compose(X2,identity_relation_of(X1)) = X2
& compose(identity_relation_of(X1),X2) = X2 ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',prove_relset_1_45) ).
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)))
=> relation_like(X3) ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p25) ).
fof(4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p27) ).
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/tmpGzpKVD/sel_SET678+3.p_1',p26) ).
fof(9,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/tmpGzpKVD/sel_SET678+3.p_1',p22) ).
fof(11,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/tmpGzpKVD/sel_SET678+3.p_1',p28) ).
fof(12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p33) ).
fof(13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> domain(X1,X2,X3) = domain_of(X3) ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p32) ).
fof(17,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p13) ).
fof(19,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/tmpGzpKVD/sel_SET678+3.p_1',p15) ).
fof(23,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/tmpGzpKVD/sel_SET678+3.p_1',p19) ).
fof(28,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p34) ).
fof(29,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p35) ).
fof(30,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(range_of(X2),X1)
=> compose(X2,identity_relation_of(X1)) = X2 ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p2) ).
fof(32,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(domain_of(X2),X1)
=> compose(identity_relation_of(X1),X2) = X2 ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p1) ).
fof(34,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p7) ).
fof(39,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpGzpKVD/sel_SET678+3.p_1',p38) ).
fof(40,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( compose(X2,identity_relation_of(X1)) = X2
& compose(identity_relation_of(X1),X2) = X2 ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(41,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(43,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)],[11,theory(equality)]) ).
fof(45,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
& ( compose(X2,identity_relation_of(X1)) != X2
| compose(identity_relation_of(X1),X2) != X2 ) ) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(46,negated_conjecture,
? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,identity_relation_of_type(X3))
& ( compose(X4,identity_relation_of(X3)) != X4
| compose(identity_relation_of(X3),X4) != X4 ) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,identity_relation_of_type(esk1_0))
& ( compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0
| compose(identity_relation_of(esk1_0),esk2_0) != esk2_0 ) ),
inference(skolemize,[status(esa)],[46]) ).
cnf(48,negated_conjecture,
( compose(identity_relation_of(esk1_0),esk2_0) != esk2_0
| compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0 ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,negated_conjecture,
ilf_type(esk2_0,identity_relation_of_type(esk1_0)),
inference(split_conjunct,[status(thm)],[47]) ).
fof(51,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| relation_like(X3) ) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(52,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6) ) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[52]) ).
cnf(54,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(66,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(67,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[66]) ).
fof(68,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)],[67]) ).
cnf(70,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[68]) ).
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)],[5]) ).
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(esk6_2(X4,X5),set_type)
& member(esk6_2(X4,X5),X4)
& ~ member(esk6_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(esk6_2(X4,X5),set_type)
& member(esk6_2(X4,X5),X4)
& ~ member(esk6_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(esk6_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk6_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk6_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(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(91,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)],[9]) ).
fof(92,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)],[91]) ).
fof(93,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)],[92]) ).
fof(94,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)],[93]) ).
cnf(96,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)],[94]) ).
fof(101,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)],[43]) ).
fof(102,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)],[101]) ).
fof(103,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)],[102]) ).
fof(104,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)],[103]) ).
cnf(106,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)],[104]) ).
fof(107,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(108,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(domain(X4,X5,X6),subset_type(X4)) ) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(domain(X4,X5,X6),subset_type(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[108]) ).
cnf(110,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(111,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| domain(X1,X2,X3) = domain_of(X3) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(112,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| domain(X4,X5,X6) = domain_of(X6) ) ) ),
inference(variable_rename,[status(thm)],[111]) ).
fof(113,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| domain(X4,X5,X6) = domain_of(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[112]) ).
cnf(114,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[113]) ).
fof(125,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,binary_relation_type)
| ( relation_like(X1)
& ilf_type(X1,set_type) ) )
& ( ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,binary_relation_type) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(126,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,binary_relation_type)
| ( relation_like(X2)
& ilf_type(X2,set_type) ) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type) ) ) ),
inference(variable_rename,[status(thm)],[125]) ).
fof(127,plain,
! [X2] :
( ( relation_like(X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ilf_type(X2,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[126]) ).
