TSTP Solution File: SWC046+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC046+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 10:08:45 EST 2010
% Result : Theorem 0.36s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 14 unt; 0 def)
% Number of atoms : 343 ( 89 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 440 ( 158 ~; 163 |; 97 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 59 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpv_BcCU/sel_SWC046+1.p_1',ax28) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpv_BcCU/sel_SWC046+1.p_1',ax20) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/tmp/tmpv_BcCU/sel_SWC046+1.p_1',ax3) ).
fof(19,axiom,
ssList(nil),
file('/tmp/tmpv_BcCU/sel_SWC046+1.p_1',ax17) ).
fof(22,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpv_BcCU/sel_SWC046+1.p_1',ax38) ).
fof(28,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X4,X5) )
| ( memberP(X3,X5)
& ( ~ memberP(X4,X5)
| ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) ) ) ) ) ) ) ) ) ),
file('/tmp/tmpv_BcCU/sel_SWC046+1.p_1',co1) ).
fof(29,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X4,X5) )
| ( memberP(X3,X5)
& ( ~ memberP(X4,X5)
| ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[28]) ).
fof(30,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[22,theory(equality)]) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X4,X5) )
| ( memberP(X3,X5)
& ( ~ memberP(X4,X5)
| ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[29,theory(equality)]) ).
fof(54,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(55,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[54]) ).
cnf(56,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(70,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk1_1(X4))
& ssItem(esk2_1(X4))
& cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[70]) ).
fof(72,plain,
! [X4] :
( ( ssList(esk1_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk2_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk2_1(X4),esk1_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[71]) ).
cnf(73,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(75,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(81,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ( ( ~ memberP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(X3,cons(X2,X4)) != X1 ) )
| memberP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(82,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssItem(X6)
| ( ( ~ memberP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(X7,cons(X6,X8)) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5 ) )
| memberP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[81]) ).
fof(83,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssItem(X6)
| ( ( ~ memberP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5 ) )
| memberP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[82]) ).
fof(84,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5
| ~ ssList(X9)
| memberP(X5,X6) )
& ( ~ memberP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5 ) ) )
| ~ ssItem(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[83]) ).
fof(85,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5
| ~ ssList(X9)
| memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( ssList(esk5_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[84]) ).
cnf(89,plain,
( memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(X3,cons(X2,X4)) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(119,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[19]) ).
fof(134,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(135,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[134]) ).
cnf(136,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(158,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& nil = X2
& X2 = X4
& X1 = X3
& nil != X1
& ! [X5] :
( ~ ssItem(X5)
| ( ( memberP(X3,X5)
| ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
| ~ memberP(X4,X5) )
& ( ~ memberP(X3,X5)
| ( memberP(X4,X5)
& ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) ) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(159,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& nil = X8
& X8 = X10
& X7 = X9
& nil != X7
& ! [X11] :
( ~ ssItem(X11)
| ( ( memberP(X9,X11)
| ? [X12] :
( ssList(X12)
& segmentP(X10,app(app(cons(X11,nil),X12),cons(X11,nil))) )
| ~ memberP(X10,X11) )
& ( ~ memberP(X9,X11)
| ( memberP(X10,X11)
& ! [X13] :
( ~ ssList(X13)
| ~ segmentP(X10,app(app(cons(X11,nil),X13),cons(X11,nil))) ) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[158]) ).
fof(160,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& nil = esk10_0
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& nil != esk9_0
& ! [X11] :
( ~ ssItem(X11)
| ( ( memberP(esk11_0,X11)
| ( ssList(esk13_1(X11))
& segmentP(esk12_0,app(app(cons(X11,nil),esk13_1(X11)),cons(X11,nil))) )
| ~ memberP(esk12_0,X11) )
& ( ~ memberP(esk11_0,X11)
| ( memberP(esk12_0,X11)
& ! [X13] :
( ~ ssList(X13)
| ~ segmentP(esk12_0,app(app(cons(X11,nil),X13),cons(X11,nil))) ) ) ) ) ) ),
inference(skolemize,[status(esa)],[159]) ).
fof(161,negated_conjecture,
! [X11,X13] :
( ( ( ( ( ( ~ ssList(X13)
| ~ segmentP(esk12_0,app(app(cons(X11,nil),X13),cons(X11,nil))) )
& memberP(esk12_0,X11) )
| ~ memberP(esk11_0,X11) )
& ( memberP(esk11_0,X11)
| ( ssList(esk13_1(X11))
& segmentP(esk12_0,app(app(cons(X11,nil),esk13_1(X11)),cons(X11,nil))) )
| ~ memberP(esk12_0,X11) ) )
| ~ ssItem(X11) )
& nil = esk10_0
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& nil != esk9_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(shift_quantors,[status(thm)],[160]) ).
