%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC076+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 10:12:27 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 17 unt; 0 def)
% Number of atoms : 392 ( 120 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 533 ( 203 ~; 189 |; 116 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 81 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpmdVccv/sel_SWC076+1.p_1',ax7) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpmdVccv/sel_SWC076+1.p_1',ax15) ).
fof(22,axiom,
ssList(nil),
file('/tmp/tmpmdVccv/sel_SWC076+1.p_1',ax17) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpmdVccv/sel_SWC076+1.p_1',ax55) ).
fof(29,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,X3),X7) != X4
| ~ equalelemsP(X3)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X6
& ? [X10] :
( ssList(X10)
& app(cons(X8,nil),X10) = X3 ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X7
& ? [X13] :
( ssList(X13)
& app(X13,cons(X11,nil)) = X3 ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
file('/tmp/tmpmdVccv/sel_SWC076+1.p_1',co1) ).
fof(30,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,X3),X7) != X4
| ~ equalelemsP(X3)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X6
& ? [X10] :
( ssList(X10)
& app(cons(X8,nil),X10) = X3 ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X7
& ? [X13] :
( ssList(X13)
& app(X13,cons(X11,nil)) = X3 ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[29]) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,X3),X7) != X4
| ~ equalelemsP(X3)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X6
& ? [X10] :
( ssList(X10)
& app(cons(X8,nil),X10) = X3 ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X7
& ? [X13] :
( ssList(X13)
& app(X13,cons(X11,nil)) = X3 ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).
fof(87,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)],[13]) ).
fof(88,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)],[87]) ).
fof(89,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)],[88]) ).
fof(90,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)],[89]) ).
fof(91,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)],[90]) ).
cnf(95,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[91]) ).
fof(119,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(120,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[119]) ).
fof(121,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[120]) ).
fof(122,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)],[121]) ).
cnf(123,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(129,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[22]) ).
fof(138,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(139,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[138]) ).
cnf(140,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[139]) ).
fof(160,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(X2,X5)
| ~ segmentP(X1,X5) )
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,X3),X7) = X4
& equalelemsP(X3)
& ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(X9,cons(X8,nil)) != X6
| ! [X10] :
( ~ ssList(X10)
| app(cons(X8,nil),X10) != X3 ) ) )
& ! [X11] :
( ~ ssItem(X11)
| ! [X12] :
( ~ ssList(X12)
| app(cons(X11,nil),X12) != X7
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X11,nil)) != X3 ) ) ) ) )
& ( nil = X4
| nil != X3 )
& ( nil != X2
| nil != X1 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(161,negated_conjecture,
? [X14] :
( ssList(X14)
& ? [X15] :
( ssList(X15)
& ? [X16] :
( ssList(X16)
& ? [X17] :
( ssList(X17)
& X15 = X17
& X14 = X16
& ! [X18] :
( ~ ssList(X18)
| ~ neq(X18,nil)
| ~ segmentP(X15,X18)
| ~ segmentP(X14,X18) )
& ? [X19] :
( ssList(X19)
& ? [X20] :
( ssList(X20)
& app(app(X19,X16),X20) = X17
& equalelemsP(X16)
& ! [X21] :
( ~ ssItem(X21)
| ! [X22] :
( ~ ssList(X22)
| app(X22,cons(X21,nil)) != X19
| ! [X23] :
( ~ ssList(X23)
| app(cons(X21,nil),X23) != X16 ) ) )
& ! [X24] :
( ~ ssItem(X24)
| ! [X25] :
( ~ ssList(X25)
| app(cons(X24,nil),X25) != X20
| ! [X26] :
( ~ ssList(X26)
| app(X26,cons(X24,nil)) != X16 ) ) ) ) )
& ( nil = X17
| nil != X16 )
& ( nil != X15
| nil != X14 ) ) ) ) ),
inference(variable_rename,[status(thm)],[160]) ).
fof(162,negated_conjecture,
( ssList(esk11_0)
& ssList(esk12_0)
& ssList(esk13_0)
& ssList(esk14_0)
& esk12_0 = esk14_0
& esk11_0 = esk13_0
& ! [X18] :
( ~ ssList(X18)
| ~ neq(X18,nil)
| ~ segmentP(esk12_0,X18)
| ~ segmentP(esk11_0,X18) )
& ssList(esk15_0)
& ssList(esk16_0)
& app(app(esk15_0,esk13_0),esk16_0) = esk14_0
& equalelemsP(esk13_0)
& ! [X21] :
( ~ ssItem(X21)
| ! [X22] :
( ~ ssList(X22)
| app(X22,cons(X21,nil)) != esk15_0
| ! [X23] :
( ~ ssList(X23)
| app(cons(X21,nil),X23) != esk13_0 ) ) )
& ! [X24] :
( ~ ssItem(X24)
| ! [X25] :
( ~ ssList(X25)
| app(cons(X24,nil),X25) != esk16_0
| ! [X26] :
( ~ ssList(X26)
| app(X26,cons(X24,nil)) != esk13_0 ) ) )
& ( nil = esk14_0
| nil != esk13_0 )
& ( nil != esk12_0
| nil != esk11_0 ) ),
inference(skolemize,[status(esa)],[161]) ).
