TSTP Solution File: SWC204+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC204+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 10:51:01 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 15 unt; 0 def)
% Number of atoms : 375 ( 146 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 482 ( 186 ~; 203 |; 69 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 52 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax28) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax24) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax22) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax78) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax15) ).
fof(26,axiom,
ssList(nil),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax17) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax18) ).
fof(29,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| neq(X1,nil) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',co1) ).
fof(30,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| neq(X1,nil) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[29]) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| neq(X1,nil) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).
fof(62,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(63,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[62]) ).
cnf(64,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(70,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssList(tl(X2)) ),
inference(variable_rename,[status(thm)],[69]) ).
cnf(71,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(95,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(96,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[95]) ).
cnf(97,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(125,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(126,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| cons(hd(X2),tl(X2)) = X2 ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(127,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[126]) ).
fof(132,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(133,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[132]) ).
fof(134,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[133]) ).
fof(135,plain,
! [X3,X4] :
( ( ~ neq(X3,X4)
| X3 != X4
| ~ ssList(X4)
| ~ ssList(X3) )
& ( X3 = X4
| neq(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[134]) ).
cnf(136,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(142,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[26]) ).
fof(143,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) != X1 ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(144,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3 ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[144]) ).
cnf(146,plain,
( ~ ssList(X1)
| cons(X2,X1) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(153,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| X4 = X5
| ! [X6] :
( ~ ssList(X6)
| tl(X4) != X6
| app(X3,X6) != X5
| ~ neq(nil,X4) ) )
& ~ neq(X1,nil) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(154,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( ( neq(X8,nil)
& ! [X11] :
( ~ ssList(X11)
| X10 = X11
| ! [X12] :
( ~ ssList(X12)
| tl(X10) != X12
| app(X9,X12) != X11
| ~ neq(nil,X10) ) )
& ~ neq(X7,nil) )
| ( neq(X8,nil)
& ~ neq(X10,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[153]) ).
fof(155,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( ( neq(esk8_0,nil)
& ! [X11] :
( ~ ssList(X11)
| esk10_0 = X11
| ! [X12] :
( ~ ssList(X12)
| tl(esk10_0) != X12
| app(esk9_0,X12) != X11
| ~ neq(nil,esk10_0) ) )
& ~ neq(esk7_0,nil) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) ) ),
inference(skolemize,[status(esa)],[154]) ).
fof(156,negated_conjecture,
! [X11,X12] :
( ( ( ( ~ ssList(X12)
| tl(esk10_0) != X12
| app(esk9_0,X12) != X11
| ~ neq(nil,esk10_0)
| ~ ssList(X11)
| esk10_0 = X11 )
& neq(esk8_0,nil)
& ~ neq(esk7_0,nil) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[155]) ).
fof(157,negated_conjecture,
! [X11,X12] :
( ( neq(esk8_0,nil)
| ~ ssList(X12)
| tl(esk10_0) != X12
| app(esk9_0,X12) != X11
| ~ neq(nil,esk10_0)
| ~ ssList(X11)
| esk10_0 = X11 )
& ( ~ neq(esk10_0,nil)
| ~ ssList(X12)
| tl(esk10_0) != X12
| app(esk9_0,X12) != X11
| ~ neq(nil,esk10_0)
| ~ ssList(X11)
| esk10_0 = X11 )
& ( neq(esk8_0,nil)
| neq(esk8_0,nil) )
& ( ~ neq(esk10_0,nil)
| neq(esk8_0,nil) )
& ( neq(esk8_0,nil)
| ~ neq(esk7_0,nil) )
& ( ~ neq(esk10_0,nil)
| ~ neq(esk7_0,nil) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[156]) ).
cnf(158,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(162,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[157]) ).
cnf(163,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[157]) ).
cnf(164,negated_conjecture,
( ~ neq(esk7_0,nil)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(167,negated_conjecture,
( neq(esk8_0,nil)
| neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(168,negated_conjecture,
( esk10_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| app(esk9_0,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(172,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[159,163,theory(equality)]) ).
cnf(173,negated_conjecture,
neq(esk10_0,nil),
inference(rw,[status(thm)],[167,163,theory(equality)]) ).
cnf(178,negated_conjecture,
( ~ neq(esk7_0,nil)
| $false ),
inference(rw,[status(thm)],[164,173,theory(equality)]) ).
