TSTP Solution File: SEU215+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU215+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 05:42:18 EST 2010
% Result : Theorem 10.34s
% Output : CNFRefutation 10.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 11 unt; 0 def)
% Number of atoms : 369 ( 69 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 501 ( 193 ~; 228 |; 56 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 65 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/tmp/tmppoZ7Q8/sel_SEU215+1.p_1',d4_funct_1) ).
fof(10,conjecture,
! [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/tmppoZ7Q8/sel_SEU215+1.p_1',t23_funct_1) ).
fof(11,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/tmp/tmppoZ7Q8/sel_SEU215+1.p_1',dt_k5_relat_1) ).
fof(14,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/tmp/tmppoZ7Q8/sel_SEU215+1.p_1',t21_funct_1) ).
fof(25,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/tmp/tmppoZ7Q8/sel_SEU215+1.p_1',fc1_funct_1) ).
fof(35,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/tmp/tmppoZ7Q8/sel_SEU215+1.p_1',t22_funct_1) ).
fof(41,negated_conjecture,
~ ! [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(assume_negation,[status(cth)],[10]) ).
fof(42,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(54,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
| ( ( X3 != apply(X1,X2)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X3 = apply(X1,X2) ) ) )
& ( in(X2,relation_dom(X1))
| ( ( X3 != apply(X1,X2)
| X3 = empty_set )
& ( X3 != empty_set
| X3 = apply(X1,X2) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(55,plain,
! [X4] :
( ~ relation(X4)
| ~ function(X4)
| ! [X5,X6] :
( ( ~ in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5) ) ) )
& ( in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| X6 = apply(X4,X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X4,X5,X6] :
( ( ( ~ in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5) ) ) )
& ( in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| X6 = apply(X4,X5) ) ) ) )
| ~ relation(X4)
| ~ function(X4) ),
inference(shift_quantors,[status(thm)],[55]) ).
fof(57,plain,
! [X4,X5,X6] :
( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != apply(X4,X5)
| X6 = empty_set
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != empty_set
| X6 = apply(X4,X5)
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[56]) ).
cnf(58,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(86,negated_conjecture,
? [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(87,negated_conjecture,
? [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)],[86]) ).
fof(88,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& relation(esk6_0)
& function(esk6_0)
& in(esk4_0,relation_dom(esk5_0))
& apply(relation_composition(esk5_0,esk6_0),esk4_0) != apply(esk6_0,apply(esk5_0,esk4_0)) ),
inference(skolemize,[status(esa)],[87]) ).
cnf(89,negated_conjecture,
apply(relation_composition(esk5_0,esk6_0),esk4_0) != apply(esk6_0,apply(esk5_0,esk4_0)),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(90,negated_conjecture,
in(esk4_0,relation_dom(esk5_0)),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(91,negated_conjecture,
function(esk6_0),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(92,negated_conjecture,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(93,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(94,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[88]) ).
fof(95,plain,
! [X1,X2] :
( ~ relation(X1)
| ~ relation(X2)
| relation(relation_composition(X1,X2)) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(96,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(relation_composition(X3,X4)) ),
inference(variable_rename,[status(thm)],[95]) ).
cnf(97,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(103,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ( ( ~ in(X1,relation_dom(relation_composition(X3,X2)))
| ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) )
& ( ~ in(X1,relation_dom(X3))
| ~ in(apply(X3,X1),relation_dom(X2))
| in(X1,relation_dom(relation_composition(X3,X2))) ) ) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(104,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ( ( ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ( in(X4,relation_dom(X6))
& in(apply(X6,X4),relation_dom(X5)) ) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5))) ) ) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ( ( ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ( in(X4,relation_dom(X6))
& in(apply(X6,X4),relation_dom(X5)) ) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5))) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[104]) ).
fof(106,plain,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X6,X4),relation_dom(X5))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[105]) ).
cnf(107,plain,
( in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[106]) ).
fof(134,plain,
! [X1,X2] :
( ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(135,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X4)
| ~ function(X4)
| ( relation(relation_composition(X3,X4))
& function(relation_composition(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X3,X4] :
( ( relation(relation_composition(X3,X4))
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X4)
| ~ function(X4) )
& ( function(relation_composition(X3,X4))
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[135]) ).
cnf(137,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(159,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_dom(relation_composition(X3,X2)))
| apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(160,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| apply(relation_composition(X6,X5),X4) = apply(X5,apply(X6,X4)) ) ),
inference(variable_rename,[status(thm)],[159]) ).
fof(161,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| apply(relation_composition(X6,X5),X4) = apply(X5,apply(X6,X4))
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[160]) ).
cnf(162,plain,
( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(210,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[58,theory(equality)]) ).
