TSTP Solution File: SEU098+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU098+1 : TPTP v5.0.0. Released v3.2.0.
% 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 04:35:25 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 14 unt; 0 def)
% Number of atoms : 247 ( 18 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 286 ( 118 ~; 128 |; 27 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-4 aty)
% Number of variables : 106 ( 6 sgn 62 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& finite(X2) )
=> finite(relation_image(X1,X2)) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',fc13_finset_1) ).
fof(7,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(cartesian_product2(X1,X2)) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',t19_finset_1) ).
fof(17,axiom,
! [X1,X2] :
( function(first_projection_as_func_of(X1,X2))
& quasi_total(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1)
& relation_of2_as_subset(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',dt_k9_funct_3) ).
fof(24,axiom,
! [X1,X2] :
( relation(first_projection(X1,X2))
& function(first_projection(X1,X2)) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',dt_k7_funct_3) ).
fof(29,axiom,
! [X1,X2,X3,X4] :
( ( function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2) )
=> function_image(X1,X2,X3,X4) = relation_image(X3,X4) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',redefinition_k2_funct_2) ).
fof(45,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',redefinition_m2_relset_1) ).
fof(51,axiom,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',t13_finset_1) ).
fof(53,axiom,
! [X1,X2] : first_projection_as_func_of(X1,X2) = first_projection(X1,X2),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',redefinition_k9_funct_3) ).
fof(58,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',t26_finset_1) ).
fof(68,axiom,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',t21_relat_1) ).
fof(69,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',t100_funct_3) ).
fof(75,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
<=> finite(X1) ) ),
file('/tmp/tmphTJ9pc/sel_SEU098+1.p_1',t29_finset_1) ).
fof(81,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
<=> finite(X1) ) ),
inference(assume_negation,[status(cth)],[75]) ).
fof(97,plain,
! [X1,X2] :
( ~ relation(X1)
| ~ function(X1)
| ~ finite(X2)
| finite(relation_image(X1,X2)) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(98,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ function(X3)
| ~ finite(X4)
| finite(relation_image(X3,X4)) ),
inference(variable_rename,[status(thm)],[97]) ).
cnf(99,plain,
( finite(relation_image(X1,X2))
| ~ finite(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[98]) ).
fof(125,plain,
! [X1,X2] :
( ~ finite(X1)
| ~ finite(X2)
| finite(cartesian_product2(X1,X2)) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(126,plain,
! [X3,X4] :
( ~ finite(X3)
| ~ finite(X4)
| finite(cartesian_product2(X3,X4)) ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(127,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X2)
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[126]) ).
fof(165,plain,
! [X3,X4] :
( function(first_projection_as_func_of(X3,X4))
& quasi_total(first_projection_as_func_of(X3,X4),cartesian_product2(X3,X4),X3)
& relation_of2_as_subset(first_projection_as_func_of(X3,X4),cartesian_product2(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[17]) ).
cnf(166,plain,
relation_of2_as_subset(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(167,plain,
quasi_total(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(168,plain,
function(first_projection_as_func_of(X1,X2)),
inference(split_conjunct,[status(thm)],[165]) ).
fof(202,plain,
! [X3,X4] :
( relation(first_projection(X3,X4))
& function(first_projection(X3,X4)) ),
inference(variable_rename,[status(thm)],[24]) ).
cnf(204,plain,
relation(first_projection(X1,X2)),
inference(split_conjunct,[status(thm)],[202]) ).
fof(219,plain,
! [X1,X2,X3,X4] :
( ~ function(X3)
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2(X3,X1,X2)
| function_image(X1,X2,X3,X4) = relation_image(X3,X4) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(220,plain,
! [X5,X6,X7,X8] :
( ~ function(X7)
| ~ quasi_total(X7,X5,X6)
| ~ relation_of2(X7,X5,X6)
| function_image(X5,X6,X7,X8) = relation_image(X7,X8) ),
inference(variable_rename,[status(thm)],[219]) ).
cnf(221,plain,
( function_image(X1,X2,X3,X4) = relation_image(X3,X4)
| ~ relation_of2(X3,X1,X2)
| ~ quasi_total(X3,X1,X2)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[220]) ).
