TSTP Solution File: SET677+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET677+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:10:21 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 200 ( 35 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 259 ( 108 ~; 109 |; 25 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 83 ( 1 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = domain(X1,X1,X2)
& X1 = range(X1,X1,X2) ) ) ) ),
file('/tmp/tmpBW1-mI/sel_SET677+3.p_1',prove_relset_1_44) ).
fof(26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpBW1-mI/sel_SET677+3.p_1',p34) ).
fof(27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,domain(X1,X2,X3))
& X2 = range(X1,X2,X3) ) ) ) ) ),
file('/tmp/tmpBW1-mI/sel_SET677+3.p_1',p2) ).
fof(29,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( X2 = domain(X2,X1,X3)
& subset(X2,range(X2,X1,X3)) ) ) ) ) ),
file('/tmp/tmpBW1-mI/sel_SET677+3.p_1',p1) ).
fof(33,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/tmpBW1-mI/sel_SET677+3.p_1',p5) ).
fof(36,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = domain(X1,X1,X2)
& X1 = range(X1,X1,X2) ) ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(41,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
& subset(identity_relation_of(X1),X2)
& ( X1 != domain(X1,X1,X2)
| X1 != range(X1,X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(42,negated_conjecture,
? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,identity_relation_of_type(X3))
& subset(identity_relation_of(X3),X4)
& ( X3 != domain(X3,X3,X4)
| X3 != range(X3,X3,X4) ) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,identity_relation_of_type(esk1_0))
& subset(identity_relation_of(esk1_0),esk2_0)
& ( esk1_0 != domain(esk1_0,esk1_0,esk2_0)
| esk1_0 != range(esk1_0,esk1_0,esk2_0) ) ),
inference(skolemize,[status(esa)],[42]) ).
cnf(44,negated_conjecture,
( esk1_0 != range(esk1_0,esk1_0,esk2_0)
| esk1_0 != domain(esk1_0,esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,negated_conjecture,
subset(identity_relation_of(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(46,negated_conjecture,
ilf_type(esk2_0,identity_relation_of_type(esk1_0)),
inference(split_conjunct,[status(thm)],[43]) ).
fof(170,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[26]) ).
cnf(171,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[170]) ).
fof(172,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ subset(identity_relation_of(X2),X3)
| ( subset(X2,domain(X1,X2,X3))
& X2 = range(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(173,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ~ subset(identity_relation_of(X5),X6)
| ( subset(X5,domain(X4,X5,X6))
& X5 = range(X4,X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[172]) ).
fof(174,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ~ subset(identity_relation_of(X5),X6)
| ( subset(X5,domain(X4,X5,X6))
& X5 = range(X4,X5,X6) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[173]) ).
fof(175,plain,
! [X4,X5,X6] :
( ( subset(X5,domain(X4,X5,X6))
| ~ subset(identity_relation_of(X5),X6)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( X5 = range(X4,X5,X6)
| ~ subset(identity_relation_of(X5),X6)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[174]) ).
cnf(176,plain,
( X2 = range(X1,X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ subset(identity_relation_of(X2),X3) ),
inference(split_conjunct,[status(thm)],[175]) ).
fof(185,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
| ~ subset(identity_relation_of(X2),X3)
| ( X2 = domain(X2,X1,X3)
& subset(X2,range(X2,X1,X3)) ) ) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(186,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X5,X4))
| ~ subset(identity_relation_of(X5),X6)
| ( X5 = domain(X5,X4,X6)
& subset(X5,range(X5,X4,X6)) ) ) ) ),
inference(variable_rename,[status(thm)],[185]) ).
fof(187,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X5,X4))
| ~ subset(identity_relation_of(X5),X6)
| ( X5 = domain(X5,X4,X6)
& subset(X5,range(X5,X4,X6)) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[186]) ).
fof(188,plain,
! [X4,X5,X6] :
( ( X5 = domain(X5,X4,X6)
| ~ subset(identity_relation_of(X5),X6)
| ~ ilf_type(X6,relation_type(X5,X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( subset(X5,range(X5,X4,X6))
| ~ subset(identity_relation_of(X5),X6)
| ~ ilf_type(X6,relation_type(X5,X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[187]) ).
cnf(190,plain,
( X2 = domain(X2,X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X2,X1))
| ~ subset(identity_relation_of(X2),X3) ),
inference(split_conjunct,[status(thm)],[188]) ).