cnf(179,negated_conjecture,
~ neq(esk7_0,nil),
inference(cn,[status(thm)],[178,theory(equality)]) ).
cnf(187,negated_conjecture,
( esk7_0 = nil
| ~ ssList(nil)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[179,136,theory(equality)]) ).
cnf(188,negated_conjecture,
( esk7_0 = nil
| $false
| ~ ssList(esk7_0) ),
inference(rw,[status(thm)],[187,142,theory(equality)]) ).
cnf(189,negated_conjecture,
( esk7_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[188,158,theory(equality)]) ).
cnf(190,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[189,theory(equality)]) ).
cnf(213,plain,
( nil = X1
| X1 != tl(X1)
| ~ ssItem(hd(X1))
| ~ ssList(tl(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[146,127,theory(equality)]) ).
cnf(244,negated_conjecture,
( esk10_0 = X1
| tl(esk10_0) != X2
| app(esk7_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[168,162,theory(equality)]) ).
cnf(245,negated_conjecture,
( esk10_0 = X1
| tl(esk10_0) != X2
| app(esk7_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| $false ),
inference(rw,[status(thm)],[244,173,theory(equality)]) ).
cnf(246,negated_conjecture,
( esk10_0 = X1
| tl(esk10_0) != X2
| app(esk7_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk10_0) ),
inference(cn,[status(thm)],[245,theory(equality)]) ).
cnf(325,negated_conjecture,
~ neq(nil,nil),
inference(rw,[status(thm)],[179,190,theory(equality)]) ).
cnf(326,negated_conjecture,
( esk10_0 = X1
| app(nil,X2) != X1
| tl(esk10_0) != X2
| ~ neq(nil,esk10_0)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[246,190,theory(equality)]) ).
cnf(335,plain,
( nil = X1
| tl(X1) != X1
| ~ ssItem(hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[213,71]) ).
cnf(336,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[335,97]) ).
cnf(366,negated_conjecture,
( esk10_0 = X1
| nil = esk10_0
| app(nil,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk10_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[326,136,theory(equality)]) ).
cnf(368,negated_conjecture,
( esk10_0 = X1
| nil = esk10_0
| app(nil,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[366,172,theory(equality)]) ).
cnf(369,negated_conjecture,
( esk10_0 = X1
| nil = esk10_0
| app(nil,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| $false
| $false ),
inference(rw,[status(thm)],[368,142,theory(equality)]) ).
cnf(370,negated_conjecture,
( esk10_0 = X1
| nil = esk10_0
| app(nil,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[369,theory(equality)]) ).
cnf(371,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(nil,tl(esk10_0)) != X1
| ~ ssList(tl(esk10_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[370,theory(equality)]) ).
cnf(372,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(nil,tl(esk10_0)) != X1
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[371,71,theory(equality)]) ).
cnf(373,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(nil,tl(esk10_0)) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[372,172,theory(equality)]) ).
cnf(374,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(nil,tl(esk10_0)) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[373,theory(equality)]) ).
cnf(375,negated_conjecture,
( esk10_0 = nil
| esk10_0 = app(nil,tl(esk10_0))
| ~ ssList(app(nil,tl(esk10_0))) ),
inference(er,[status(thm)],[374,theory(equality)]) ).
cnf(377,negated_conjecture,
( tl(esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0)) ),
inference(spm,[status(thm)],[375,64,theory(equality)]) ).
cnf(381,negated_conjecture,
( tl(esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[377,71,theory(equality)]) ).
cnf(382,negated_conjecture,
( tl(esk10_0) = esk10_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[381,172,theory(equality)]) ).
cnf(383,negated_conjecture,
( tl(esk10_0) = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[382,theory(equality)]) ).
cnf(388,negated_conjecture,
( nil = esk10_0
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[336,383,theory(equality)]) ).
cnf(401,negated_conjecture,
( nil = esk10_0
| $false ),
inference(rw,[status(thm)],[388,172,theory(equality)]) ).
cnf(402,negated_conjecture,
nil = esk10_0,
inference(cn,[status(thm)],[401,theory(equality)]) ).
cnf(405,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[173,402,theory(equality)]) ).
cnf(406,negated_conjecture,
$false,
inference(sr,[status(thm)],[405,325,theory(equality)]) ).
cnf(407,negated_conjecture,
$false,
406,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC204+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpYyV4pP/sel_SWC204+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC204+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC204+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC204+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
%
%------------------------------------------------------------------------------