TSTP Solution File: KLE145+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE145+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 12:37:10 EST 2010
% Result : Theorem 99.98s
% Output : CNFRefutation 99.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 111 ( 81 unt; 0 def)
% Number of atoms : 145 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 30 ~; 28 |; 2 &)
% ( 1 <=>; 3 =>; 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; 2 con; 0-2 aty)
% Number of variables : 181 ( 3 sgn 75 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',multiplicative_left_identity) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',additive_commutativity) ).
fof(6,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',multiplicative_right_identity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',idempotence) ).
fof(8,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',star_induction2) ).
fof(9,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X3),X2),X3)
=> leq(multiplication(star(X1),X2),X3) ),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',star_induction1) ).
fof(10,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',infty_unfold1) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',additive_associativity) ).
fof(12,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',infty_coinduction) ).
fof(13,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',distributivity2) ).
fof(14,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',distributivity1) ).
fof(15,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',star_unfold1) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',order) ).
fof(17,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',multiplicative_associativity) ).
fof(18,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',star_unfold2) ).
fof(19,conjecture,
! [X4] : star(strong_iteration(X4)) = strong_iteration(X4),
file('/tmp/tmpgb1nti/sel_KLE145+1.p_2',goals) ).
fof(20,negated_conjecture,
~ ! [X4] : star(strong_iteration(X4)) = strong_iteration(X4),
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(35,plain,
! [X1,X2,X3] :
( ~ leq(addition(multiplication(X3,X1),X2),X3)
| leq(multiplication(X2,star(X1)),X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(36,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X6,X4),X5),X6)
| leq(multiplication(X5,star(X4)),X6) ),
inference(variable_rename,[status(thm)],[35]) ).
cnf(37,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X1,X2,X3] :
( ~ leq(addition(multiplication(X1,X3),X2),X3)
| leq(multiplication(star(X1),X2),X3) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(39,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X4,X6),X5),X6)
| leq(multiplication(star(X4),X5),X6) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(multiplication(X1,X3),X2),X3) ),
inference(split_conjunct,[status(thm)],[39]) ).
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(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(52,plain,
! [X2] : addition(one,multiplication(X2,star(X2))) = star(X2),
inference(variable_rename,[status(thm)],[15]) ).
cnf(53,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[52]) ).
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(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] : star(strong_iteration(X4)) != strong_iteration(X4),
inference(fof_nnf,[status(thm)],[20]) ).
fof(63,negated_conjecture,
? [X5] : star(strong_iteration(X5)) != strong_iteration(X5),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
star(strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
star(strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,plain,
leq(X1,X1),
inference(spm,[status(thm)],[56,34,theory(equality)]) ).
cnf(91,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[44,34,theory(equality)]) ).
cnf(105,plain,
addition(one,multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))) = star(multiplication(X1,X2)),
inference(spm,[status(thm)],[53,59,theory(equality)]) ).
cnf(106,plain,
addition(star(X1),X2) = addition(one,addition(multiplication(X1,star(X1)),X2)),
inference(spm,[status(thm)],[44,53,theory(equality)]) ).
cnf(110,plain,
addition(star(X1),X2) = addition(one,addition(multiplication(star(X1),X1),X2)),
inference(spm,[status(thm)],[44,61,theory(equality)]) ).
cnf(112,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[42,28,theory(equality)]) ).
cnf(116,plain,
addition(strong_iteration(X1),X2) = addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)),
inference(spm,[status(thm)],[44,112,theory(equality)]) ).
cnf(123,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[51,32,theory(equality)]) ).
cnf(154,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[49,24,theory(equality)]) ).
cnf(184,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[47,28,theory(equality)]) ).
cnf(192,plain,
( leq(multiplication(multiplication(X1,X2),star(X3)),X1)
| ~ leq(multiplication(X1,addition(X3,X2)),X1) ),
inference(spm,[status(thm)],[37,51,theory(equality)]) ).
cnf(198,plain,
( leq(multiplication(X1,multiplication(X2,star(X3))),X1)
| ~ leq(multiplication(X1,addition(X3,X2)),X1) ),
inference(rw,[status(thm)],[192,59,theory(equality)]) ).
cnf(204,plain,
( leq(multiplication(star(X1),multiplication(X1,X2)),X2)
| ~ leq(multiplication(X1,X2),X2) ),
inference(spm,[status(thm)],[40,34,theory(equality)]) ).
cnf(242,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[91,53,theory(equality)]) ).
cnf(252,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[56,91,theory(equality)]) ).
cnf(966,plain,
leq(X1,multiplication(X1,addition(one,X2))),
inference(spm,[status(thm)],[252,123,theory(equality)]) ).
cnf(1238,plain,
leq(X1,multiplication(X1,star(X2))),
inference(spm,[status(thm)],[966,53,theory(equality)]) ).
cnf(1974,plain,
addition(one,multiplication(X1,star(X1))) = addition(star(X1),multiplication(X1,star(X1))),
inference(spm,[status(thm)],[106,34,theory(equality)]) ).
cnf(2029,plain,
star(X1) = addition(star(X1),multiplication(X1,star(X1))),
inference(rw,[status(thm)],[1974,53,theory(equality)]) ).
cnf(2030,plain,
star(X1) = multiplication(addition(one,X1),star(X1)),
inference(rw,[status(thm)],[2029,154,theory(equality)]) ).
cnf(2396,plain,
multiplication(strong_iteration(X1),star(multiplication(X1,strong_iteration(X1)))) = star(multiplication(X1,strong_iteration(X1))),
inference(spm,[status(thm)],[2030,112,theory(equality)]) ).
cnf(2409,plain,
leq(addition(one,X1),star(X1)),
inference(spm,[status(thm)],[1238,2030,theory(equality)]) ).
