TSTP Solution File: SWC106+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC106+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 10:17:43 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 68 ( 15 unt; 0 def)
% Number of atoms : 318 ( 80 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 398 ( 148 ~; 150 |; 74 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 53 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpFdTAyu/sel_SWC106+1.p_1',ax21) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpFdTAyu/sel_SWC106+1.p_1',ax6) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpFdTAyu/sel_SWC106+1.p_1',ax15) ).
fof(20,axiom,
ssList(nil),
file('/tmp/tmpFdTAyu/sel_SWC106+1.p_1',ax17) ).
fof(26,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X3
| app(X6,cons(X5,nil)) != X4 ) ) )
| ( neq(X1,nil)
& rearsegP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpFdTAyu/sel_SWC106+1.p_1',co1) ).
fof(27,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X3
| app(X6,cons(X5,nil)) != X4 ) ) )
| ( neq(X1,nil)
& rearsegP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[26]) ).
fof(28,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X3
| app(X6,cons(X5,nil)) != X4 ) ) )
| ( neq(X1,nil)
& rearsegP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(70,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(72,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(91,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ rearsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X3,X2) != X1 )
| rearsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(92,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X6,X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[91]) ).
fof(93,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[92]) ).
fof(94,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5) )
& ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[93]) ).
fof(95,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk5_2(X4,X5))
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(esk5_2(X4,X5),X5) = X4
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[94]) ).
cnf(98,plain,
( rearsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X3,X2) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[95]) ).
fof(107,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(108,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[108]) ).
fof(110,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)],[109]) ).
cnf(111,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(117,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[20]) ).
fof(140,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& cons(X5,nil) = X3
& app(X6,cons(X5,nil)) = X4 ) )
& ( ~ neq(X1,nil)
| ~ rearsegP(X2,X1) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(141,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( ( neq(X8,nil)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& cons(X11,nil) = X9
& app(X12,cons(X11,nil)) = X10 ) )
& ( ~ neq(X7,nil)
| ~ rearsegP(X8,X7) ) )
| ( neq(X8,nil)
& ~ neq(X10,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[140]) ).
fof(142,negated_conjecture,
( ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& esk7_0 = esk9_0
& esk6_0 = esk8_0
& ( ( neq(esk7_0,nil)
& ssItem(esk10_0)
& ssList(esk11_0)
& cons(esk10_0,nil) = esk8_0
& app(esk11_0,cons(esk10_0,nil)) = esk9_0
& ( ~ neq(esk6_0,nil)
| ~ rearsegP(esk7_0,esk6_0) ) )
| ( neq(esk7_0,nil)
& ~ neq(esk9_0,nil) ) ) ),
inference(skolemize,[status(esa)],[141]) ).
fof(143,negated_conjecture,
( ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& esk7_0 = esk9_0
& esk6_0 = esk8_0
& ( neq(esk7_0,nil)
| neq(esk7_0,nil) )
& ( ~ neq(esk9_0,nil)
| neq(esk7_0,nil) )
& ( neq(esk7_0,nil)
| ssItem(esk10_0) )
& ( ~ neq(esk9_0,nil)
| ssItem(esk10_0) )
& ( neq(esk7_0,nil)
| ssList(esk11_0) )
& ( ~ neq(esk9_0,nil)
| ssList(esk11_0) )
& ( neq(esk7_0,nil)
| cons(esk10_0,nil) = esk8_0 )
& ( ~ neq(esk9_0,nil)
| cons(esk10_0,nil) = esk8_0 )
& ( neq(esk7_0,nil)
| app(esk11_0,cons(esk10_0,nil)) = esk9_0 )
& ( ~ neq(esk9_0,nil)
| app(esk11_0,cons(esk10_0,nil)) = esk9_0 )
& ( neq(esk7_0,nil)
| ~ neq(esk6_0,nil)
| ~ rearsegP(esk7_0,esk6_0) )
& ( ~ neq(esk9_0,nil)
| ~ neq(esk6_0,nil)
| ~ rearsegP(esk7_0,esk6_0) ) ),
inference(distribute,[status(thm)],[142]) ).
cnf(144,negated_conjecture,
( ~ rearsegP(esk7_0,esk6_0)
| ~ neq(esk6_0,nil)
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(146,negated_conjecture,
( app(esk11_0,cons(esk10_0,nil)) = esk9_0
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(148,negated_conjecture,
( cons(esk10_0,nil) = esk8_0
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(150,negated_conjecture,
( ssList(esk11_0)
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(152,negated_conjecture,
( ssItem(esk10_0)
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(155,negated_conjecture,
( neq(esk7_0,nil)
| neq(esk7_0,nil) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(156,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[143]) ).
cnf(157,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[143]) ).
cnf(160,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(161,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(168,negated_conjecture,
( ssList(esk11_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[150,157,theory(equality)]),155,theory(equality)]) ).
cnf(169,negated_conjecture,
ssList(esk11_0),
inference(cn,[status(thm)],[168,theory(equality)]) ).
cnf(170,negated_conjecture,
( ssItem(esk10_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[152,157,theory(equality)]),155,theory(equality)]) ).
