TSTP Solution File: KLE039+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE039+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 11:58:34 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 69 unt; 0 def)
% Number of atoms : 105 ( 58 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 16 |; 2 &)
% ( 1 <=>; 1 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 133 ( 3 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',star_induction_right) ).
fof(2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',left_distributivity) ).
fof(3,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',additive_commutativity) ).
fof(4,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',additive_idempotence) ).
fof(5,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',multiplicative_associativity) ).
fof(6,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',star_unfold_left) ).
fof(7,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',additive_associativity) ).
fof(8,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',multiplicative_right_identity) ).
fof(9,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',star_unfold_right) ).
fof(10,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',right_distributivity) ).
fof(12,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',order) ).
fof(13,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',multiplicative_left_identity) ).
fof(14,conjecture,
! [X4] : star(star(X4)) = star(X4),
file('/tmp/tmp3sJvUv/sel_KLE039+1.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X4] : star(star(X4)) = star(X4),
inference(assume_negation,[status(cth)],[14]) ).
fof(16,plain,
! [X1,X2,X3] :
( ~ leq(addition(multiplication(X1,X2),X3),X1)
| leq(multiplication(X3,star(X2)),X1) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(17,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X4,X5),X6),X4)
| leq(multiplication(X6,star(X5)),X4) ),
inference(variable_rename,[status(thm)],[16]) ).
cnf(18,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(24,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[5]) ).
cnf(26,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X2] : leq(addition(one,multiplication(star(X2),X2)),star(X2)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(28,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[7]) ).
cnf(30,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[8]) ).
cnf(32,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X2] : leq(addition(one,multiplication(X2,star(X2))),star(X2)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(34,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(36,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(40,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(41,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[40]) ).
cnf(42,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(44,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[13]) ).
cnf(45,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,negated_conjecture,
? [X4] : star(star(X4)) != star(X4),
inference(fof_nnf,[status(thm)],[15]) ).
fof(47,negated_conjecture,
? [X5] : star(star(X5)) != star(X5),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,negated_conjecture,
star(star(esk1_0)) != star(esk1_0),
inference(skolemize,[status(esa)],[47]) ).
cnf(49,negated_conjecture,
star(star(esk1_0)) != star(esk1_0),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(54,plain,
leq(X1,X1),
inference(spm,[status(thm)],[42,24,theory(equality)]) ).
cnf(70,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[30,24,theory(equality)]) ).
cnf(81,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(spm,[status(thm)],[43,34,theory(equality)]) ).
cnf(82,plain,
addition(addition(one,multiplication(star(X1),X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[43,28,theory(equality)]) ).
cnf(83,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[81,30,theory(equality)]),22,theory(equality)]) ).
cnf(84,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[82,30,theory(equality)]),22,theory(equality)]) ).
cnf(87,plain,
( leq(multiplication(multiplication(X1,X2),star(X2)),X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(spm,[status(thm)],[18,24,theory(equality)]) ).
cnf(91,plain,
( leq(multiplication(X1,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[87,26,theory(equality)]) ).
cnf(98,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[36,32,theory(equality)]) ).
cnf(109,plain,
( leq(multiplication(multiplication(X1,X2),star(X3)),X1)
| ~ leq(multiplication(X1,addition(X3,X2)),X1) ),
inference(spm,[status(thm)],[18,36,theory(equality)]) ).
cnf(123,plain,
( leq(multiplication(X1,multiplication(X2,star(X3))),X1)
| ~ leq(multiplication(X1,addition(X3,X2)),X1) ),
inference(rw,[status(thm)],[109,26,theory(equality)]) ).
cnf(126,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[20,45,theory(equality)]) ).
cnf(175,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[70,22,theory(equality)]) ).
cnf(177,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[42,70,theory(equality)]) ).
cnf(335,plain,
leq(X1,multiplication(X1,addition(one,X2))),
inference(spm,[status(thm)],[177,98,theory(equality)]) ).
cnf(1802,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[83,126,theory(equality)]) ).
cnf(1805,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[70,1802,theory(equality)]) ).
cnf(1814,plain,
addition(multiplication(addition(one,X1),star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[175,1802,theory(equality)]) ).
cnf(1854,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1814,22,theory(equality)]),126,theory(equality)]),70,theory(equality)]) ).
cnf(1866,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[84,98,theory(equality)]) ).
cnf(1878,plain,
addition(multiplication(star(X1),addition(one,X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[175,1866,theory(equality)]) ).
cnf(1920,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1878,22,theory(equality)]),98,theory(equality)]),70,theory(equality)]) ).
cnf(1939,plain,
leq(X1,multiplication(X1,star(X2))),
inference(spm,[status(thm)],[335,1805,theory(equality)]) ).
cnf(2036,plain,
multiplication(star(X1),star(star(X1))) = star(star(X1)),
inference(spm,[status(thm)],[1854,1805,theory(equality)]) ).
cnf(2082,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(spm,[status(thm)],[1920,22,theory(equality)]) ).
cnf(2190,plain,
leq(addition(one,X1),star(X1)),
inference(spm,[status(thm)],[1939,1854,theory(equality)]) ).
cnf(2206,plain,
leq(addition(X1,one),star(X1)),
inference(spm,[status(thm)],[2190,22,theory(equality)]) ).
cnf(2226,plain,
addition(addition(X1,one),star(X1)) = star(X1),
inference(spm,[status(thm)],[43,2206,theory(equality)]) ).
cnf(2231,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2226,30,theory(equality)]),1805,theory(equality)]) ).
cnf(4788,plain,
( leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(spm,[status(thm)],[123,2082,theory(equality)]) ).
cnf(4818,plain,
( leq(multiplication(star(X1),star(X1)),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(rw,[status(thm)],[4788,45,theory(equality)]) ).
cnf(4819,plain,
( leq(multiplication(star(X1),star(X1)),star(X1))
| $false ),
inference(rw,[status(thm)],[4818,54,theory(equality)]) ).
cnf(4820,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[4819,theory(equality)]) ).
cnf(5162,plain,
leq(multiplication(star(X1),multiplication(star(X1),star(star(X1)))),star(X1)),
inference(spm,[status(thm)],[91,4820,theory(equality)]) ).
cnf(5166,plain,
leq(star(star(X1)),star(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5162,2036,theory(equality)]),2036,theory(equality)]) ).
cnf(5168,plain,
addition(star(star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[43,5166,theory(equality)]) ).
cnf(5171,plain,
star(star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5168,22,theory(equality)]),2231,theory(equality)]) ).
cnf(5272,negated_conjecture,
$false,
inference(rw,[status(thm)],[49,5171,theory(equality)]) ).
cnf(5273,negated_conjecture,
$false,
inference(cn,[status(thm)],[5272,theory(equality)]) ).
cnf(5274,negated_conjecture,
$false,
5273,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE039+1.p
% --creating new selector for [KLE002+0.ax]
% -running prover on /tmp/tmp3sJvUv/sel_KLE039+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE039+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE039+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE039+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
%
%------------------------------------------------------------------------------