TSTP Solution File: SWC092+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC092+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 10:16:08 EST 2010
% Result : Theorem 0.65s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 69 ( 16 unt; 0 def)
% Number of atoms : 392 ( 98 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 535 ( 212 ~; 201 |; 99 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 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 : 133 ( 0 sgn 73 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(11,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpJHVST9/sel_SWC092+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/tmpJHVST9/sel_SWC092+1.p_1',ax7) ).
fof(33,axiom,
ssList(nil),
file('/tmp/tmpJHVST9/sel_SWC092+1.p_1',ax17) ).
fof(37,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpJHVST9/sel_SWC092+1.p_1',ax55) ).
fof(40,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpJHVST9/sel_SWC092+1.p_1',ax15) ).
fof(43,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ( app(X3,X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X6
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(X10,cons(X9,nil)) = X3
& lt(X9,X7) ) ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
file('/tmp/tmpJHVST9/sel_SWC092+1.p_1',co1) ).
fof(44,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ( app(X3,X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X6
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(X10,cons(X9,nil)) = X3
& lt(X9,X7) ) ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[43]) ).
fof(47,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ( app(X3,X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X6
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(X10,cons(X9,nil)) = X3
& lt(X9,X7) ) ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[44,theory(equality)]) ).
fof(86,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(87,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[86]) ).
cnf(88,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[87]) ).
fof(126,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(127,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)],[126]) ).
fof(128,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)],[127]) ).
fof(129,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)],[128]) ).
fof(130,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)],[129]) ).
cnf(134,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(195,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[33]) ).
fof(217,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(218,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[217]) ).
cnf(219,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[218]) ).
fof(227,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(228,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[227]) ).
fof(229,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[228]) ).
fof(230,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)],[229]) ).
cnf(231,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[230]) ).
cnf(232,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[230]) ).
fof(240,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(X2,X5)
| ~ segmentP(X1,X5) )
& ? [X6] :
( ssList(X6)
& app(X3,X6) = X4
& strictorderedP(X3)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X6
| ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(X10,cons(X9,nil)) != X3
| ~ lt(X9,X7) ) ) ) ) )
& ( nil = X4
| nil != X3 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(241,negated_conjecture,
? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& X12 = X14
& X11 = X13
& neq(X12,nil)
& ! [X15] :
( ~ ssList(X15)
| ~ neq(X15,nil)
| ~ segmentP(X12,X15)
| ~ segmentP(X11,X15) )
& ? [X16] :
( ssList(X16)
& app(X13,X16) = X14
& strictorderedP(X13)
& ! [X17] :
( ~ ssItem(X17)
| ! [X18] :
( ~ ssList(X18)
| app(cons(X17,nil),X18) != X16
| ! [X19] :
( ~ ssItem(X19)
| ! [X20] :
( ~ ssList(X20)
| app(X20,cons(X19,nil)) != X13
| ~ lt(X19,X17) ) ) ) ) )
& ( nil = X14
| nil != X13 ) ) ) ) ),
inference(variable_rename,[status(thm)],[240]) ).
fof(242,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)
& ! [X15] :
( ~ ssList(X15)
| ~ neq(X15,nil)
| ~ segmentP(esk14_0,X15)
| ~ segmentP(esk13_0,X15) )
& ssList(esk17_0)
& app(esk15_0,esk17_0) = esk16_0
& strictorderedP(esk15_0)
& ! [X17] :
( ~ ssItem(X17)
| ! [X18] :
( ~ ssList(X18)
| app(cons(X17,nil),X18) != esk17_0
| ! [X19] :
( ~ ssItem(X19)
| ! [X20] :
( ~ ssList(X20)
| app(X20,cons(X19,nil)) != esk15_0
| ~ lt(X19,X17) ) ) ) )
& ( nil = esk16_0
| nil != esk15_0 ) ),
inference(skolemize,[status(esa)],[241]) ).
fof(243,negated_conjecture,
! [X15,X17,X18,X19,X20] :
( ( ~ ssList(X20)
| app(X20,cons(X19,nil)) != esk15_0
| ~ lt(X19,X17)
| ~ ssItem(X19)
| ~ ssList(X18)
| app(cons(X17,nil),X18) != esk17_0
| ~ ssItem(X17) )
& app(esk15_0,esk17_0) = esk16_0
& strictorderedP(esk15_0)
& ssList(esk17_0)
& ( ~ ssList(X15)
| ~ neq(X15,nil)
| ~ segmentP(esk14_0,X15)
| ~ segmentP(esk13_0,X15) )
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& neq(esk14_0,nil)
& ( nil = esk16_0
| nil != esk15_0 )
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(shift_quantors,[status(thm)],[242]) ).
