TSTP Solution File: SWC104+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC104+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 10:17:30 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 56 ( 17 unt; 0 def)
% Number of atoms : 307 ( 89 equ)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 408 ( 157 ~; 143 |; 87 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 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 : 94 ( 0 sgn 58 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmpt0AdIl/sel_SWC104+1.p_1',ax5) ).
fof(29,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpt0AdIl/sel_SWC104+1.p_1',ax15) ).
fof(31,axiom,
ssList(nil),
file('/tmp/tmpt0AdIl/sel_SWC104+1.p_1',ax17) ).
fof(38,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ totalorderedP(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
& leq(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( neq(X1,nil)
& frontsegP(X2,X1) ) ) ) ) ) ),
file('/tmp/tmpt0AdIl/sel_SWC104+1.p_1',co1) ).
fof(39,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ totalorderedP(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
& leq(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( neq(X1,nil)
& frontsegP(X2,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[38]) ).
fof(40,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ totalorderedP(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
& leq(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( neq(X1,nil)
& frontsegP(X2,X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[39,theory(equality)]) ).
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)],[23]) ).
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(esk3_2(X4,X5))
& app(X5,esk3_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(esk3_2(X4,X5))
& app(X5,esk3_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(esk3_2(X4,X5))
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(X5,esk3_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]) ).
fof(166,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(167,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[166]) ).
fof(168,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[167]) ).
fof(169,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)],[168]) ).
cnf(170,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(171,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(176,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[31]) ).
fof(213,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& ? [X5] :
( ssList(X5)
& app(X3,X5) = X4
& totalorderedP(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
| ~ leq(X8,X6) ) ) ) ) )
& ( nil = X4
| nil != X3 )
& ( ~ neq(X1,nil)
| ~ frontsegP(X2,X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(214,negated_conjecture,
? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& X11 = X13
& X10 = X12
& neq(X11,nil)
& ? [X14] :
( ssList(X14)
& app(X12,X14) = X13
& totalorderedP(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
| ~ leq(X17,X15) ) ) ) ) )
& ( nil = X13
| nil != X12 )
& ( ~ neq(X10,nil)
| ~ frontsegP(X11,X10) ) ) ) ) ),
inference(variable_rename,[status(thm)],[213]) ).
fof(215,negated_conjecture,
( ssList(esk12_0)
& ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& neq(esk13_0,nil)
& ssList(esk16_0)
& app(esk14_0,esk16_0) = esk15_0
& totalorderedP(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
| ~ leq(X17,X15) ) ) ) )
& ( nil = esk15_0
| nil != esk14_0 )
& ( ~ neq(esk12_0,nil)
| ~ frontsegP(esk13_0,esk12_0) ) ),
inference(skolemize,[status(esa)],[214]) ).
fof(216,negated_conjecture,
! [X15,X16,X17,X18] :
( ( ~ ssList(X18)
| app(X18,cons(X17,nil)) != esk14_0
| ~ leq(X17,X15)
| ~ ssItem(X17)
| ~ ssList(X16)
| app(cons(X15,nil),X16) != esk16_0
| ~ ssItem(X15) )
& app(esk14_0,esk16_0) = esk15_0
& totalorderedP(esk14_0)
& ssList(esk16_0)
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& neq(esk13_0,nil)
& ( nil = esk15_0
| nil != esk14_0 )
& ( ~ 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)],[215]) ).
cnf(217,negated_conjecture,
ssList(esk12_0),
inference(split_conjunct,[status(thm)],[216]) ).
cnf(218,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[216]) ).
cnf(221,negated_conjecture,
( ~ frontsegP(esk13_0,esk12_0)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[216]) ).
cnf(222,negated_conjecture,
( nil = esk15_0
| nil != esk14_0 ),
inference(split_conjunct,[status(thm)],[216]) ).
cnf(223,negated_conjecture,
neq(esk13_0,nil),
inference(split_conjunct,[status(thm)],[216]) ).
cnf(224,negated_conjecture,
esk12_0 = esk14_0,
inference(split_conjunct,[status(thm)],[216]) ).
cnf(225,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[216]) ).
cnf(226,negated_conjecture,
ssList(esk16_0),
inference(split_conjunct,[status(thm)],[216]) ).
