TSTP Solution File: SWC244+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC244+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 11:04:05 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 7 unt; 0 def)
% Number of atoms : 359 ( 82 equ)
% Maximal formula atoms : 39 ( 6 avg)
% Number of connectives : 490 ( 189 ~; 174 |; 104 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 131 ( 0 sgn 63 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp9wZydm/sel_SWC244+1.p_1',ax81) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp9wZydm/sel_SWC244+1.p_1',ax28) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmp9wZydm/sel_SWC244+1.p_1',ax20) ).
fof(34,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp9wZydm/sel_SWC244+1.p_1',ax16) ).
fof(35,axiom,
ssList(nil),
file('/tmp/tmp9wZydm/sel_SWC244+1.p_1',ax17) ).
fof(39,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmp9wZydm/sel_SWC244+1.p_1',ax38) ).
fof(50,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ equalelemsP(X3)
| nil = X1
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,cons(X6,nil)),X8) = X1
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X7,X9)
| ~ memberP(X8,X9)
| ~ lt(X6,X9)
| leq(X6,X9) ) ) ) ) ) ) ) ) ) ),
file('/tmp/tmp9wZydm/sel_SWC244+1.p_1',co1) ).
fof(51,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ equalelemsP(X3)
| nil = X1
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,cons(X6,nil)),X8) = X1
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X7,X9)
| ~ memberP(X8,X9)
| ~ lt(X6,X9)
| leq(X6,X9) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[50]) ).
fof(54,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[39,theory(equality)]) ).
fof(55,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ equalelemsP(X3)
| nil = X1
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,cons(X6,nil)),X8) = X1
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X7,X9)
| ~ memberP(X8,X9)
| ~ lt(X6,X9)
| leq(X6,X9) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[51,theory(equality)]) ).
fof(71,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(72,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[71]) ).
fof(73,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[72]) ).
cnf(74,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[73]) ).
fof(88,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(89,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[88]) ).
cnf(90,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
fof(110,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(111,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk1_1(X4))
& ssItem(esk2_1(X4))
& cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[111]) ).
fof(113,plain,
! [X4] :
( ( ssList(esk1_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk2_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk2_1(X4),esk1_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[112]) ).
cnf(114,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[113]) ).
cnf(115,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[113]) ).
cnf(116,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[113]) ).
fof(210,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(211,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[210]) ).
fof(212,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[211]) ).
cnf(213,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[212]) ).
cnf(214,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[35]) ).
fof(233,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(234,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[233]) ).
cnf(235,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[234]) ).
fof(285,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& frontsegP(X4,X3)
& equalelemsP(X3)
& nil != X1
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X3,X5)
| ~ frontsegP(X4,X5)
| ~ segmentP(X5,X3)
| ~ equalelemsP(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| app(app(X7,cons(X6,nil)),X8) != X1
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& memberP(X8,X9)
& lt(X6,X9)
& ~ leq(X6,X9) ) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(286,negated_conjecture,
? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& X11 = X13
& X10 = X12
& frontsegP(X13,X12)
& equalelemsP(X12)
& nil != X10
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X12,X14)
| ~ frontsegP(X13,X14)
| ~ segmentP(X14,X12)
| ~ equalelemsP(X14) )
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != X10
| ? [X18] :
( ssItem(X18)
& memberP(X16,X18)
& memberP(X17,X18)
& lt(X15,X18)
& ~ leq(X15,X18) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[285]) ).
fof(287,negated_conjecture,
( ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& ssList(esk17_0)
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& frontsegP(esk17_0,esk16_0)
& equalelemsP(esk16_0)
& nil != esk14_0
& ! [X14] :
( ~ ssList(X14)
| ~ neq(esk16_0,X14)
| ~ frontsegP(esk17_0,X14)
| ~ segmentP(X14,esk16_0)
| ~ equalelemsP(X14) )
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk14_0
| ( ssItem(esk18_3(X15,X16,X17))
& memberP(X16,esk18_3(X15,X16,X17))
& memberP(X17,esk18_3(X15,X16,X17))
& lt(X15,esk18_3(X15,X16,X17))
& ~ leq(X15,esk18_3(X15,X16,X17)) ) ) ) ) ),
inference(skolemize,[status(esa)],[286]) ).
