TSTP Solution File: SET682+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET682+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:10:54 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 150 ( 22 unt; 0 def)
% Number of atoms : 650 ( 18 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 827 ( 327 ~; 347 |; 95 &)
% ( 7 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 308 ( 11 sgn 161 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(X5,range(X1,X2,X3)) ) ) ) ) ) ),
file('/tmp/tmpBQXFId/sel_SET682+3.p_1',prove_relset_1_49) ).
fof(2,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpBQXFId/sel_SET682+3.p_1',p24) ).
fof(4,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/tmpBQXFId/sel_SET682+3.p_1',p20) ).
fof(5,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/tmpBQXFId/sel_SET682+3.p_1',p23) ).
fof(6,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/tmpBQXFId/sel_SET682+3.p_1',p22) ).
fof(7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpBQXFId/sel_SET682+3.p_1',p10) ).
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/tmpBQXFId/sel_SET682+3.p_1',p12) ).
fof(11,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/tmpBQXFId/sel_SET682+3.p_1',p14) ).
fof(12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpBQXFId/sel_SET682+3.p_1',p15) ).
fof(15,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/tmpBQXFId/sel_SET682+3.p_1',p18) ).
fof(17,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/tmpBQXFId/sel_SET682+3.p_1',p2) ).
fof(19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
=> ? [X3] :
( ilf_type(X3,set_type)
& member(X3,range_of(X2)) ) ) ) ),
file('/tmp/tmpBQXFId/sel_SET682+3.p_1',p1) ).
fof(20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpBQXFId/sel_SET682+3.p_1',p6) ).
fof(22,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/tmpBQXFId/sel_SET682+3.p_1',p4) ).
fof(26,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(X5,range(X1,X2,X3)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(27,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(X5,range(X1,X2,X3)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[26,theory(equality)]) ).
fof(28,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
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)],[20,theory(equality)]) ).
fof(30,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)],[22,theory(equality)]) ).
fof(32,negated_conjecture,
? [X1] :
( ~ empty(X1)
& ilf_type(X1,set_type)
& ? [X2] :
( ~ empty(X2)
& ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X1,X2))
& ? [X4] :
( ilf_type(X4,member_type(X1))
& member(X4,domain(X1,X2,X3))
& ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(X5,range(X1,X2,X3)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(33,negated_conjecture,
? [X6] :
( ~ empty(X6)
& ilf_type(X6,set_type)
& ? [X7] :
( ~ empty(X7)
& ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,relation_type(X6,X7))
& ? [X9] :
( ilf_type(X9,member_type(X6))
& member(X9,domain(X6,X7,X8))
& ! [X10] :
( ~ ilf_type(X10,member_type(X7))
| ~ member(X10,range(X6,X7,X8)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,negated_conjecture,
( ~ empty(esk1_0)
& ilf_type(esk1_0,set_type)
& ~ empty(esk2_0)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,relation_type(esk1_0,esk2_0))
& ilf_type(esk4_0,member_type(esk1_0))
& member(esk4_0,domain(esk1_0,esk2_0,esk3_0))
& ! [X10] :
( ~ ilf_type(X10,member_type(esk2_0))
| ~ member(X10,range(esk1_0,esk2_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[33]) ).
fof(35,negated_conjecture,
! [X10] :
( ( ~ ilf_type(X10,member_type(esk2_0))
| ~ member(X10,range(esk1_0,esk2_0,esk3_0)) )
& member(esk4_0,domain(esk1_0,esk2_0,esk3_0))
& ilf_type(esk4_0,member_type(esk1_0))
& ilf_type(esk3_0,relation_type(esk1_0,esk2_0))
& ~ empty(esk2_0)
& ilf_type(esk2_0,set_type)
& ~ empty(esk1_0)
& ilf_type(esk1_0,set_type) ),
inference(shift_quantors,[status(thm)],[34]) ).
cnf(40,negated_conjecture,
ilf_type(esk3_0,relation_type(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(42,negated_conjecture,
member(esk4_0,domain(esk1_0,esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(43,negated_conjecture,
( ~ member(X1,range(esk1_0,esk2_0,esk3_0))
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(44,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[2]) ).
cnf(45,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[44]) ).
fof(50,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)],[4]) ).
fof(51,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)],[50]) ).
fof(52,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)],[51]) ).
cnf(53,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)],[52]) ).
fof(54,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)],[5]) ).
fof(55,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)],[54]) ).
fof(56,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)],[55]) ).
cnf(57,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)],[56]) ).
fof(58,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)],[6]) ).
fof(59,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)],[58]) ).
fof(60,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)],[59]) ).
cnf(61,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)],[60]) ).
fof(62,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)],[7]) ).
fof(63,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)],[62]) ).
fof(64,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)],[63]) ).
cnf(65,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)],[64]) ).
fof(71,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(72,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)],[71]) ).