fof(285,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)],[45]) ).
fof(286,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)],[285]) ).
cnf(288,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[286]) ).
fof(317,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| ~ finite(X2)
| finite(X1) ),
inference(fof_nnf,[status(thm)],[51]) ).
fof(318,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ finite(X4)
| finite(X3) ),
inference(variable_rename,[status(thm)],[317]) ).
cnf(319,plain,
( finite(X1)
| ~ finite(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[318]) ).
fof(323,plain,
! [X3,X4] : first_projection_as_func_of(X3,X4) = first_projection(X3,X4),
inference(variable_rename,[status(thm)],[53]) ).
cnf(324,plain,
first_projection_as_func_of(X1,X2) = first_projection(X1,X2),
inference(split_conjunct,[status(thm)],[323]) ).
fof(339,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ~ finite(relation_dom(X1))
| finite(relation_rng(X1)) ),
inference(fof_nnf,[status(thm)],[58]) ).
fof(340,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ finite(relation_dom(X2))
| finite(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[339]) ).
cnf(341,plain,
( finite(relation_rng(X1))
| ~ finite(relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[340]) ).
fof(375,plain,
! [X1] :
( ~ relation(X1)
| subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
inference(fof_nnf,[status(thm)],[68]) ).
fof(376,plain,
! [X2] :
( ~ relation(X2)
| subset(X2,cartesian_product2(relation_dom(X2),relation_rng(X2))) ),
inference(variable_rename,[status(thm)],[375]) ).
cnf(377,plain,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[376]) ).
fof(378,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1) ),
inference(fof_nnf,[status(thm)],[69]) ).
fof(379,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| function_image(cartesian_product2(relation_dom(X2),relation_rng(X2)),relation_dom(X2),first_projection_as_func_of(relation_dom(X2),relation_rng(X2)),X2) = relation_dom(X2) ),
inference(variable_rename,[status(thm)],[378]) ).
cnf(380,plain,
( function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[379]) ).
fof(405,negated_conjecture,
? [X1] :
( relation(X1)
& function(X1)
& ( ~ finite(relation_dom(X1))
| ~ finite(X1) )
& ( finite(relation_dom(X1))
| finite(X1) ) ),
inference(fof_nnf,[status(thm)],[81]) ).
fof(406,negated_conjecture,
? [X2] :
( relation(X2)
& function(X2)
& ( ~ finite(relation_dom(X2))
| ~ finite(X2) )
& ( finite(relation_dom(X2))
| finite(X2) ) ),
inference(variable_rename,[status(thm)],[405]) ).
fof(407,negated_conjecture,
( relation(esk27_0)
& function(esk27_0)
& ( ~ finite(relation_dom(esk27_0))
| ~ finite(esk27_0) )
& ( finite(relation_dom(esk27_0))
| finite(esk27_0) ) ),
inference(skolemize,[status(esa)],[406]) ).
cnf(408,negated_conjecture,
( finite(esk27_0)
| finite(relation_dom(esk27_0)) ),
inference(split_conjunct,[status(thm)],[407]) ).
cnf(409,negated_conjecture,
( ~ finite(esk27_0)
| ~ finite(relation_dom(esk27_0)) ),
inference(split_conjunct,[status(thm)],[407]) ).
cnf(410,negated_conjecture,
function(esk27_0),
inference(split_conjunct,[status(thm)],[407]) ).
cnf(411,negated_conjecture,
relation(esk27_0),
inference(split_conjunct,[status(thm)],[407]) ).
cnf(437,plain,
relation(first_projection_as_func_of(X1,X2)),
inference(rw,[status(thm)],[204,324,theory(equality)]),
[unfolding] ).
cnf(594,plain,
( finite(X1)
| ~ finite(cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(spm,[status(thm)],[319,377,theory(equality)]) ).
cnf(615,plain,
( relation_image(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation_of2(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1))
| ~ quasi_total(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1))
| ~ function(first_projection_as_func_of(relation_dom(X1),relation_rng(X1))) ),
inference(spm,[status(thm)],[380,221,theory(equality)]) ).
