TSTP Solution File: KLE140+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE140+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sat Dec 25 12:40:15 EST 2010
% Result : Theorem 10.91s
% Output : CNFRefutation 10.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 36 unt; 0 def)
% Number of atoms : 76 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 17 ~; 13 |; 5 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 4 sgn 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',multiplicative_left_identity) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',multiplicative_right_identity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',idempotence) ).
fof(10,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',infty_unfold1) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',additive_associativity) ).
fof(12,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',infty_coinduction) ).
fof(13,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',distributivity2) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',order) ).
fof(19,conjecture,
! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
file('/tmp/tmpqQRXLB/sel_KLE140+1.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(23,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(24,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(28,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[27]) ).
fof(31,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(32,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(34,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[33]) ).
fof(41,plain,
! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
inference(variable_rename,[status(thm)],[10]) ).
cnf(42,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[11]) ).
cnf(44,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,plain,
! [X1,X2,X3] :
( ~ leq(X3,addition(multiplication(X1,X3),X2))
| leq(X3,multiplication(strong_iteration(X1),X2)) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(46,plain,
! [X4,X5,X6] :
( ~ leq(X6,addition(multiplication(X4,X6),X5))
| leq(X6,multiplication(strong_iteration(X4),X5)) ),
inference(variable_rename,[status(thm)],[45]) ).
cnf(47,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(49,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[48]) ).
fof(54,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(55,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[54]) ).
cnf(56,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(57,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(62,negated_conjecture,
? [X4,X5] :
( leq(X4,X5)
& ~ leq(strong_iteration(X4),strong_iteration(X5)) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(63,negated_conjecture,
? [X6,X7] :
( leq(X6,X7)
& ~ leq(strong_iteration(X6),strong_iteration(X7)) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0)) ),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0)),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(66,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[57,66,theory(equality)]) ).
cnf(93,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[44,34,theory(equality)]) ).
cnf(114,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[42,28,theory(equality)]) ).
cnf(118,plain,
addition(strong_iteration(X1),X2) = addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)),
inference(spm,[status(thm)],[44,114,theory(equality)]) ).
cnf(156,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[49,24,theory(equality)]) ).
cnf(186,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[47,28,theory(equality)]) ).
cnf(258,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[56,93,theory(equality)]) ).
cnf(1494,plain,
leq(X1,multiplication(addition(one,X2),X1)),
inference(spm,[status(thm)],[258,156,theory(equality)]) ).
cnf(2958,plain,
addition(one,multiplication(addition(X1,X2),strong_iteration(X1))) = addition(strong_iteration(X1),multiplication(X2,strong_iteration(X1))),
inference(spm,[status(thm)],[118,49,theory(equality)]) ).
cnf(3013,plain,
addition(one,multiplication(addition(X1,X2),strong_iteration(X1))) = multiplication(addition(one,X2),strong_iteration(X1)),
inference(rw,[status(thm)],[2958,156,theory(equality)]) ).
cnf(328947,plain,
( leq(strong_iteration(X1),multiplication(strong_iteration(addition(X1,X2)),one))
| ~ leq(strong_iteration(X1),multiplication(addition(one,X2),strong_iteration(X1))) ),
inference(spm,[status(thm)],[186,3013,theory(equality)]) ).
cnf(329673,plain,
( leq(strong_iteration(X1),strong_iteration(addition(X1,X2)))
| ~ leq(strong_iteration(X1),multiplication(addition(one,X2),strong_iteration(X1))) ),
inference(rw,[status(thm)],[328947,32,theory(equality)]) ).
cnf(329674,plain,
( leq(strong_iteration(X1),strong_iteration(addition(X1,X2)))
| $false ),
inference(rw,[status(thm)],[329673,1494,theory(equality)]) ).
cnf(329675,plain,
leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),
inference(cn,[status(thm)],[329674,theory(equality)]) ).
cnf(329833,negated_conjecture,
leq(strong_iteration(esk1_0),strong_iteration(esk2_0)),
inference(spm,[status(thm)],[329675,67,theory(equality)]) ).
cnf(330013,negated_conjecture,
$false,
inference(sr,[status(thm)],[329833,65,theory(equality)]) ).
cnf(330014,negated_conjecture,
$false,
330013,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE140+1.p
% --creating new selector for [KLE004+0.ax]
% -running prover on /tmp/tmpqQRXLB/sel_KLE140+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE140+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE140+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE140+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
%
%------------------------------------------------------------------------------