TSTP Solution File: SWC243+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC243+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 11:04:01 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 7 unt; 0 def)
% Number of atoms : 311 ( 82 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 414 ( 161 ~; 148 |; 82 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 123 ( 0 sgn 58 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax81) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax28) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax20) ).
fof(27,axiom,
ssList(nil),
file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax17) ).
fof(31,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax38) ).
fof(35,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax16) ).
fof(38,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ totalorderedP(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) ) ) ) ) ) ) ) ) ) ),
file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',co1) ).
fof(39,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ totalorderedP(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) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[38]) ).
fof(42,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(43,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ totalorderedP(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) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[39,theory(equality)]) ).
fof(75,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(76,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[75]) ).
fof(77,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[76]) ).
cnf(78,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(87,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(88,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[87]) ).
cnf(89,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(102,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(103,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,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)],[103]) ).
fof(105,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)],[104]) ).
cnf(106,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(107,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(108,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(159,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[27]) ).
fof(184,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(185,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[184]) ).
cnf(186,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[185]) ).
fof(204,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(205,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[204]) ).
fof(206,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[205]) ).
cnf(207,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[206]) ).
fof(218,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& totalorderedP(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) ) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(219,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& totalorderedP(X11)
& nil != X9
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != X9
| ? [X16] :
( ssItem(X16)
& memberP(X14,X16)
& memberP(X15,X16)
& lt(X13,X16)
& ~ leq(X13,X16) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[218]) ).
fof(220,negated_conjecture,
( ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& totalorderedP(esk15_0)
& nil != esk13_0
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk13_0
| ( ssItem(esk17_3(X13,X14,X15))
& memberP(X14,esk17_3(X13,X14,X15))
& memberP(X15,esk17_3(X13,X14,X15))
& lt(X13,esk17_3(X13,X14,X15))
& ~ leq(X13,esk17_3(X13,X14,X15)) ) ) ) ) ),
inference(skolemize,[status(esa)],[219]) ).
fof(221,negated_conjecture,
! [X13,X14,X15] :
( ( ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk13_0
| ( ssItem(esk17_3(X13,X14,X15))
& memberP(X14,esk17_3(X13,X14,X15))
& memberP(X15,esk17_3(X13,X14,X15))
& lt(X13,esk17_3(X13,X14,X15))
& ~ leq(X13,esk17_3(X13,X14,X15)) )
| ~ ssList(X14)
| ~ ssItem(X13) )
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& totalorderedP(esk15_0)
& nil != esk13_0
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(shift_quantors,[status(thm)],[220]) ).
fof(222,negated_conjecture,
! [X13,X14,X15] :
( ( ssItem(esk17_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk13_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( memberP(X14,esk17_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk13_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( memberP(X15,esk17_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk13_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( lt(X13,esk17_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk13_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( ~ leq(X13,esk17_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk13_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& totalorderedP(esk15_0)
& nil != esk13_0
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(distribute,[status(thm)],[221]) ).
cnf(223,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[222]) ).
cnf(227,negated_conjecture,
nil != esk13_0,
inference(split_conjunct,[status(thm)],[222]) ).
cnf(234,negated_conjecture,
( memberP(X2,esk17_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk13_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[222]) ).
cnf(235,negated_conjecture,
( ssItem(esk17_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk13_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[222]) ).
cnf(425,negated_conjecture,
( ~ ssItem(esk17_3(X1,nil,X2))
| app(app(nil,cons(X1,nil)),X2) != esk13_0
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[186,234,theory(equality)]) ).
cnf(428,negated_conjecture,
( ~ ssItem(esk17_3(X1,nil,X2))
| app(app(nil,cons(X1,nil)),X2) != esk13_0
| ~ ssList(X2)
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[425,159,theory(equality)]) ).
cnf(429,negated_conjecture,
( ~ ssItem(esk17_3(X1,nil,X2))
| app(app(nil,cons(X1,nil)),X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[428,theory(equality)]) ).
cnf(1000,negated_conjecture,
( app(app(nil,cons(X1,nil)),X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[429,235,theory(equality)]) ).
cnf(1001,negated_conjecture,
( app(app(nil,cons(X1,nil)),X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1000,159,theory(equality)]) ).
cnf(1002,negated_conjecture,
( app(app(nil,cons(X1,nil)),X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1001,theory(equality)]) ).
cnf(1004,negated_conjecture,
( app(cons(X1,nil),X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[1002,89,theory(equality)]) ).
cnf(1103,negated_conjecture,
( cons(X1,X2) != esk13_0
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[1004,78,theory(equality)]) ).
cnf(1184,negated_conjecture,
( cons(X1,X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1103,207,theory(equality)]) ).
cnf(1185,negated_conjecture,
( cons(X1,X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1184,159,theory(equality)]) ).
cnf(1186,negated_conjecture,
( cons(X1,X2) != esk13_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1185,theory(equality)]) ).
cnf(1207,negated_conjecture,
( nil = X1
| X1 != esk13_0
| ~ ssList(esk1_1(X1))
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1186,106,theory(equality)]) ).
cnf(1299,negated_conjecture,
( nil = X1
| X1 != esk13_0
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1207,107]) ).
cnf(1300,negated_conjecture,
( nil = X1
| X1 != esk13_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1299,108]) ).
cnf(1301,negated_conjecture,
nil = esk13_0,
inference(spm,[status(thm)],[1300,223,theory(equality)]) ).
cnf(1311,negated_conjecture,
$false,
inference(sr,[status(thm)],[1301,227,theory(equality)]) ).
cnf(1312,negated_conjecture,
$false,
1311,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC243+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp_gn9gL/sel_SWC243+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC243+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC243+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC243+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
%
%------------------------------------------------------------------------------