cnf(616,plain,
( relation_image(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation_of2(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1))
| $false
| ~ function(first_projection_as_func_of(relation_dom(X1),relation_rng(X1))) ),
inference(rw,[status(thm)],[615,167,theory(equality)]) ).
cnf(617,plain,
( relation_image(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation_of2(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1))
| $false
| $false ),
inference(rw,[status(thm)],[616,168,theory(equality)]) ).
cnf(618,plain,
( relation_image(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation_of2(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1)) ),
inference(cn,[status(thm)],[617,theory(equality)]) ).
cnf(1104,plain,
( finite(X1)
| ~ relation(X1)
| ~ finite(relation_rng(X1))
| ~ finite(relation_dom(X1)) ),
inference(spm,[status(thm)],[594,127,theory(equality)]) ).
cnf(1112,plain,
( finite(X1)
| ~ finite(relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[1104,341,theory(equality)]) ).
cnf(1126,negated_conjecture,
( finite(esk27_0)
| ~ function(esk27_0)
| ~ relation(esk27_0) ),
inference(spm,[status(thm)],[1112,408,theory(equality)]) ).
cnf(1133,negated_conjecture,
( finite(esk27_0)
| $false
| ~ relation(esk27_0) ),
inference(rw,[status(thm)],[1126,410,theory(equality)]) ).
cnf(1134,negated_conjecture,
( finite(esk27_0)
| $false
| $false ),
inference(rw,[status(thm)],[1133,411,theory(equality)]) ).
cnf(1135,negated_conjecture,
finite(esk27_0),
inference(cn,[status(thm)],[1134,theory(equality)]) ).
cnf(1140,negated_conjecture,
( ~ finite(relation_dom(esk27_0))
| $false ),
inference(rw,[status(thm)],[409,1135,theory(equality)]) ).
cnf(1141,negated_conjecture,
~ finite(relation_dom(esk27_0)),
inference(cn,[status(thm)],[1140,theory(equality)]) ).
cnf(1426,plain,
( relation_image(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation_of2_as_subset(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1)) ),
inference(spm,[status(thm)],[618,288,theory(equality)]) ).
cnf(1437,plain,
( relation_image(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| $false ),
inference(rw,[status(thm)],[1426,166,theory(equality)]) ).
cnf(1438,plain,
( relation_image(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cn,[status(thm)],[1437,theory(equality)]) ).
cnf(2110,plain,
( finite(relation_dom(X1))
| ~ finite(X1)
| ~ function(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)))
| ~ relation(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)))
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[99,1438,theory(equality)]) ).
cnf(2124,plain,
( finite(relation_dom(X1))
| ~ finite(X1)
| $false
| ~ relation(first_projection_as_func_of(relation_dom(X1),relation_rng(X1)))
| ~ function(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[2110,168,theory(equality)]) ).
cnf(2125,plain,
( finite(relation_dom(X1))
| ~ finite(X1)
| $false
| $false
| ~ function(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[2124,437,theory(equality)]) ).
cnf(2126,plain,
( finite(relation_dom(X1))
| ~ finite(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cn,[status(thm)],[2125,theory(equality)]) ).
cnf(2179,negated_conjecture,
( ~ finite(esk27_0)
| ~ function(esk27_0)
| ~ relation(esk27_0) ),
inference(spm,[status(thm)],[1141,2126,theory(equality)]) ).
cnf(2188,negated_conjecture,
( $false
| ~ function(esk27_0)
| ~ relation(esk27_0) ),
inference(rw,[status(thm)],[2179,1135,theory(equality)]) ).
cnf(2189,negated_conjecture,
( $false
| $false
| ~ relation(esk27_0) ),
inference(rw,[status(thm)],[2188,410,theory(equality)]) ).
cnf(2190,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[2189,411,theory(equality)]) ).
cnf(2191,negated_conjecture,
$false,
inference(cn,[status(thm)],[2190,theory(equality)]) ).
cnf(2192,negated_conjecture,
$false,
2191,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU098+1.p
% --creating new selector for []
% -running prover on /tmp/tmphTJ9pc/sel_SEU098+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU098+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU098+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU098+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
%
%------------------------------------------------------------------------------