TSTP Solution File: SEU225+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU225+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 05:52:34 EST 2010
% Result : Theorem 28.23s
% Output : CNFRefutation 28.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 12 unt; 0 def)
% Number of atoms : 206 ( 72 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 259 ( 105 ~; 109 |; 34 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 2 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('/tmp/tmp-uvTRq/sel_SEU225+2.p_1',t94_relat_1) ).
fof(29,axiom,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('/tmp/tmp-uvTRq/sel_SEU225+2.p_1',t71_relat_1) ).
fof(104,axiom,
! [X1] : relation(identity_relation(X1)),
file('/tmp/tmp-uvTRq/sel_SEU225+2.p_1',dt_k6_relat_1) ).
fof(117,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/tmp/tmp-uvTRq/sel_SEU225+2.p_1',t72_funct_1) ).
fof(164,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/tmp/tmp-uvTRq/sel_SEU225+2.p_1',fc2_funct_1) ).
fof(186,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/tmp-uvTRq/sel_SEU225+2.p_1',t23_funct_1) ).
fof(209,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/tmp/tmp-uvTRq/sel_SEU225+2.p_1',t34_funct_1) ).
fof(241,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[117]) ).
fof(298,plain,
! [X1,X2] :
( ~ relation(X2)
| relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(299,plain,
! [X3,X4] :
( ~ relation(X4)
| relation_dom_restriction(X4,X3) = relation_composition(identity_relation(X3),X4) ),
inference(variable_rename,[status(thm)],[298]) ).
cnf(300,plain,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[299]) ).
fof(395,plain,
! [X2] :
( relation_dom(identity_relation(X2)) = X2
& relation_rng(identity_relation(X2)) = X2 ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(397,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[395]) ).
fof(689,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[104]) ).
cnf(690,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[689]) ).
fof(743,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& function(X3)
& in(X2,X1)
& apply(relation_dom_restriction(X3,X1),X2) != apply(X3,X2) ),
inference(fof_nnf,[status(thm)],[241]) ).
fof(744,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& function(X6)
& in(X5,X4)
& apply(relation_dom_restriction(X6,X4),X5) != apply(X6,X5) ),
inference(variable_rename,[status(thm)],[743]) ).
fof(745,negated_conjecture,
( relation(esk39_0)
& function(esk39_0)
& in(esk38_0,esk37_0)
& apply(relation_dom_restriction(esk39_0,esk37_0),esk38_0) != apply(esk39_0,esk38_0) ),
inference(skolemize,[status(esa)],[744]) ).
cnf(746,negated_conjecture,
apply(relation_dom_restriction(esk39_0,esk37_0),esk38_0) != apply(esk39_0,esk38_0),
inference(split_conjunct,[status(thm)],[745]) ).
cnf(747,negated_conjecture,
in(esk38_0,esk37_0),
inference(split_conjunct,[status(thm)],[745]) ).
cnf(748,negated_conjecture,
function(esk39_0),
inference(split_conjunct,[status(thm)],[745]) ).
cnf(749,negated_conjecture,
relation(esk39_0),
inference(split_conjunct,[status(thm)],[745]) ).
fof(927,plain,
! [X2] :
( relation(identity_relation(X2))
& function(identity_relation(X2)) ),
inference(variable_rename,[status(thm)],[164]) ).
cnf(928,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[927]) ).
fof(1030,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)],[186]) ).
fof(1031,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)],[1030]) ).
fof(1032,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)],[1031]) ).
cnf(1033,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)],[1032]) ).
fof(1107,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ( ( X2 != identity_relation(X1)
| ( relation_dom(X2) = X1
& ! [X3] :
( ~ in(X3,X1)
| apply(X2,X3) = X3 ) ) )
& ( relation_dom(X2) != X1
| ? [X3] :
( in(X3,X1)
& apply(X2,X3) != X3 )
| X2 = identity_relation(X1) ) ) ),
inference(fof_nnf,[status(thm)],[209]) ).
fof(1108,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ( ( X5 != identity_relation(X4)
| ( relation_dom(X5) = X4
& ! [X6] :
( ~ in(X6,X4)
| apply(X5,X6) = X6 ) ) )
& ( relation_dom(X5) != X4
| ? [X7] :
( in(X7,X4)
& apply(X5,X7) != X7 )
| X5 = identity_relation(X4) ) ) ),
inference(variable_rename,[status(thm)],[1107]) ).
fof(1109,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ( ( X5 != identity_relation(X4)
| ( relation_dom(X5) = X4
& ! [X6] :
( ~ in(X6,X4)
| apply(X5,X6) = X6 ) ) )
& ( relation_dom(X5) != X4
| ( in(esk64_2(X4,X5),X4)
& apply(X5,esk64_2(X4,X5)) != esk64_2(X4,X5) )
| X5 = identity_relation(X4) ) ) ),
inference(skolemize,[status(esa)],[1108]) ).
