TSTP Solution File: SWC118+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC118+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 10:20:22 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 54 ( 16 unt; 0 def)
% Number of atoms : 384 ( 117 equ)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 533 ( 203 ~; 184 |; 122 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 82 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmpbsbtHN/sel_SWC118+1.p_1',ax7) ).
fof(26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpbsbtHN/sel_SWC118+1.p_1',ax15) ).
fof(28,axiom,
ssList(nil),
file('/tmp/tmpbsbtHN/sel_SWC118+1.p_1',ax17) ).
fof(37,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X3),X6) != X4
| ~ totalorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& leq(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& leq(X13,X11) ) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
file('/tmp/tmpbsbtHN/sel_SWC118+1.p_1',co1) ).
fof(38,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X3),X6) != X4
| ~ totalorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& leq(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& leq(X13,X11) ) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 )
| ( 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
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X3),X6) != X4
| ~ totalorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& leq(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& leq(X13,X11) ) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[38,theory(equality)]) ).
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(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
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,X3),X6) = X4
& totalorderedP(X3)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X5
| ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X3
| ~ leq(X7,X9) ) ) ) )
& ! [X11] :
( ~ ssItem(X11)
| ! [X12] :
( ~ ssList(X12)
| app(cons(X11,nil),X12) != X6
| ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| app(X14,cons(X13,nil)) != X3
| ~ leq(X13,X11) ) ) ) ) ) )
& ( nil = X4
| nil != X3 )
& ( nil != X2
| nil != X1 )
& ( ~ neq(X1,nil)
| ~ segmentP(X2,X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(207,negated_conjecture,
? [X15] :
( ssList(X15)
& ? [X16] :
( ssList(X16)
& ? [X17] :
( ssList(X17)
& ? [X18] :
( ssList(X18)
& X16 = X18
& X15 = X17
& ? [X19] :
( ssList(X19)
& ? [X20] :
( ssList(X20)
& app(app(X19,X17),X20) = X18
& totalorderedP(X17)
& ! [X21] :
( ~ ssItem(X21)
| ! [X22] :
( ~ ssList(X22)
| app(X22,cons(X21,nil)) != X19
| ! [X23] :
( ~ ssItem(X23)
| ! [X24] :
( ~ ssList(X24)
| app(cons(X23,nil),X24) != X17
| ~ leq(X21,X23) ) ) ) )
& ! [X25] :
( ~ ssItem(X25)
| ! [X26] :
( ~ ssList(X26)
| app(cons(X25,nil),X26) != X20
| ! [X27] :
( ~ ssItem(X27)
| ! [X28] :
( ~ ssList(X28)
| app(X28,cons(X27,nil)) != X17
| ~ leq(X27,X25) ) ) ) ) ) )
& ( nil = X18
| nil != X17 )
& ( nil != X16
| nil != X15 )
& ( ~ neq(X15,nil)
| ~ segmentP(X16,X15) ) ) ) ) ),
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
& ssList(esk17_0)
& ssList(esk18_0)
& app(app(esk17_0,esk15_0),esk18_0) = esk16_0
& totalorderedP(esk15_0)
& ! [X21] :
( ~ ssItem(X21)
| ! [X22] :
( ~ ssList(X22)
| app(X22,cons(X21,nil)) != esk17_0
| ! [X23] :
( ~ ssItem(X23)
| ! [X24] :
( ~ ssList(X24)
| app(cons(X23,nil),X24) != esk15_0
| ~ leq(X21,X23) ) ) ) )
& ! [X25] :
( ~ ssItem(X25)
| ! [X26] :
( ~ ssList(X26)
| app(cons(X25,nil),X26) != esk18_0
| ! [X27] :
( ~ ssItem(X27)
| ! [X28] :
( ~ ssList(X28)
| app(X28,cons(X27,nil)) != esk15_0
| ~ leq(X27,X25) ) ) ) )
& ( nil = esk16_0
| nil != esk15_0 )
& ( nil != esk14_0
| nil != esk13_0 )
& ( ~ neq(esk13_0,nil)
| ~ segmentP(esk14_0,esk13_0) ) ),
inference(skolemize,[status(esa)],[207]) ).
