TSTP Solution File: SWC402+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC402+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 11:43:56 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 343 ( 66 equ)
% Maximal formula atoms : 29 ( 7 avg)
% Number of connectives : 482 ( 184 ~; 173 |; 107 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Maximal term depth : 3 ( 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 : 126 ( 0 sgn 76 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpCgq1CK/sel_SWC402+1.p_1',ax26) ).
fof(24,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpCgq1CK/sel_SWC402+1.p_1',ax36) ).
fof(32,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,X3),X6) != X4
| ~ totalorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& leq(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& leq(X13,X11) ) ) ) ) ) )
| ! [X15] :
( ~ ssItem(X15)
| ~ memberP(X1,X15)
| memberP(X2,X15) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
file('/tmp/tmpCgq1CK/sel_SWC402+1.p_1',co1) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,X3),X6) != X4
| ~ totalorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& leq(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& leq(X13,X11) ) ) ) ) ) )
| ! [X15] :
( ~ ssItem(X15)
| ~ memberP(X1,X15)
| memberP(X2,X15) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[32]) ).
fof(35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,X3),X6) != X4
| ~ totalorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& leq(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& leq(X13,X11) ) ) ) ) ) )
| ! [X15] :
( ~ ssItem(X15)
| ~ memberP(X1,X15)
| memberP(X2,X15) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).
fof(86,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(87,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[86]) ).
fof(88,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[87]) ).
cnf(89,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(137,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ( ( ~ memberP(app(X2,X3),X1)
| memberP(X2,X1)
| memberP(X3,X1) )
& ( ( ~ memberP(X2,X1)
& ~ memberP(X3,X1) )
| memberP(app(X2,X3),X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(138,plain,
! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ memberP(app(X5,X6),X4)
| memberP(X5,X4)
| memberP(X6,X4) )
& ( ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) )
| memberP(app(X5,X6),X4) ) ) ) ) ),
inference(variable_rename,[status(thm)],[137]) ).
fof(139,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ( ( ~ memberP(app(X5,X6),X4)
| memberP(X5,X4)
| memberP(X6,X4) )
& ( ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) )
| memberP(app(X5,X6),X4) ) )
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(shift_quantors,[status(thm)],[138]) ).
fof(140,plain,
! [X4,X5,X6] :
( ( ~ memberP(app(X5,X6),X4)
| memberP(X5,X4)
| memberP(X6,X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) )
& ( ~ memberP(X5,X4)
| memberP(app(X5,X6),X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) )
& ( ~ memberP(X6,X4)
| memberP(app(X5,X6),X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ) ),
inference(distribute,[status(thm)],[139]) ).
cnf(141,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(split_conjunct,[status(thm)],[140]) ).
cnf(142,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,X1) ),
inference(split_conjunct,[status(thm)],[140]) ).
fof(184,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,X3),X6) = X4
& totalorderedP(X3)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X5
| ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X3
| ~ leq(X7,X9) ) ) ) )
& ! [X11] :
( ~ ssItem(X11)
| ! [X12] :
( ~ ssList(X12)
| app(cons(X11,nil),X12) != X6
| ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| app(X14,cons(X13,nil)) != X3
| ~ leq(X13,X11) ) ) ) ) ) )
& ? [X15] :
( ssItem(X15)
& memberP(X1,X15)
& ~ memberP(X2,X15) )
& ( nil = X4
| nil != X3 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(185,negated_conjecture,
? [X16] :
( ssList(X16)
& ? [X17] :
( ssList(X17)
& ? [X18] :
( ssList(X18)
& ? [X19] :
( ssList(X19)
& X17 = X19
& X16 = X18
& ? [X20] :
( ssList(X20)
& ? [X21] :
( ssList(X21)
& app(app(X20,X18),X21) = X19
& totalorderedP(X18)
& ! [X22] :
( ~ ssItem(X22)
| ! [X23] :
( ~ ssList(X23)
| app(X23,cons(X22,nil)) != X20
| ! [X24] :
( ~ ssItem(X24)
| ! [X25] :
( ~ ssList(X25)
| app(cons(X24,nil),X25) != X18
| ~ leq(X22,X24) ) ) ) )
& ! [X26] :
( ~ ssItem(X26)
| ! [X27] :
( ~ ssList(X27)
| app(cons(X26,nil),X27) != X21
| ! [X28] :
( ~ ssItem(X28)
| ! [X29] :
( ~ ssList(X29)
| app(X29,cons(X28,nil)) != X18
| ~ leq(X28,X26) ) ) ) ) ) )
& ? [X30] :
( ssItem(X30)
& memberP(X16,X30)
& ~ memberP(X17,X30) )
& ( nil = X19
| nil != X18 ) ) ) ) ),
inference(variable_rename,[status(thm)],[184]) ).
fof(186,negated_conjecture,
( ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& ssList(esk17_0)
& ssList(esk18_0)
& app(app(esk17_0,esk15_0),esk18_0) = esk16_0
& totalorderedP(esk15_0)
& ! [X22] :
( ~ ssItem(X22)
| ! [X23] :
( ~ ssList(X23)
| app(X23,cons(X22,nil)) != esk17_0
| ! [X24] :
( ~ ssItem(X24)
| ! [X25] :
( ~ ssList(X25)
| app(cons(X24,nil),X25) != esk15_0
| ~ leq(X22,X24) ) ) ) )
& ! [X26] :
( ~ ssItem(X26)
| ! [X27] :
( ~ ssList(X27)
| app(cons(X26,nil),X27) != esk18_0
| ! [X28] :
( ~ ssItem(X28)
| ! [X29] :
( ~ ssList(X29)
| app(X29,cons(X28,nil)) != esk15_0
| ~ leq(X28,X26) ) ) ) )
& ssItem(esk19_0)
& memberP(esk13_0,esk19_0)
& ~ memberP(esk14_0,esk19_0)
& ( nil = esk16_0
| nil != esk15_0 ) ),
inference(skolemize,[status(esa)],[185]) ).