cnf(128,plain,
( ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1) ),
inference(split_conjunct,[status(thm)],[127]) ).
fof(134,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)],[19]) ).
fof(135,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)],[134]) ).
fof(136,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)],[135]) ).
fof(137,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)],[136]) ).
cnf(139,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)],[137]) ).
fof(152,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)],[23]) ).
fof(153,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)],[152]) ).
fof(154,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(esk11_2(X4,X5),set_type)
& member(esk11_2(X4,X5),X4)
& ~ member(esk11_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[153]) ).
fof(155,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk11_2(X4,X5),set_type)
& member(esk11_2(X4,X5),X4)
& ~ member(esk11_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[154]) ).
fof(156,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(esk11_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk11_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk11_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[155]) ).
cnf(157,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[156]) ).
cnf(158,plain,
( subset(X1,X2)
| member(esk11_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[156]) ).
fof(180,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| range(X1,X2,X3) = range_of(X3) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(181,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| range(X4,X5,X6) = range_of(X6) ) ) ),
inference(variable_rename,[status(thm)],[180]) ).
fof(182,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| range(X4,X5,X6) = range_of(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[181]) ).
cnf(183,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[182]) ).
fof(184,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(185,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(range(X4,X5,X6),subset_type(X5)) ) ) ),
inference(variable_rename,[status(thm)],[184]) ).
fof(186,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(range(X4,X5,X6),subset_type(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[185]) ).
cnf(187,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[186]) ).
fof(188,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ~ subset(range_of(X2),X1)
| compose(X2,identity_relation_of(X1)) = X2 ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(189,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,binary_relation_type)
| ~ subset(range_of(X4),X3)
| compose(X4,identity_relation_of(X3)) = X4 ) ),
inference(variable_rename,[status(thm)],[188]) ).
fof(190,plain,
! [X3,X4] :
( ~ ilf_type(X4,binary_relation_type)
| ~ subset(range_of(X4),X3)
| compose(X4,identity_relation_of(X3)) = X4
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[189]) ).
cnf(191,plain,
( compose(X2,identity_relation_of(X1)) = X2
| ~ ilf_type(X1,set_type)
| ~ subset(range_of(X2),X1)
| ~ ilf_type(X2,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[190]) ).
fof(201,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ~ subset(domain_of(X2),X1)
| compose(identity_relation_of(X1),X2) = X2 ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(202,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,binary_relation_type)
| ~ subset(domain_of(X4),X3)
| compose(identity_relation_of(X3),X4) = X4 ) ),
inference(variable_rename,[status(thm)],[201]) ).
fof(203,plain,
! [X3,X4] :
( ~ ilf_type(X4,binary_relation_type)
| ~ subset(domain_of(X4),X3)
| compose(identity_relation_of(X3),X4) = X4
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[202]) ).
cnf(204,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ ilf_type(X1,set_type)
| ~ subset(domain_of(X2),X1)
| ~ ilf_type(X2,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[203]) ).
fof(208,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,identity_relation_of_type(X1))
| ilf_type(X2,relation_type(X1,X1)) )
& ( ~ ilf_type(X2,relation_type(X1,X1))
| ilf_type(X2,identity_relation_of_type(X1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(209,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3)) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3)) ) ) ) ),
inference(variable_rename,[status(thm)],[208]) ).
fof(210,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3)) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[209]) ).
fof(211,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[210]) ).
cnf(213,plain,
( ilf_type(X2,relation_type(X1,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(split_conjunct,[status(thm)],[211]) ).
fof(240,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[39]) ).
cnf(241,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[240]) ).
cnf(245,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[70,241,theory(equality)]) ).
cnf(246,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[245,theory(equality)]) ).
cnf(260,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[128,241,theory(equality)]) ).
cnf(261,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[260,theory(equality)]) ).
cnf(299,plain,
( compose(X2,identity_relation_of(X1)) = X2
| ~ ilf_type(X2,binary_relation_type)
| $false
| ~ subset(range_of(X2),X1) ),
inference(rw,[status(thm)],[191,241,theory(equality)]) ).
