TSTP Solution File: SWC373+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC373+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 11:39:58 EST 2010
% Result : Theorem 0.32s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 7
% Syntax : Number of formulae : 83 ( 20 unt; 0 def)
% Number of atoms : 334 ( 61 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 414 ( 163 ~; 178 |; 49 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 69 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpHYWpAd/sel_SWC373+1.p_1',ax84) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpHYWpAd/sel_SWC373+1.p_1',ax6) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpHYWpAd/sel_SWC373+1.p_1',ax7) ).
fof(21,axiom,
ssList(nil),
file('/tmp/tmpHYWpAd/sel_SWC373+1.p_1',ax17) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/tmp/tmpHYWpAd/sel_SWC373+1.p_1',ax50) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/tmp/tmpHYWpAd/sel_SWC373+1.p_1',ax51) ).
fof(31,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ rearsegP(X4,X3)
| segmentP(X2,X1) ) ) ) ) ),
file('/tmp/tmpHYWpAd/sel_SWC373+1.p_1',co1) ).
fof(32,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ rearsegP(X4,X3)
| segmentP(X2,X1) ) ) ) ) ),
inference(assume_negation,[status(cth)],[31]) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ rearsegP(X4,X3)
| segmentP(X2,X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[32,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(35,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(90,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ rearsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X3,X2) != X1 )
| rearsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(91,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X6,X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[91]) ).
fof(93,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5) )
& ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[92]) ).
fof(94,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk5_2(X4,X5))
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(esk5_2(X4,X5),X5) = X4
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[93]) ).
cnf(95,plain,
( app(esk5_2(X1,X2),X2) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[94]) ).
cnf(96,plain,
( ssList(esk5_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(98,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(app(X3,X2),X4) != X1 ) )
| segmentP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(99,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,X6),X8) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk6_2(X5,X6))
& ssList(esk7_2(X5,X6))
& app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk6_2(X5,X6))
& ssList(esk7_2(X5,X6))
& app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk7_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(106,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(130,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[21]) ).
fof(131,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ rearsegP(X1,X2)
| rearsegP(app(X3,X1),X2) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(132,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ rearsegP(X4,X5)
| rearsegP(app(X6,X4),X5) ) ) ),
inference(variable_rename,[status(thm)],[131]) ).
fof(133,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ rearsegP(X4,X5)
| rearsegP(app(X6,X4),X5)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[132]) ).
cnf(134,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[133]) ).
fof(135,plain,
! [X1] :
( ~ ssList(X1)
| rearsegP(X1,nil) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(136,plain,
! [X2] :
( ~ ssList(X2)
| rearsegP(X2,nil) ),
inference(variable_rename,[status(thm)],[135]) ).
cnf(137,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(165,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& rearsegP(X4,X3)
& ~ segmentP(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(166,negated_conjecture,
? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& X6 = X8
& X5 = X7
& rearsegP(X8,X7)
& ~ segmentP(X6,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& rearsegP(esk11_0,esk10_0)
& ~ segmentP(esk9_0,esk8_0) ),
inference(skolemize,[status(esa)],[166]) ).
cnf(168,negated_conjecture,
~ segmentP(esk9_0,esk8_0),
inference(split_conjunct,[status(thm)],[167]) ).
cnf(169,negated_conjecture,
rearsegP(esk11_0,esk10_0),
inference(split_conjunct,[status(thm)],[167]) ).
cnf(170,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[167]) ).
cnf(171,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[167]) ).
cnf(172,negated_conjecture,
ssList(esk11_0),
inference(split_conjunct,[status(thm)],[167]) ).
cnf(175,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[167]) ).
cnf(179,negated_conjecture,
rearsegP(esk11_0,esk8_0),
inference(rw,[status(thm)],[169,170,theory(equality)]) ).
cnf(180,negated_conjecture,
~ segmentP(esk11_0,esk8_0),
inference(rw,[status(thm)],[168,171,theory(equality)]) ).
cnf(206,negated_conjecture,
( ssList(esk5_2(esk11_0,esk8_0))
| ~ ssList(esk8_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[96,179,theory(equality)]) ).
cnf(209,negated_conjecture,
( ssList(esk5_2(esk11_0,esk8_0))
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[206,175,theory(equality)]) ).
cnf(210,negated_conjecture,
( ssList(esk5_2(esk11_0,esk8_0))
| $false
| $false ),
inference(rw,[status(thm)],[209,172,theory(equality)]) ).
cnf(211,negated_conjecture,
ssList(esk5_2(esk11_0,esk8_0)),
inference(cn,[status(thm)],[210,theory(equality)]) ).
cnf(254,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[134,137,theory(equality)]) ).
cnf(258,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[254,130,theory(equality)]) ).
cnf(259,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[258,theory(equality)]) ).
cnf(260,negated_conjecture,
( app(esk5_2(esk11_0,esk8_0),esk8_0) = esk11_0
| ~ ssList(esk8_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[95,179,theory(equality)]) ).
cnf(263,negated_conjecture,
( app(esk5_2(esk11_0,esk8_0),esk8_0) = esk11_0
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[260,175,theory(equality)]) ).
