%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC323+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 11:28:19 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 84 ( 16 unt; 0 def)
% Number of atoms : 330 ( 144 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 390 ( 144 ~; 158 |; 69 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 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 : 77 ( 0 sgn 46 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpAvY1RQ/sel_SWC323+1.p_1',ax84) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpAvY1RQ/sel_SWC323+1.p_1',ax15) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpAvY1RQ/sel_SWC323+1.p_1',ax16) ).
fof(12,axiom,
ssList(nil),
file('/tmp/tmpAvY1RQ/sel_SWC323+1.p_1',ax17) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpAvY1RQ/sel_SWC323+1.p_1',ax28) ).
fof(19,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(X5,X6) = X2
& app(X6,X5) = X1 ) )
| ( nil != X3
& nil = X4 )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(cons(X7,nil),X8) != X4
| app(X8,cons(X7,nil)) != X3 ) ) )
& neq(X4,nil) ) ) ) ) ) ),
file('/tmp/tmpAvY1RQ/sel_SWC323+1.p_1',co1) ).
fof(20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(X5,X6) = X2
& app(X6,X5) = X1 ) )
| ( nil != X3
& nil = X4 )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(cons(X7,nil),X8) != X4
| app(X8,cons(X7,nil)) != X3 ) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(38,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(39,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(63,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(64,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[64]) ).
fof(66,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)],[65]) ).
cnf(67,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(70,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(72,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(73,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[12]) ).
fof(80,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(81,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[80]) ).
cnf(82,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(101,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != X2
| app(X6,X5) != X1 ) )
& ( nil = X3
| nil != X4 )
& ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X4
& app(X8,cons(X7,nil)) = X3 ) )
| ~ neq(X4,nil) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(102,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& ! [X13] :
( ~ ssList(X13)
| ! [X14] :
( ~ ssList(X14)
| app(X13,X14) != X10
| app(X14,X13) != X9 ) )
& ( nil = X11
| nil != X12 )
& ( ? [X15] :
( ssItem(X15)
& ? [X16] :
( ssList(X16)
& app(cons(X15,nil),X16) = X12
& app(X16,cons(X15,nil)) = X11 ) )
| ~ neq(X12,nil) ) ) ) ) ),
inference(variable_rename,[status(thm)],[101]) ).
fof(103,negated_conjecture,
( ssList(esk5_0)
& ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ! [X13] :
( ~ ssList(X13)
| ! [X14] :
( ~ ssList(X14)
| app(X13,X14) != esk6_0
| app(X14,X13) != esk5_0 ) )
& ( nil = esk7_0
| nil != esk8_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(esk8_0,nil) ) ),
inference(skolemize,[status(esa)],[102]) ).
fof(104,negated_conjecture,
! [X13,X14] :
( ( ~ ssList(X14)
| app(X13,X14) != esk6_0
| app(X14,X13) != esk5_0
| ~ ssList(X13) )
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_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(esk8_0,nil) )
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0) ),
inference(shift_quantors,[status(thm)],[103]) ).
fof(105,negated_conjecture,
! [X13,X14] :
( ( ~ ssList(X14)
| app(X13,X14) != esk6_0
| app(X14,X13) != esk5_0
| ~ ssList(X13) )
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_0 )
& ( ssItem(esk9_0)
| ~ neq(esk8_0,nil) )
& ( ssList(esk10_0)
| ~ neq(esk8_0,nil) )
& ( app(cons(esk9_0,nil),esk10_0) = esk8_0
| ~ neq(esk8_0,nil) )
& ( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| ~ neq(esk8_0,nil) )
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0) ),
inference(distribute,[status(thm)],[104]) ).
cnf(106,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(107,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(110,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(111,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(112,negated_conjecture,
( ssList(esk10_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(113,negated_conjecture,
( ssItem(esk9_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(114,negated_conjecture,
( nil = esk7_0
| nil != esk8_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(115,negated_conjecture,
esk5_0 = esk7_0,
inference(split_conjunct,[status(thm)],[105]) ).
cnf(116,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[105]) ).
cnf(117,negated_conjecture,
( ~ ssList(X1)
| app(X2,X1) != esk5_0
| app(X1,X2) != esk6_0
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(118,negated_conjecture,
ssList(esk7_0),
inference(rw,[status(thm)],[106,115,theory(equality)]) ).
cnf(119,negated_conjecture,
ssList(esk8_0),
inference(rw,[status(thm)],[107,116,theory(equality)]) ).
cnf(130,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[113,67,theory(equality)]) ).
