TSTP Solution File: SEU292+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU292+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 06:53:29 EST 2010
% Result : Theorem 0.38s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 14 unt; 0 def)
% Number of atoms : 234 ( 72 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 278 ( 103 ~; 111 |; 45 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 113 ( 4 sgn 70 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/tmp/tmpWiNEcG/sel_SEU292+1.p_1',cc1_relset_1) ).
fof(13,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/tmp/tmpWiNEcG/sel_SEU292+1.p_1',redefinition_k4_relset_1) ).
fof(18,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
file('/tmp/tmpWiNEcG/sel_SEU292+1.p_1',t21_funct_2) ).
fof(28,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmpWiNEcG/sel_SEU292+1.p_1',redefinition_m2_relset_1) ).
fof(33,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/tmp/tmpWiNEcG/sel_SEU292+1.p_1',dt_m2_relset_1) ).
fof(41,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/tmp/tmpWiNEcG/sel_SEU292+1.p_1',t23_funct_1) ).
fof(55,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
file('/tmp/tmpWiNEcG/sel_SEU292+1.p_1',d1_funct_2) ).
fof(57,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[18]) ).
fof(74,plain,
! [X1,X2,X3] :
( ~ element(X3,powerset(cartesian_product2(X1,X2)))
| relation(X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(75,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(cartesian_product2(X4,X5)))
| relation(X6) ),
inference(variable_rename,[status(thm)],[74]) ).
cnf(76,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(114,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(115,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| relation_dom_as_subset(X4,X5,X6) = relation_dom(X6) ),
inference(variable_rename,[status(thm)],[114]) ).
cnf(116,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(128,negated_conjecture,
? [X1,X2,X3,X4] :
( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2)
& ? [X5] :
( relation(X5)
& function(X5)
& in(X3,X1)
& X2 != empty_set
& apply(relation_composition(X4,X5),X3) != apply(X5,apply(X4,X3)) ) ),
inference(fof_nnf,[status(thm)],[57]) ).
fof(129,negated_conjecture,
? [X6,X7,X8,X9] :
( function(X9)
& quasi_total(X9,X6,X7)
& relation_of2_as_subset(X9,X6,X7)
& ? [X10] :
( relation(X10)
& function(X10)
& in(X8,X6)
& X7 != empty_set
& apply(relation_composition(X9,X10),X8) != apply(X10,apply(X9,X8)) ) ),
inference(variable_rename,[status(thm)],[128]) ).
fof(130,negated_conjecture,
( function(esk11_0)
& quasi_total(esk11_0,esk8_0,esk9_0)
& relation_of2_as_subset(esk11_0,esk8_0,esk9_0)
& relation(esk12_0)
& function(esk12_0)
& in(esk10_0,esk8_0)
& esk9_0 != empty_set
& apply(relation_composition(esk11_0,esk12_0),esk10_0) != apply(esk12_0,apply(esk11_0,esk10_0)) ),
inference(skolemize,[status(esa)],[129]) ).
cnf(131,negated_conjecture,
apply(relation_composition(esk11_0,esk12_0),esk10_0) != apply(esk12_0,apply(esk11_0,esk10_0)),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(132,negated_conjecture,
esk9_0 != empty_set,
inference(split_conjunct,[status(thm)],[130]) ).
cnf(133,negated_conjecture,
in(esk10_0,esk8_0),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(134,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(135,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(136,negated_conjecture,
relation_of2_as_subset(esk11_0,esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(137,negated_conjecture,
quasi_total(esk11_0,esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(138,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[130]) ).
fof(167,plain,
! [X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X1,X2)
| relation_of2(X3,X1,X2) )
& ( ~ relation_of2(X3,X1,X2)
| relation_of2_as_subset(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(168,plain,
! [X4,X5,X6] :
( ( ~ relation_of2_as_subset(X6,X4,X5)
| relation_of2(X6,X4,X5) )
& ( ~ relation_of2(X6,X4,X5)
| relation_of2_as_subset(X6,X4,X5) ) ),
inference(variable_rename,[status(thm)],[167]) ).
cnf(169,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[168]) ).
cnf(170,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[168]) ).
fof(181,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| element(X3,powerset(cartesian_product2(X1,X2))) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(182,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| element(X6,powerset(cartesian_product2(X4,X5))) ),
inference(variable_rename,[status(thm)],[181]) ).
cnf(183,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[182]) ).
fof(208,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_dom(X2))
| apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(209,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4)) ) ),
inference(variable_rename,[status(thm)],[208]) ).
fof(210,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4))
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[209]) ).
cnf(211,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[210]) ).