fof(73,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)],[72]) ).
fof(74,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)],[73]) ).
cnf(76,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)],[74]) ).
fof(81,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)],[11]) ).
fof(82,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)],[81]) ).
fof(83,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(esk7_2(X4,X5),set_type)
& member(esk7_2(X4,X5),X4)
& ~ member(esk7_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[82]) ).
fof(84,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk7_2(X4,X5),set_type)
& member(esk7_2(X4,X5),X4)
& ~ member(esk7_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[83]) ).
fof(85,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(esk7_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk7_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk7_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[84]) ).
cnf(89,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)],[85]) ).
fof(90,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(91,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,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)],[91]) ).
cnf(94,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(109,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)],[15]) ).
fof(110,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)],[109]) ).
fof(111,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)],[110]) ).
cnf(112,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)],[111]) ).
fof(117,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)],[17]) ).
fof(118,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)],[117]) ).
fof(119,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)],[118]) ).
fof(120,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)],[119]) ).
cnf(122,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)],[120]) ).
fof(128,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2))
| ? [X3] :
( ilf_type(X3,set_type)
& member(X3,range_of(X2)) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(129,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ~ member(X4,domain_of(X5))
| ? [X6] :
( ilf_type(X6,set_type)
& member(X6,range_of(X5)) ) ) ),
inference(variable_rename,[status(thm)],[128]) ).
fof(130,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ~ member(X4,domain_of(X5))
| ( ilf_type(esk12_2(X4,X5),set_type)
& member(esk12_2(X4,X5),range_of(X5)) ) ) ),
inference(skolemize,[status(esa)],[129]) ).
fof(131,plain,
! [X4,X5] :
( ~ ilf_type(X5,binary_relation_type)
| ~ member(X4,domain_of(X5))
| ( ilf_type(esk12_2(X4,X5),set_type)
& member(esk12_2(X4,X5),range_of(X5)) )
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[130]) ).
fof(132,plain,
! [X4,X5] :
( ( ilf_type(esk12_2(X4,X5),set_type)
| ~ member(X4,domain_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk12_2(X4,X5),range_of(X5))
| ~ member(X4,domain_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[131]) ).
cnf(133,plain,
( member(esk12_2(X1,X2),range_of(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2)) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(135,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(136,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)],[135]) ).
fof(137,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk13_1(X3),set_type)
& member(esk13_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[136]) ).
fof(138,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk13_1(X3),set_type)
& member(esk13_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[137]) ).
fof(139,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk13_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk13_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[138]) ).
cnf(140,plain,
( empty(X1)
| member(esk13_1(X1),X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(142,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[139]) ).
fof(146,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)],[30]) ).
fof(147,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)],[146]) ).
fof(148,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)],[147]) ).
fof(149,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)],[148]) ).
cnf(150,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)],[149]) ).
cnf(151,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)],[149]) ).
cnf(167,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[94,45,theory(equality)]) ).
cnf(168,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[167,theory(equality)]) ).
cnf(176,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[65,45,theory(equality)]) ).
cnf(177,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[176,theory(equality)]) ).
cnf(185,plain,
( empty(X1)
| member(esk13_1(X1),X1)
| $false ),
inference(rw,[status(thm)],[140,45,theory(equality)]) ).
cnf(186,plain,
( empty(X1)
| member(esk13_1(X1),X1) ),
inference(cn,[status(thm)],[185,theory(equality)]) ).
cnf(204,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[142,45,theory(equality)]) ).
cnf(205,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[204,45,theory(equality)]) ).
cnf(206,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[205,theory(equality)]) ).
cnf(210,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[150,45,theory(equality)]) ).
cnf(211,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[210,45,theory(equality)]) ).
cnf(212,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[211,theory(equality)]) ).
cnf(213,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[212,206]) ).
cnf(220,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[151,45,theory(equality)]) ).
cnf(221,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[220,45,theory(equality)]) ).
cnf(222,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[221,theory(equality)]) ).
cnf(235,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)],[53,45,theory(equality)]) ).
cnf(236,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[235,45,theory(equality)]) ).
cnf(237,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[236,theory(equality)]) ).
cnf(238,negated_conjecture,
domain(esk1_0,esk2_0,esk3_0) = domain_of(esk3_0),
inference(spm,[status(thm)],[237,40,theory(equality)]) ).
cnf(240,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)],[61,45,theory(equality)]) ).
cnf(241,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[240,45,theory(equality)]) ).
cnf(242,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[241,theory(equality)]) ).
cnf(243,negated_conjecture,
range(esk1_0,esk2_0,esk3_0) = range_of(esk3_0),
inference(spm,[status(thm)],[242,40,theory(equality)]) ).
cnf(245,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[112,45,theory(equality)]) ).
cnf(246,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[245,45,theory(equality)]) ).
cnf(247,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[246,theory(equality)]) ).
