TSTP Solution File: SWC100+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC100+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 10:17:09 EST 2010
% Result : Theorem 0.32s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 15 unt; 0 def)
% Number of atoms : 417 ( 167 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 564 ( 214 ~; 209 |; 117 &)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 72 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp7OI-fI/sel_SWC100+1.p_1',ax83) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmp7OI-fI/sel_SWC100+1.p_1',ax5) ).
fof(35,axiom,
ssList(nil),
file('/tmp/tmp7OI-fI/sel_SWC100+1.p_1',ax17) ).
fof(40,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmp7OI-fI/sel_SWC100+1.p_1',ax15) ).
fof(44,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& frontsegP(X2,X1) ) ) ) ) ) ) ) ),
file('/tmp/tmp7OI-fI/sel_SWC100+1.p_1',co1) ).
fof(45,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& frontsegP(X2,X1) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[44]) ).
fof(48,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& frontsegP(X2,X1) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[45,theory(equality)]) ).
fof(64,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( nil != app(X1,X2)
| ( nil = X2
& nil = X1 ) )
& ( nil != X2
| nil != X1
| nil = app(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(65,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[65]) ).
fof(67,plain,
! [X3,X4] :
( ( nil = X4
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil = X3
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[66]) ).
cnf(69,plain,
( nil = X1
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(135,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X2,X3) != X1 )
| frontsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(136,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X5,X6) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[135]) ).
fof(137,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(X5,esk5_2(X4,X5)) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[136]) ).
fof(138,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5) )
& ( ~ frontsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(X5,esk5_2(X4,X5)) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[137]) ).
fof(139,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk5_2(X4,X5))
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(X5,esk5_2(X4,X5)) = X4
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[138]) ).
cnf(142,plain,
( frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(197,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[35]) ).
fof(228,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(229,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[228]) ).
fof(230,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[229]) ).
fof(231,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)],[230]) ).
cnf(232,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[231]) ).
cnf(233,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[231]) ).
fof(247,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ? [X5] :
( ssList(X5)
& app(X3,X5) = X4
& strictorderedP(X3)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X5
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(X9,cons(X8,nil)) != X3
| ~ lt(X8,X6) ) ) ) ) )
& ( nil = X4
| nil != X3 )
& ( ( nil = X2
& nil != X1 )
| ( neq(X2,nil)
& ( ~ neq(X1,nil)
| ~ frontsegP(X2,X1) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[48]) ).
fof(248,negated_conjecture,
? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& X11 = X13
& X10 = X12
& ? [X14] :
( ssList(X14)
& app(X12,X14) = X13
& strictorderedP(X12)
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| app(cons(X15,nil),X16) != X14
| ! [X17] :
( ~ ssItem(X17)
| ! [X18] :
( ~ ssList(X18)
| app(X18,cons(X17,nil)) != X12
| ~ lt(X17,X15) ) ) ) ) )
& ( nil = X13
| nil != X12 )
& ( ( nil = X11
& nil != X10 )
| ( neq(X11,nil)
& ( ~ neq(X10,nil)
| ~ frontsegP(X11,X10) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[247]) ).
fof(249,negated_conjecture,
( ssList(esk12_0)
& ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& ssList(esk16_0)
& app(esk14_0,esk16_0) = esk15_0
& strictorderedP(esk14_0)
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| app(cons(X15,nil),X16) != esk16_0
| ! [X17] :
( ~ ssItem(X17)
| ! [X18] :
( ~ ssList(X18)
| app(X18,cons(X17,nil)) != esk14_0
| ~ lt(X17,X15) ) ) ) )
& ( nil = esk15_0
| nil != esk14_0 )
& ( ( nil = esk13_0
& nil != esk12_0 )
| ( neq(esk13_0,nil)
& ( ~ neq(esk12_0,nil)
| ~ frontsegP(esk13_0,esk12_0) ) ) ) ),
inference(skolemize,[status(esa)],[248]) ).
