TSTP Solution File: KLE148+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE148+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 12:38:13 EST 2010
% Result : Theorem 2.11s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 44 unt; 0 def)
% Number of atoms : 83 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 20 ~; 14 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 7 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',left_annihilation) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',additive_identity) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',multiplicative_right_identity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',idempotence) ).
fof(10,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',infty_unfold1) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',additive_associativity) ).
fof(14,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',distributivity1) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',order) ).
fof(17,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',multiplicative_associativity) ).
fof(19,conjecture,
! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,strong_iteration(X5)),X4) )
& leq(X4,multiplication(X4,strong_iteration(X5))) ),
file('/tmp/tmpW6vaKL/sel_KLE148+2.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,strong_iteration(X5)),X4) )
& leq(X4,multiplication(X4,strong_iteration(X5))) ),
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(25,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[25]) ).
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(50,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(51,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[50]) ).
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,X5] :
( ( multiplication(X4,X5) = zero
& ~ leq(multiplication(X4,strong_iteration(X5)),X4) )
| ~ leq(X4,multiplication(X4,strong_iteration(X5))) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(63,negated_conjecture,
? [X6,X7] :
( ( multiplication(X6,X7) = zero
& ~ leq(multiplication(X6,strong_iteration(X7)),X6) )
| ~ leq(X6,multiplication(X6,strong_iteration(X7))) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
( ( multiplication(esk1_0,esk2_0) = zero
& ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) )
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ),
inference(skolemize,[status(esa)],[63]) ).
fof(65,negated_conjecture,
( ( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) )
& ( ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0)
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ) ),
inference(distribute,[status(thm)],[64]) ).
cnf(66,negated_conjecture,
( ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0)))
| ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) ),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(67,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(75,plain,
leq(X1,X1),
inference(spm,[status(thm)],[56,34,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(125,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[51,32,theory(equality)]) ).
cnf(254,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[56,93,theory(equality)]) ).
cnf(1194,plain,
leq(X1,multiplication(X1,addition(one,X2))),
inference(spm,[status(thm)],[254,125,theory(equality)]) ).
cnf(1246,plain,
leq(X1,multiplication(X1,strong_iteration(X2))),
inference(spm,[status(thm)],[1194,114,theory(equality)]) ).
cnf(1293,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| $false ),
inference(rw,[status(thm)],[67,1246,theory(equality)]) ).
cnf(1294,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(cn,[status(thm)],[1293,theory(equality)]) ).
cnf(1295,negated_conjecture,
( $false
| ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) ),
inference(rw,[status(thm)],[66,1246,theory(equality)]) ).
cnf(1296,negated_conjecture,
~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0),
inference(cn,[status(thm)],[1295,theory(equality)]) ).
cnf(1303,negated_conjecture,
multiplication(zero,X1) = multiplication(esk1_0,multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[59,1294,theory(equality)]) ).
cnf(1312,negated_conjecture,
zero = multiplication(esk1_0,multiplication(esk2_0,X1)),
inference(rw,[status(thm)],[1303,22,theory(equality)]) ).
cnf(1412,negated_conjecture,
addition(esk1_0,zero) = multiplication(esk1_0,addition(one,multiplication(esk2_0,X1))),
inference(spm,[status(thm)],[125,1312,theory(equality)]) ).
cnf(1423,negated_conjecture,
esk1_0 = multiplication(esk1_0,addition(one,multiplication(esk2_0,X1))),
inference(rw,[status(thm)],[1412,26,theory(equality)]) ).
cnf(64668,negated_conjecture,
multiplication(esk1_0,strong_iteration(esk2_0)) = esk1_0,
inference(spm,[status(thm)],[1423,114,theory(equality)]) ).
cnf(64924,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1296,64668,theory(equality)]),75,theory(equality)]) ).
cnf(64925,negated_conjecture,
$false,
inference(cn,[status(thm)],[64924,theory(equality)]) ).
cnf(64926,negated_conjecture,
$false,
64925,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE148+2.p
% --creating new selector for [KLE004+0.ax]
% -running prover on /tmp/tmpW6vaKL/sel_KLE148+2.p_1 with time limit 29
% -prover status Theorem
% Problem KLE148+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE148+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE148+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
%
%------------------------------------------------------------------------------