TSTP Solution File: SWC124+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC124+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 10:20:54 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 16 unt; 0 def)
% Number of atoms : 350 ( 99 equ)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 469 ( 182 ~; 172 |; 93 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 66 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(11,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpvJsc29/sel_SWC124+1.p_1',ax28) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpvJsc29/sel_SWC124+1.p_1',ax7) ).
fof(26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpvJsc29/sel_SWC124+1.p_1',ax15) ).
fof(28,axiom,
ssList(nil),
file('/tmp/tmpvJsc29/sel_SWC124+1.p_1',ax17) ).
fof(37,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)
& segmentP(X2,X1) ) ) ) ) ) ),
file('/tmp/tmpvJsc29/sel_SWC124+1.p_1',co1) ).
fof(38,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)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[37]) ).
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)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[38,theory(equality)]) ).
fof(83,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(84,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[83]) ).
cnf(85,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(123,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)],[20]) ).
fof(124,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)],[123]) ).
fof(125,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[124]) ).
fof(126,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[125]) ).
fof(127,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk5_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[126]) ).
cnf(131,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[127]) ).
fof(154,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(155,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[155]) ).
fof(157,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)],[156]) ).
cnf(158,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(164,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[28]) ).
fof(206,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)
| ~ segmentP(X2,X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(207,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)
| ~ segmentP(X11,X10) ) ) ) ) ),
inference(variable_rename,[status(thm)],[206]) ).
fof(208,negated_conjecture,
( ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& neq(esk14_0,nil)
& ssList(esk17_0)
& app(esk15_0,esk17_0) = esk16_0
& totalorderedP(esk15_0)
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| app(cons(X15,nil),X16) != esk17_0
| ! [X17] :
( ~ ssItem(X17)
| ! [X18] :
( ~ ssList(X18)
| app(X18,cons(X17,nil)) != esk15_0
| ~ leq(X17,X15) ) ) ) )
& ( nil = esk16_0
| nil != esk15_0 )
& ( ~ neq(esk13_0,nil)
| ~ segmentP(esk14_0,esk13_0) ) ),
inference(skolemize,[status(esa)],[207]) ).
fof(209,negated_conjecture,
! [X15,X16,X17,X18] :
( ( ~ ssList(X18)
| app(X18,cons(X17,nil)) != esk15_0
| ~ leq(X17,X15)
| ~ ssItem(X17)
| ~ ssList(X16)
| app(cons(X15,nil),X16) != esk17_0
| ~ ssItem(X15) )
& app(esk15_0,esk17_0) = esk16_0
& totalorderedP(esk15_0)
& ssList(esk17_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& neq(esk14_0,nil)
& ( nil = esk16_0
| nil != esk15_0 )
& ( ~ neq(esk13_0,nil)
| ~ segmentP(esk14_0,esk13_0) )
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(shift_quantors,[status(thm)],[208]) ).
cnf(210,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(211,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(214,negated_conjecture,
( ~ segmentP(esk14_0,esk13_0)
| ~ neq(esk13_0,nil) ),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(215,negated_conjecture,
( nil = esk16_0
| nil != esk15_0 ),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(216,negated_conjecture,
neq(esk14_0,nil),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(217,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[209]) ).
cnf(218,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[209]) ).
cnf(219,negated_conjecture,
ssList(esk17_0),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(221,negated_conjecture,
app(esk15_0,esk17_0) = esk16_0,
inference(split_conjunct,[status(thm)],[209]) ).
cnf(223,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[210,217,theory(equality)]) ).
cnf(224,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[211,218,theory(equality)]) ).
cnf(225,negated_conjecture,
neq(esk16_0,nil),
inference(rw,[status(thm)],[216,218,theory(equality)]) ).
cnf(227,negated_conjecture,
( neq(nil,nil)
| esk15_0 != nil ),
inference(spm,[status(thm)],[225,215,theory(equality)]) ).
cnf(229,negated_conjecture,
( ~ neq(esk15_0,nil)
| ~ segmentP(esk14_0,esk13_0) ),
inference(rw,[status(thm)],[214,217,theory(equality)]) ).
cnf(230,negated_conjecture,
( ~ neq(esk15_0,nil)
| ~ segmentP(esk16_0,esk15_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[229,218,theory(equality)]),217,theory(equality)]) ).
cnf(241,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0)
| ~ ssList(nil)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[230,158,theory(equality)]) ).
cnf(242,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0)
| $false
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[241,164,theory(equality)]) ).
cnf(243,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[242,theory(equality)]) ).
cnf(259,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[159,theory(equality)]) ).
cnf(352,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[131,85,theory(equality)]) ).
cnf(360,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[352,164,theory(equality)]) ).
cnf(361,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[360,theory(equality)]) ).
cnf(491,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0)
| $false ),
inference(rw,[status(thm)],[243,223,theory(equality)]) ).
cnf(492,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0) ),
inference(cn,[status(thm)],[491,theory(equality)]) ).
cnf(501,negated_conjecture,
( ~ ssList(nil)
| esk15_0 != nil ),
inference(spm,[status(thm)],[259,227,theory(equality)]) ).
cnf(502,negated_conjecture,
( $false
| esk15_0 != nil ),
inference(rw,[status(thm)],[501,164,theory(equality)]) ).
cnf(503,negated_conjecture,
esk15_0 != nil,
inference(cn,[status(thm)],[502,theory(equality)]) ).
cnf(2479,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| ~ ssList(esk15_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[361,221,theory(equality)]) ).
cnf(2498,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2479,223,theory(equality)]) ).
cnf(2499,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2498,theory(equality)]) ).
cnf(2651,negated_conjecture,
( esk15_0 = nil
| ~ ssList(esk17_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[492,2499,theory(equality)]) ).
cnf(2661,negated_conjecture,
( esk15_0 = nil
| ~ ssList(esk17_0)
| $false ),
inference(rw,[status(thm)],[2651,224,theory(equality)]) ).
cnf(2662,negated_conjecture,
( esk15_0 = nil
| ~ ssList(esk17_0) ),
inference(cn,[status(thm)],[2661,theory(equality)]) ).
cnf(2663,negated_conjecture,
~ ssList(esk17_0),
inference(sr,[status(thm)],[2662,503,theory(equality)]) ).
cnf(2694,negated_conjecture,
$false,
inference(sr,[status(thm)],[219,2663,theory(equality)]) ).
cnf(2695,negated_conjecture,
$false,
2694,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC124+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpvJsc29/sel_SWC124+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC124+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC124+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC124+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
%
%------------------------------------------------------------------------------