TSTP Solution File: SWC417+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC417+1 : TPTP v5.0.0. Released v2.4.0.
% 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 11:46:52 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 13 unt; 0 def)
% Number of atoms : 284 ( 89 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 349 ( 125 ~; 122 |; 80 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 47 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpoMmMex/sel_SWC417+1.p_1',ax84) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpoMmMex/sel_SWC417+1.p_1',ax16) ).
fof(12,axiom,
ssList(nil),
file('/tmp/tmpoMmMex/sel_SWC417+1.p_1',ax17) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpoMmMex/sel_SWC417+1.p_1',ax28) ).
fof(19,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(cons(X8,nil),X9) != X4
| app(X9,cons(X8,nil)) != X3 ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpoMmMex/sel_SWC417+1.p_1',co1) ).
fof(20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(cons(X8,nil),X9) != X4
| app(X9,cons(X8,nil)) != X3 ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(cons(X8,nil),X9) != X4
| app(X9,cons(X8,nil)) != X3 ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).
fof(39,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(40,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[39]) ).
cnf(41,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(70,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(71,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[71]) ).
cnf(73,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[12]) ).
fof(81,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(82,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[81]) ).
cnf(83,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(102,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(app(X6,cons(X5,nil)),X7) != X2
| app(app(X7,cons(X5,nil)),X6) != X1 ) ) )
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X4
& app(X9,cons(X8,nil)) = X3 ) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(103,negated_conjecture,
? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& X11 = X13
& X10 = X12
& ( ( neq(X11,nil)
& ! [X14] :
( ~ ssItem(X14)
| ! [X15] :
( ~ ssList(X15)
| ! [X16] :
( ~ ssList(X16)
| app(app(X15,cons(X14,nil)),X16) != X11
| app(app(X16,cons(X14,nil)),X15) != X10 ) ) )
& ? [X17] :
( ssItem(X17)
& ? [X18] :
( ssList(X18)
& app(cons(X17,nil),X18) = X13
& app(X18,cons(X17,nil)) = X12 ) ) )
| ( neq(X11,nil)
& ~ neq(X13,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,negated_conjecture,
( ssList(esk5_0)
& ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( ( neq(esk6_0,nil)
& ! [X14] :
( ~ ssItem(X14)
| ! [X15] :
( ~ ssList(X15)
| ! [X16] :
( ~ ssList(X16)
| app(app(X15,cons(X14,nil)),X16) != esk6_0
| app(app(X16,cons(X14,nil)),X15) != esk5_0 ) ) )
& ssItem(esk9_0)
& ssList(esk10_0)
& app(cons(esk9_0,nil),esk10_0) = esk8_0
& app(esk10_0,cons(esk9_0,nil)) = esk7_0 )
| ( neq(esk6_0,nil)
& ~ neq(esk8_0,nil) ) ) ),
inference(skolemize,[status(esa)],[103]) ).
fof(105,negated_conjecture,
! [X14,X15,X16] :
( ( ( ( ~ ssList(X16)
| app(app(X15,cons(X14,nil)),X16) != esk6_0
| app(app(X16,cons(X14,nil)),X15) != esk5_0
| ~ ssList(X15)
| ~ ssItem(X14) )
& neq(esk6_0,nil)
& ssItem(esk9_0)
& ssList(esk10_0)
& app(cons(esk9_0,nil),esk10_0) = esk8_0
& app(esk10_0,cons(esk9_0,nil)) = esk7_0 )
| ( neq(esk6_0,nil)
& ~ neq(esk8_0,nil) ) )
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0) ),
inference(shift_quantors,[status(thm)],[104]) ).
fof(106,negated_conjecture,
! [X14,X15,X16] :
( ( neq(esk6_0,nil)
| ~ ssList(X16)
| app(app(X15,cons(X14,nil)),X16) != esk6_0
| app(app(X16,cons(X14,nil)),X15) != esk5_0
| ~ ssList(X15)
| ~ ssItem(X14) )
& ( ~ neq(esk8_0,nil)
| ~ ssList(X16)
| app(app(X15,cons(X14,nil)),X16) != esk6_0
| app(app(X16,cons(X14,nil)),X15) != esk5_0
| ~ ssList(X15)
| ~ ssItem(X14) )
& ( neq(esk6_0,nil)
| neq(esk6_0,nil) )
& ( ~ neq(esk8_0,nil)
| neq(esk6_0,nil) )
& ( neq(esk6_0,nil)
| ssItem(esk9_0) )
& ( ~ neq(esk8_0,nil)
| ssItem(esk9_0) )
& ( neq(esk6_0,nil)
| ssList(esk10_0) )
& ( ~ neq(esk8_0,nil)
| ssList(esk10_0) )
& ( neq(esk6_0,nil)
| app(cons(esk9_0,nil),esk10_0) = esk8_0 )
& ( ~ neq(esk8_0,nil)
| app(cons(esk9_0,nil),esk10_0) = esk8_0 )
& ( neq(esk6_0,nil)
| app(esk10_0,cons(esk9_0,nil)) = esk7_0 )
& ( ~ neq(esk8_0,nil)
| app(esk10_0,cons(esk9_0,nil)) = esk7_0 )
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0) ),
inference(distribute,[status(thm)],[105]) ).