fof(288,negated_conjecture,
! [X14,X15,X16,X17] :
( ( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk14_0
| ( ssItem(esk18_3(X15,X16,X17))
& memberP(X16,esk18_3(X15,X16,X17))
& memberP(X17,esk18_3(X15,X16,X17))
& lt(X15,esk18_3(X15,X16,X17))
& ~ leq(X15,esk18_3(X15,X16,X17)) )
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( ~ ssList(X14)
| ~ neq(esk16_0,X14)
| ~ frontsegP(esk17_0,X14)
| ~ segmentP(X14,esk16_0)
| ~ equalelemsP(X14) )
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& frontsegP(esk17_0,esk16_0)
& equalelemsP(esk16_0)
& nil != esk14_0
& ssList(esk17_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0) ),
inference(shift_quantors,[status(thm)],[287]) ).
fof(289,negated_conjecture,
! [X14,X15,X16,X17] :
( ( ssItem(esk18_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk14_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X16,esk18_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk14_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X17,esk18_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk14_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( lt(X15,esk18_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk14_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( ~ leq(X15,esk18_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk14_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( ~ ssList(X14)
| ~ neq(esk16_0,X14)
| ~ frontsegP(esk17_0,X14)
| ~ segmentP(X14,esk16_0)
| ~ equalelemsP(X14) )
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& frontsegP(esk17_0,esk16_0)
& equalelemsP(esk16_0)
& nil != esk14_0
& ssList(esk17_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0) ),
inference(distribute,[status(thm)],[288]) ).
cnf(290,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(294,negated_conjecture,
nil != esk14_0,
inference(split_conjunct,[status(thm)],[289]) ).
cnf(303,negated_conjecture,
( memberP(X2,esk18_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk14_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(304,negated_conjecture,
( ssItem(esk18_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk14_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(607,negated_conjecture,
( ~ ssItem(esk18_3(X1,nil,X2))
| app(app(nil,cons(X1,nil)),X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[235,303,theory(equality)]) ).
cnf(610,negated_conjecture,
( ~ ssItem(esk18_3(X1,nil,X2))
| app(app(nil,cons(X1,nil)),X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[607,214,theory(equality)]) ).
cnf(611,negated_conjecture,
( ~ ssItem(esk18_3(X1,nil,X2))
| app(app(nil,cons(X1,nil)),X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[610,theory(equality)]) ).
cnf(1365,negated_conjecture,
( app(app(nil,cons(X1,nil)),X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[611,304,theory(equality)]) ).
cnf(1366,negated_conjecture,
( app(app(nil,cons(X1,nil)),X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[1365,214,theory(equality)]) ).
cnf(1367,negated_conjecture,
( app(app(nil,cons(X1,nil)),X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1366,theory(equality)]) ).
cnf(1369,negated_conjecture,
( app(cons(X1,nil),X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[1367,90,theory(equality)]) ).
cnf(1555,negated_conjecture,
( cons(X1,X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[1369,74,theory(equality)]) ).
cnf(1659,negated_conjecture,
( cons(X1,X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1555,213,theory(equality)]) ).
cnf(1660,negated_conjecture,
( cons(X1,X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[1659,214,theory(equality)]) ).
cnf(1661,negated_conjecture,
( cons(X1,X2) != esk14_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1660,theory(equality)]) ).
cnf(1662,negated_conjecture,
( nil = X1
| X1 != esk14_0
| ~ ssItem(esk2_1(X1))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1661,114,theory(equality)]) ).
cnf(2072,negated_conjecture,
( nil = X1
| X1 != esk14_0
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1662,116]) ).
cnf(2073,negated_conjecture,
( nil = X1
| X1 != esk14_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2072,115]) ).
cnf(2074,negated_conjecture,
nil = esk14_0,
inference(spm,[status(thm)],[2073,290,theory(equality)]) ).
cnf(2086,negated_conjecture,
$false,
inference(sr,[status(thm)],[2074,294,theory(equality)]) ).
cnf(2087,negated_conjecture,
$false,
2086,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC244+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp9wZydm/sel_SWC244+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC244+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC244+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC244+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
%
%------------------------------------------------------------------------------