TSTP Solution File: KLE139+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE139+2 : 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 12:39:20 EST 2010
% Result : Theorem 7.52s
% Output : CNFRefutation 7.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 31 unt; 0 def)
% Number of atoms : 63 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 13 |; 4 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 1 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',left_annihilation) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',additive_commutativity) ).
fof(5,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',isolation) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',idempotence) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',additive_associativity) ).
fof(13,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',distributivity2) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',order) ).
fof(17,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',multiplicative_associativity) ).
fof(18,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',star_unfold2) ).
fof(19,conjecture,
! [X4] :
( leq(strong_iteration(X4),addition(multiplication(strong_iteration(X4),X4),one))
& leq(addition(multiplication(strong_iteration(X4),X4),one),strong_iteration(X4)) ),
file('/tmp/tmp77e_De/sel_KLE139+2.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(X4),addition(multiplication(strong_iteration(X4),X4),one))
& leq(addition(multiplication(strong_iteration(X4),X4),one),strong_iteration(X4)) ),
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(29,plain,
! [X2] : strong_iteration(X2) = addition(star(X2),multiplication(strong_iteration(X2),zero)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(30,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[29]) ).
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(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(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]) ).
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(60,plain,
! [X2] : addition(one,multiplication(star(X2),X2)) = star(X2),
inference(variable_rename,[status(thm)],[18]) ).
cnf(61,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[60]) ).
fof(62,negated_conjecture,
? [X4] :
( ~ leq(strong_iteration(X4),addition(multiplication(strong_iteration(X4),X4),one))
| ~ leq(addition(multiplication(strong_iteration(X4),X4),one),strong_iteration(X4)) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(63,negated_conjecture,
? [X5] :
( ~ leq(strong_iteration(X5),addition(multiplication(strong_iteration(X5),X5),one))
| ~ leq(addition(multiplication(strong_iteration(X5),X5),one),strong_iteration(X5)) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),addition(multiplication(strong_iteration(esk1_0),esk1_0),one))
| ~ leq(addition(multiplication(strong_iteration(esk1_0),esk1_0),one),strong_iteration(esk1_0)) ),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
( ~ leq(addition(multiplication(strong_iteration(esk1_0),esk1_0),one),strong_iteration(esk1_0))
| ~ leq(strong_iteration(esk1_0),addition(multiplication(strong_iteration(esk1_0),esk1_0),one)) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,plain,
leq(X1,X1),
inference(spm,[status(thm)],[56,34,theory(equality)]) ).
cnf(74,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),addition(one,multiplication(strong_iteration(esk1_0),esk1_0)))
| ~ leq(addition(multiplication(strong_iteration(esk1_0),esk1_0),one),strong_iteration(esk1_0)) ),
inference(rw,[status(thm)],[65,28,theory(equality)]) ).
cnf(75,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),addition(one,multiplication(strong_iteration(esk1_0),esk1_0)))
| ~ leq(addition(one,multiplication(strong_iteration(esk1_0),esk1_0)),strong_iteration(esk1_0)) ),
inference(rw,[status(thm)],[74,28,theory(equality)]) ).
cnf(112,plain,
addition(star(X1),X2) = addition(one,addition(multiplication(star(X1),X1),X2)),
inference(spm,[status(thm)],[44,61,theory(equality)]) ).
cnf(2353,plain,
addition(one,multiplication(addition(star(X1),X2),X1)) = addition(star(X1),multiplication(X2,X1)),
inference(spm,[status(thm)],[112,49,theory(equality)]) ).
cnf(265137,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = addition(star(X1),multiplication(multiplication(strong_iteration(X1),zero),X1)),
inference(spm,[status(thm)],[2353,30,theory(equality)]) ).
cnf(265883,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[265137,59,theory(equality)]),22,theory(equality)]),30,theory(equality)]) ).
cnf(267157,negated_conjecture,
( $false
| ~ leq(addition(one,multiplication(strong_iteration(esk1_0),esk1_0)),strong_iteration(esk1_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[75,265883,theory(equality)]),67,theory(equality)]) ).
cnf(267158,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[267157,265883,theory(equality)]),67,theory(equality)]) ).
cnf(267159,negated_conjecture,
$false,
inference(cn,[status(thm)],[267158,theory(equality)]) ).
cnf(267160,negated_conjecture,
$false,
267159,
[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/KLE139+2.p
% --creating new selector for [KLE004+0.ax]
% -running prover on /tmp/tmp77e_De/sel_KLE139+2.p_1 with time limit 29
% -prover status Theorem
% Problem KLE139+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE139+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE139+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
%
%------------------------------------------------------------------------------