fof(250,negated_conjecture,
! [X15,X16,X17,X18] :
( ( ~ ssList(X18)
| app(X18,cons(X17,nil)) != esk14_0
| ~ lt(X17,X15)
| ~ ssItem(X17)
| ~ ssList(X16)
| app(cons(X15,nil),X16) != esk16_0
| ~ ssItem(X15) )
& app(esk14_0,esk16_0) = esk15_0
& strictorderedP(esk14_0)
& ssList(esk16_0)
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& ( nil = esk15_0
| nil != esk14_0 )
& ( ( nil = esk13_0
& nil != esk12_0 )
| ( neq(esk13_0,nil)
& ( ~ neq(esk12_0,nil)
| ~ frontsegP(esk13_0,esk12_0) ) ) )
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0)
& ssList(esk12_0) ),
inference(shift_quantors,[status(thm)],[249]) ).
fof(251,negated_conjecture,
! [X15,X16,X17,X18] :
( ( ~ ssList(X18)
| app(X18,cons(X17,nil)) != esk14_0
| ~ lt(X17,X15)
| ~ ssItem(X17)
| ~ ssList(X16)
| app(cons(X15,nil),X16) != esk16_0
| ~ ssItem(X15) )
& app(esk14_0,esk16_0) = esk15_0
& strictorderedP(esk14_0)
& ssList(esk16_0)
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& ( nil = esk15_0
| nil != esk14_0 )
& ( neq(esk13_0,nil)
| nil = esk13_0 )
& ( ~ neq(esk12_0,nil)
| ~ frontsegP(esk13_0,esk12_0)
| nil = esk13_0 )
& ( neq(esk13_0,nil)
| nil != esk12_0 )
& ( ~ neq(esk12_0,nil)
| ~ frontsegP(esk13_0,esk12_0)
| nil != esk12_0 )
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0)
& ssList(esk12_0) ),
inference(distribute,[status(thm)],[250]) ).
cnf(252,negated_conjecture,
ssList(esk12_0),
inference(split_conjunct,[status(thm)],[251]) ).
cnf(253,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[251]) ).
cnf(257,negated_conjecture,
( neq(esk13_0,nil)
| nil != esk12_0 ),
inference(split_conjunct,[status(thm)],[251]) ).
cnf(258,negated_conjecture,
( nil = esk13_0
| ~ frontsegP(esk13_0,esk12_0)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[251]) ).
cnf(260,negated_conjecture,
( nil = esk15_0
| nil != esk14_0 ),
inference(split_conjunct,[status(thm)],[251]) ).
cnf(261,negated_conjecture,
esk12_0 = esk14_0,
inference(split_conjunct,[status(thm)],[251]) ).
cnf(262,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[251]) ).
cnf(263,negated_conjecture,
ssList(esk16_0),
inference(split_conjunct,[status(thm)],[251]) ).
cnf(265,negated_conjecture,
app(esk14_0,esk16_0) = esk15_0,
inference(split_conjunct,[status(thm)],[251]) ).
cnf(272,negated_conjecture,
( esk13_0 = nil
| esk14_0 != nil ),
inference(rw,[status(thm)],[260,262,theory(equality)]) ).
cnf(273,negated_conjecture,
( esk13_0 = nil
| esk12_0 != nil ),
inference(rw,[status(thm)],[272,261,theory(equality)]) ).
cnf(276,negated_conjecture,
app(esk12_0,esk16_0) = esk15_0,
inference(rw,[status(thm)],[265,261,theory(equality)]) ).
cnf(277,negated_conjecture,
app(esk12_0,esk16_0) = esk13_0,
inference(rw,[status(thm)],[276,262,theory(equality)]) ).
cnf(278,negated_conjecture,
( neq(nil,nil)
| esk12_0 != nil ),
inference(spm,[status(thm)],[257,273,theory(equality)]) ).