fof(250,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ( ( ( X2 = empty_set
& X1 != empty_set )
| ( ( ~ quasi_total(X3,X1,X2)
| X1 = relation_dom_as_subset(X1,X2,X3) )
& ( X1 != relation_dom_as_subset(X1,X2,X3)
| quasi_total(X3,X1,X2) ) ) )
& ( X2 != empty_set
| X1 = empty_set
| ( ( ~ quasi_total(X3,X1,X2)
| X3 = empty_set )
& ( X3 != empty_set
| quasi_total(X3,X1,X2) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(251,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| ( ( ( X5 = empty_set
& X4 != empty_set )
| ( ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5) ) ) )
& ( X5 != empty_set
| X4 = empty_set
| ( ( ~ quasi_total(X6,X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| quasi_total(X6,X4,X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[250]) ).
fof(252,plain,
! [X4,X5,X6] :
( ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6)
| X5 = empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5)
| X5 = empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6)
| X4 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5)
| X4 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( ~ quasi_total(X6,X4,X5)
| X6 = empty_set
| X4 = empty_set
| X5 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X6 != empty_set
| quasi_total(X6,X4,X5)
| X4 = empty_set
| X5 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) ) ),
inference(distribute,[status(thm)],[251]) ).
cnf(258,plain,
( X3 = empty_set
| X2 = relation_dom_as_subset(X2,X3,X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[252]) ).
cnf(312,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[76,183,theory(equality)]) ).
cnf(318,plain,
( X1 = relation_dom(X3)
| empty_set = X2
| ~ relation_of2(X3,X1,X2)
| ~ relation_of2_as_subset(X3,X1,X2)
| ~ quasi_total(X3,X1,X2) ),
inference(spm,[status(thm)],[116,258,theory(equality)]) ).
cnf(332,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk11_0))
| ~ function(esk12_0)
| ~ function(esk11_0)
| ~ relation(esk12_0)
| ~ relation(esk11_0) ),
inference(spm,[status(thm)],[131,211,theory(equality)]) ).
cnf(335,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk11_0))
| $false
| ~ function(esk11_0)
| ~ relation(esk12_0)
| ~ relation(esk11_0) ),
inference(rw,[status(thm)],[332,134,theory(equality)]) ).
cnf(336,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk11_0))
| $false
| $false
| ~ relation(esk12_0)
| ~ relation(esk11_0) ),
inference(rw,[status(thm)],[335,138,theory(equality)]) ).
cnf(337,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk11_0))
| $false
| $false
| $false
| ~ relation(esk11_0) ),
inference(rw,[status(thm)],[336,135,theory(equality)]) ).
cnf(338,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk11_0))
| ~ relation(esk11_0) ),
inference(cn,[status(thm)],[337,theory(equality)]) ).
cnf(386,negated_conjecture,
relation(esk11_0),
inference(spm,[status(thm)],[312,136,theory(equality)]) ).
cnf(388,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk11_0))
| $false ),
inference(rw,[status(thm)],[338,386,theory(equality)]) ).
cnf(389,negated_conjecture,
~ in(esk10_0,relation_dom(esk11_0)),
inference(cn,[status(thm)],[388,theory(equality)]) ).
cnf(564,plain,
( X1 = relation_dom(X3)
| empty_set = X2
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2(X3,X1,X2) ),
inference(csr,[status(thm)],[318,169]) ).
cnf(568,plain,
( X1 = relation_dom(X2)
| empty_set = X3
| ~ quasi_total(X2,X1,X3)
| ~ relation_of2_as_subset(X2,X1,X3) ),
inference(spm,[status(thm)],[564,170,theory(equality)]) ).
cnf(3454,negated_conjecture,
( esk8_0 = relation_dom(esk11_0)
| empty_set = esk9_0
| ~ relation_of2_as_subset(esk11_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[568,137,theory(equality)]) ).
cnf(3463,negated_conjecture,
( esk8_0 = relation_dom(esk11_0)
| empty_set = esk9_0
| $false ),
inference(rw,[status(thm)],[3454,136,theory(equality)]) ).
cnf(3464,negated_conjecture,
( esk8_0 = relation_dom(esk11_0)
| empty_set = esk9_0 ),
inference(cn,[status(thm)],[3463,theory(equality)]) ).
cnf(3465,negated_conjecture,
relation_dom(esk11_0) = esk8_0,
inference(sr,[status(thm)],[3464,132,theory(equality)]) ).
cnf(3488,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[389,3465,theory(equality)]),133,theory(equality)]) ).
cnf(3489,negated_conjecture,
$false,
inference(cn,[status(thm)],[3488,theory(equality)]) ).
cnf(3490,negated_conjecture,
$false,
3489,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU292+1.p
% --creating new selector for []
% -running prover on /tmp/tmpWiNEcG/sel_SEU292+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU292+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU292+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU292+1.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
%
%------------------------------------------------------------------------------