cnf(360,plain,
( in(X1,relation_dom(relation_composition(X2,X3)))
| apply(X3,apply(X2,X1)) = empty_set
| ~ in(X1,relation_dom(X2))
| ~ function(X2)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3) ),
inference(spm,[status(thm)],[107,210,theory(equality)]) ).
cnf(361,plain,
( apply(X1,apply(X2,X3)) = apply(relation_composition(X2,X1),X3)
| apply(relation_composition(X2,X1),X3) = empty_set
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(relation_composition(X2,X1))
| ~ relation(relation_composition(X2,X1)) ),
inference(spm,[status(thm)],[162,210,theory(equality)]) ).
cnf(5846,plain,
( apply(X1,apply(X2,X3)) = apply(relation_composition(X2,X1),X3)
| apply(X1,apply(X2,X3)) = empty_set
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X3,relation_dom(X2)) ),
inference(spm,[status(thm)],[162,360,theory(equality)]) ).
cnf(6018,plain,
( apply(X1,apply(X2,X3)) = apply(relation_composition(X2,X1),X3)
| apply(relation_composition(X2,X1),X3) = empty_set
| ~ function(relation_composition(X2,X1))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[361,97]) ).
cnf(6019,plain,
( apply(X1,apply(X2,X3)) = apply(relation_composition(X2,X1),X3)
| apply(relation_composition(X2,X1),X3) = empty_set
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[6018,137]) ).
cnf(6022,negated_conjecture,
( apply(relation_composition(esk5_0,esk6_0),esk4_0) = empty_set
| ~ function(esk5_0)
| ~ function(esk6_0)
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(spm,[status(thm)],[89,6019,theory(equality)]) ).
cnf(6049,negated_conjecture,
( apply(relation_composition(esk5_0,esk6_0),esk4_0) = empty_set
| $false
| ~ function(esk6_0)
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[6022,93,theory(equality)]) ).
cnf(6050,negated_conjecture,
( apply(relation_composition(esk5_0,esk6_0),esk4_0) = empty_set
| $false
| $false
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[6049,91,theory(equality)]) ).
cnf(6051,negated_conjecture,
( apply(relation_composition(esk5_0,esk6_0),esk4_0) = empty_set
| $false
| $false
| $false
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[6050,94,theory(equality)]) ).
cnf(6052,negated_conjecture,
( apply(relation_composition(esk5_0,esk6_0),esk4_0) = empty_set
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[6051,92,theory(equality)]) ).
cnf(6053,negated_conjecture,
apply(relation_composition(esk5_0,esk6_0),esk4_0) = empty_set,
inference(cn,[status(thm)],[6052,theory(equality)]) ).
cnf(6069,negated_conjecture,
apply(esk6_0,apply(esk5_0,esk4_0)) != empty_set,
inference(rw,[status(thm)],[89,6053,theory(equality)]) ).
cnf(206880,negated_conjecture,
( apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set
| apply(relation_composition(esk5_0,esk6_0),esk4_0) != empty_set
| ~ in(esk4_0,relation_dom(esk5_0))
| ~ function(esk5_0)
| ~ function(esk6_0)
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(spm,[status(thm)],[6069,5846,theory(equality)]) ).
cnf(206990,negated_conjecture,
( apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set
| $false
| ~ in(esk4_0,relation_dom(esk5_0))
| ~ function(esk5_0)
| ~ function(esk6_0)
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[206880,6053,theory(equality)]) ).
cnf(206991,negated_conjecture,
( apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set
| $false
| $false
| ~ function(esk5_0)
| ~ function(esk6_0)
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[206990,90,theory(equality)]) ).
cnf(206992,negated_conjecture,
( apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set
| $false
| $false
| $false
| ~ function(esk6_0)
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[206991,93,theory(equality)]) ).
cnf(206993,negated_conjecture,
( apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set
| $false
| $false
| $false
| $false
| ~ relation(esk5_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[206992,91,theory(equality)]) ).
cnf(206994,negated_conjecture,
( apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set
| $false
| $false
| $false
| $false
| $false
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[206993,94,theory(equality)]) ).
cnf(206995,negated_conjecture,
( apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set
| $false
| $false
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[206994,92,theory(equality)]) ).
cnf(206996,negated_conjecture,
apply(esk6_0,apply(esk5_0,esk4_0)) = empty_set,
inference(cn,[status(thm)],[206995,theory(equality)]) ).
cnf(206997,negated_conjecture,
$false,
inference(sr,[status(thm)],[206996,6069,theory(equality)]) ).
cnf(206998,negated_conjecture,
$false,
206997,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU215+1.p
% --creating new selector for []
% -running prover on /tmp/tmppoZ7Q8/sel_SEU215+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU215+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU215+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU215+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
%
%------------------------------------------------------------------------------