fof(162,negated_conjecture,
! [X11,X13] :
( ( ~ ssList(X13)
| ~ segmentP(esk12_0,app(app(cons(X11,nil),X13),cons(X11,nil)))
| ~ memberP(esk11_0,X11)
| ~ ssItem(X11) )
& ( memberP(esk12_0,X11)
| ~ memberP(esk11_0,X11)
| ~ ssItem(X11) )
& ( ssList(esk13_1(X11))
| memberP(esk11_0,X11)
| ~ memberP(esk12_0,X11)
| ~ ssItem(X11) )
& ( segmentP(esk12_0,app(app(cons(X11,nil),esk13_1(X11)),cons(X11,nil)))
| memberP(esk11_0,X11)
| ~ memberP(esk12_0,X11)
| ~ ssItem(X11) )
& nil = esk10_0
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& nil != esk9_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(distribute,[status(thm)],[161]) ).
cnf(163,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(167,negated_conjecture,
nil != esk9_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(168,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(169,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(170,negated_conjecture,
nil = esk10_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(173,negated_conjecture,
( memberP(esk12_0,X1)
| ~ ssItem(X1)
| ~ memberP(esk11_0,X1) ),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(177,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[163,168,theory(equality)]) ).
cnf(178,negated_conjecture,
esk12_0 = nil,
inference(rw,[status(thm)],[169,170,theory(equality)]) ).
cnf(181,negated_conjecture,
esk11_0 != nil,
inference(rw,[status(thm)],[167,168,theory(equality)]) ).
cnf(185,negated_conjecture,
( memberP(nil,X1)
| ~ ssItem(X1)
| ~ memberP(esk11_0,X1) ),
inference(rw,[status(thm)],[173,178,theory(equality)]) ).
cnf(186,negated_conjecture,
( ~ memberP(esk11_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[185,136]) ).
cnf(274,plain,
( memberP(X1,esk2_1(X2))
| nil = X2
| app(X3,X2) != X1
| ~ ssItem(esk2_1(X2))
| ~ ssList(esk1_1(X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[89,73,theory(equality)]) ).
cnf(1652,plain,
( nil = X2
| memberP(X1,esk2_1(X2))
| app(X3,X2) != X1
| ~ ssItem(esk2_1(X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[274,75]) ).
cnf(1653,plain,
( nil = X2
| memberP(X1,esk2_1(X2))
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[1652,74]) ).
cnf(1655,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1653,56,theory(equality)]) ).
cnf(1661,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1655,119,theory(equality)]) ).
cnf(1662,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1661,theory(equality)]) ).
cnf(1663,plain,
( nil = X1
| memberP(X1,esk2_1(X1))
| ~ ssList(X1) ),
inference(er,[status(thm)],[1662,theory(equality)]) ).
cnf(1674,negated_conjecture,
( nil = esk11_0
| ~ ssItem(esk2_1(esk11_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[186,1663,theory(equality)]) ).
cnf(1685,negated_conjecture,
( nil = esk11_0
| ~ ssItem(esk2_1(esk11_0))
| $false ),
inference(rw,[status(thm)],[1674,177,theory(equality)]) ).
cnf(1686,negated_conjecture,
( nil = esk11_0
| ~ ssItem(esk2_1(esk11_0)) ),
inference(cn,[status(thm)],[1685,theory(equality)]) ).
cnf(1687,negated_conjecture,
~ ssItem(esk2_1(esk11_0)),
inference(sr,[status(thm)],[1686,181,theory(equality)]) ).
cnf(1688,negated_conjecture,
( nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1687,74,theory(equality)]) ).
cnf(1689,negated_conjecture,
( nil = esk11_0
| $false ),
inference(rw,[status(thm)],[1688,177,theory(equality)]) ).
cnf(1690,negated_conjecture,
nil = esk11_0,
inference(cn,[status(thm)],[1689,theory(equality)]) ).
cnf(1691,negated_conjecture,
$false,
inference(sr,[status(thm)],[1690,181,theory(equality)]) ).
cnf(1692,negated_conjecture,
$false,
1691,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC046+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpv_BcCU/sel_SWC046+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC046+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC046+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC046+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
%
%------------------------------------------------------------------------------