TSTP Solution File: SWC211+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC211+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 10:52:01 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 7
% Syntax : Number of formulae : 86 ( 17 unt; 0 def)
% Number of atoms : 366 ( 166 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 437 ( 157 ~; 186 |; 71 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 61 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpzVVRZ7/sel_SWC211+1.p_1',ax83) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpzVVRZ7/sel_SWC211+1.p_1',ax81) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpzVVRZ7/sel_SWC211+1.p_1',ax20) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpzVVRZ7/sel_SWC211+1.p_1',ax15) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpzVVRZ7/sel_SWC211+1.p_1',ax16) ).
fof(12,axiom,
ssList(nil),
file('/tmp/tmpzVVRZ7/sel_SWC211+1.p_1',ax17) ).
fof(19,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)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| neq(X1,nil)
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
file('/tmp/tmpzVVRZ7/sel_SWC211+1.p_1',co1) ).
fof(20,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)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| neq(X1,nil)
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(21,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)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| neq(X1,nil)
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).
fof(42,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( nil != app(X1,X2)
| ( nil = X2
& nil = X1 ) )
& ( nil != X2
| nil != X1
| nil = app(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(43,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[43]) ).
fof(45,plain,
! [X3,X4] :
( ( nil = X4
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil = X3
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[44]) ).
cnf(47,plain,
( nil = X1
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(48,plain,
( nil = X2
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(53,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(54,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[54]) ).
cnf(56,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(58,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk3_1(X4))
& ssItem(esk4_1(X4))
& cons(esk4_1(X4),esk3_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[58]) ).
fof(60,plain,
! [X4] :
( ( ssList(esk3_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk4_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk4_1(X4),esk3_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[59]) ).
cnf(61,plain,
( nil = X1
| cons(esk4_1(X1),esk3_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[60]) ).
cnf(62,plain,
( nil = X1
| ssItem(esk4_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[60]) ).
cnf(63,plain,
( nil = X1
| ssList(esk3_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(64,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(65,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[65]) ).
fof(67,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)],[66]) ).
cnf(68,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(70,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(71,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[71]) ).
cnf(73,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[12]) ).
fof(102,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)
| app(X6,cons(X5,nil)) = X3
| app(cons(X5,nil),X6) != X4 ) )
& ~ neq(X1,nil)
& ( nil = X3
| nil != X4 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(103,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)
| app(X12,cons(X11,nil)) = X9
| app(cons(X11,nil),X12) != X10 ) )
& ~ neq(X7,nil)
& ( nil = X9
| nil != X10 ) ) ) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,negated_conjecture,
( ssList(esk5_0)
& ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& neq(esk6_0,nil)
& ! [X11] :
( ~ ssItem(X11)
| ! [X12] :
( ~ ssList(X12)
| app(X12,cons(X11,nil)) = esk7_0
| app(cons(X11,nil),X12) != esk8_0 ) )
& ~ neq(esk5_0,nil)
& ( nil = esk7_0
| nil != esk8_0 ) ),
inference(skolemize,[status(esa)],[103]) ).
fof(105,negated_conjecture,
! [X11,X12] :
( ( ~ ssList(X12)
| app(X12,cons(X11,nil)) = esk7_0
| app(cons(X11,nil),X12) != esk8_0
| ~ ssItem(X11) )
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& neq(esk6_0,nil)
& ~ neq(esk5_0,nil)
& ( nil = esk7_0
| nil != esk8_0 )
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0) ),
inference(shift_quantors,[status(thm)],[104]) ).
cnf(107,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(108,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(111,negated_conjecture,
~ neq(esk5_0,nil),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(112,negated_conjecture,
neq(esk6_0,nil),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(113,negated_conjecture,
esk5_0 = esk7_0,
inference(split_conjunct,[status(thm)],[105]) ).
cnf(114,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[105]) ).
cnf(115,negated_conjecture,
( app(X2,cons(X1,nil)) = esk7_0
| ~ ssItem(X1)
| app(cons(X1,nil),X2) != esk8_0
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(117,negated_conjecture,
ssList(esk8_0),
inference(rw,[status(thm)],[107,114,theory(equality)]) ).
cnf(118,negated_conjecture,
neq(esk8_0,nil),
inference(rw,[status(thm)],[112,114,theory(equality)]) ).
cnf(119,negated_conjecture,
~ neq(esk7_0,nil),
inference(rw,[status(thm)],[111,113,theory(equality)]) ).
cnf(127,negated_conjecture,
( esk7_0 = nil
| ~ ssList(nil)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[119,68,theory(equality)]) ).
cnf(128,negated_conjecture,
( esk7_0 = nil
| $false
| ~ ssList(esk7_0) ),
inference(rw,[status(thm)],[127,74,theory(equality)]) ).
cnf(129,negated_conjecture,
( esk7_0 = nil
| ~ ssList(esk7_0) ),
inference(cn,[status(thm)],[128,theory(equality)]) ).
cnf(221,negated_conjecture,
esk7_0 = nil,
inference(spm,[status(thm)],[129,108,theory(equality)]) ).
cnf(226,negated_conjecture,
~ neq(nil,nil),
inference(rw,[status(thm)],[119,221,theory(equality)]) ).
cnf(230,negated_conjecture,
( app(X1,cons(X2,nil)) = nil
| app(cons(X2,nil),X1) != esk8_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(rw,[status(thm)],[115,221,theory(equality)]) ).
