TSTP Solution File: SWC003+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC003+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 10:03:52 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 13 unt; 0 def)
% Number of atoms : 395 ( 101 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 517 ( 189 ~; 192 |; 108 &)
% ( 1 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 67 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpi_Pdbd/sel_SWC003+1.p_1',ax21) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpi_Pdbd/sel_SWC003+1.p_1',ax15) ).
fof(22,axiom,
ssList(nil),
file('/tmp/tmpi_Pdbd/sel_SWC003+1.p_1',ax17) ).
fof(28,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpi_Pdbd/sel_SWC003+1.p_1',ax16) ).
fof(30,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X4
| app(X9,X10) != X3
| ? [X11] :
( ssItem(X11)
& X8 != X11
& memberP(X4,X11)
& geq(X11,X8) ) ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpi_Pdbd/sel_SWC003+1.p_1',co1) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X4
| app(X9,X10) != X3
| ? [X11] :
( ssItem(X11)
& X8 != X11
& memberP(X4,X11)
& geq(X11,X8) ) ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[30]) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X4
| app(X9,X10) != X3
| ? [X11] :
( ssItem(X11)
& X8 != X11
& memberP(X4,X11)
& geq(X11,X8) ) ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(82,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(83,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[82]) ).
fof(84,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[83]) ).
cnf(85,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(123,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(124,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[123]) ).
fof(125,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[124]) ).
fof(126,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)],[125]) ).
cnf(127,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[126]) ).
cnf(133,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[22]) ).
fof(161,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(162,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[161]) ).
fof(163,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[162]) ).
cnf(164,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[163]) ).
fof(168,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(app(X5,X6),X7) != X2
| app(X5,X7) != X1
| ~ neq(X6,nil) ) ) )
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& app(app(X9,cons(X8,nil)),X10) = X4
& app(X9,X10) = X3
& ! [X11] :
( ~ ssItem(X11)
| X8 = X11
| ~ memberP(X4,X11)
| ~ geq(X11,X8) ) ) ) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(169,negated_conjecture,
? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& ? [X15] :
( ssList(X15)
& X13 = X15
& X12 = X14
& ( ( neq(X13,nil)
& ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| ! [X18] :
( ~ ssList(X18)
| app(app(X16,X17),X18) != X13
| app(X16,X18) != X12
| ~ neq(X17,nil) ) ) )
& ? [X19] :
( ssItem(X19)
& ? [X20] :
( ssList(X20)
& ? [X21] :
( ssList(X21)
& app(app(X20,cons(X19,nil)),X21) = X15
& app(X20,X21) = X14
& ! [X22] :
( ~ ssItem(X22)
| X19 = X22
| ~ memberP(X15,X22)
| ~ geq(X22,X19) ) ) ) ) )
| ( neq(X13,nil)
& ~ neq(X15,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[168]) ).
fof(170,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( ( neq(esk8_0,nil)
& ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| ! [X18] :
( ~ ssList(X18)
| app(app(X16,X17),X18) != esk8_0
| app(X16,X18) != esk7_0
| ~ neq(X17,nil) ) ) )
& ssItem(esk11_0)
& ssList(esk12_0)
& ssList(esk13_0)
& app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
& app(esk12_0,esk13_0) = esk9_0
& ! [X22] :
( ~ ssItem(X22)
| esk11_0 = X22
| ~ memberP(esk10_0,X22)
| ~ geq(X22,esk11_0) ) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) ) ),
inference(skolemize,[status(esa)],[169]) ).
fof(171,negated_conjecture,
! [X16,X17,X18,X22] :
( ( ( ( ~ ssItem(X22)
| esk11_0 = X22
| ~ memberP(esk10_0,X22)
| ~ geq(X22,esk11_0) )
& app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
& app(esk12_0,esk13_0) = esk9_0
& ssList(esk13_0)
& ssList(esk12_0)
& ssItem(esk11_0)
& ( ~ ssList(X18)
| app(app(X16,X17),X18) != esk8_0
| app(X16,X18) != esk7_0
| ~ neq(X17,nil)
| ~ ssList(X17)
| ~ ssList(X16) )
& neq(esk8_0,nil) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[170]) ).
fof(172,negated_conjecture,
! [X16,X17,X18,X22] :
( ( neq(esk8_0,nil)
| ~ ssItem(X22)
| esk11_0 = X22
| ~ memberP(esk10_0,X22)
| ~ geq(X22,esk11_0) )
& ( ~ neq(esk10_0,nil)
| ~ ssItem(X22)
| esk11_0 = X22
| ~ memberP(esk10_0,X22)
| ~ geq(X22,esk11_0) )
& ( neq(esk8_0,nil)
| app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0 )
& ( ~ neq(esk10_0,nil)
| app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0 )
& ( neq(esk8_0,nil)
| app(esk12_0,esk13_0) = esk9_0 )
& ( ~ neq(esk10_0,nil)
| app(esk12_0,esk13_0) = esk9_0 )
& ( neq(esk8_0,nil)
| ssList(esk13_0) )
& ( ~ neq(esk10_0,nil)
| ssList(esk13_0) )
& ( neq(esk8_0,nil)
| ssList(esk12_0) )
& ( ~ neq(esk10_0,nil)
| ssList(esk12_0) )
& ( neq(esk8_0,nil)
| ssItem(esk11_0) )
& ( ~ neq(esk10_0,nil)
| ssItem(esk11_0) )
& ( neq(esk8_0,nil)
| ~ ssList(X18)
| app(app(X16,X17),X18) != esk8_0
| app(X16,X18) != esk7_0
| ~ neq(X17,nil)
| ~ ssList(X17)
| ~ ssList(X16) )
& ( ~ neq(esk10_0,nil)
| ~ ssList(X18)
| app(app(X16,X17),X18) != esk8_0
| app(X16,X18) != esk7_0
| ~ neq(X17,nil)
| ~ ssList(X17)
| ~ ssList(X16) )
& ( neq(esk8_0,nil)
| neq(esk8_0,nil) )
& ( ~ neq(esk10_0,nil)
| neq(esk8_0,nil) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[171]) ).