cnf(2471,plain,
leq(addition(X1,one),star(X1)),
inference(spm,[status(thm)],[2409,28,theory(equality)]) ).
cnf(2498,plain,
addition(one,multiplication(star(X1),X1)) = addition(star(X1),multiplication(star(X1),X1)),
inference(spm,[status(thm)],[110,34,theory(equality)]) ).
cnf(2554,plain,
star(X1) = addition(star(X1),multiplication(star(X1),X1)),
inference(rw,[status(thm)],[2498,61,theory(equality)]) ).
cnf(2555,plain,
star(X1) = multiplication(star(X1),addition(one,X1)),
inference(rw,[status(thm)],[2554,123,theory(equality)]) ).
cnf(2648,plain,
addition(addition(X1,one),star(X1)) = star(X1),
inference(spm,[status(thm)],[57,2471,theory(equality)]) ).
cnf(2656,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2648,44,theory(equality)]),242,theory(equality)]) ).
cnf(3333,plain,
addition(one,star(multiplication(X1,strong_iteration(X1)))) = addition(strong_iteration(X1),star(multiplication(X1,strong_iteration(X1)))),
inference(spm,[status(thm)],[116,2656,theory(equality)]) ).
cnf(3380,plain,
star(multiplication(X1,strong_iteration(X1))) = addition(strong_iteration(X1),star(multiplication(X1,strong_iteration(X1)))),
inference(rw,[status(thm)],[3333,242,theory(equality)]) ).
cnf(5538,plain,
multiplication(star(star(X1)),star(X1)) = star(star(X1)),
inference(spm,[status(thm)],[2555,242,theory(equality)]) ).
cnf(5575,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(spm,[status(thm)],[2555,28,theory(equality)]) ).
cnf(10653,plain,
( leq(multiplication(X1,star(multiplication(X2,X1))),multiplication(strong_iteration(X2),one))
| ~ leq(multiplication(X1,star(multiplication(X2,X1))),star(multiplication(X2,X1))) ),
inference(spm,[status(thm)],[184,105,theory(equality)]) ).
cnf(10702,plain,
( leq(multiplication(X1,star(multiplication(X2,X1))),strong_iteration(X2))
| ~ leq(multiplication(X1,star(multiplication(X2,X1))),star(multiplication(X2,X1))) ),
inference(rw,[status(thm)],[10653,32,theory(equality)]) ).
cnf(12250,plain,
( leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(spm,[status(thm)],[198,5575,theory(equality)]) ).
cnf(12297,plain,
( leq(multiplication(star(X1),star(X1)),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(rw,[status(thm)],[12250,24,theory(equality)]) ).
cnf(12298,plain,
( leq(multiplication(star(X1),star(X1)),star(X1))
| $false ),
inference(rw,[status(thm)],[12297,67,theory(equality)]) ).
cnf(12299,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[12298,theory(equality)]) ).
cnf(19586,plain,
addition(multiplication(star(X1),star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[57,12299,theory(equality)]) ).
cnf(19593,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[19586,28,theory(equality)]),123,theory(equality)]),242,theory(equality)]) ).
cnf(19645,plain,
( leq(multiplication(star(star(X1)),star(X1)),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(spm,[status(thm)],[204,19593,theory(equality)]) ).
cnf(19702,plain,
( leq(multiplication(star(star(X1)),star(X1)),star(X1))
| $false ),
inference(rw,[status(thm)],[19645,67,theory(equality)]) ).
cnf(19703,plain,
leq(multiplication(star(star(X1)),star(X1)),star(X1)),
inference(cn,[status(thm)],[19702,theory(equality)]) ).
cnf(100906,plain,
leq(star(star(X1)),star(X1)),
inference(rw,[status(thm)],[19703,5538,theory(equality)]) ).
cnf(100911,plain,
addition(star(star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[57,100906,theory(equality)]) ).
cnf(100916,plain,
star(star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[100911,28,theory(equality)]),2656,theory(equality)]) ).
cnf(1903631,plain,
( leq(star(multiplication(X1,strong_iteration(X1))),strong_iteration(X1))
| ~ leq(star(multiplication(X1,strong_iteration(X1))),star(multiplication(X1,strong_iteration(X1)))) ),
inference(spm,[status(thm)],[10702,2396,theory(equality)]) ).
cnf(1903876,plain,
( leq(star(multiplication(X1,strong_iteration(X1))),strong_iteration(X1))
| $false ),
inference(rw,[status(thm)],[1903631,67,theory(equality)]) ).
cnf(1903877,plain,
leq(star(multiplication(X1,strong_iteration(X1))),strong_iteration(X1)),
inference(cn,[status(thm)],[1903876,theory(equality)]) ).
cnf(1904318,plain,
addition(star(multiplication(X1,strong_iteration(X1))),strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[57,1903877,theory(equality)]) ).
cnf(1904379,plain,
star(multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1904318,28,theory(equality)]),3380,theory(equality)]) ).
cnf(1904629,plain,
star(strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[100916,1904379,theory(equality)]) ).
cnf(1909631,negated_conjecture,
$false,
inference(rw,[status(thm)],[65,1904629,theory(equality)]) ).
cnf(1909632,negated_conjecture,
$false,
inference(cn,[status(thm)],[1909631,theory(equality)]) ).
cnf(1909633,negated_conjecture,
$false,
1909632,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE145+1.p
% --creating new selector for [KLE004+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpgb1nti/sel_KLE145+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpgb1nti/sel_KLE145+1.p_2 with time limit 81
% -prover status Theorem
% Problem KLE145+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE145+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE145+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
%
%------------------------------------------------------------------------------