fof(209,negated_conjecture,
! [X21,X22,X23,X24,X25,X26,X27,X28] :
( ( ~ ssList(X28)
| app(X28,cons(X27,nil)) != esk15_0
| ~ leq(X27,X25)
| ~ ssItem(X27)
| ~ ssList(X26)
| app(cons(X25,nil),X26) != esk18_0
| ~ ssItem(X25) )
& ( ~ ssList(X24)
| app(cons(X23,nil),X24) != esk15_0
| ~ leq(X21,X23)
| ~ ssItem(X23)
| ~ ssList(X22)
| app(X22,cons(X21,nil)) != esk17_0
| ~ ssItem(X21) )
& app(app(esk17_0,esk15_0),esk18_0) = esk16_0
& totalorderedP(esk15_0)
& ssList(esk18_0)
& ssList(esk17_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& ( nil = esk16_0
| nil != esk15_0 )
& ( nil != esk14_0
| nil != esk13_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 != esk13_0
| nil != esk14_0 ),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(216,negated_conjecture,
( nil = esk16_0
| nil != esk15_0 ),
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(220,negated_conjecture,
ssList(esk18_0),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(222,negated_conjecture,
app(app(esk17_0,esk15_0),esk18_0) = esk16_0,
inference(split_conjunct,[status(thm)],[209]) ).
cnf(225,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[210,217,theory(equality)]) ).
cnf(226,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[211,218,theory(equality)]) ).
cnf(229,negated_conjecture,
( esk15_0 != nil
| esk14_0 != nil ),
inference(rw,[status(thm)],[215,217,theory(equality)]) ).
cnf(230,negated_conjecture,
( esk15_0 != nil
| esk16_0 != nil ),
inference(rw,[status(thm)],[229,218,theory(equality)]) ).
cnf(231,negated_conjecture,
esk15_0 != nil,
inference(csr,[status(thm)],[230,216]) ).
cnf(232,negated_conjecture,
( ~ neq(esk15_0,nil)
| ~ segmentP(esk14_0,esk13_0) ),
inference(rw,[status(thm)],[214,217,theory(equality)]) ).
cnf(233,negated_conjecture,
( ~ neq(esk15_0,nil)
| ~ segmentP(esk16_0,esk15_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[232,218,theory(equality)]),217,theory(equality)]) ).
cnf(245,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0)
| ~ ssList(nil)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[233,158,theory(equality)]) ).
cnf(246,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0)
| $false
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[245,164,theory(equality)]) ).
cnf(247,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[246,theory(equality)]) ).
cnf(248,negated_conjecture,
( ~ segmentP(esk16_0,esk15_0)
| ~ ssList(esk15_0) ),
inference(sr,[status(thm)],[247,231,theory(equality)]) ).
cnf(356,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| ~ ssList(esk15_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[131,222,theory(equality)]) ).
cnf(502,negated_conjecture,
( ~ segmentP(esk16_0,esk15_0)
| $false ),
inference(rw,[status(thm)],[248,225,theory(equality)]) ).
cnf(503,negated_conjecture,
~ segmentP(esk16_0,esk15_0),
inference(cn,[status(thm)],[502,theory(equality)]) ).
cnf(1014,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[356,225,theory(equality)]) ).
cnf(1015,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1014,theory(equality)]) ).
cnf(1016,negated_conjecture,
( ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[503,1015,theory(equality)]) ).
cnf(1020,negated_conjecture,
( ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| $false ),
inference(rw,[status(thm)],[1016,226,theory(equality)]) ).
cnf(1021,negated_conjecture,
( ~ ssList(esk18_0)
| ~ ssList(esk17_0) ),
inference(cn,[status(thm)],[1020,theory(equality)]) ).
cnf(1030,negated_conjecture,
~ ssList(esk17_0),
inference(spm,[status(thm)],[1021,220,theory(equality)]) ).
cnf(1053,negated_conjecture,
$false,
inference(sr,[status(thm)],[219,1030,theory(equality)]) ).
cnf(1054,negated_conjecture,
$false,
1053,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC118+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpbsbtHN/sel_SWC118+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC118+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC118+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC118+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
%
%------------------------------------------------------------------------------