cnf(300,plain,
( compose(X2,identity_relation_of(X1)) = X2
| ~ ilf_type(X2,binary_relation_type)
| ~ subset(range_of(X2),X1) ),
inference(cn,[status(thm)],[299,theory(equality)]) ).
cnf(302,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ ilf_type(X2,binary_relation_type)
| $false
| ~ subset(domain_of(X2),X1) ),
inference(rw,[status(thm)],[204,241,theory(equality)]) ).
cnf(303,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ ilf_type(X2,binary_relation_type)
| ~ subset(domain_of(X2),X1) ),
inference(cn,[status(thm)],[302,theory(equality)]) ).
cnf(305,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[54,241,theory(equality)]) ).
cnf(306,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[305,241,theory(equality)]) ).
cnf(307,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[306,theory(equality)]) ).
cnf(315,plain,
( ilf_type(X2,relation_type(X1,X1))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(rw,[status(thm)],[213,241,theory(equality)]) ).
cnf(316,plain,
( ilf_type(X2,relation_type(X1,X1))
| $false
| $false
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(rw,[status(thm)],[315,241,theory(equality)]) ).
cnf(317,plain,
( ilf_type(X2,relation_type(X1,X1))
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(cn,[status(thm)],[316,theory(equality)]) ).
cnf(318,negated_conjecture,
ilf_type(esk2_0,relation_type(esk1_0,esk1_0)),
inference(spm,[status(thm)],[317,49,theory(equality)]) ).
cnf(324,plain,
( subset(X1,X2)
| member(esk11_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[158,241,theory(equality)]) ).
cnf(325,plain,
( subset(X1,X2)
| member(esk11_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[324,241,theory(equality)]) ).
cnf(326,plain,
( subset(X1,X2)
| member(esk11_2(X1,X2),X1) ),
inference(cn,[status(thm)],[325,theory(equality)]) ).
cnf(333,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)],[96,241,theory(equality)]) ).
cnf(334,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[333,241,theory(equality)]) ).
cnf(335,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[334,theory(equality)]) ).
cnf(342,plain,
( subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk11_2(X1,X2),X2) ),
inference(rw,[status(thm)],[157,241,theory(equality)]) ).
cnf(343,plain,
( subset(X1,X2)
| $false
| $false
| ~ member(esk11_2(X1,X2),X2) ),
inference(rw,[status(thm)],[342,241,theory(equality)]) ).
cnf(344,plain,
( subset(X1,X2)
| ~ member(esk11_2(X1,X2),X2) ),
inference(cn,[status(thm)],[343,theory(equality)]) ).
cnf(347,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[106,241,theory(equality)]) ).
cnf(348,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[347,241,theory(equality)]) ).
cnf(349,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[348,theory(equality)]) ).
cnf(351,plain,
( empty(power_set(X1))
| member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(spm,[status(thm)],[349,335,theory(equality)]) ).
cnf(352,plain,
( member(X2,power_set(X1))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(sr,[status(thm)],[351,246,theory(equality)]) ).
cnf(378,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[114,241,theory(equality)]) ).
cnf(379,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[378,241,theory(equality)]) ).
cnf(380,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[379,theory(equality)]) ).
cnf(381,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[183,241,theory(equality)]) ).
cnf(382,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[381,241,theory(equality)]) ).
cnf(383,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[382,theory(equality)]) ).
cnf(384,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)],[139,241,theory(equality)]) ).
cnf(385,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[384,241,theory(equality)]) ).
cnf(386,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[385,theory(equality)]) ).
cnf(387,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[307,386,theory(equality)]) ).
cnf(408,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)],[79,241,theory(equality)]) ).
cnf(409,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[408,241,theory(equality)]) ).
cnf(410,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[409,241,theory(equality)]) ).
cnf(411,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[410,theory(equality)]) ).
cnf(417,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[110,241,theory(equality)]) ).
cnf(418,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[417,241,theory(equality)]) ).
cnf(419,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[418,theory(equality)]) ).
cnf(421,plain,
( ilf_type(domain_of(X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[419,380,theory(equality)]) ).
cnf(423,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[187,241,theory(equality)]) ).
cnf(424,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[423,241,theory(equality)]) ).
cnf(425,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[424,theory(equality)]) ).