fof(1110,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ in(X6,X4)
| apply(X5,X6) = X6 )
& relation_dom(X5) = X4 )
| X5 != identity_relation(X4) )
& ( relation_dom(X5) != X4
| ( in(esk64_2(X4,X5),X4)
& apply(X5,esk64_2(X4,X5)) != esk64_2(X4,X5) )
| X5 = identity_relation(X4) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[1109]) ).
fof(1111,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| apply(X5,X6) = X6
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( relation_dom(X5) = X4
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk64_2(X4,X5),X4)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( apply(X5,esk64_2(X4,X5)) != esk64_2(X4,X5)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[1110]) ).
cnf(1115,plain,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[1111]) ).
cnf(2320,negated_conjecture,
( apply(X1,esk38_0) = esk38_0
| identity_relation(esk37_0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[1115,747,theory(equality)]) ).
cnf(4018,plain,
( apply(relation_dom_restriction(X2,X1),X3) = apply(X2,apply(identity_relation(X1),X3))
| ~ function(X2)
| ~ function(identity_relation(X1))
| ~ in(X3,relation_dom(identity_relation(X1)))
| ~ relation(X2)
| ~ relation(identity_relation(X1)) ),
inference(spm,[status(thm)],[1033,300,theory(equality)]) ).
cnf(4024,plain,
( apply(relation_dom_restriction(X2,X1),X3) = apply(X2,apply(identity_relation(X1),X3))
| ~ function(X2)
| $false
| ~ in(X3,relation_dom(identity_relation(X1)))
| ~ relation(X2)
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[4018,928,theory(equality)]) ).
cnf(4025,plain,
( apply(relation_dom_restriction(X2,X1),X3) = apply(X2,apply(identity_relation(X1),X3))
| ~ function(X2)
| $false
| ~ in(X3,X1)
| ~ relation(X2)
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[4024,397,theory(equality)]) ).
cnf(4026,plain,
( apply(relation_dom_restriction(X2,X1),X3) = apply(X2,apply(identity_relation(X1),X3))
| ~ function(X2)
| $false
| ~ in(X3,X1)
| ~ relation(X2)
| $false ),
inference(rw,[status(thm)],[4025,690,theory(equality)]) ).
cnf(4027,plain,
( apply(relation_dom_restriction(X2,X1),X3) = apply(X2,apply(identity_relation(X1),X3))
| ~ function(X2)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(cn,[status(thm)],[4026,theory(equality)]) ).
cnf(39729,negated_conjecture,
( apply(identity_relation(esk37_0),esk38_0) = esk38_0
| ~ function(identity_relation(esk37_0))
| ~ relation(identity_relation(esk37_0)) ),
inference(er,[status(thm)],[2320,theory(equality)]) ).
cnf(39734,negated_conjecture,
( apply(identity_relation(esk37_0),esk38_0) = esk38_0
| $false
| ~ relation(identity_relation(esk37_0)) ),
inference(rw,[status(thm)],[39729,928,theory(equality)]) ).
cnf(39735,negated_conjecture,
( apply(identity_relation(esk37_0),esk38_0) = esk38_0
| $false
| $false ),
inference(rw,[status(thm)],[39734,690,theory(equality)]) ).
cnf(39736,negated_conjecture,
apply(identity_relation(esk37_0),esk38_0) = esk38_0,
inference(cn,[status(thm)],[39735,theory(equality)]) ).
cnf(322406,negated_conjecture,
( apply(X1,esk38_0) = apply(relation_dom_restriction(X1,esk37_0),esk38_0)
| ~ function(X1)
| ~ in(esk38_0,esk37_0)
| ~ relation(X1) ),
inference(spm,[status(thm)],[4027,39736,theory(equality)]) ).
cnf(322498,negated_conjecture,
( apply(X1,esk38_0) = apply(relation_dom_restriction(X1,esk37_0),esk38_0)
| ~ function(X1)
| $false
| ~ relation(X1) ),
inference(rw,[status(thm)],[322406,747,theory(equality)]) ).
cnf(322499,negated_conjecture,
( apply(X1,esk38_0) = apply(relation_dom_restriction(X1,esk37_0),esk38_0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cn,[status(thm)],[322498,theory(equality)]) ).
cnf(322606,negated_conjecture,
( ~ function(esk39_0)
| ~ relation(esk39_0) ),
inference(spm,[status(thm)],[746,322499,theory(equality)]) ).
cnf(322628,negated_conjecture,
( $false
| ~ relation(esk39_0) ),
inference(rw,[status(thm)],[322606,748,theory(equality)]) ).
cnf(322629,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[322628,749,theory(equality)]) ).
cnf(322630,negated_conjecture,
$false,
inference(cn,[status(thm)],[322629,theory(equality)]) ).
cnf(322631,negated_conjecture,
$false,
322630,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU225+2.p
% --creating new selector for []
% -running prover on /tmp/tmp-uvTRq/sel_SEU225+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU225+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU225+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU225+2.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
%
%------------------------------------------------------------------------------