TSTP Solution File: KLE002+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE002+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 11:37:06 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 19 unt; 0 def)
% Number of atoms : 43 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 6 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 1 sgn 26 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmppY7469/sel_KLE002+1.p_1',left_distributivity) ).
fof(3,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmppY7469/sel_KLE002+1.p_1',additive_idempotence) ).
fof(5,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmppY7469/sel_KLE002+1.p_1',additive_associativity) ).
fof(7,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmppY7469/sel_KLE002+1.p_1',order) ).
fof(8,conjecture,
! [X4,X5,X6] :
( leq(X4,X5)
=> leq(multiplication(X4,X6),multiplication(X5,X6)) ),
file('/tmp/tmppY7469/sel_KLE002+1.p_1',goals) ).
fof(9,negated_conjecture,
~ ! [X4,X5,X6] :
( leq(X4,X5)
=> leq(multiplication(X4,X6),multiplication(X5,X6)) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(10,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(11,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[10]) ).
fof(14,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(15,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[5]) ).
cnf(19,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[18]) ).
fof(22,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(23,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[22]) ).
cnf(24,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(26,negated_conjecture,
? [X4,X5,X6] :
( leq(X4,X5)
& ~ leq(multiplication(X4,X6),multiplication(X5,X6)) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(27,negated_conjecture,
? [X7,X8,X9] :
( leq(X7,X8)
& ~ leq(multiplication(X7,X9),multiplication(X8,X9)) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(multiplication(esk1_0,esk3_0),multiplication(esk2_0,esk3_0)) ),
inference(skolemize,[status(esa)],[27]) ).
cnf(29,negated_conjecture,
~ leq(multiplication(esk1_0,esk3_0),multiplication(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(39,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[19,15,theory(equality)]) ).
cnf(53,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[25,30,theory(equality)]) ).
cnf(113,negated_conjecture,
multiplication(esk2_0,X1) = addition(multiplication(esk1_0,X1),multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[11,53,theory(equality)]) ).
cnf(352,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[24,39,theory(equality)]) ).
cnf(1002,negated_conjecture,
leq(multiplication(esk1_0,X1),multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[352,113,theory(equality)]) ).
cnf(1413,negated_conjecture,
$false,
inference(rw,[status(thm)],[29,1002,theory(equality)]) ).
cnf(1414,negated_conjecture,
$false,
inference(cn,[status(thm)],[1413,theory(equality)]) ).
cnf(1415,negated_conjecture,
$false,
1414,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE002+1.p
% --creating new selector for [KLE001+0.ax]
% -running prover on /tmp/tmppY7469/sel_KLE002+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE002+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE002+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE002+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
%
%------------------------------------------------------------------------------