cnf(427,plain,
( ilf_type(range_of(X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[425,383,theory(equality)]) ).
cnf(521,negated_conjecture,
relation_like(esk2_0),
inference(spm,[status(thm)],[387,318,theory(equality)]) ).
cnf(530,negated_conjecture,
ilf_type(esk2_0,binary_relation_type),
inference(spm,[status(thm)],[261,521,theory(equality)]) ).
cnf(879,negated_conjecture,
ilf_type(domain_of(esk2_0),subset_type(esk1_0)),
inference(spm,[status(thm)],[421,318,theory(equality)]) ).
cnf(887,negated_conjecture,
member(domain_of(esk2_0),power_set(esk1_0)),
inference(spm,[status(thm)],[352,879,theory(equality)]) ).
cnf(890,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,domain_of(esk2_0)) ),
inference(spm,[status(thm)],[411,887,theory(equality)]) ).
cnf(906,negated_conjecture,
( member(esk11_2(domain_of(esk2_0),X1),esk1_0)
| subset(domain_of(esk2_0),X1) ),
inference(spm,[status(thm)],[890,326,theory(equality)]) ).
cnf(968,negated_conjecture,
ilf_type(range_of(esk2_0),subset_type(esk1_0)),
inference(spm,[status(thm)],[427,318,theory(equality)]) ).
cnf(977,negated_conjecture,
member(range_of(esk2_0),power_set(esk1_0)),
inference(spm,[status(thm)],[352,968,theory(equality)]) ).
cnf(980,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,range_of(esk2_0)) ),
inference(spm,[status(thm)],[411,977,theory(equality)]) ).
cnf(1047,negated_conjecture,
( member(esk11_2(range_of(esk2_0),X1),esk1_0)
| subset(range_of(esk2_0),X1) ),
inference(spm,[status(thm)],[980,326,theory(equality)]) ).
cnf(1288,negated_conjecture,
subset(domain_of(esk2_0),esk1_0),
inference(spm,[status(thm)],[344,906,theory(equality)]) ).
cnf(1290,negated_conjecture,
( compose(identity_relation_of(esk1_0),esk2_0) = esk2_0
| ~ ilf_type(esk2_0,binary_relation_type) ),
inference(spm,[status(thm)],[303,1288,theory(equality)]) ).
cnf(1292,negated_conjecture,
( compose(identity_relation_of(esk1_0),esk2_0) = esk2_0
| $false ),
inference(rw,[status(thm)],[1290,530,theory(equality)]) ).
cnf(1293,negated_conjecture,
compose(identity_relation_of(esk1_0),esk2_0) = esk2_0,
inference(cn,[status(thm)],[1292,theory(equality)]) ).
cnf(1297,negated_conjecture,
( compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0
| $false ),
inference(rw,[status(thm)],[48,1293,theory(equality)]) ).
cnf(1298,negated_conjecture,
compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0,
inference(cn,[status(thm)],[1297,theory(equality)]) ).
cnf(1334,negated_conjecture,
subset(range_of(esk2_0),esk1_0),
inference(spm,[status(thm)],[344,1047,theory(equality)]) ).
cnf(1336,negated_conjecture,
( compose(esk2_0,identity_relation_of(esk1_0)) = esk2_0
| ~ ilf_type(esk2_0,binary_relation_type) ),
inference(spm,[status(thm)],[300,1334,theory(equality)]) ).
cnf(1338,negated_conjecture,
( compose(esk2_0,identity_relation_of(esk1_0)) = esk2_0
| $false ),
inference(rw,[status(thm)],[1336,530,theory(equality)]) ).
cnf(1339,negated_conjecture,
compose(esk2_0,identity_relation_of(esk1_0)) = esk2_0,
inference(cn,[status(thm)],[1338,theory(equality)]) ).
cnf(1340,negated_conjecture,
$false,
inference(sr,[status(thm)],[1339,1298,theory(equality)]) ).
cnf(1341,negated_conjecture,
$false,
1340,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET678+3.p
% --creating new selector for []
% -running prover on /tmp/tmpGzpKVD/sel_SET678+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET678+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET678+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET678+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
%
%------------------------------------------------------------------------------