TSTP Solution File: KLE150+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE150+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 : Sat Dec 25 12:38:48 EST 2010
% Result : Theorem 0.32s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 21 unt; 0 def)
% Number of atoms : 49 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 11 |; 4 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 41 ( 1 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpkwxUyw/sel_KLE150+2.p_1',left_annihilation) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpkwxUyw/sel_KLE150+2.p_1',additive_commutativity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpkwxUyw/sel_KLE150+2.p_1',idempotence) ).
fof(10,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/tmp/tmpkwxUyw/sel_KLE150+2.p_1',infty_unfold1) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpkwxUyw/sel_KLE150+2.p_1',order) ).
fof(17,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpkwxUyw/sel_KLE150+2.p_1',multiplicative_associativity) ).
fof(19,conjecture,
! [X4] :
( leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero)))
& leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero))) ),
file('/tmp/tmpkwxUyw/sel_KLE150+2.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero)))
& leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero))) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(21,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[1]) ).
cnf(22,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[21]) ).
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(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(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]) ).
fof(58,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[17]) ).
cnf(59,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[58]) ).
fof(62,negated_conjecture,
? [X4] :
( ~ leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero)))
| ~ leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero))) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(63,negated_conjecture,
? [X5] :
( ~ leq(strong_iteration(multiplication(X5,zero)),addition(one,multiplication(X5,zero)))
| ~ leq(addition(one,multiplication(X5,zero)),strong_iteration(multiplication(X5,zero))) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
( ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero)))
| ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero))) ),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
( ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero)))
| ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero))) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,plain,
leq(X1,X1),
inference(spm,[status(thm)],[56,34,theory(equality)]) ).
cnf(112,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[42,28,theory(equality)]) ).
cnf(115,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[112,59,theory(equality)]) ).
cnf(3020,plain,
addition(one,multiplication(X1,zero)) = strong_iteration(multiplication(X1,zero)),
inference(spm,[status(thm)],[115,22,theory(equality)]) ).
cnf(5709,negated_conjecture,
( $false
| ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[65,3020,theory(equality)]),67,theory(equality)]) ).
cnf(5710,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5709,3020,theory(equality)]),67,theory(equality)]) ).
cnf(5711,negated_conjecture,
$false,
inference(cn,[status(thm)],[5710,theory(equality)]) ).
cnf(5712,negated_conjecture,
$false,
5711,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE150+2.p
% --creating new selector for [KLE004+0.ax]
% -running prover on /tmp/tmpkwxUyw/sel_KLE150+2.p_1 with time limit 29
% -prover status Theorem
% Problem KLE150+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE150+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE150+2.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
%
%------------------------------------------------------------------------------