cnf(244,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(245,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(248,negated_conjecture,
( nil = esk16_0
| nil != esk15_0 ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(249,negated_conjecture,
neq(esk14_0,nil),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(250,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[243]) ).
cnf(251,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[243]) ).
cnf(252,negated_conjecture,
( ~ segmentP(esk13_0,X1)
| ~ segmentP(esk14_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(253,negated_conjecture,
ssList(esk17_0),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(255,negated_conjecture,
app(esk15_0,esk17_0) = esk16_0,
inference(split_conjunct,[status(thm)],[243]) ).
cnf(257,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[244,250,theory(equality)]) ).
cnf(258,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[245,251,theory(equality)]) ).
cnf(259,negated_conjecture,
neq(esk16_0,nil),
inference(rw,[status(thm)],[249,251,theory(equality)]) ).
cnf(261,negated_conjecture,
( neq(nil,nil)
| esk15_0 != nil ),
inference(spm,[status(thm)],[259,248,theory(equality)]) ).
cnf(288,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[232,theory(equality)]) ).
cnf(302,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk15_0,X1)
| ~ segmentP(esk14_0,X1) ),
inference(rw,[status(thm)],[252,250,theory(equality)]) ).
cnf(303,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk15_0,X1)
| ~ segmentP(esk16_0,X1) ),
inference(rw,[status(thm)],[302,251,theory(equality)]) ).
cnf(306,negated_conjecture,
( X1 = nil
| ~ segmentP(esk15_0,X1)
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[303,231,theory(equality)]) ).
cnf(307,negated_conjecture,
( X1 = nil
| ~ segmentP(esk15_0,X1)
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[306,195,theory(equality)]) ).
cnf(308,negated_conjecture,
( X1 = nil
| ~ segmentP(esk15_0,X1)
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[307,theory(equality)]) ).
cnf(434,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[134,88,theory(equality)]) ).
cnf(444,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[434,195,theory(equality)]) ).
cnf(445,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[444,theory(equality)]) ).
cnf(546,negated_conjecture,
( ~ ssList(nil)
| esk15_0 != nil ),
inference(spm,[status(thm)],[288,261,theory(equality)]) ).
cnf(549,negated_conjecture,
( $false
| esk15_0 != nil ),
inference(rw,[status(thm)],[546,195,theory(equality)]) ).
cnf(550,negated_conjecture,
esk15_0 != nil,
inference(cn,[status(thm)],[549,theory(equality)]) ).
cnf(9732,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| ~ ssList(esk15_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[445,255,theory(equality)]) ).
cnf(9776,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[9732,257,theory(equality)]) ).
cnf(9777,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[9776,theory(equality)]) ).
cnf(10009,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk15_0,esk15_0)
| ~ ssList(esk15_0)
| ~ ssList(esk17_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[308,9777,theory(equality)]) ).
cnf(10018,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk15_0,esk15_0)
| $false
| ~ ssList(esk17_0)
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[10009,257,theory(equality)]) ).
cnf(10019,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk15_0,esk15_0)
| $false
| ~ ssList(esk17_0)
| $false ),
inference(rw,[status(thm)],[10018,258,theory(equality)]) ).
cnf(10020,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk15_0,esk15_0)
| ~ ssList(esk17_0) ),
inference(cn,[status(thm)],[10019,theory(equality)]) ).
cnf(10021,negated_conjecture,
( ~ segmentP(esk15_0,esk15_0)
| ~ ssList(esk17_0) ),
inference(sr,[status(thm)],[10020,550,theory(equality)]) ).
cnf(10066,negated_conjecture,
( ~ ssList(esk17_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[10021,219,theory(equality)]) ).
cnf(10069,negated_conjecture,
( ~ ssList(esk17_0)
| $false ),
inference(rw,[status(thm)],[10066,257,theory(equality)]) ).
cnf(10070,negated_conjecture,
~ ssList(esk17_0),
inference(cn,[status(thm)],[10069,theory(equality)]) ).
cnf(10077,negated_conjecture,
$false,
inference(sr,[status(thm)],[253,10070,theory(equality)]) ).
cnf(10078,negated_conjecture,
$false,
10077,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC092+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpJHVST9/sel_SWC092+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC092+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC092+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC092+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
%
%------------------------------------------------------------------------------