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)],[33]) ).
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]) ).
cnf(300,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)],[213,171,theory(equality)]) ).
cnf(301,plain,
( ilf_type(X2,relation_type(X1,X1))
| $false
| $false
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(rw,[status(thm)],[300,171,theory(equality)]) ).
cnf(302,plain,
( ilf_type(X2,relation_type(X1,X1))
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(cn,[status(thm)],[301,theory(equality)]) ).
cnf(303,negated_conjecture,
ilf_type(esk2_0,relation_type(esk1_0,esk1_0)),
inference(spm,[status(thm)],[302,46,theory(equality)]) ).
cnf(408,plain,
( domain(X2,X1,X3) = X2
| $false
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X2,X1)) ),
inference(rw,[status(thm)],[190,171,theory(equality)]) ).
cnf(409,plain,
( domain(X2,X1,X3) = X2
| $false
| $false
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X2,X1)) ),
inference(rw,[status(thm)],[408,171,theory(equality)]) ).
cnf(410,plain,
( domain(X2,X1,X3) = X2
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X2,X1)) ),
inference(cn,[status(thm)],[409,theory(equality)]) ).
cnf(413,plain,
( range(X1,X2,X3) = X2
| $false
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[176,171,theory(equality)]) ).
cnf(414,plain,
( range(X1,X2,X3) = X2
| $false
| $false
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[413,171,theory(equality)]) ).
cnf(415,plain,
( range(X1,X2,X3) = X2
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[414,theory(equality)]) ).
cnf(416,negated_conjecture,
( domain(esk1_0,esk1_0,esk2_0) != esk1_0
| ~ subset(identity_relation_of(esk1_0),esk2_0)
| ~ ilf_type(esk2_0,relation_type(esk1_0,esk1_0)) ),
inference(spm,[status(thm)],[44,415,theory(equality)]) ).
cnf(419,negated_conjecture,
( domain(esk1_0,esk1_0,esk2_0) != esk1_0
| $false
| ~ ilf_type(esk2_0,relation_type(esk1_0,esk1_0)) ),
inference(rw,[status(thm)],[416,45,theory(equality)]) ).
cnf(420,negated_conjecture,
( domain(esk1_0,esk1_0,esk2_0) != esk1_0
| ~ ilf_type(esk2_0,relation_type(esk1_0,esk1_0)) ),
inference(cn,[status(thm)],[419,theory(equality)]) ).
cnf(488,negated_conjecture,
( domain(esk1_0,esk1_0,esk2_0) != esk1_0
| $false ),
inference(rw,[status(thm)],[420,303,theory(equality)]) ).
cnf(489,negated_conjecture,
domain(esk1_0,esk1_0,esk2_0) != esk1_0,
inference(cn,[status(thm)],[488,theory(equality)]) ).
cnf(490,negated_conjecture,
( ~ subset(identity_relation_of(esk1_0),esk2_0)
| ~ ilf_type(esk2_0,relation_type(esk1_0,esk1_0)) ),
inference(spm,[status(thm)],[489,410,theory(equality)]) ).
cnf(491,negated_conjecture,
( $false
| ~ ilf_type(esk2_0,relation_type(esk1_0,esk1_0)) ),
inference(rw,[status(thm)],[490,45,theory(equality)]) ).
cnf(492,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[491,303,theory(equality)]) ).
cnf(493,negated_conjecture,
$false,
inference(cn,[status(thm)],[492,theory(equality)]) ).
cnf(494,negated_conjecture,
$false,
493,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET677+3.p
% --creating new selector for []
% -running prover on /tmp/tmpBW1-mI/sel_SET677+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET677+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET677+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET677+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
%
%------------------------------------------------------------------------------