TSTP Solution File: SEU290+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU290+1 : TPTP v5.0.0. Released v3.3.0.
% 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 06:52:22 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 10 unt; 0 def)
% Number of atoms : 291 ( 100 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 373 ( 138 ~; 156 |; 62 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 136 ( 4 sgn 84 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/tmp/tmp_6K20p/sel_SEU290+1.p_1',cc1_relset_1) ).
fof(12,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/tmp/tmp_6K20p/sel_SEU290+1.p_1',redefinition_k4_relset_1) ).
fof(14,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
file('/tmp/tmp_6K20p/sel_SEU290+1.p_1',t6_funct_2) ).
fof(15,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/tmp/tmp_6K20p/sel_SEU290+1.p_1',d5_funct_1) ).
fof(28,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmp_6K20p/sel_SEU290+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/tmp_6K20p/sel_SEU290+1.p_1',dt_m2_relset_1) ).
fof(54,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/tmp_6K20p/sel_SEU290+1.p_1',d1_funct_2) ).
fof(56,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
inference(assume_negation,[status(cth)],[14]) ).
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(109,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(110,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| relation_dom_as_subset(X4,X5,X6) = relation_dom(X6) ),
inference(variable_rename,[status(thm)],[109]) ).
cnf(111,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[110]) ).
fof(114,negated_conjecture,
? [X1,X2,X3,X4] :
( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2)
& in(X3,X1)
& X2 != empty_set
& ~ in(apply(X4,X3),relation_rng(X4)) ),
inference(fof_nnf,[status(thm)],[56]) ).
fof(115,negated_conjecture,
? [X5,X6,X7,X8] :
( function(X8)
& quasi_total(X8,X5,X6)
& relation_of2_as_subset(X8,X5,X6)
& in(X7,X5)
& X6 != empty_set
& ~ in(apply(X8,X7),relation_rng(X8)) ),
inference(variable_rename,[status(thm)],[114]) ).
fof(116,negated_conjecture,
( function(esk11_0)
& quasi_total(esk11_0,esk8_0,esk9_0)
& relation_of2_as_subset(esk11_0,esk8_0,esk9_0)
& in(esk10_0,esk8_0)
& esk9_0 != empty_set
& ~ in(apply(esk11_0,esk10_0),relation_rng(esk11_0)) ),
inference(skolemize,[status(esa)],[115]) ).
cnf(117,negated_conjecture,
~ in(apply(esk11_0,esk10_0),relation_rng(esk11_0)),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(118,negated_conjecture,
esk9_0 != empty_set,
inference(split_conjunct,[status(thm)],[116]) ).
cnf(119,negated_conjecture,
in(esk10_0,esk8_0),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(120,negated_conjecture,
relation_of2_as_subset(esk11_0,esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(121,negated_conjecture,
quasi_total(esk11_0,esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(122,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[116]) ).
fof(123,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2] :
( ( X2 != relation_rng(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| X3 != apply(X1,X4) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X1))
| X3 != apply(X1,X4) ) )
& ( in(X3,X2)
| ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) )
| X2 = relation_rng(X1) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(124,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] :
( in(X8,relation_dom(X5))
& X7 = apply(X5,X8) ) )
& ( ! [X9] :
( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9) )
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] :
( ~ in(X11,relation_dom(X5))
| X10 != apply(X5,X11) ) )
& ( in(X10,X6)
| ? [X12] :
( in(X12,relation_dom(X5))
& X10 = apply(X5,X12) ) ) )
| X6 = relation_rng(X5) ) ) ),
inference(variable_rename,[status(thm)],[123]) ).
fof(125,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ( in(esk12_3(X5,X6,X7),relation_dom(X5))
& X7 = apply(X5,esk12_3(X5,X6,X7)) ) )
& ( ! [X9] :
( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9) )
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk13_2(X5,X6),X6)
| ! [X11] :
( ~ in(X11,relation_dom(X5))
| esk13_2(X5,X6) != apply(X5,X11) ) )
& ( in(esk13_2(X5,X6),X6)
| ( in(esk14_2(X5,X6),relation_dom(X5))
& esk13_2(X5,X6) = apply(X5,esk14_2(X5,X6)) ) ) )
| X6 = relation_rng(X5) ) ) ),
inference(skolemize,[status(esa)],[124]) ).
