TSTP Solution File: SWC371+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC371+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 11:39:47 EST 2010
% Result : Theorem 0.70s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 261 ( 74 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 348 ( 128 ~; 119 |; 82 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 56 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(11,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpoJdGe8/sel_SWC371+1.p_1',ax28) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpoJdGe8/sel_SWC371+1.p_1',ax7) ).
fof(26,axiom,
ssList(nil),
file('/tmp/tmpoJdGe8/sel_SWC371+1.p_1',ax17) ).
fof(35,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [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) ) ) ) ) ) )
| segmentP(X2,X1)
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
file('/tmp/tmpoJdGe8/sel_SWC371+1.p_1',co1) ).
fof(36,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [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) ) ) ) ) ) )
| segmentP(X2,X1)
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[35]) ).
fof(37,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [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) ) ) ) ) ) )
| segmentP(X2,X1)
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).
fof(81,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(82,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[81]) ).
cnf(83,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(115,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)],[19]) ).
fof(116,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)],[115]) ).
fof(117,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)],[116]) ).
fof(118,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)],[117]) ).
fof(119,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)],[118]) ).
cnf(123,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[119]) ).
cnf(150,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[26]) ).
fof(192,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ? [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) ) ) ) ) )
& ~ segmentP(X2,X1)
& ( nil = X4
| nil != X3 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(193,negated_conjecture,
? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& X11 = X13
& X10 = X12
& ? [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) ) ) ) ) )
& ~ segmentP(X11,X10)
& ( nil = X13
| nil != X12 ) ) ) ) ),
inference(variable_rename,[status(thm)],[192]) ).
fof(194,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)
& 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) ) ) ) )
& ~ segmentP(esk14_0,esk13_0)
& ( nil = esk16_0
| nil != esk15_0 ) ),
inference(skolemize,[status(esa)],[193]) ).
fof(195,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
& ~ segmentP(esk14_0,esk13_0)
& ( nil = esk16_0
| nil != esk15_0 )
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(shift_quantors,[status(thm)],[194]) ).
cnf(196,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(197,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(201,negated_conjecture,
~ segmentP(esk14_0,esk13_0),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(202,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[195]) ).
cnf(203,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[195]) ).
cnf(204,negated_conjecture,
ssList(esk17_0),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(206,negated_conjecture,
app(esk15_0,esk17_0) = esk16_0,
inference(split_conjunct,[status(thm)],[195]) ).
cnf(208,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[196,202,theory(equality)]) ).
cnf(209,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[197,203,theory(equality)]) ).
cnf(210,negated_conjecture,
~ segmentP(esk16_0,esk15_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[201,203,theory(equality)]),202,theory(equality)]) ).
cnf(372,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[123,83,theory(equality)]) ).
cnf(382,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[372,150,theory(equality)]) ).
cnf(383,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[382,theory(equality)]) ).
cnf(10102,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| ~ ssList(esk15_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[383,206,theory(equality)]) ).
cnf(10145,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[10102,208,theory(equality)]) ).
cnf(10146,negated_conjecture,
( segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[10145,theory(equality)]) ).
cnf(11675,negated_conjecture,
( ~ ssList(esk17_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[210,10146,theory(equality)]) ).
cnf(11680,negated_conjecture,
( ~ ssList(esk17_0)
| $false ),
inference(rw,[status(thm)],[11675,209,theory(equality)]) ).
cnf(11681,negated_conjecture,
~ ssList(esk17_0),
inference(cn,[status(thm)],[11680,theory(equality)]) ).
cnf(11696,negated_conjecture,
$false,
inference(sr,[status(thm)],[204,11681,theory(equality)]) ).
cnf(11697,negated_conjecture,
$false,
11696,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC371+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpoJdGe8/sel_SWC371+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC371+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC371+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC371+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
%
%------------------------------------------------------------------------------