TSTP Solution File: SWC348+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC348+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 11:36:50 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 17 unt; 0 def)
% Number of atoms : 312 ( 66 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 382 ( 149 ~; 160 |; 49 &)
% ( 3 <=>; 21 =>; 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 : 80 ( 0 sgn 52 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
strictorderedP(nil),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',ax69) ).
fof(3,axiom,
! [X1] :
( ssItem(X1)
=> strictorderedP(cons(X1,nil)) ),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',ax68) ).
fof(21,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',ax4) ).
fof(31,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',ax58) ).
fof(34,axiom,
ssList(nil),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',ax17) ).
fof(36,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',ax53) ).
fof(41,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',ax15) ).
fof(45,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)
& strictorderedP(X1) ) ) ) ) ) ),
file('/tmp/tmpCwj6It/sel_SWC348+1.p_1',co1) ).
fof(46,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)
& strictorderedP(X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[45]) ).
fof(50,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)
& strictorderedP(X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[46,theory(equality)]) ).
cnf(55,plain,
strictorderedP(nil),
inference(split_conjunct,[status(thm)],[2]) ).
fof(56,plain,
! [X1] :
( ~ ssItem(X1)
| strictorderedP(cons(X1,nil)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(57,plain,
! [X2] :
( ~ ssItem(X2)
| strictorderedP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[56]) ).
cnf(58,plain,
( strictorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(133,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)],[21]) ).
fof(134,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)],[133]) ).
fof(135,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)],[134]) ).
fof(136,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)],[135]) ).
fof(137,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)],[136]) ).
cnf(138,plain,
( cons(esk7_1(X1),nil) = X1
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(139,plain,
( ssItem(esk7_1(X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(188,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(189,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[188]) ).
fof(190,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[189]) ).
cnf(191,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(192,plain,
( nil = X1
| ~ ssList(X1)
| ~ segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(201,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[34]) ).
fof(215,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(216,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[215]) ).
fof(217,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[216]) ).
cnf(218,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[217]) ).
fof(233,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(234,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[233]) ).
fof(235,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[234]) ).
fof(236,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)],[235]) ).
cnf(237,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[236]) ).
fof(252,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)
| ~ strictorderedP(X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[50]) ).
fof(253,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)
| ~ strictorderedP(X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[252]) ).
fof(254,negated_conjecture,
( ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& ssList(esk17_0)
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& segmentP(esk17_0,esk16_0)
& ( singletonP(esk16_0)
| ~ neq(esk17_0,nil) )
& ( ~ segmentP(esk15_0,esk14_0)
| ~ strictorderedP(esk14_0) ) ),
inference(skolemize,[status(esa)],[253]) ).
cnf(255,negated_conjecture,
( ~ strictorderedP(esk14_0)
| ~ segmentP(esk15_0,esk14_0) ),
inference(split_conjunct,[status(thm)],[254]) ).
cnf(256,negated_conjecture,
( singletonP(esk16_0)
| ~ neq(esk17_0,nil) ),
inference(split_conjunct,[status(thm)],[254]) ).
cnf(257,negated_conjecture,
segmentP(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[254]) ).
cnf(258,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[254]) ).
cnf(259,negated_conjecture,
esk15_0 = esk17_0,
inference(split_conjunct,[status(thm)],[254]) ).
cnf(262,negated_conjecture,
ssList(esk15_0),
inference(split_conjunct,[status(thm)],[254]) ).
cnf(263,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[254]) ).
cnf(266,negated_conjecture,
ssList(esk17_0),
inference(rw,[status(thm)],[262,259,theory(equality)]) ).
cnf(267,negated_conjecture,
segmentP(esk17_0,esk14_0),
inference(rw,[status(thm)],[257,258,theory(equality)]) ).
cnf(268,negated_conjecture,
( singletonP(esk14_0)
| ~ neq(esk17_0,nil) ),
inference(rw,[status(thm)],[256,258,theory(equality)]) ).
cnf(269,negated_conjecture,
( ~ strictorderedP(esk14_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[255,259,theory(equality)]),267,theory(equality)]) ).
cnf(270,negated_conjecture,
~ strictorderedP(esk14_0),
inference(cn,[status(thm)],[269,theory(equality)]) ).
cnf(272,negated_conjecture,
( singletonP(esk14_0)
| esk17_0 = nil
| ~ ssList(nil)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[268,237,theory(equality)]) ).
