TSTP Solution File: SWC332+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC332+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 11:30:43 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 18 unt; 0 def)
% Number of atoms : 239 ( 56 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 279 ( 103 ~; 108 |; 48 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 40 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpl9Zpe5/sel_SWC332+1.p_1',ax4) ).
fof(17,axiom,
equalelemsP(nil),
file('/tmp/tmpl9Zpe5/sel_SWC332+1.p_1',ax74) ).
fof(18,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/tmp/tmpl9Zpe5/sel_SWC332+1.p_1',ax73) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpl9Zpe5/sel_SWC332+1.p_1',ax58) ).
fof(21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpl9Zpe5/sel_SWC332+1.p_1',ax15) ).
fof(23,axiom,
ssList(nil),
file('/tmp/tmpl9Zpe5/sel_SWC332+1.p_1',ax17) ).
fof(31,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ( ~ singletonP(X3)
& neq(X4,nil) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ) ),
file('/tmp/tmpl9Zpe5/sel_SWC332+1.p_1',co1) ).
fof(32,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ( ~ singletonP(X3)
& neq(X4,nil) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[31]) ).
fof(34,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ( ~ singletonP(X3)
& neq(X4,nil) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[32,theory(equality)]) ).
fof(94,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ singletonP(X1)
| ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) )
& ( ! [X2] :
( ~ ssItem(X2)
| cons(X2,nil) != X1 )
| singletonP(X1) ) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(95,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(variable_rename,[status(thm)],[94]) ).
fof(96,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ( ssItem(esk7_1(X3))
& cons(esk7_1(X3),nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(skolemize,[status(esa)],[95]) ).
fof(97,plain,
! [X3,X5] :
( ( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3) )
& ( ~ singletonP(X3)
| ( ssItem(esk7_1(X3))
& cons(esk7_1(X3),nil) = X3 ) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[96]) ).
fof(98,plain,
! [X3,X5] :
( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3)
| ~ ssList(X3) )
& ( ssItem(esk7_1(X3))
| ~ singletonP(X3)
| ~ ssList(X3) )
& ( cons(esk7_1(X3),nil) = X3
| ~ singletonP(X3)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[97]) ).
cnf(99,plain,
( cons(esk7_1(X1),nil) = X1
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[98]) ).
cnf(100,plain,
( ssItem(esk7_1(X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[98]) ).
cnf(112,plain,
equalelemsP(nil),
inference(split_conjunct,[status(thm)],[17]) ).
fof(113,plain,
! [X1] :
( ~ ssItem(X1)
| equalelemsP(cons(X1,nil)) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(114,plain,
! [X2] :
( ~ ssItem(X2)
| equalelemsP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[113]) ).
cnf(115,plain,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[114]) ).
fof(120,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(121,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[120]) ).
fof(122,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[121]) ).
cnf(124,plain,
( nil = X1
| ~ ssList(X1)
| ~ segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[122]) ).
fof(125,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(126,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[125]) ).
fof(127,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[126]) ).
fof(128,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)],[127]) ).
cnf(129,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(135,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[23]) ).
fof(172,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& segmentP(X4,X3)
& ( singletonP(X3)
| ~ neq(X4,nil) )
& ( ~ segmentP(X2,X1)
| ~ equalelemsP(X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(173,negated_conjecture,
? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& X6 = X8
& X5 = X7
& segmentP(X8,X7)
& ( singletonP(X7)
| ~ neq(X8,nil) )
& ( ~ segmentP(X6,X5)
| ~ equalelemsP(X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[172]) ).
fof(174,negated_conjecture,
( ssList(esk12_0)
& ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& segmentP(esk15_0,esk14_0)
& ( singletonP(esk14_0)
| ~ neq(esk15_0,nil) )
& ( ~ segmentP(esk13_0,esk12_0)
| ~ equalelemsP(esk12_0) ) ),
inference(skolemize,[status(esa)],[173]) ).