cnf(177,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[172]) ).
cnf(178,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[172]) ).
cnf(180,negated_conjecture,
( neq(esk8_0,nil)
| neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(181,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X2,nil)
| app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk8_0
| ~ ssList(X3)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(183,negated_conjecture,
( ssItem(esk11_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(185,negated_conjecture,
( ssList(esk12_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(187,negated_conjecture,
( ssList(esk13_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(189,negated_conjecture,
( app(esk12_0,esk13_0) = esk9_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(191,negated_conjecture,
( app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[172]) ).
cnf(198,negated_conjecture,
neq(esk10_0,nil),
inference(rw,[status(thm)],[180,178,theory(equality)]) ).
cnf(202,negated_conjecture,
( ssItem(esk11_0)
| $false ),
inference(rw,[status(thm)],[183,198,theory(equality)]) ).
cnf(203,negated_conjecture,
ssItem(esk11_0),
inference(cn,[status(thm)],[202,theory(equality)]) ).
cnf(204,negated_conjecture,
( ssList(esk12_0)
| $false ),
inference(rw,[status(thm)],[185,198,theory(equality)]) ).
cnf(205,negated_conjecture,
ssList(esk12_0),
inference(cn,[status(thm)],[204,theory(equality)]) ).
cnf(206,negated_conjecture,
( ssList(esk13_0)
| $false ),
inference(rw,[status(thm)],[187,198,theory(equality)]) ).
cnf(207,negated_conjecture,
ssList(esk13_0),
inference(cn,[status(thm)],[206,theory(equality)]) ).
cnf(213,negated_conjecture,
( app(esk12_0,esk13_0) = esk7_0
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[189,177,theory(equality)]) ).
cnf(214,negated_conjecture,
( app(esk12_0,esk13_0) = esk7_0
| $false ),
inference(rw,[status(thm)],[213,198,theory(equality)]) ).
cnf(215,negated_conjecture,
app(esk12_0,esk13_0) = esk7_0,
inference(cn,[status(thm)],[214,theory(equality)]) ).
cnf(228,negated_conjecture,
( app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
| $false ),
inference(rw,[status(thm)],[191,198,theory(equality)]) ).
cnf(229,negated_conjecture,
app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0,
inference(cn,[status(thm)],[228,theory(equality)]) ).
cnf(497,negated_conjecture,
( app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk10_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[181,178,theory(equality)]) ).
cnf(498,negated_conjecture,
( app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk10_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil)
| $false ),
inference(rw,[status(thm)],[497,198,theory(equality)]) ).
cnf(499,negated_conjecture,
( app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk10_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil) ),
inference(cn,[status(thm)],[498,theory(equality)]) ).
cnf(502,negated_conjecture,
( app(esk12_0,esk13_0) != esk7_0
| ~ neq(cons(esk11_0,nil),nil)
| ~ ssList(esk13_0)
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[499,229,theory(equality)]) ).
cnf(517,negated_conjecture,
( $false
| ~ neq(cons(esk11_0,nil),nil)
| ~ ssList(esk13_0)
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[502,215,theory(equality)]) ).
cnf(518,negated_conjecture,
( $false
| ~ neq(cons(esk11_0,nil),nil)
| $false
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[517,207,theory(equality)]) ).
cnf(519,negated_conjecture,
( $false
| ~ neq(cons(esk11_0,nil),nil)
| $false
| ~ ssList(cons(esk11_0,nil))
| $false ),
inference(rw,[status(thm)],[518,205,theory(equality)]) ).
cnf(520,negated_conjecture,
( ~ neq(cons(esk11_0,nil),nil)
| ~ ssList(cons(esk11_0,nil)) ),
inference(cn,[status(thm)],[519,theory(equality)]) ).
cnf(536,negated_conjecture,
( cons(esk11_0,nil) = nil
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[520,127,theory(equality)]) ).
cnf(537,negated_conjecture,
( cons(esk11_0,nil) = nil
| ~ ssList(cons(esk11_0,nil))
| $false ),
inference(rw,[status(thm)],[536,133,theory(equality)]) ).
cnf(538,negated_conjecture,
( cons(esk11_0,nil) = nil
| ~ ssList(cons(esk11_0,nil)) ),
inference(cn,[status(thm)],[537,theory(equality)]) ).
cnf(539,negated_conjecture,
( cons(esk11_0,nil) = nil
| ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[538,164,theory(equality)]) ).
cnf(540,negated_conjecture,
( cons(esk11_0,nil) = nil
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[539,133,theory(equality)]) ).
cnf(541,negated_conjecture,
( cons(esk11_0,nil) = nil
| $false
| $false ),
inference(rw,[status(thm)],[540,203,theory(equality)]) ).
cnf(542,negated_conjecture,
cons(esk11_0,nil) = nil,
inference(cn,[status(thm)],[541,theory(equality)]) ).
cnf(544,negated_conjecture,
( ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[85,542,theory(equality)]) ).
cnf(565,negated_conjecture,
( $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[544,133,theory(equality)]) ).
cnf(566,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[565,203,theory(equality)]) ).
cnf(567,negated_conjecture,
$false,
inference(cn,[status(thm)],[566,theory(equality)]) ).
cnf(568,negated_conjecture,
$false,
567,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC003+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpi_Pdbd/sel_SWC003+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC003+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC003+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC003+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
%
%------------------------------------------------------------------------------