cnf(107,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(111,negated_conjecture,
esk5_0 = esk7_0,
inference(split_conjunct,[status(thm)],[106]) ).
cnf(112,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[106]) ).
cnf(113,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(115,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(117,negated_conjecture,
( ssList(esk10_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(119,negated_conjecture,
( ssItem(esk9_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(122,negated_conjecture,
( neq(esk6_0,nil)
| neq(esk6_0,nil) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(123,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X3,cons(X1,nil)),X2) != esk5_0
| app(app(X2,cons(X1,nil)),X3) != esk6_0
| ~ ssList(X3)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(131,negated_conjecture,
( ssItem(esk9_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[119,112,theory(equality)]),122,theory(equality)]) ).
cnf(132,negated_conjecture,
ssItem(esk9_0),
inference(cn,[status(thm)],[131,theory(equality)]) ).
cnf(133,negated_conjecture,
( ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[117,112,theory(equality)]),122,theory(equality)]) ).
cnf(134,negated_conjecture,
ssList(esk10_0),
inference(cn,[status(thm)],[133,theory(equality)]) ).
cnf(148,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk5_0
| ~ neq(esk8_0,nil) ),
inference(rw,[status(thm)],[113,111,theory(equality)]) ).
cnf(149,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk5_0
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[148,112,theory(equality)]),122,theory(equality)]) ).
cnf(150,negated_conjecture,
app(esk10_0,cons(esk9_0,nil)) = esk5_0,
inference(cn,[status(thm)],[149,theory(equality)]) ).
cnf(157,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk6_0
| ~ neq(esk8_0,nil) ),
inference(rw,[status(thm)],[115,112,theory(equality)]) ).
cnf(158,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk6_0
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[157,112,theory(equality)]),122,theory(equality)]) ).
cnf(159,negated_conjecture,
app(cons(esk9_0,nil),esk10_0) = esk6_0,
inference(cn,[status(thm)],[158,theory(equality)]) ).
cnf(302,negated_conjecture,
( app(app(X3,cons(X1,nil)),X2) != esk5_0
| app(app(X2,cons(X1,nil)),X3) != esk6_0
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[123,112,theory(equality)]),122,theory(equality)]) ).
cnf(303,negated_conjecture,
( app(app(X3,cons(X1,nil)),X2) != esk5_0
| app(app(X2,cons(X1,nil)),X3) != esk6_0
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[302,theory(equality)]) ).
cnf(304,negated_conjecture,
( app(esk5_0,X1) != esk5_0
| app(app(X1,cons(esk9_0,nil)),esk10_0) != esk6_0
| ~ ssList(esk10_0)
| ~ ssList(X1)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[303,150,theory(equality)]) ).
cnf(310,negated_conjecture,
( app(esk5_0,X1) != esk5_0
| app(app(X1,cons(esk9_0,nil)),esk10_0) != esk6_0
| $false
| ~ ssList(X1)
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[304,134,theory(equality)]) ).
cnf(311,negated_conjecture,
( app(esk5_0,X1) != esk5_0
| app(app(X1,cons(esk9_0,nil)),esk10_0) != esk6_0
| $false
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[310,132,theory(equality)]) ).
cnf(312,negated_conjecture,
( app(esk5_0,X1) != esk5_0
| app(app(X1,cons(esk9_0,nil)),esk10_0) != esk6_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[311,theory(equality)]) ).
cnf(401,negated_conjecture,
( app(app(nil,cons(esk9_0,nil)),esk10_0) != esk6_0
| ~ ssList(nil)
| ~ ssList(esk5_0) ),
inference(spm,[status(thm)],[312,41,theory(equality)]) ).
cnf(402,negated_conjecture,
( app(app(nil,cons(esk9_0,nil)),esk10_0) != esk6_0
| $false
| ~ ssList(esk5_0) ),
inference(rw,[status(thm)],[401,74,theory(equality)]) ).
cnf(403,negated_conjecture,
( app(app(nil,cons(esk9_0,nil)),esk10_0) != esk6_0
| $false
| $false ),
inference(rw,[status(thm)],[402,107,theory(equality)]) ).
cnf(404,negated_conjecture,
app(app(nil,cons(esk9_0,nil)),esk10_0) != esk6_0,
inference(cn,[status(thm)],[403,theory(equality)]) ).
cnf(405,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) != esk6_0
| ~ ssList(cons(esk9_0,nil)) ),
inference(spm,[status(thm)],[404,83,theory(equality)]) ).
cnf(407,negated_conjecture,
( $false
| ~ ssList(cons(esk9_0,nil)) ),
inference(rw,[status(thm)],[405,159,theory(equality)]) ).
cnf(408,negated_conjecture,
~ ssList(cons(esk9_0,nil)),
inference(cn,[status(thm)],[407,theory(equality)]) ).
cnf(413,negated_conjecture,
( ~ ssList(nil)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[408,73,theory(equality)]) ).
cnf(414,negated_conjecture,
( $false
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[413,74,theory(equality)]) ).
cnf(415,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[414,132,theory(equality)]) ).
cnf(416,negated_conjecture,
$false,
inference(cn,[status(thm)],[415,theory(equality)]) ).
cnf(417,negated_conjecture,
$false,
416,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC417+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpoMmMex/sel_SWC417+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC417+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC417+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC417+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
%
%------------------------------------------------------------------------------