cnf(273,negated_conjecture,
( singletonP(esk14_0)
| esk17_0 = nil
| $false
| ~ ssList(esk17_0) ),
inference(rw,[status(thm)],[272,201,theory(equality)]) ).
cnf(274,negated_conjecture,
( singletonP(esk14_0)
| esk17_0 = nil
| ~ ssList(esk17_0) ),
inference(cn,[status(thm)],[273,theory(equality)]) ).
cnf(299,plain,
( strictorderedP(X1)
| ~ ssItem(esk7_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[58,138,theory(equality)]) ).
cnf(310,negated_conjecture,
( segmentP(X1,esk14_0)
| ~ segmentP(X1,esk17_0)
| ~ ssList(esk14_0)
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[218,267,theory(equality)]) ).
cnf(314,negated_conjecture,
( segmentP(X1,esk14_0)
| ~ segmentP(X1,esk17_0)
| $false
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[310,263,theory(equality)]) ).
cnf(315,negated_conjecture,
( segmentP(X1,esk14_0)
| ~ segmentP(X1,esk17_0)
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[314,theory(equality)]) ).
cnf(562,negated_conjecture,
( singletonP(esk14_0)
| esk17_0 = nil
| $false ),
inference(rw,[status(thm)],[274,266,theory(equality)]) ).
cnf(563,negated_conjecture,
( singletonP(esk14_0)
| esk17_0 = nil ),
inference(cn,[status(thm)],[562,theory(equality)]) ).
cnf(606,negated_conjecture,
( segmentP(X1,esk14_0)
| ~ segmentP(X1,esk17_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[315,266,theory(equality)]) ).
cnf(607,negated_conjecture,
( segmentP(X1,esk14_0)
| ~ segmentP(X1,esk17_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[606,theory(equality)]) ).
cnf(609,negated_conjecture,
( segmentP(nil,esk14_0)
| ~ ssList(nil)
| nil != esk17_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[607,191,theory(equality)]) ).
cnf(615,negated_conjecture,
( segmentP(nil,esk14_0)
| $false
| nil != esk17_0
| ~ ssList(esk17_0) ),
inference(rw,[status(thm)],[609,201,theory(equality)]) ).
cnf(616,negated_conjecture,
( segmentP(nil,esk14_0)
| $false
| nil != esk17_0
| $false ),
inference(rw,[status(thm)],[615,266,theory(equality)]) ).
cnf(617,negated_conjecture,
( segmentP(nil,esk14_0)
| nil != esk17_0 ),
inference(cn,[status(thm)],[616,theory(equality)]) ).
cnf(620,negated_conjecture,
( nil = esk14_0
| ~ ssList(esk14_0)
| esk17_0 != nil ),
inference(spm,[status(thm)],[192,617,theory(equality)]) ).
cnf(623,negated_conjecture,
( nil = esk14_0
| $false
| esk17_0 != nil ),
inference(rw,[status(thm)],[620,263,theory(equality)]) ).
cnf(624,negated_conjecture,
( nil = esk14_0
| esk17_0 != nil ),
inference(cn,[status(thm)],[623,theory(equality)]) ).
cnf(655,plain,
( strictorderedP(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[299,139]) ).
cnf(656,negated_conjecture,
( strictorderedP(esk14_0)
| esk17_0 = nil
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[655,563,theory(equality)]) ).
cnf(657,negated_conjecture,
( strictorderedP(esk14_0)
| esk17_0 = nil
| $false ),
inference(rw,[status(thm)],[656,263,theory(equality)]) ).
cnf(658,negated_conjecture,
( strictorderedP(esk14_0)
| esk17_0 = nil ),
inference(cn,[status(thm)],[657,theory(equality)]) ).
cnf(659,negated_conjecture,
esk17_0 = nil,
inference(sr,[status(thm)],[658,270,theory(equality)]) ).
cnf(667,negated_conjecture,
( esk14_0 = nil
| $false ),
inference(rw,[status(thm)],[624,659,theory(equality)]) ).
cnf(668,negated_conjecture,
esk14_0 = nil,
inference(cn,[status(thm)],[667,theory(equality)]) ).
cnf(681,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[270,668,theory(equality)]),55,theory(equality)]) ).
cnf(682,negated_conjecture,
$false,
inference(cn,[status(thm)],[681,theory(equality)]) ).
cnf(683,negated_conjecture,
$false,
682,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC348+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpCwj6It/sel_SWC348+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC348+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC348+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC348+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
%
%------------------------------------------------------------------------------