cnf(228,negated_conjecture,
app(esk14_0,esk16_0) = esk15_0,
inference(split_conjunct,[status(thm)],[216]) ).
cnf(230,negated_conjecture,
ssList(esk14_0),
inference(rw,[status(thm)],[217,224,theory(equality)]) ).
cnf(231,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[218,225,theory(equality)]) ).
cnf(232,negated_conjecture,
neq(esk15_0,nil),
inference(rw,[status(thm)],[223,225,theory(equality)]) ).
cnf(234,negated_conjecture,
( neq(nil,nil)
| esk14_0 != nil ),
inference(spm,[status(thm)],[232,222,theory(equality)]) ).
cnf(236,negated_conjecture,
( ~ frontsegP(esk15_0,esk14_0)
| ~ neq(esk12_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[221,225,theory(equality)]),224,theory(equality)]) ).
cnf(237,negated_conjecture,
( ~ frontsegP(esk15_0,esk14_0)
| ~ neq(esk14_0,nil) ),
inference(rw,[status(thm)],[236,224,theory(equality)]) ).
cnf(248,negated_conjecture,
( esk14_0 = nil
| ~ frontsegP(esk15_0,esk14_0)
| ~ ssList(nil)
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[237,170,theory(equality)]) ).
cnf(249,negated_conjecture,
( esk14_0 = nil
| ~ frontsegP(esk15_0,esk14_0)
| $false
| ~ ssList(esk14_0) ),
inference(rw,[status(thm)],[248,176,theory(equality)]) ).
cnf(250,negated_conjecture,
( esk14_0 = nil
| ~ frontsegP(esk15_0,esk14_0)
| ~ ssList(esk14_0) ),
inference(cn,[status(thm)],[249,theory(equality)]) ).
cnf(266,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[171,theory(equality)]) ).
cnf(291,negated_conjecture,
( frontsegP(X1,esk14_0)
| esk15_0 != X1
| ~ ssList(esk16_0)
| ~ ssList(esk14_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[142,228,theory(equality)]) ).
cnf(496,negated_conjecture,
( ~ ssList(nil)
| esk14_0 != nil ),
inference(spm,[status(thm)],[266,234,theory(equality)]) ).
cnf(497,negated_conjecture,
( $false
| esk14_0 != nil ),
inference(rw,[status(thm)],[496,176,theory(equality)]) ).
cnf(498,negated_conjecture,
esk14_0 != nil,
inference(cn,[status(thm)],[497,theory(equality)]) ).
cnf(499,negated_conjecture,
( esk14_0 = nil
| ~ frontsegP(esk15_0,esk14_0)
| $false ),
inference(rw,[status(thm)],[250,230,theory(equality)]) ).
cnf(500,negated_conjecture,
( esk14_0 = nil
| ~ frontsegP(esk15_0,esk14_0) ),
inference(cn,[status(thm)],[499,theory(equality)]) ).
cnf(501,negated_conjecture,
~ frontsegP(esk15_0,esk14_0),
inference(sr,[status(thm)],[500,498,theory(equality)]) ).
cnf(539,negated_conjecture,
( frontsegP(X1,esk14_0)
| esk15_0 != X1
| ~ ssList(esk16_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[291,230,theory(equality)]) ).
cnf(540,negated_conjecture,
( frontsegP(X1,esk14_0)
| esk15_0 != X1
| ~ ssList(esk16_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[539,theory(equality)]) ).
cnf(541,negated_conjecture,
( ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[501,540,theory(equality)]) ).
cnf(545,negated_conjecture,
( ~ ssList(esk16_0)
| $false ),
inference(rw,[status(thm)],[541,231,theory(equality)]) ).
cnf(546,negated_conjecture,
~ ssList(esk16_0),
inference(cn,[status(thm)],[545,theory(equality)]) ).
cnf(568,negated_conjecture,
$false,
inference(sr,[status(thm)],[226,546,theory(equality)]) ).
cnf(569,negated_conjecture,
$false,
568,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC104+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpt0AdIl/sel_SWC104+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC104+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC104+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC104+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
%
%------------------------------------------------------------------------------