TSTP Solution File: SWC013+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC013+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 10:05:22 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 11 unt; 0 def)
% Number of atoms : 386 ( 143 equ)
% Maximal formula atoms : 38 ( 6 avg)
% Number of connectives : 548 ( 223 ~; 222 |; 84 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 53 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax22) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax15) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax16) ).
fof(20,axiom,
ssList(nil),
file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax17) ).
fof(23,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| ? [X7] :
( ssList(X7)
& X1 = X7
& ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X7
& hd(X2) = X8
& neq(nil,X2) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpah920q/sel_SWC013+1.p_1',co1) ).
fof(24,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| ? [X7] :
( ssList(X7)
& X1 = X7
& ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X7
& hd(X2) = X8
& neq(nil,X2) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(25,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| ? [X7] :
( ssList(X7)
& X1 = X7
& ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X7
& hd(X2) = X8
& neq(nil,X2) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(78,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(79,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[78]) ).
cnf(80,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(102,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(103,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[103]) ).
fof(105,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)],[104]) ).
cnf(106,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(107,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[105]) ).
fof(108,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(109,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[108]) ).
fof(110,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[109]) ).
cnf(111,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(112,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[20]) ).
fof(123,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| X3 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X4) != X6
| ~ neq(nil,X4) ) )
& ! [X7] :
( ~ ssList(X7)
| X1 != X7
| ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X7
| hd(X2) != X8
| ~ neq(nil,X2) ) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(124,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& ( ( neq(X10,nil)
& ! [X13] :
( ~ ssList(X13)
| X11 = X13
| ! [X14] :
( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(X12) != X14
| ~ neq(nil,X12) ) )
& ! [X15] :
( ~ ssList(X15)
| X9 != X15
| ! [X16] :
( ~ ssItem(X16)
| cons(X16,nil) != X15
| hd(X10) != X16
| ~ neq(nil,X10) ) ) )
| ( neq(X10,nil)
& ~ neq(X12,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[123]) ).
fof(125,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)
& ! [X13] :
( ~ ssList(X13)
| esk8_0 = X13
| ! [X14] :
( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk9_0) != X14
| ~ neq(nil,esk9_0) ) )
& ! [X15] :
( ~ ssList(X15)
| esk6_0 != X15
| ! [X16] :
( ~ ssItem(X16)
| cons(X16,nil) != X15
| hd(esk7_0) != X16
| ~ neq(nil,esk7_0) ) ) )
| ( neq(esk7_0,nil)
& ~ neq(esk9_0,nil) ) ) ),
inference(skolemize,[status(esa)],[124]) ).
fof(126,negated_conjecture,
! [X13,X14,X15,X16] :
( ( ( ( ~ ssItem(X16)
| cons(X16,nil) != X15
| hd(esk7_0) != X16
| ~ neq(nil,esk7_0)
| ~ ssList(X15)
| esk6_0 != X15 )
& ( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk9_0) != X14
| ~ neq(nil,esk9_0)
| ~ ssList(X13)
| esk8_0 = X13 )
& neq(esk7_0,nil) )
| ( neq(esk7_0,nil)
& ~ neq(esk9_0,nil) ) )
& esk7_0 = esk9_0
& esk6_0 = esk8_0
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0) ),
inference(shift_quantors,[status(thm)],[125]) ).
fof(127,negated_conjecture,
! [X13,X14,X15,X16] :
( ( neq(esk7_0,nil)
| ~ ssItem(X16)
| cons(X16,nil) != X15
| hd(esk7_0) != X16
| ~ neq(nil,esk7_0)
| ~ ssList(X15)
| esk6_0 != X15 )
& ( ~ neq(esk9_0,nil)
| ~ ssItem(X16)
| cons(X16,nil) != X15
| hd(esk7_0) != X16
| ~ neq(nil,esk7_0)
| ~ ssList(X15)
| esk6_0 != X15 )
& ( neq(esk7_0,nil)
| ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk9_0) != X14
| ~ neq(nil,esk9_0)
| ~ ssList(X13)
| esk8_0 = X13 )
& ( ~ neq(esk9_0,nil)
| ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk9_0) != X14
| ~ neq(nil,esk9_0)
| ~ ssList(X13)
| esk8_0 = X13 )
& ( neq(esk7_0,nil)
| neq(esk7_0,nil) )
& ( ~ neq(esk9_0,nil)
| neq(esk7_0,nil) )
& esk7_0 = esk9_0
& esk6_0 = esk8_0
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0) ),
inference(distribute,[status(thm)],[126]) ).
cnf(129,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[127]) ).
cnf(132,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[127]) ).
cnf(133,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[127]) ).
cnf(135,negated_conjecture,
( neq(esk7_0,nil)
| neq(esk7_0,nil) ),
inference(split_conjunct,[status(thm)],[127]) ).
