TSTP Solution File: SEU305+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU305+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 07:03:55 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 13 unt; 0 def)
% Number of atoms : 269 ( 49 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 318 ( 104 ~; 138 |; 52 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 51 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
file('/tmp/tmpoSSjis/sel_SEU305+1.p_1',redefinition_k3_lattices) ).
fof(16,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
file('/tmp/tmpoSSjis/sel_SEU305+1.p_1',commutativity_k3_lattices) ).
fof(22,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
file('/tmp/tmpoSSjis/sel_SEU305+1.p_1',d3_lattices) ).
fof(32,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
file('/tmp/tmpoSSjis/sel_SEU305+1.p_1',t26_lattices) ).
fof(43,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
inference(assume_negation,[status(cth)],[32]) ).
fof(46,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(49,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).
fof(51,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[22,theory(equality)]) ).
fof(53,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[43,theory(equality)]) ).
fof(71,plain,
! [X1,X2,X3] :
( empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join_commut(X1,X2,X3) = join(X1,X2,X3) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(72,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_commutative(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| join_commut(X4,X5,X6) = join(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[71]) ).
cnf(73,plain,
( join_commut(X1,X2,X3) = join(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(105,plain,
! [X1,X2,X3] :
( empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(106,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_commutative(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| join_commut(X4,X5,X6) = join_commut(X4,X6,X5) ),
inference(variable_rename,[status(thm)],[105]) ).
cnf(107,plain,
( join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(split_conjunct,[status(thm)],[106]) ).
fof(121,plain,
! [X1] :
( empty_carrier(X1)
| ~ join_semilatt_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ( ( ~ below(X1,X2,X3)
| join(X1,X2,X3) = X3 )
& ( join(X1,X2,X3) != X3
| below(X1,X2,X3) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[51]) ).
fof(122,plain,
! [X4] :
( empty_carrier(X4)
| ~ join_semilatt_str(X4)
| ! [X5] :
( ~ element(X5,the_carrier(X4))
| ! [X6] :
( ~ element(X6,the_carrier(X4))
| ( ( ~ below(X4,X5,X6)
| join(X4,X5,X6) = X6 )
& ( join(X4,X5,X6) != X6
| below(X4,X5,X6) ) ) ) ) ),
inference(variable_rename,[status(thm)],[121]) ).
fof(123,plain,
! [X4,X5,X6] :
( ~ element(X6,the_carrier(X4))
| ( ( ~ below(X4,X5,X6)
| join(X4,X5,X6) = X6 )
& ( join(X4,X5,X6) != X6
| below(X4,X5,X6) ) )
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) ),
inference(shift_quantors,[status(thm)],[122]) ).
fof(124,plain,
! [X4,X5,X6] :
( ( ~ below(X4,X5,X6)
| join(X4,X5,X6) = X6
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) )
& ( join(X4,X5,X6) != X6
| below(X4,X5,X6)
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) ) ),
inference(distribute,[status(thm)],[123]) ).
cnf(126,plain,
( empty_carrier(X1)
| join(X1,X2,X3) = X3
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[124]) ).
fof(153,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& ? [X3] :
( element(X3,the_carrier(X1))
& below(X1,X2,X3)
& below(X1,X3,X2)
& X2 != X3 ) ) ),
inference(fof_nnf,[status(thm)],[53]) ).
fof(154,negated_conjecture,
? [X4] :
( ~ empty_carrier(X4)
& join_commutative(X4)
& join_semilatt_str(X4)
& ? [X5] :
( element(X5,the_carrier(X4))
& ? [X6] :
( element(X6,the_carrier(X4))
& below(X4,X5,X6)
& below(X4,X6,X5)
& X5 != X6 ) ) ),
inference(variable_rename,[status(thm)],[153]) ).
fof(155,negated_conjecture,
( ~ empty_carrier(esk5_0)
& join_commutative(esk5_0)
& join_semilatt_str(esk5_0)
& element(esk6_0,the_carrier(esk5_0))
& element(esk7_0,the_carrier(esk5_0))
& below(esk5_0,esk6_0,esk7_0)
& below(esk5_0,esk7_0,esk6_0)
& esk6_0 != esk7_0 ),
inference(skolemize,[status(esa)],[154]) ).
cnf(156,negated_conjecture,
esk6_0 != esk7_0,
inference(split_conjunct,[status(thm)],[155]) ).
cnf(157,negated_conjecture,
below(esk5_0,esk7_0,esk6_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(158,negated_conjecture,
below(esk5_0,esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(159,negated_conjecture,
element(esk7_0,the_carrier(esk5_0)),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(160,negated_conjecture,
element(esk6_0,the_carrier(esk5_0)),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(161,negated_conjecture,
join_semilatt_str(esk5_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(162,negated_conjecture,
join_commutative(esk5_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(163,negated_conjecture,
~ empty_carrier(esk5_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(216,negated_conjecture,
( join(esk5_0,esk6_0,esk7_0) = esk7_0
| empty_carrier(esk5_0)
| ~ element(esk7_0,the_carrier(esk5_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(spm,[status(thm)],[126,158,theory(equality)]) ).