cnf(249,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)],[76,45,theory(equality)]) ).
cnf(250,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[249,45,theory(equality)]) ).
cnf(251,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(280,plain,
( member(esk12_2(X1,X2),range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| $false
| ~ member(X1,domain_of(X2)) ),
inference(rw,[status(thm)],[133,45,theory(equality)]) ).
cnf(281,plain,
( member(esk12_2(X1,X2),range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2)) ),
inference(cn,[status(thm)],[280,theory(equality)]) ).
cnf(283,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)],[122,45,theory(equality)]) ).
cnf(284,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[283,45,theory(equality)]) ).
cnf(285,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[284,theory(equality)]) ).
cnf(286,negated_conjecture,
ilf_type(esk3_0,subset_type(cross_product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[285,40,theory(equality)]) ).
cnf(292,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)],[89,45,theory(equality)]) ).
cnf(293,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[292,45,theory(equality)]) ).
cnf(294,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[293,45,theory(equality)]) ).
cnf(295,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(309,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)],[57,45,theory(equality)]) ).
cnf(310,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[309,45,theory(equality)]) ).
cnf(311,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[310,theory(equality)]) ).
cnf(312,negated_conjecture,
ilf_type(range(esk1_0,esk2_0,esk3_0),subset_type(esk2_0)),
inference(spm,[status(thm)],[311,40,theory(equality)]) ).
cnf(318,negated_conjecture,
member(esk4_0,domain_of(esk3_0)),
inference(rw,[status(thm)],[42,238,theory(equality)]) ).
cnf(319,negated_conjecture,
( ~ member(X1,range_of(esk3_0))
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(rw,[status(thm)],[43,243,theory(equality)]) ).
cnf(323,negated_conjecture,
( empty(range_of(esk3_0))
| ~ ilf_type(esk13_1(range_of(esk3_0)),member_type(esk2_0)) ),
inference(spm,[status(thm)],[319,186,theory(equality)]) ).
cnf(344,negated_conjecture,
relation_like(esk3_0),
inference(spm,[status(thm)],[247,286,theory(equality)]) ).
cnf(348,negated_conjecture,
ilf_type(esk3_0,binary_relation_type),
inference(spm,[status(thm)],[177,344,theory(equality)]) ).
cnf(350,negated_conjecture,
( member(esk12_2(X1,esk3_0),range_of(esk3_0))
| ~ member(X1,domain_of(esk3_0)) ),
inference(spm,[status(thm)],[281,348,theory(equality)]) ).
cnf(391,negated_conjecture,
ilf_type(range_of(esk3_0),subset_type(esk2_0)),
inference(rw,[status(thm)],[312,243,theory(equality)]) ).
cnf(392,negated_conjecture,
ilf_type(range_of(esk3_0),member_type(power_set(esk2_0))),
inference(spm,[status(thm)],[251,391,theory(equality)]) ).
cnf(434,negated_conjecture,
( member(range_of(esk3_0),power_set(esk2_0))
| empty(power_set(esk2_0)) ),
inference(spm,[status(thm)],[222,392,theory(equality)]) ).
cnf(436,negated_conjecture,
member(range_of(esk3_0),power_set(esk2_0)),
inference(sr,[status(thm)],[434,168,theory(equality)]) ).
cnf(441,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,range_of(esk3_0)) ),
inference(spm,[status(thm)],[295,436,theory(equality)]) ).
cnf(517,negated_conjecture,
( member(esk13_1(range_of(esk3_0)),esk2_0)
| empty(range_of(esk3_0)) ),
inference(spm,[status(thm)],[441,186,theory(equality)]) ).
cnf(541,negated_conjecture,
( ilf_type(esk13_1(range_of(esk3_0)),member_type(esk2_0))
| empty(range_of(esk3_0)) ),
inference(spm,[status(thm)],[213,517,theory(equality)]) ).
cnf(671,negated_conjecture,
empty(range_of(esk3_0)),
inference(csr,[status(thm)],[541,323]) ).
cnf(698,negated_conjecture,
member(esk12_2(esk4_0,esk3_0),range_of(esk3_0)),
inference(spm,[status(thm)],[350,318,theory(equality)]) ).
cnf(724,negated_conjecture,
~ empty(range_of(esk3_0)),
inference(spm,[status(thm)],[206,698,theory(equality)]) ).
cnf(729,negated_conjecture,
$false,
inference(rw,[status(thm)],[724,671,theory(equality)]) ).
cnf(730,negated_conjecture,
$false,
inference(cn,[status(thm)],[729,theory(equality)]) ).
cnf(731,negated_conjecture,
$false,
730,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET682+3.p
% --creating new selector for []
% -running prover on /tmp/tmpBQXFId/sel_SET682+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET682+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET682+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET682+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
%
%------------------------------------------------------------------------------