fof(163,negated_conjecture,
! [X18,X21,X22,X23,X24,X25,X26] :
( ( ~ ssList(X26)
| app(X26,cons(X24,nil)) != esk13_0
| ~ ssList(X25)
| app(cons(X24,nil),X25) != esk16_0
| ~ ssItem(X24) )
& ( ~ ssList(X23)
| app(cons(X21,nil),X23) != esk13_0
| ~ ssList(X22)
| app(X22,cons(X21,nil)) != esk15_0
| ~ ssItem(X21) )
& app(app(esk15_0,esk13_0),esk16_0) = esk14_0
& equalelemsP(esk13_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ( ~ ssList(X18)
| ~ neq(X18,nil)
| ~ segmentP(esk12_0,X18)
| ~ segmentP(esk11_0,X18) )
& esk12_0 = esk14_0
& esk11_0 = esk13_0
& ( nil = esk14_0
| nil != esk13_0 )
& ( nil != esk12_0
| nil != esk11_0 )
& ssList(esk14_0)
& ssList(esk13_0)
& ssList(esk12_0)
& ssList(esk11_0) ),
inference(shift_quantors,[status(thm)],[162]) ).
cnf(164,negated_conjecture,
ssList(esk11_0),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(165,negated_conjecture,
ssList(esk12_0),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(168,negated_conjecture,
( nil != esk11_0
| nil != esk12_0 ),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(169,negated_conjecture,
( nil = esk14_0
| nil != esk13_0 ),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(170,negated_conjecture,
esk11_0 = esk13_0,
inference(split_conjunct,[status(thm)],[163]) ).
cnf(171,negated_conjecture,
esk12_0 = esk14_0,
inference(split_conjunct,[status(thm)],[163]) ).
cnf(172,negated_conjecture,
( ~ segmentP(esk11_0,X1)
| ~ segmentP(esk12_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(173,negated_conjecture,
ssList(esk15_0),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(174,negated_conjecture,
ssList(esk16_0),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(176,negated_conjecture,
app(app(esk15_0,esk13_0),esk16_0) = esk14_0,
inference(split_conjunct,[status(thm)],[163]) ).
cnf(179,negated_conjecture,
ssList(esk13_0),
inference(rw,[status(thm)],[164,170,theory(equality)]) ).
cnf(180,negated_conjecture,
ssList(esk14_0),
inference(rw,[status(thm)],[165,171,theory(equality)]) ).
cnf(181,negated_conjecture,
( esk13_0 != nil
| esk12_0 != nil ),
inference(rw,[status(thm)],[168,170,theory(equality)]) ).
cnf(182,negated_conjecture,
( esk13_0 != nil
| esk14_0 != nil ),
inference(rw,[status(thm)],[181,171,theory(equality)]) ).
cnf(183,negated_conjecture,
esk13_0 != nil,
inference(csr,[status(thm)],[182,169]) ).
cnf(217,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk13_0,X1)
| ~ segmentP(esk12_0,X1) ),
inference(rw,[status(thm)],[172,170,theory(equality)]) ).
cnf(218,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk13_0,X1)
| ~ segmentP(esk14_0,X1) ),
inference(rw,[status(thm)],[217,171,theory(equality)]) ).
cnf(220,negated_conjecture,
( ~ segmentP(esk14_0,esk13_0)
| ~ neq(esk13_0,nil)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[218,140,theory(equality)]) ).
cnf(313,negated_conjecture,
( segmentP(X1,esk13_0)
| esk14_0 != X1
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[95,176,theory(equality)]) ).
cnf(396,negated_conjecture,
( ~ segmentP(esk14_0,esk13_0)
| ~ neq(esk13_0,nil)
| $false ),
inference(rw,[status(thm)],[220,179,theory(equality)]) ).
cnf(397,negated_conjecture,
( ~ segmentP(esk14_0,esk13_0)
| ~ neq(esk13_0,nil) ),
inference(cn,[status(thm)],[396,theory(equality)]) ).
cnf(532,negated_conjecture,
( segmentP(X1,esk13_0)
| esk14_0 != X1
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[313,179,theory(equality)]) ).
cnf(533,negated_conjecture,
( segmentP(X1,esk13_0)
| esk14_0 != X1
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[532,theory(equality)]) ).
cnf(534,negated_conjecture,
( segmentP(X1,esk13_0)
| esk14_0 != X1
| ~ ssList(esk15_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[533,174,theory(equality)]) ).
cnf(535,negated_conjecture,
( segmentP(X1,esk13_0)
| esk14_0 != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[534,173,theory(equality)]) ).
cnf(536,negated_conjecture,
( segmentP(esk14_0,esk13_0)
| ~ ssList(esk14_0) ),
inference(er,[status(thm)],[535,theory(equality)]) ).
cnf(537,negated_conjecture,
( segmentP(esk14_0,esk13_0)
| $false ),
inference(rw,[status(thm)],[536,180,theory(equality)]) ).
cnf(538,negated_conjecture,
segmentP(esk14_0,esk13_0),
inference(cn,[status(thm)],[537,theory(equality)]) ).
cnf(545,negated_conjecture,
( $false
| ~ neq(esk13_0,nil) ),
inference(rw,[status(thm)],[397,538,theory(equality)]) ).
cnf(546,negated_conjecture,
~ neq(esk13_0,nil),
inference(cn,[status(thm)],[545,theory(equality)]) ).
cnf(565,negated_conjecture,
( esk13_0 = nil
| ~ ssList(nil)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[546,123,theory(equality)]) ).
cnf(567,negated_conjecture,
( esk13_0 = nil
| $false
| ~ ssList(esk13_0) ),
inference(rw,[status(thm)],[565,129,theory(equality)]) ).
cnf(568,negated_conjecture,
( esk13_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[567,179,theory(equality)]) ).
cnf(569,negated_conjecture,
esk13_0 = nil,
inference(cn,[status(thm)],[568,theory(equality)]) ).
cnf(570,negated_conjecture,
$false,
inference(sr,[status(thm)],[569,183,theory(equality)]) ).
cnf(571,negated_conjecture,
$false,
570,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC076+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpmdVccv/sel_SWC076+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC076+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC076+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC076+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
%
%------------------------------------------------------------------------------