cnf(171,negated_conjecture,
ssItem(esk10_0),
inference(cn,[status(thm)],[170,theory(equality)]) ).
cnf(180,negated_conjecture,
( cons(esk10_0,nil) = esk6_0
| ~ neq(esk9_0,nil) ),
inference(rw,[status(thm)],[148,156,theory(equality)]) ).
cnf(181,negated_conjecture,
( cons(esk10_0,nil) = esk6_0
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[180,157,theory(equality)]),155,theory(equality)]) ).
cnf(182,negated_conjecture,
cons(esk10_0,nil) = esk6_0,
inference(cn,[status(thm)],[181,theory(equality)]) ).
cnf(195,negated_conjecture,
( esk6_0 != nil
| ~ ssItem(esk10_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[72,182,theory(equality)]) ).
cnf(196,negated_conjecture,
( esk6_0 != nil
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[195,171,theory(equality)]) ).
cnf(197,negated_conjecture,
( esk6_0 != nil
| $false
| $false ),
inference(rw,[status(thm)],[196,117,theory(equality)]) ).
cnf(198,negated_conjecture,
esk6_0 != nil,
inference(cn,[status(thm)],[197,theory(equality)]) ).
cnf(206,negated_conjecture,
( app(esk11_0,esk6_0) = esk9_0
| ~ neq(esk9_0,nil) ),
inference(rw,[status(thm)],[146,182,theory(equality)]) ).
cnf(207,negated_conjecture,
( app(esk11_0,esk6_0) = esk7_0
| ~ neq(esk9_0,nil) ),
inference(rw,[status(thm)],[206,157,theory(equality)]) ).
cnf(208,negated_conjecture,
( app(esk11_0,esk6_0) = esk7_0
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[207,157,theory(equality)]),155,theory(equality)]) ).
cnf(209,negated_conjecture,
app(esk11_0,esk6_0) = esk7_0,
inference(cn,[status(thm)],[208,theory(equality)]) ).
cnf(215,negated_conjecture,
( ~ rearsegP(esk7_0,esk6_0)
| ~ neq(esk6_0,nil)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[144,157,theory(equality)]),155,theory(equality)]) ).
cnf(216,negated_conjecture,
( ~ rearsegP(esk7_0,esk6_0)
| ~ neq(esk6_0,nil) ),
inference(cn,[status(thm)],[215,theory(equality)]) ).
cnf(217,negated_conjecture,
( esk6_0 = nil
| ~ rearsegP(esk7_0,esk6_0)
| ~ ssList(nil)
| ~ ssList(esk6_0) ),
inference(spm,[status(thm)],[216,111,theory(equality)]) ).
cnf(218,negated_conjecture,
( esk6_0 = nil
| ~ rearsegP(esk7_0,esk6_0)
| $false
| ~ ssList(esk6_0) ),
inference(rw,[status(thm)],[217,117,theory(equality)]) ).
cnf(219,negated_conjecture,
( esk6_0 = nil
| ~ rearsegP(esk7_0,esk6_0)
| $false
| $false ),
inference(rw,[status(thm)],[218,161,theory(equality)]) ).
cnf(220,negated_conjecture,
( esk6_0 = nil
| ~ rearsegP(esk7_0,esk6_0) ),
inference(cn,[status(thm)],[219,theory(equality)]) ).
cnf(265,negated_conjecture,
( rearsegP(X1,esk6_0)
| esk7_0 != X1
| ~ ssList(esk11_0)
| ~ ssList(esk6_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[98,209,theory(equality)]) ).
cnf(269,negated_conjecture,
( rearsegP(X1,esk6_0)
| esk7_0 != X1
| $false
| ~ ssList(esk6_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[265,169,theory(equality)]) ).
cnf(270,negated_conjecture,
( rearsegP(X1,esk6_0)
| esk7_0 != X1
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[269,161,theory(equality)]) ).
cnf(271,negated_conjecture,
( rearsegP(X1,esk6_0)
| esk7_0 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[270,theory(equality)]) ).
cnf(416,negated_conjecture,
~ rearsegP(esk7_0,esk6_0),
inference(sr,[status(thm)],[220,198,theory(equality)]) ).
cnf(638,negated_conjecture,
( rearsegP(esk7_0,esk6_0)
| ~ ssList(esk7_0) ),
inference(er,[status(thm)],[271,theory(equality)]) ).
cnf(639,negated_conjecture,
( rearsegP(esk7_0,esk6_0)
| $false ),
inference(rw,[status(thm)],[638,160,theory(equality)]) ).
cnf(640,negated_conjecture,
rearsegP(esk7_0,esk6_0),
inference(cn,[status(thm)],[639,theory(equality)]) ).
cnf(641,negated_conjecture,
$false,
inference(sr,[status(thm)],[640,416,theory(equality)]) ).
cnf(642,negated_conjecture,
$false,
641,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC106+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpFdTAyu/sel_SWC106+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC106+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC106+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC106+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
%
%------------------------------------------------------------------------------