TSTP Solution File: SWC313+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC313+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 11:25:57 EST 2010
% Result : Theorem 0.36s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 12 unt; 0 def)
% Number of atoms : 318 ( 152 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 407 ( 147 ~; 153 |; 89 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 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 : 104 ( 0 sgn 55 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpN0vB7q/sel_SWC313+1.p_1',ax81) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpN0vB7q/sel_SWC313+1.p_1',ax20) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpN0vB7q/sel_SWC313+1.p_1',ax15) ).
fof(12,axiom,
ssList(nil),
file('/tmp/tmpN0vB7q/sel_SWC313+1.p_1',ax17) ).
fof(19,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ( nil != X3
& nil = X4 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X2
& app(X8,cons(X7,nil)) = X1 ) ) ) ) ) ) ) ) ),
file('/tmp/tmpN0vB7q/sel_SWC313+1.p_1',co1) ).
fof(20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ( nil != X3
& nil = X4 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X2
& app(X8,cons(X7,nil)) = X1 ) ) ) ) ) ) ) ) ),
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
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ( nil != X3
& nil = X4 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X2
& app(X8,cons(X7,nil)) = X1 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).
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(69,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
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
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X5,nil)) = X3
| app(cons(X5,nil),X6) != X4 ) )
& ( nil = X3
| nil != X4 )
& ( ( nil = X2
& nil != X1 )
| ( neq(X2,nil)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X2
| app(X8,cons(X7,nil)) != X1 ) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(103,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| app(X14,cons(X13,nil)) = X11
| app(cons(X13,nil),X14) != X12 ) )
& ( nil = X11
| nil != X12 )
& ( ( nil = X10
& nil != X9 )
| ( neq(X10,nil)
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| app(cons(X15,nil),X16) != X10
| app(X16,cons(X15,nil)) != X9 ) ) ) ) ) ) ) ),
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
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| app(X14,cons(X13,nil)) = esk7_0
| app(cons(X13,nil),X14) != esk8_0 ) )
& ( nil = esk7_0
| nil != esk8_0 )
& ( ( nil = esk6_0
& nil != esk5_0 )
| ( neq(esk6_0,nil)
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| app(cons(X15,nil),X16) != esk6_0
| app(X16,cons(X15,nil)) != esk5_0 ) ) ) ) ),
inference(skolemize,[status(esa)],[103]) ).
fof(105,negated_conjecture,
! [X13,X14,X15,X16] :
( ( ( ( ~ ssList(X16)
| app(cons(X15,nil),X16) != esk6_0
| app(X16,cons(X15,nil)) != esk5_0
| ~ ssItem(X15) )
& neq(esk6_0,nil) )
| ( nil = esk6_0
& nil != esk5_0 ) )
& ( ~ ssList(X14)
| app(X14,cons(X13,nil)) = esk7_0
| app(cons(X13,nil),X14) != esk8_0
| ~ ssItem(X13) )
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_0 )
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0) ),
inference(shift_quantors,[status(thm)],[104]) ).
fof(106,negated_conjecture,
! [X13,X14,X15,X16] :
( ( nil = esk6_0
| ~ ssList(X16)
| app(cons(X15,nil),X16) != esk6_0
| app(X16,cons(X15,nil)) != esk5_0
| ~ ssItem(X15) )
& ( nil != esk5_0
| ~ ssList(X16)
| app(cons(X15,nil),X16) != esk6_0
| app(X16,cons(X15,nil)) != esk5_0
| ~ ssItem(X15) )
& ( nil = esk6_0
| neq(esk6_0,nil) )
& ( nil != esk5_0
| neq(esk6_0,nil) )
& ( ~ ssList(X14)
| app(X14,cons(X13,nil)) = esk7_0
| app(cons(X13,nil),X14) != esk8_0
| ~ ssItem(X13) )
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_0 )
& ssList(esk8_0)
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0) ),
inference(distribute,[status(thm)],[105]) ).