cnf(136,negated_conjecture,
( esk8_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk9_0)
| hd(esk9_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[127]) ).
cnf(138,negated_conjecture,
( esk6_0 != X1
| ~ ssList(X1)
| ~ neq(nil,esk7_0)
| hd(esk7_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[127]) ).
cnf(158,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[107,theory(equality)]) ).
cnf(231,negated_conjecture,
( esk6_0 = X1
| hd(esk9_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk9_0)
| ~ neq(esk9_0,nil) ),
inference(rw,[status(thm)],[136,132,theory(equality)]) ).
cnf(232,negated_conjecture,
( esk6_0 = X1
| hd(esk7_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk9_0)
| ~ neq(esk9_0,nil) ),
inference(rw,[status(thm)],[231,133,theory(equality)]) ).
cnf(233,negated_conjecture,
( esk6_0 = X1
| hd(esk7_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk7_0)
| ~ neq(esk9_0,nil) ),
inference(rw,[status(thm)],[232,133,theory(equality)]) ).
cnf(234,negated_conjecture,
( esk6_0 = X1
| hd(esk7_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk7_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[233,133,theory(equality)]),135,theory(equality)]) ).
cnf(235,negated_conjecture,
( esk6_0 = X1
| hd(esk7_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk7_0) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(262,negated_conjecture,
( esk6_0 != X1
| hd(esk7_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk7_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[138,133,theory(equality)]),135,theory(equality)]) ).
cnf(263,negated_conjecture,
( esk6_0 != X1
| hd(esk7_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk7_0) ),
inference(cn,[status(thm)],[262,theory(equality)]) ).
cnf(264,negated_conjecture,
( cons(X2,nil) != X1
| hd(esk7_0) != X2
| ~ neq(nil,esk7_0)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[263,235]) ).
cnf(265,negated_conjecture,
( nil = esk7_0
| cons(X1,nil) != X2
| hd(esk7_0) != X1
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(esk7_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[264,106,theory(equality)]) ).
cnf(267,negated_conjecture,
( nil = esk7_0
| cons(X1,nil) != X2
| hd(esk7_0) != X1
| ~ ssItem(X1)
| ~ ssList(X2)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[265,129,theory(equality)]) ).
cnf(268,negated_conjecture,
( nil = esk7_0
| cons(X1,nil) != X2
| hd(esk7_0) != X1
| ~ ssItem(X1)
| ~ ssList(X2)
| $false
| $false ),
inference(rw,[status(thm)],[267,112,theory(equality)]) ).
cnf(269,negated_conjecture,
( nil = esk7_0
| cons(X1,nil) != X2
| hd(esk7_0) != X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[268,theory(equality)]) ).
cnf(276,negated_conjecture,
( esk7_0 = nil
| cons(hd(esk7_0),nil) != X1
| ~ ssItem(hd(esk7_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[269,theory(equality)]) ).
cnf(307,negated_conjecture,
( esk7_0 = nil
| cons(hd(esk7_0),nil) != X1
| ~ ssList(X1)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[276,80,theory(equality)]) ).
cnf(308,negated_conjecture,
( esk7_0 = nil
| cons(hd(esk7_0),nil) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[307,129,theory(equality)]) ).
cnf(309,negated_conjecture,
( esk7_0 = nil
| cons(hd(esk7_0),nil) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[308,theory(equality)]) ).
cnf(310,negated_conjecture,
( esk7_0 = nil
| ~ ssList(cons(hd(esk7_0),nil)) ),
inference(er,[status(thm)],[309,theory(equality)]) ).
cnf(311,negated_conjecture,
( esk7_0 = nil
| ~ ssItem(hd(esk7_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[310,111,theory(equality)]) ).
cnf(312,negated_conjecture,
( esk7_0 = nil
| ~ ssItem(hd(esk7_0))
| $false ),
inference(rw,[status(thm)],[311,112,theory(equality)]) ).
cnf(313,negated_conjecture,
( esk7_0 = nil
| ~ ssItem(hd(esk7_0)) ),
inference(cn,[status(thm)],[312,theory(equality)]) ).
cnf(314,negated_conjecture,
( esk7_0 = nil
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[313,80,theory(equality)]) ).
cnf(315,negated_conjecture,
( esk7_0 = nil
| $false ),
inference(rw,[status(thm)],[314,129,theory(equality)]) ).
cnf(316,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[315,theory(equality)]) ).
cnf(317,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[135,316,theory(equality)]) ).
cnf(332,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[158,317,theory(equality)]) ).
cnf(334,negated_conjecture,
$false,
inference(rw,[status(thm)],[332,112,theory(equality)]) ).
cnf(335,negated_conjecture,
$false,
inference(cn,[status(thm)],[334,theory(equality)]) ).
cnf(336,negated_conjecture,
$false,
335,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC013+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpah920q/sel_SWC013+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC013+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC013+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC013+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
%
%------------------------------------------------------------------------------