TSTP Solution File: SWC240+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC240+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 11:03:40 EST 2010
% Result : Theorem 0.38s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 7 unt; 0 def)
% Number of atoms : 376 ( 99 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 515 ( 198 ~; 188 |; 102 &)
% ( 1 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 147 ( 0 sgn 72 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax81) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax28) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax20) ).
fof(20,axiom,
ssList(nil),
file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax17) ).
fof(25,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax93) ).
fof(28,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax16) ).
fof(30,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X3,X10) ) ) ) ) ) ) ),
file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',co1) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X3,X10) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[30]) ).
fof(35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X3,X10) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(50,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(51,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[51]) ).
cnf(53,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(62,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(63,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[62]) ).
cnf(64,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(77,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(78,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk1_1(X4))
& ssItem(esk2_1(X4))
& cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[78]) ).
fof(80,plain,
! [X4] :
( ( ssList(esk1_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk2_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk2_1(X4),esk1_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[79]) ).
cnf(81,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(82,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(83,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(121,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[20]) ).
fof(143,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ( ( ~ lt(X1,X2)
| ( X1 != X2
& leq(X1,X2) ) )
& ( X1 = X2
| ~ leq(X1,X2)
| lt(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(144,plain,
! [X3] :
( ~ ssItem(X3)
| ! [X4] :
( ~ ssItem(X4)
| ( ( ~ lt(X3,X4)
| ( X3 != X4
& leq(X3,X4) ) )
& ( X3 = X4
| ~ leq(X3,X4)
| lt(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ( ( ~ lt(X3,X4)
| ( X3 != X4
& leq(X3,X4) ) )
& ( X3 = X4
| ~ leq(X3,X4)
| lt(X3,X4) ) )
| ~ ssItem(X3) ),
inference(shift_quantors,[status(thm)],[144]) ).
fof(146,plain,
! [X3,X4] :
( ( X3 != X4
| ~ lt(X3,X4)
| ~ ssItem(X4)
| ~ ssItem(X3) )
& ( leq(X3,X4)
| ~ lt(X3,X4)
| ~ ssItem(X4)
| ~ ssItem(X3) )
& ( X3 = X4
| ~ leq(X3,X4)
| lt(X3,X4)
| ~ ssItem(X4)
| ~ ssItem(X3) ) ),
inference(distribute,[status(thm)],[145]) ).
cnf(148,plain,
( leq(X1,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2) ),
inference(split_conjunct,[status(thm)],[146]) ).
fof(160,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(161,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[160]) ).
fof(162,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[161]) ).
cnf(163,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[162]) ).
fof(167,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& nil != X1
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(app(X6,cons(X5,nil)),X7) != X1
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& memberP(X7,X8)
& lt(X5,X8)
& ~ leq(X5,X8) ) ) ) )
& ? [X9] :
( ssItem(X9)
& ! [X10] :
( ~ ssItem(X10)
| X9 = X10
| ~ memberP(X3,X10) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(168,negated_conjecture,
? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& X12 = X14
& X11 = X13
& nil != X11
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != X11
| ? [X18] :
( ssItem(X18)
& memberP(X16,X18)
& memberP(X17,X18)
& lt(X15,X18)
& ~ leq(X15,X18) ) ) ) )
& ? [X19] :
( ssItem(X19)
& ! [X20] :
( ~ ssItem(X20)
| X19 = X20
| ~ memberP(X13,X20) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& nil != esk7_0
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ( ssItem(esk11_3(X15,X16,X17))
& memberP(X16,esk11_3(X15,X16,X17))
& memberP(X17,esk11_3(X15,X16,X17))
& lt(X15,esk11_3(X15,X16,X17))
& ~ leq(X15,esk11_3(X15,X16,X17)) ) ) ) )
& ssItem(esk12_0)
& ! [X20] :
( ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk9_0,X20) ) ),
inference(skolemize,[status(esa)],[168]) ).
fof(170,negated_conjecture,
! [X15,X16,X17,X20] :
( ( ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk9_0,X20) )
& ssItem(esk12_0)
& ( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ( ssItem(esk11_3(X15,X16,X17))
& memberP(X16,esk11_3(X15,X16,X17))
& memberP(X17,esk11_3(X15,X16,X17))
& lt(X15,esk11_3(X15,X16,X17))
& ~ leq(X15,esk11_3(X15,X16,X17)) )
| ~ ssList(X16)
| ~ ssItem(X15) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& nil != esk7_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[169]) ).
fof(171,negated_conjecture,
! [X15,X16,X17,X20] :
( ( ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk9_0,X20) )
& ssItem(esk12_0)
& ( ssItem(esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X16,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X17,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( lt(X15,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( ~ leq(X15,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& nil != esk7_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[170]) ).
cnf(172,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(176,negated_conjecture,
nil != esk7_0,
inference(split_conjunct,[status(thm)],[171]) ).
cnf(179,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk7_0
| ~ ssList(X3)
| ~ leq(X1,esk11_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(180,negated_conjecture,
( lt(X1,esk11_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk7_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(183,negated_conjecture,
( ssItem(esk11_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk7_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(278,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk7_0
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ lt(X2,esk11_3(X2,X1,X3))
| ~ ssItem(esk11_3(X2,X1,X3)) ),
inference(spm,[status(thm)],[179,148,theory(equality)]) ).
cnf(3050,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk7_0
| ~ lt(X2,esk11_3(X2,X1,X3))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[278,183]) ).
cnf(3051,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk7_0
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[3050,180]) ).
cnf(3053,negated_conjecture,
( app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[3051,64,theory(equality)]) ).
cnf(3065,negated_conjecture,
( app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false
| ~ ssList(cons(X1,nil)) ),
inference(rw,[status(thm)],[3053,121,theory(equality)]) ).
cnf(3066,negated_conjecture,
( app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[3065,theory(equality)]) ).
cnf(3207,negated_conjecture,
( cons(X1,X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[3066,53,theory(equality)]) ).
cnf(3269,negated_conjecture,
( cons(X1,X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3207,163,theory(equality)]) ).
cnf(3270,negated_conjecture,
( cons(X1,X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[3269,121,theory(equality)]) ).
cnf(3271,negated_conjecture,
( cons(X1,X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[3270,theory(equality)]) ).
cnf(3272,negated_conjecture,
( nil = X1
| X1 != esk7_0
| ~ ssItem(esk2_1(X1))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[3271,81,theory(equality)]) ).
cnf(3279,negated_conjecture,
( nil = X1
| X1 != esk7_0
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[3272,83]) ).
cnf(3280,negated_conjecture,
( nil = X1
| X1 != esk7_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[3279,82]) ).
cnf(3281,negated_conjecture,
nil = esk7_0,
inference(spm,[status(thm)],[3280,172,theory(equality)]) ).
cnf(3289,negated_conjecture,
$false,
inference(sr,[status(thm)],[3281,176,theory(equality)]) ).
cnf(3290,negated_conjecture,
$false,
3289,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC240+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpo8PqqB/sel_SWC240+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC240+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC240+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC240+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
%
%------------------------------------------------------------------------------