%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC024+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 10:06:37 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 20 unt; 0 def)
% Number of atoms : 365 ( 94 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 472 ( 182 ~; 174 |; 90 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 73 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/tmp/tmpY0XeRm/sel_SWC024+1.p_1',ax42) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpY0XeRm/sel_SWC024+1.p_1',ax26) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpY0XeRm/sel_SWC024+1.p_1',ax46) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmpY0XeRm/sel_SWC024+1.p_1',ax5) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpY0XeRm/sel_SWC024+1.p_1',ax15) ).
fof(26,axiom,
ssList(nil),
file('/tmp/tmpY0XeRm/sel_SWC024+1.p_1',ax17) ).
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)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ( app(X3,X6) != X4
| ~ equalelemsP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X6
& ? [X9] :
( ssList(X9)
& app(X9,cons(X7,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
file('/tmp/tmpY0XeRm/sel_SWC024+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)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ( app(X3,X6) != X4
| ~ equalelemsP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X6
& ? [X9] :
( ssList(X9)
& app(X9,cons(X7,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[30]) ).
fof(32,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ( app(X3,X6) != X4
| ~ equalelemsP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X6
& ? [X9] :
( ssList(X9)
& app(X9,cons(X7,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(62,plain,
! [X1] :
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(63,plain,
! [X2] :
( ~ ssList(X2)
| frontsegP(X2,X2) ),
inference(variable_rename,[status(thm)],[62]) ).
cnf(64,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(70,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(72,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(77,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(nil,X1)
| nil = X1 )
& ( nil != X1
| frontsegP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(78,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(nil,X2)
| nil = X2 )
& ( nil != X2
| frontsegP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,plain,
! [X2] :
( ( ~ frontsegP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| frontsegP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[78]) ).
cnf(80,plain,
( frontsegP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(102,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X2,X3) != X1 )
| frontsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(103,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X5,X6) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ( ssList(esk3_2(X4,X5))
& app(X5,esk3_2(X4,X5)) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[103]) ).
fof(105,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5) )
& ( ~ frontsegP(X4,X5)
| ( ssList(esk3_2(X4,X5))
& app(X5,esk3_2(X4,X5)) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[104]) ).
fof(106,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk3_2(X4,X5))
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(X5,esk3_2(X4,X5)) = X4
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[105]) ).
cnf(109,plain,
( frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[106]) ).
fof(140,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(141,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[140]) ).
fof(142,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[141]) ).
fof(143,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)],[142]) ).
cnf(144,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(150,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[26]) ).
fof(167,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ frontsegP(X2,X5)
| ~ frontsegP(X1,X5) )
& ? [X6] :
( ssList(X6)
& app(X3,X6) = X4
& equalelemsP(X3)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X6
| ! [X9] :
( ~ ssList(X9)
| app(X9,cons(X7,nil)) != X3 ) ) ) )
& ( nil = X4
| nil != X3 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(168,negated_conjecture,
? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& X11 = X13
& X10 = X12
& neq(X11,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ frontsegP(X11,X14)
| ~ frontsegP(X10,X14) )
& ? [X15] :
( ssList(X15)
& app(X12,X15) = X13
& equalelemsP(X12)
& ! [X16] :
( ~ ssItem(X16)
| ! [X17] :
( ~ ssList(X17)
| app(cons(X16,nil),X17) != X15
| ! [X18] :
( ~ ssList(X18)
| app(X18,cons(X16,nil)) != X12 ) ) ) )
& ( nil = X13
| nil != X12 ) ) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,negated_conjecture,
( ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& ssList(esk13_0)
& esk11_0 = esk13_0
& esk10_0 = esk12_0
& neq(esk11_0,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ frontsegP(esk11_0,X14)
| ~ frontsegP(esk10_0,X14) )
& ssList(esk14_0)
& app(esk12_0,esk14_0) = esk13_0
& equalelemsP(esk12_0)
& ! [X16] :
( ~ ssItem(X16)
| ! [X17] :
( ~ ssList(X17)
| app(cons(X16,nil),X17) != esk14_0
| ! [X18] :
( ~ ssList(X18)
| app(X18,cons(X16,nil)) != esk12_0 ) ) )
& ( nil = esk13_0
| nil != esk12_0 ) ),
inference(skolemize,[status(esa)],[168]) ).
fof(170,negated_conjecture,
! [X14,X16,X17,X18] :
( ( ~ ssList(X18)
| app(X18,cons(X16,nil)) != esk12_0
| ~ ssList(X17)
| app(cons(X16,nil),X17) != esk14_0
| ~ ssItem(X16) )
& app(esk12_0,esk14_0) = esk13_0
& equalelemsP(esk12_0)
& ssList(esk14_0)
& ( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ frontsegP(esk11_0,X14)
| ~ frontsegP(esk10_0,X14) )
& esk11_0 = esk13_0
& esk10_0 = esk12_0
& neq(esk11_0,nil)
& ( nil = esk13_0
| nil != esk12_0 )
& ssList(esk13_0)
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0) ),
inference(shift_quantors,[status(thm)],[169]) ).