cnf(131,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[112,67,theory(equality)]) ).
cnf(132,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[110,67,theory(equality)]) ).
cnf(133,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[111,67,theory(equality)]) ).
cnf(134,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[130,73,theory(equality)]) ).
cnf(135,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[134,theory(equality)]) ).
cnf(136,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[131,73,theory(equality)]) ).
cnf(137,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[136,theory(equality)]) ).
cnf(138,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[132,73,theory(equality)]) ).
cnf(139,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[138,theory(equality)]) ).
cnf(140,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[133,73,theory(equality)]) ).
cnf(141,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[140,theory(equality)]) ).
cnf(153,negated_conjecture,
( app(X2,X1) != esk7_0
| app(X1,X2) != esk6_0
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[117,115,theory(equality)]) ).
cnf(154,negated_conjecture,
( app(X2,X1) != esk7_0
| app(X1,X2) != esk8_0
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[153,116,theory(equality)]) ).
cnf(155,negated_conjecture,
( X1 != esk7_0
| app(nil,X1) != esk8_0
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[154,40,theory(equality)]) ).
cnf(157,negated_conjecture,
( X1 != esk7_0
| app(nil,X1) != esk8_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[155,73,theory(equality)]) ).
cnf(158,negated_conjecture,
( X1 != esk7_0
| app(nil,X1) != esk8_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[157,theory(equality)]) ).
cnf(243,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[135,119,theory(equality)]) ).
cnf(244,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil ),
inference(cn,[status(thm)],[243,theory(equality)]) ).
cnf(249,negated_conjecture,
( app(nil,esk7_0) != esk8_0
| ~ ssList(esk7_0) ),
inference(er,[status(thm)],[158,theory(equality)]) ).
cnf(250,negated_conjecture,
( app(nil,esk7_0) != esk8_0
| $false ),
inference(rw,[status(thm)],[249,118,theory(equality)]) ).
cnf(251,negated_conjecture,
app(nil,esk7_0) != esk8_0,
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(252,negated_conjecture,
( esk7_0 != esk8_0
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[251,82,theory(equality)]) ).
cnf(253,negated_conjecture,
( esk7_0 != esk8_0
| $false ),
inference(rw,[status(thm)],[252,118,theory(equality)]) ).
cnf(254,negated_conjecture,
esk7_0 != esk8_0,
inference(cn,[status(thm)],[253,theory(equality)]) ).
cnf(258,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[137,119,theory(equality)]) ).
cnf(259,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil ),
inference(cn,[status(thm)],[258,theory(equality)]) ).
cnf(262,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[139,119,theory(equality)]) ).
cnf(263,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| esk8_0 = nil ),
inference(cn,[status(thm)],[262,theory(equality)]) ).
cnf(267,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) != esk8_0
| ~ ssList(esk10_0)
| ~ ssList(cons(esk9_0,nil)) ),
inference(spm,[status(thm)],[154,263,theory(equality)]) ).
cnf(280,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) != esk8_0
| ~ ssList(cons(esk9_0,nil)) ),
inference(csr,[status(thm)],[267,259]) ).
cnf(281,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) != esk8_0
| ~ ssList(nil)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[280,72,theory(equality)]) ).
cnf(282,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) != esk8_0
| $false
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[281,73,theory(equality)]) ).
cnf(283,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) != esk8_0
| ~ ssItem(esk9_0) ),
inference(cn,[status(thm)],[282,theory(equality)]) ).
cnf(284,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) != esk8_0 ),
inference(csr,[status(thm)],[283,244]) ).
cnf(289,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[141,119,theory(equality)]) ).
cnf(290,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| esk8_0 = nil ),
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(291,negated_conjecture,
esk8_0 = nil,
inference(csr,[status(thm)],[290,284]) ).
cnf(297,negated_conjecture,
esk7_0 != nil,
inference(rw,[status(thm)],[254,291,theory(equality)]) ).
cnf(313,negated_conjecture,
( esk7_0 = nil
| $false ),
inference(rw,[status(thm)],[114,291,theory(equality)]) ).
cnf(314,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[313,theory(equality)]) ).
cnf(321,negated_conjecture,
$false,
inference(rw,[status(thm)],[297,314,theory(equality)]) ).
cnf(322,negated_conjecture,
$false,
inference(cn,[status(thm)],[321,theory(equality)]) ).
cnf(323,negated_conjecture,
$false,
322,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC323+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpAvY1RQ/sel_SWC323+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC323+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC323+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC323+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
%
%------------------------------------------------------------------------------