fof(187,negated_conjecture,
! [X22,X23,X24,X25,X26,X27,X28,X29] :
( ( ~ ssList(X29)
| app(X29,cons(X28,nil)) != esk15_0
| ~ leq(X28,X26)
| ~ ssItem(X28)
| ~ ssList(X27)
| app(cons(X26,nil),X27) != esk18_0
| ~ ssItem(X26) )
& ( ~ ssList(X25)
| app(cons(X24,nil),X25) != esk15_0
| ~ leq(X22,X24)
| ~ ssItem(X24)
| ~ ssList(X23)
| app(X23,cons(X22,nil)) != esk17_0
| ~ ssItem(X22) )
& ssList(esk18_0)
& app(app(esk17_0,esk15_0),esk18_0) = esk16_0
& totalorderedP(esk15_0)
& ssList(esk17_0)
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& ssItem(esk19_0)
& memberP(esk13_0,esk19_0)
& ~ memberP(esk14_0,esk19_0)
& ( nil = esk16_0
| nil != esk15_0 )
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(shift_quantors,[status(thm)],[186]) ).
cnf(188,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(192,negated_conjecture,
~ memberP(esk14_0,esk19_0),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(193,negated_conjecture,
memberP(esk13_0,esk19_0),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(194,negated_conjecture,
ssItem(esk19_0),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(195,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[187]) ).
cnf(196,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[187]) ).
cnf(198,negated_conjecture,
ssList(esk17_0),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(200,negated_conjecture,
app(app(esk17_0,esk15_0),esk18_0) = esk16_0,
inference(split_conjunct,[status(thm)],[187]) ).
cnf(201,negated_conjecture,
ssList(esk18_0),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(204,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[188,195,theory(equality)]) ).
cnf(206,negated_conjecture,
memberP(esk15_0,esk19_0),
inference(rw,[status(thm)],[193,195,theory(equality)]) ).
cnf(209,negated_conjecture,
~ memberP(esk16_0,esk19_0),
inference(rw,[status(thm)],[192,196,theory(equality)]) ).
cnf(266,negated_conjecture,
( memberP(esk16_0,X1)
| ~ memberP(app(esk17_0,esk15_0),X1)
| ~ ssList(esk18_0)
| ~ ssList(app(esk17_0,esk15_0))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[142,200,theory(equality)]) ).
cnf(2067,negated_conjecture,
( memberP(esk16_0,X1)
| ~ ssList(app(esk17_0,esk15_0))
| ~ ssList(esk18_0)
| ~ ssItem(X1)
| ~ memberP(esk15_0,X1)
| ~ ssList(esk15_0)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[266,141,theory(equality)]) ).
cnf(2073,negated_conjecture,
( memberP(esk16_0,X1)
| ~ ssList(app(esk17_0,esk15_0))
| ~ ssList(esk18_0)
| ~ ssItem(X1)
| ~ memberP(esk15_0,X1)
| $false
| ~ ssList(esk17_0) ),
inference(rw,[status(thm)],[2067,204,theory(equality)]) ).
cnf(2074,negated_conjecture,
( memberP(esk16_0,X1)
| ~ ssList(app(esk17_0,esk15_0))
| ~ ssList(esk18_0)
| ~ ssItem(X1)
| ~ memberP(esk15_0,X1)
| ~ ssList(esk17_0) ),
inference(cn,[status(thm)],[2073,theory(equality)]) ).
cnf(2792,negated_conjecture,
( ~ memberP(esk15_0,esk19_0)
| ~ ssList(app(esk17_0,esk15_0))
| ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| ~ ssItem(esk19_0) ),
inference(spm,[status(thm)],[209,2074,theory(equality)]) ).
cnf(2795,negated_conjecture,
( $false
| ~ ssList(app(esk17_0,esk15_0))
| ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| ~ ssItem(esk19_0) ),
inference(rw,[status(thm)],[2792,206,theory(equality)]) ).
cnf(2796,negated_conjecture,
( $false
| ~ ssList(app(esk17_0,esk15_0))
| ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| $false ),
inference(rw,[status(thm)],[2795,194,theory(equality)]) ).
cnf(2797,negated_conjecture,
( ~ ssList(app(esk17_0,esk15_0))
| ~ ssList(esk18_0)
| ~ ssList(esk17_0) ),
inference(cn,[status(thm)],[2796,theory(equality)]) ).
cnf(2800,negated_conjecture,
( ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[2797,89,theory(equality)]) ).
cnf(2803,negated_conjecture,
( ~ ssList(esk18_0)
| ~ ssList(esk17_0)
| $false ),
inference(rw,[status(thm)],[2800,204,theory(equality)]) ).
cnf(2804,negated_conjecture,
( ~ ssList(esk18_0)
| ~ ssList(esk17_0) ),
inference(cn,[status(thm)],[2803,theory(equality)]) ).
cnf(2820,negated_conjecture,
~ ssList(esk17_0),
inference(spm,[status(thm)],[2804,201,theory(equality)]) ).
cnf(2831,negated_conjecture,
$false,
inference(sr,[status(thm)],[198,2820,theory(equality)]) ).
cnf(2832,negated_conjecture,
$false,
2831,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC402+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpCgq1CK/sel_SWC402+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC402+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC402+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC402+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
%
%------------------------------------------------------------------------------