cnf(171,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(174,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(175,negated_conjecture,
( nil = esk13_0
| nil != esk12_0 ),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(176,negated_conjecture,
neq(esk11_0,nil),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(177,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[170]) ).
cnf(178,negated_conjecture,
esk11_0 = esk13_0,
inference(split_conjunct,[status(thm)],[170]) ).
cnf(179,negated_conjecture,
( ~ frontsegP(esk10_0,X1)
| ~ frontsegP(esk11_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(180,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(182,negated_conjecture,
app(esk12_0,esk14_0) = esk13_0,
inference(split_conjunct,[status(thm)],[170]) ).
cnf(184,negated_conjecture,
ssList(esk12_0),
inference(rw,[status(thm)],[171,177,theory(equality)]) ).
cnf(186,negated_conjecture,
neq(esk13_0,nil),
inference(rw,[status(thm)],[176,178,theory(equality)]) ).
cnf(187,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(er,[status(thm)],[80,theory(equality)]) ).
cnf(188,plain,
( frontsegP(nil,nil)
| $false ),
inference(rw,[status(thm)],[187,150,theory(equality)]) ).
cnf(189,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[188,theory(equality)]) ).
cnf(223,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(esk12_0,X1)
| ~ frontsegP(esk11_0,X1) ),
inference(rw,[status(thm)],[179,177,theory(equality)]) ).
cnf(224,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(esk12_0,X1)
| ~ frontsegP(esk13_0,X1) ),
inference(rw,[status(thm)],[223,178,theory(equality)]) ).
cnf(225,negated_conjecture,
( ~ frontsegP(esk12_0,esk13_0)
| ~ frontsegP(esk13_0,esk13_0)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[224,186,theory(equality)]) ).
cnf(226,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk12_0,X1)
| ~ frontsegP(esk13_0,X1)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[224,144,theory(equality)]) ).
cnf(228,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk12_0,X1)
| ~ frontsegP(esk13_0,X1)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[226,150,theory(equality)]) ).
cnf(229,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk12_0,X1)
| ~ frontsegP(esk13_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[228,theory(equality)]) ).
cnf(230,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(er,[status(thm)],[109,theory(equality)]) ).
cnf(371,negated_conjecture,
( ~ frontsegP(esk12_0,esk13_0)
| ~ ssList(esk13_0) ),
inference(csr,[status(thm)],[225,64]) ).
cnf(372,negated_conjecture,
~ frontsegP(esk12_0,esk13_0),
inference(spm,[status(thm)],[371,174,theory(equality)]) ).
cnf(393,negated_conjecture,
( esk12_0 = nil
| ~ frontsegP(esk13_0,esk12_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[229,64,theory(equality)]) ).
cnf(394,negated_conjecture,
( esk12_0 = nil
| ~ frontsegP(esk13_0,esk12_0)
| $false ),
inference(rw,[status(thm)],[393,184,theory(equality)]) ).
cnf(395,negated_conjecture,
( esk12_0 = nil
| ~ frontsegP(esk13_0,esk12_0) ),
inference(cn,[status(thm)],[394,theory(equality)]) ).
cnf(566,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[230,72]) ).
cnf(567,negated_conjecture,
( frontsegP(esk13_0,esk12_0)
| ~ ssList(esk14_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[566,182,theory(equality)]) ).
cnf(579,negated_conjecture,
( frontsegP(esk13_0,esk12_0)
| ~ ssList(esk14_0)
| $false ),
inference(rw,[status(thm)],[567,184,theory(equality)]) ).
cnf(580,negated_conjecture,
( frontsegP(esk13_0,esk12_0)
| ~ ssList(esk14_0) ),
inference(cn,[status(thm)],[579,theory(equality)]) ).
cnf(608,negated_conjecture,
frontsegP(esk13_0,esk12_0),
inference(spm,[status(thm)],[580,180,theory(equality)]) ).
cnf(615,negated_conjecture,
( esk12_0 = nil
| $false ),
inference(rw,[status(thm)],[395,608,theory(equality)]) ).
cnf(616,negated_conjecture,
esk12_0 = nil,
inference(cn,[status(thm)],[615,theory(equality)]) ).
cnf(640,negated_conjecture,
~ frontsegP(nil,esk13_0),
inference(rw,[status(thm)],[372,616,theory(equality)]) ).
cnf(645,negated_conjecture,
( esk13_0 = nil
| $false ),
inference(rw,[status(thm)],[175,616,theory(equality)]) ).
cnf(646,negated_conjecture,
esk13_0 = nil,
inference(cn,[status(thm)],[645,theory(equality)]) ).
cnf(675,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[640,646,theory(equality)]),189,theory(equality)]) ).
cnf(676,negated_conjecture,
$false,
inference(cn,[status(thm)],[675,theory(equality)]) ).
cnf(677,negated_conjecture,
$false,
676,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC024+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpY0XeRm/sel_SWC024+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC024+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC024+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC024+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
%
%------------------------------------------------------------------------------