cnf(242,negated_conjecture,
( app(X1,cons(X2,nil)) = nil
| cons(X2,X1) != esk8_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[230,56,theory(equality)]) ).
cnf(249,negated_conjecture,
( app(esk3_1(X1),cons(esk4_1(X1),nil)) = nil
| nil = X1
| X1 != esk8_0
| ~ ssList(esk3_1(X1))
| ~ ssItem(esk4_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[242,61,theory(equality)]) ).
cnf(2261,negated_conjecture,
( app(esk3_1(X1),cons(esk4_1(X1),nil)) = nil
| nil = X1
| X1 != esk8_0
| ~ ssList(esk3_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[249,62]) ).
cnf(2262,negated_conjecture,
( app(esk3_1(X1),cons(esk4_1(X1),nil)) = nil
| nil = X1
| X1 != esk8_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2261,63]) ).
cnf(2263,negated_conjecture,
( app(esk3_1(esk8_0),cons(esk4_1(esk8_0),nil)) = nil
| nil = esk8_0
| ~ ssList(esk8_0) ),
inference(er,[status(thm)],[2262,theory(equality)]) ).
cnf(2264,negated_conjecture,
( app(esk3_1(esk8_0),cons(esk4_1(esk8_0),nil)) = nil
| nil = esk8_0
| $false ),
inference(rw,[status(thm)],[2263,117,theory(equality)]) ).
cnf(2265,negated_conjecture,
( app(esk3_1(esk8_0),cons(esk4_1(esk8_0),nil)) = nil
| nil = esk8_0 ),
inference(cn,[status(thm)],[2264,theory(equality)]) ).
cnf(2268,negated_conjecture,
( nil = esk3_1(esk8_0)
| esk8_0 = nil
| ~ ssList(cons(esk4_1(esk8_0),nil))
| ~ ssList(esk3_1(esk8_0)) ),
inference(spm,[status(thm)],[47,2265,theory(equality)]) ).
cnf(2290,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| ~ ssList(cons(esk4_1(esk8_0),nil))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[2268,63,theory(equality)]) ).
cnf(2291,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| ~ ssList(cons(esk4_1(esk8_0),nil))
| $false ),
inference(rw,[status(thm)],[2290,117,theory(equality)]) ).
cnf(2292,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| ~ ssList(cons(esk4_1(esk8_0),nil)) ),
inference(cn,[status(thm)],[2291,theory(equality)]) ).
cnf(2293,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssItem(esk4_1(esk8_0)) ),
inference(spm,[status(thm)],[2292,73,theory(equality)]) ).
cnf(2295,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| $false
| ~ ssItem(esk4_1(esk8_0)) ),
inference(rw,[status(thm)],[2293,74,theory(equality)]) ).
cnf(2296,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| ~ ssItem(esk4_1(esk8_0)) ),
inference(cn,[status(thm)],[2295,theory(equality)]) ).
cnf(2297,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[2296,62,theory(equality)]) ).
cnf(2298,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[2297,117,theory(equality)]) ).
cnf(2299,negated_conjecture,
( esk3_1(esk8_0) = nil
| esk8_0 = nil ),
inference(cn,[status(thm)],[2298,theory(equality)]) ).
cnf(2301,negated_conjecture,
( cons(esk4_1(esk8_0),nil) = esk8_0
| nil = esk8_0
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[61,2299,theory(equality)]) ).
cnf(2309,negated_conjecture,
( cons(esk4_1(esk8_0),nil) = esk8_0
| nil = esk8_0
| $false ),
inference(rw,[status(thm)],[2301,117,theory(equality)]) ).
cnf(2310,negated_conjecture,
( cons(esk4_1(esk8_0),nil) = esk8_0
| nil = esk8_0 ),
inference(cn,[status(thm)],[2309,theory(equality)]) ).
cnf(2367,negated_conjecture,
( app(esk3_1(esk8_0),esk8_0) = nil
| esk8_0 = nil ),
inference(spm,[status(thm)],[2265,2310,theory(equality)]) ).
cnf(2486,negated_conjecture,
( nil = esk8_0
| ~ ssList(esk8_0)
| ~ ssList(esk3_1(esk8_0)) ),
inference(spm,[status(thm)],[48,2367,theory(equality)]) ).
cnf(2510,negated_conjecture,
( nil = esk8_0
| $false
| ~ ssList(esk3_1(esk8_0)) ),
inference(rw,[status(thm)],[2486,117,theory(equality)]) ).
cnf(2511,negated_conjecture,
( nil = esk8_0
| ~ ssList(esk3_1(esk8_0)) ),
inference(cn,[status(thm)],[2510,theory(equality)]) ).
cnf(2551,negated_conjecture,
( esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[2511,63,theory(equality)]) ).
cnf(2553,negated_conjecture,
( esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[2551,117,theory(equality)]) ).
cnf(2554,negated_conjecture,
esk8_0 = nil,
inference(cn,[status(thm)],[2553,theory(equality)]) ).
cnf(2559,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[118,2554,theory(equality)]) ).
cnf(2560,negated_conjecture,
$false,
inference(sr,[status(thm)],[2559,226,theory(equality)]) ).
cnf(2561,negated_conjecture,
$false,
2560,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC211+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpzVVRZ7/sel_SWC211+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC211+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC211+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC211+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
%
%------------------------------------------------------------------------------