cnf(264,negated_conjecture,
( app(esk5_2(esk11_0,esk8_0),esk8_0) = esk11_0
| $false
| $false ),
inference(rw,[status(thm)],[263,172,theory(equality)]) ).
cnf(265,negated_conjecture,
app(esk5_2(esk11_0,esk8_0),esk8_0) = esk11_0,
inference(cn,[status(thm)],[264,theory(equality)]) ).
cnf(471,negated_conjecture,
( segmentP(X1,esk8_0)
| app(esk11_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(esk5_2(esk11_0,esk8_0))
| ~ ssList(esk8_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[106,265,theory(equality)]) ).
cnf(499,negated_conjecture,
( segmentP(X1,esk8_0)
| app(esk11_0,X2) != X1
| ~ ssList(X2)
| $false
| ~ ssList(esk8_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[471,211,theory(equality)]) ).
cnf(500,negated_conjecture,
( segmentP(X1,esk8_0)
| app(esk11_0,X2) != X1
| ~ ssList(X2)
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[499,175,theory(equality)]) ).
cnf(501,negated_conjecture,
( segmentP(X1,esk8_0)
| app(esk11_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[500,theory(equality)]) ).
cnf(743,negated_conjecture,
( rearsegP(esk11_0,nil)
| ~ ssList(esk5_2(esk11_0,esk8_0))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[259,265,theory(equality)]) ).
cnf(756,negated_conjecture,
( rearsegP(esk11_0,nil)
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[743,211,theory(equality)]) ).
cnf(757,negated_conjecture,
( rearsegP(esk11_0,nil)
| $false
| $false ),
inference(rw,[status(thm)],[756,175,theory(equality)]) ).
cnf(758,negated_conjecture,
rearsegP(esk11_0,nil),
inference(cn,[status(thm)],[757,theory(equality)]) ).
cnf(774,negated_conjecture,
( ssList(esk5_2(esk11_0,nil))
| ~ ssList(nil)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[96,758,theory(equality)]) ).
cnf(777,negated_conjecture,
( app(esk5_2(esk11_0,nil),nil) = esk11_0
| ~ ssList(nil)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[95,758,theory(equality)]) ).
cnf(781,negated_conjecture,
( ssList(esk5_2(esk11_0,nil))
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[774,130,theory(equality)]) ).
cnf(782,negated_conjecture,
( ssList(esk5_2(esk11_0,nil))
| $false
| $false ),
inference(rw,[status(thm)],[781,172,theory(equality)]) ).
cnf(783,negated_conjecture,
ssList(esk5_2(esk11_0,nil)),
inference(cn,[status(thm)],[782,theory(equality)]) ).
cnf(790,negated_conjecture,
( app(esk5_2(esk11_0,nil),nil) = esk11_0
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[777,130,theory(equality)]) ).
cnf(791,negated_conjecture,
( app(esk5_2(esk11_0,nil),nil) = esk11_0
| $false
| $false ),
inference(rw,[status(thm)],[790,172,theory(equality)]) ).
cnf(792,negated_conjecture,
app(esk5_2(esk11_0,nil),nil) = esk11_0,
inference(cn,[status(thm)],[791,theory(equality)]) ).
cnf(947,negated_conjecture,
( esk11_0 = esk5_2(esk11_0,nil)
| ~ ssList(esk5_2(esk11_0,nil)) ),
inference(spm,[status(thm)],[36,792,theory(equality)]) ).
cnf(964,negated_conjecture,
( esk11_0 = esk5_2(esk11_0,nil)
| $false ),
inference(rw,[status(thm)],[947,783,theory(equality)]) ).
cnf(965,negated_conjecture,
esk11_0 = esk5_2(esk11_0,nil),
inference(cn,[status(thm)],[964,theory(equality)]) ).
cnf(1019,negated_conjecture,
app(esk11_0,nil) = esk11_0,
inference(rw,[status(thm)],[792,965,theory(equality)]) ).
cnf(1625,negated_conjecture,
( segmentP(X1,esk8_0)
| esk11_0 != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[501,1019,theory(equality)]) ).
cnf(1627,negated_conjecture,
( segmentP(X1,esk8_0)
| esk11_0 != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1625,130,theory(equality)]) ).
cnf(1628,negated_conjecture,
( segmentP(X1,esk8_0)
| esk11_0 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1627,theory(equality)]) ).
cnf(1632,negated_conjecture,
( segmentP(esk11_0,esk8_0)
| ~ ssList(esk11_0) ),
inference(er,[status(thm)],[1628,theory(equality)]) ).
cnf(1633,negated_conjecture,
( segmentP(esk11_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[1632,172,theory(equality)]) ).
cnf(1634,negated_conjecture,
segmentP(esk11_0,esk8_0),
inference(cn,[status(thm)],[1633,theory(equality)]) ).
cnf(1635,negated_conjecture,
$false,
inference(sr,[status(thm)],[1634,180,theory(equality)]) ).
cnf(1636,negated_conjecture,
$false,
1635,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC373+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpHYWpAd/sel_SWC373+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC373+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC373+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC373+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
%
%------------------------------------------------------------------------------