fof(126,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(X11,relation_dom(X5))
| esk13_2(X5,X6) != apply(X5,X11)
| ~ in(esk13_2(X5,X6),X6) )
& ( in(esk13_2(X5,X6),X6)
| ( in(esk14_2(X5,X6),relation_dom(X5))
& esk13_2(X5,X6) = apply(X5,esk14_2(X5,X6)) ) ) )
| X6 = relation_rng(X5) )
& ( ( ( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9)
| in(X7,X6) )
& ( ~ in(X7,X6)
| ( in(esk12_3(X5,X6,X7),relation_dom(X5))
& X7 = apply(X5,esk12_3(X5,X6,X7)) ) ) )
| X6 != relation_rng(X5) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[125]) ).
fof(127,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(X11,relation_dom(X5))
| esk13_2(X5,X6) != apply(X5,X11)
| ~ in(esk13_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk14_2(X5,X6),relation_dom(X5))
| in(esk13_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk13_2(X5,X6) = apply(X5,esk14_2(X5,X6))
| in(esk13_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk12_3(X5,X6,X7),relation_dom(X5))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,esk12_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[126]) ).
cnf(130,plain,
( in(X3,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[127]) ).
fof(173,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(174,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)],[173]) ).
cnf(175,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[174]) ).
cnf(176,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[174]) ).
fof(187,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(188,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| element(X6,powerset(cartesian_product2(X4,X5))) ),
inference(variable_rename,[status(thm)],[187]) ).
cnf(189,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[188]) ).
fof(246,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)],[54]) ).
fof(247,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)],[246]) ).
fof(248,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)],[247]) ).
cnf(254,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)],[248]) ).
cnf(306,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[76,189,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)],[111,254,theory(equality)]) ).
cnf(326,plain,
( in(apply(X1,X2),X3)
| relation_rng(X1) != X3
| ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[130,theory(equality)]) ).
cnf(504,negated_conjecture,
relation(esk11_0),
inference(spm,[status(thm)],[306,120,theory(equality)]) ).
cnf(817,plain,
( X1 = relation_dom(X3)
| empty_set = X2
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2(X3,X1,X2) ),
inference(csr,[status(thm)],[318,175]) ).
cnf(821,plain,
( X1 = relation_dom(X2)
| empty_set = X3
| ~ quasi_total(X2,X1,X3)
| ~ relation_of2_as_subset(X2,X1,X3) ),
inference(spm,[status(thm)],[817,176,theory(equality)]) ).
cnf(937,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)],[821,121,theory(equality)]) ).
cnf(941,negated_conjecture,
( esk8_0 = relation_dom(esk11_0)
| empty_set = esk9_0
| $false ),
inference(rw,[status(thm)],[937,120,theory(equality)]) ).
cnf(942,negated_conjecture,
( esk8_0 = relation_dom(esk11_0)
| empty_set = esk9_0 ),
inference(cn,[status(thm)],[941,theory(equality)]) ).
cnf(943,negated_conjecture,
relation_dom(esk11_0) = esk8_0,
inference(sr,[status(thm)],[942,118,theory(equality)]) ).
cnf(1061,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk11_0))
| ~ function(esk11_0)
| ~ relation(esk11_0) ),
inference(spm,[status(thm)],[117,326,theory(equality)]) ).
cnf(1094,negated_conjecture,
( $false
| ~ function(esk11_0)
| ~ relation(esk11_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1061,943,theory(equality)]),119,theory(equality)]) ).
cnf(1095,negated_conjecture,
( $false
| $false
| ~ relation(esk11_0) ),
inference(rw,[status(thm)],[1094,122,theory(equality)]) ).
cnf(1096,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[1095,504,theory(equality)]) ).
cnf(1097,negated_conjecture,
$false,
inference(cn,[status(thm)],[1096,theory(equality)]) ).
cnf(1098,negated_conjecture,
$false,
1097,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU290+1.p
% --creating new selector for []
% -running prover on /tmp/tmp_6K20p/sel_SEU290+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU290+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU290+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU290+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
%
%------------------------------------------------------------------------------