cnf(292,negated_conjecture,
( esk13_0 = nil
| esk12_0 = nil
| ~ frontsegP(esk13_0,esk12_0)
| ~ ssList(nil)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[258,232,theory(equality)]) ).
cnf(293,negated_conjecture,
( esk13_0 = nil
| esk12_0 = nil
| ~ frontsegP(esk13_0,esk12_0)
| $false
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[292,197,theory(equality)]) ).
cnf(294,negated_conjecture,
( esk13_0 = nil
| esk12_0 = nil
| ~ frontsegP(esk13_0,esk12_0)
| $false
| $false ),
inference(rw,[status(thm)],[293,252,theory(equality)]) ).
cnf(295,negated_conjecture,
( esk13_0 = nil
| esk12_0 = nil
| ~ frontsegP(esk13_0,esk12_0) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(314,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[233,theory(equality)]) ).
cnf(322,negated_conjecture,
( nil = esk12_0
| esk13_0 != nil
| ~ ssList(esk16_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[69,277,theory(equality)]) ).
cnf(325,negated_conjecture,
( nil = esk12_0
| esk13_0 != nil
| ~ ssList(esk16_0)
| $false ),
inference(rw,[status(thm)],[322,252,theory(equality)]) ).
cnf(326,negated_conjecture,
( nil = esk12_0
| esk13_0 != nil
| ~ ssList(esk16_0) ),
inference(cn,[status(thm)],[325,theory(equality)]) ).
cnf(348,negated_conjecture,
( frontsegP(X1,esk12_0)
| esk13_0 != X1
| ~ ssList(esk16_0)
| ~ ssList(esk12_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[142,277,theory(equality)]) ).
cnf(353,negated_conjecture,
( frontsegP(X1,esk12_0)
| esk13_0 != X1
| ~ ssList(esk16_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[348,252,theory(equality)]) ).
cnf(354,negated_conjecture,
( frontsegP(X1,esk12_0)
| esk13_0 != X1
| ~ ssList(esk16_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[353,theory(equality)]) ).
cnf(569,negated_conjecture,
( ~ ssList(nil)
| esk12_0 != nil ),
inference(spm,[status(thm)],[314,278,theory(equality)]) ).
cnf(570,negated_conjecture,
( $false
| esk12_0 != nil ),
inference(rw,[status(thm)],[569,197,theory(equality)]) ).
cnf(571,negated_conjecture,
esk12_0 != nil,
inference(cn,[status(thm)],[570,theory(equality)]) ).
cnf(575,negated_conjecture,
( esk13_0 != nil
| ~ ssList(esk16_0) ),
inference(sr,[status(thm)],[326,571,theory(equality)]) ).
cnf(576,negated_conjecture,
esk13_0 != nil,
inference(spm,[status(thm)],[575,263,theory(equality)]) ).
cnf(580,negated_conjecture,
( esk13_0 = nil
| ~ frontsegP(esk13_0,esk12_0) ),
inference(sr,[status(thm)],[295,571,theory(equality)]) ).
cnf(606,negated_conjecture,
( esk13_0 = nil
| ~ ssList(esk16_0)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[580,354,theory(equality)]) ).
cnf(615,negated_conjecture,
( esk13_0 = nil
| ~ ssList(esk16_0)
| $false ),
inference(rw,[status(thm)],[606,253,theory(equality)]) ).
cnf(616,negated_conjecture,
( esk13_0 = nil
| ~ ssList(esk16_0) ),
inference(cn,[status(thm)],[615,theory(equality)]) ).
cnf(617,negated_conjecture,
~ ssList(esk16_0),
inference(sr,[status(thm)],[616,576,theory(equality)]) ).
cnf(630,negated_conjecture,
$false,
inference(sr,[status(thm)],[263,617,theory(equality)]) ).
cnf(631,negated_conjecture,
$false,
630,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC100+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp7OI-fI/sel_SWC100+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC100+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC100+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC100+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
%
%------------------------------------------------------------------------------