cnf(175,negated_conjecture,
( ~ equalelemsP(esk12_0)
| ~ segmentP(esk13_0,esk12_0) ),
inference(split_conjunct,[status(thm)],[174]) ).
cnf(176,negated_conjecture,
( singletonP(esk14_0)
| ~ neq(esk15_0,nil) ),
inference(split_conjunct,[status(thm)],[174]) ).
cnf(177,negated_conjecture,
segmentP(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[174]) ).
cnf(178,negated_conjecture,
esk12_0 = esk14_0,
inference(split_conjunct,[status(thm)],[174]) ).
cnf(179,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[174]) ).
cnf(182,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[174]) ).
cnf(183,negated_conjecture,
ssList(esk12_0),
inference(split_conjunct,[status(thm)],[174]) ).
cnf(186,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[182,179,theory(equality)]) ).
cnf(187,negated_conjecture,
segmentP(esk15_0,esk12_0),
inference(rw,[status(thm)],[177,178,theory(equality)]) ).
cnf(188,negated_conjecture,
( singletonP(esk12_0)
| ~ neq(esk15_0,nil) ),
inference(rw,[status(thm)],[176,178,theory(equality)]) ).
cnf(192,negated_conjecture,
( ~ equalelemsP(esk12_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[175,179,theory(equality)]),187,theory(equality)]) ).
cnf(193,negated_conjecture,
~ equalelemsP(esk12_0),
inference(cn,[status(thm)],[192,theory(equality)]) ).
cnf(194,negated_conjecture,
( singletonP(esk12_0)
| esk15_0 = nil
| ~ ssList(nil)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[188,129,theory(equality)]) ).
cnf(195,negated_conjecture,
( singletonP(esk12_0)
| esk15_0 = nil
| $false
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[194,135,theory(equality)]) ).
cnf(196,negated_conjecture,
( singletonP(esk12_0)
| esk15_0 = nil
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[195,theory(equality)]) ).
cnf(231,plain,
( equalelemsP(X1)
| ~ ssItem(esk7_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[115,99,theory(equality)]) ).
cnf(410,negated_conjecture,
( singletonP(esk12_0)
| esk15_0 = nil
| $false ),
inference(rw,[status(thm)],[196,186,theory(equality)]) ).
cnf(411,negated_conjecture,
( singletonP(esk12_0)
| esk15_0 = nil ),
inference(cn,[status(thm)],[410,theory(equality)]) ).
cnf(462,plain,
( equalelemsP(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[231,100]) ).
cnf(463,negated_conjecture,
( equalelemsP(esk12_0)
| esk15_0 = nil
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[462,411,theory(equality)]) ).
cnf(464,negated_conjecture,
( equalelemsP(esk12_0)
| esk15_0 = nil
| $false ),
inference(rw,[status(thm)],[463,183,theory(equality)]) ).
cnf(465,negated_conjecture,
( equalelemsP(esk12_0)
| esk15_0 = nil ),
inference(cn,[status(thm)],[464,theory(equality)]) ).
cnf(466,negated_conjecture,
esk15_0 = nil,
inference(sr,[status(thm)],[465,193,theory(equality)]) ).
cnf(474,negated_conjecture,
segmentP(nil,esk12_0),
inference(rw,[status(thm)],[187,466,theory(equality)]) ).
cnf(482,negated_conjecture,
( nil = esk12_0
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[124,474,theory(equality)]) ).
cnf(489,negated_conjecture,
( nil = esk12_0
| $false ),
inference(rw,[status(thm)],[482,183,theory(equality)]) ).
cnf(490,negated_conjecture,
nil = esk12_0,
inference(cn,[status(thm)],[489,theory(equality)]) ).
cnf(515,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[193,490,theory(equality)]),112,theory(equality)]) ).
cnf(516,negated_conjecture,
$false,
inference(cn,[status(thm)],[515,theory(equality)]) ).
cnf(517,negated_conjecture,
$false,
516,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC332+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpl9Zpe5/sel_SWC332+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC332+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC332+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC332+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
%
%------------------------------------------------------------------------------