cnf(217,negated_conjecture,
( join(esk5_0,esk7_0,esk6_0) = esk6_0
| empty_carrier(esk5_0)
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ element(esk7_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(spm,[status(thm)],[126,157,theory(equality)]) ).
cnf(218,negated_conjecture,
( join(esk5_0,esk6_0,esk7_0) = esk7_0
| empty_carrier(esk5_0)
| $false
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[216,159,theory(equality)]) ).
cnf(219,negated_conjecture,
( join(esk5_0,esk6_0,esk7_0) = esk7_0
| empty_carrier(esk5_0)
| $false
| $false
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[218,160,theory(equality)]) ).
cnf(220,negated_conjecture,
( join(esk5_0,esk6_0,esk7_0) = esk7_0
| empty_carrier(esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[219,161,theory(equality)]) ).
cnf(221,negated_conjecture,
( join(esk5_0,esk6_0,esk7_0) = esk7_0
| empty_carrier(esk5_0) ),
inference(cn,[status(thm)],[220,theory(equality)]) ).
cnf(222,negated_conjecture,
join(esk5_0,esk6_0,esk7_0) = esk7_0,
inference(sr,[status(thm)],[221,163,theory(equality)]) ).
cnf(223,negated_conjecture,
( join(esk5_0,esk7_0,esk6_0) = esk6_0
| empty_carrier(esk5_0)
| $false
| ~ element(esk7_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[217,160,theory(equality)]) ).
cnf(224,negated_conjecture,
( join(esk5_0,esk7_0,esk6_0) = esk6_0
| empty_carrier(esk5_0)
| $false
| $false
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[223,159,theory(equality)]) ).
cnf(225,negated_conjecture,
( join(esk5_0,esk7_0,esk6_0) = esk6_0
| empty_carrier(esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[224,161,theory(equality)]) ).
cnf(226,negated_conjecture,
( join(esk5_0,esk7_0,esk6_0) = esk6_0
| empty_carrier(esk5_0) ),
inference(cn,[status(thm)],[225,theory(equality)]) ).
cnf(227,negated_conjecture,
join(esk5_0,esk7_0,esk6_0) = esk6_0,
inference(sr,[status(thm)],[226,163,theory(equality)]) ).
cnf(229,plain,
( join(X1,X2,X3) = join_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(spm,[status(thm)],[107,73,theory(equality)]) ).
cnf(305,plain,
( join(X1,X3,X2) = join(X1,X2,X3)
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(spm,[status(thm)],[73,229,theory(equality)]) ).
cnf(500,negated_conjecture,
( join(esk5_0,esk6_0,esk7_0) = esk6_0
| empty_carrier(esk5_0)
| ~ join_commutative(esk5_0)
| ~ element(esk7_0,the_carrier(esk5_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(spm,[status(thm)],[227,305,theory(equality)]) ).
cnf(506,negated_conjecture,
( esk7_0 = esk6_0
| empty_carrier(esk5_0)
| ~ join_commutative(esk5_0)
| ~ element(esk7_0,the_carrier(esk5_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[500,222,theory(equality)]) ).
cnf(507,negated_conjecture,
( esk7_0 = esk6_0
| empty_carrier(esk5_0)
| $false
| ~ element(esk7_0,the_carrier(esk5_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[506,162,theory(equality)]) ).
cnf(508,negated_conjecture,
( esk7_0 = esk6_0
| empty_carrier(esk5_0)
| $false
| $false
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[507,159,theory(equality)]) ).
cnf(509,negated_conjecture,
( esk7_0 = esk6_0
| empty_carrier(esk5_0)
| $false
| $false
| $false
| ~ join_semilatt_str(esk5_0) ),
inference(rw,[status(thm)],[508,160,theory(equality)]) ).
cnf(510,negated_conjecture,
( esk7_0 = esk6_0
| empty_carrier(esk5_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[509,161,theory(equality)]) ).
cnf(511,negated_conjecture,
( esk7_0 = esk6_0
| empty_carrier(esk5_0) ),
inference(cn,[status(thm)],[510,theory(equality)]) ).
cnf(512,negated_conjecture,
empty_carrier(esk5_0),
inference(sr,[status(thm)],[511,156,theory(equality)]) ).
cnf(513,negated_conjecture,
$false,
inference(sr,[status(thm)],[512,163,theory(equality)]) ).
cnf(514,negated_conjecture,
$false,
513,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU305+1.p
% --creating new selector for []
% -running prover on /tmp/tmpoSSjis/sel_SEU305+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU305+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU305+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU305+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
%
%------------------------------------------------------------------------------