cnf(108,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(111,negated_conjecture,
( nil = esk7_0
| nil != esk8_0 ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(112,negated_conjecture,
esk5_0 = esk7_0,
inference(split_conjunct,[status(thm)],[106]) ).
cnf(113,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[106]) ).
cnf(114,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)],[106]) ).
cnf(115,negated_conjecture,
( neq(esk6_0,nil)
| nil != esk5_0 ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(118,negated_conjecture,
( nil = esk6_0
| ~ ssItem(X1)
| app(X2,cons(X1,nil)) != esk5_0
| app(cons(X1,nil),X2) != esk6_0
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(123,negated_conjecture,
( esk5_0 = nil
| esk8_0 != nil ),
inference(rw,[status(thm)],[111,112,theory(equality)]) ).
cnf(124,negated_conjecture,
( esk5_0 = nil
| esk6_0 != nil ),
inference(rw,[status(thm)],[123,113,theory(equality)]) ).
cnf(141,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[69,theory(equality)]) ).
cnf(163,negated_conjecture,
( app(X2,cons(X1,nil)) = esk5_0
| app(cons(X1,nil),X2) != esk8_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[114,112,theory(equality)]) ).
cnf(164,negated_conjecture,
( app(X2,cons(X1,nil)) = esk5_0
| app(cons(X1,nil),X2) != esk6_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[163,113,theory(equality)]) ).
cnf(184,negated_conjecture,
( esk6_0 = nil
| app(cons(X1,nil),X2) != esk6_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[118,164]) ).
cnf(186,negated_conjecture,
( esk6_0 = nil
| cons(X1,X2) != esk6_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[184,56,theory(equality)]) ).
cnf(335,negated_conjecture,
( esk6_0 = nil
| nil = X1
| X1 != esk6_0
| ~ ssList(esk3_1(X1))
| ~ ssItem(esk4_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[186,61,theory(equality)]) ).
cnf(2673,negated_conjecture,
( esk6_0 = nil
| nil = X1
| X1 != esk6_0
| ~ ssList(esk3_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[335,62]) ).
cnf(2674,negated_conjecture,
( esk6_0 = nil
| nil = X1
| X1 != esk6_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2673,63]) ).
cnf(2675,negated_conjecture,
( esk6_0 = nil
| ~ ssList(esk6_0) ),
inference(er,[status(thm)],[2674,theory(equality)]) ).
cnf(2676,negated_conjecture,
( esk6_0 = nil
| $false ),
inference(rw,[status(thm)],[2675,108,theory(equality)]) ).
cnf(2677,negated_conjecture,
esk6_0 = nil,
inference(cn,[status(thm)],[2676,theory(equality)]) ).
cnf(2720,negated_conjecture,
( neq(nil,nil)
| esk5_0 != nil ),
inference(rw,[status(thm)],[115,2677,theory(equality)]) ).
cnf(2723,negated_conjecture,
( esk5_0 = nil
| $false ),
inference(rw,[status(thm)],[124,2677,theory(equality)]) ).
cnf(2724,negated_conjecture,
esk5_0 = nil,
inference(cn,[status(thm)],[2723,theory(equality)]) ).
cnf(2729,negated_conjecture,
( neq(nil,nil)
| $false ),
inference(rw,[status(thm)],[2720,2724,theory(equality)]) ).
cnf(2730,negated_conjecture,
neq(nil,nil),
inference(cn,[status(thm)],[2729,theory(equality)]) ).
cnf(2732,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[141,2730,theory(equality)]) ).
cnf(2733,negated_conjecture,
$false,
inference(rw,[status(thm)],[2732,74,theory(equality)]) ).
cnf(2734,negated_conjecture,
$false,
inference(cn,[status(thm)],[2733,theory(equality)]) ).
cnf(2735,negated_conjecture,
$false,
2734,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC313+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpN0vB7q/sel_SWC313+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC313+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC313+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC313+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
%
%------------------------------------------------------------------------------