%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE170+1.002 : TPTP v5.2.0. Released v5.2.0.
% 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 : Mon Feb 28 18:27:17 EST 2011
% Result : Theorem 1.08s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 64 unt; 0 def)
% Number of atoms : 78 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 6 |; 2 &)
% ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 4 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',multiplicative_left_identity) ).
fof(2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',left_distributivity) ).
fof(3,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',additive_commutativity) ).
fof(4,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',additive_idempotence) ).
fof(6,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',order) ).
fof(7,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',additive_associativity) ).
fof(8,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',multiplicative_right_identity) ).
fof(9,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/tmp/tmp0haApJ/sel_KLE170+1.002.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/tmp0haApJ/sel_KLE170+1.002.p_1',right_distributivity) ).
fof(14,conjecture,
leq(multiplication(a,a),star(a)),
file('/tmp/tmp0haApJ/sel_KLE170+1.002.p_1',a) ).
fof(15,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(assume_negation,[status(cth)],[14]) ).
fof(16,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(17,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[1]) ).
cnf(18,plain,
multiplication(one,X1) = X1,
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(28,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(29,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[28]) ).
cnf(30,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(32,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[7]) ).
cnf(33,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[8]) ).
cnf(35,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,plain,
! [X2] : leq(addition(one,multiplication(X2,star(X2))),star(X2)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(37,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(39,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(47,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(68,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[33,24,theory(equality)]) ).
cnf(70,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[22,33,theory(equality)]) ).
cnf(72,plain,
addition(addition(X2,X1),X3) = addition(X1,addition(X2,X3)),
inference(spm,[status(thm)],[33,22,theory(equality)]) ).
cnf(77,plain,
addition(X2,addition(X1,X3)) = addition(X1,addition(X2,X3)),
inference(rw,[status(thm)],[72,33,theory(equality)]) ).
cnf(79,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(spm,[status(thm)],[31,37,theory(equality)]) ).
cnf(81,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[79,33,theory(equality)]),22,theory(equality)]) ).
cnf(96,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[39,35,theory(equality)]) ).
cnf(124,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[20,18,theory(equality)]) ).
cnf(173,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[68,22,theory(equality)]) ).
cnf(175,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[30,68,theory(equality)]) ).
cnf(191,plain,
leq(multiplication(X1,X2),multiplication(X1,addition(X2,X3))),
inference(spm,[status(thm)],[175,39,theory(equality)]) ).
cnf(333,plain,
leq(X1,multiplication(X1,addition(one,X2))),
inference(spm,[status(thm)],[175,96,theory(equality)]) ).
cnf(455,plain,
addition(X1,multiplication(X2,addition(one,X3))) = addition(multiplication(X2,X3),addition(X1,X2)),
inference(spm,[status(thm)],[70,96,theory(equality)]) ).
cnf(514,plain,
addition(X1,multiplication(X2,addition(one,X3))) = addition(X2,addition(multiplication(X2,X3),X1)),
inference(rw,[status(thm)],[455,70,theory(equality)]) ).
cnf(806,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(spm,[status(thm)],[96,124,theory(equality)]) ).
cnf(1800,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[81,124,theory(equality)]) ).
cnf(1803,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[68,1800,theory(equality)]) ).
cnf(1812,plain,
addition(multiplication(addition(one,X1),star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[173,1800,theory(equality)]) ).
cnf(1852,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1812,22,theory(equality)]),124,theory(equality)]),68,theory(equality)]) ).
cnf(1937,plain,
leq(X1,multiplication(X1,star(X2))),
inference(spm,[status(thm)],[333,1803,theory(equality)]) ).
cnf(2188,plain,
leq(addition(one,X1),star(X1)),
inference(spm,[status(thm)],[1937,1852,theory(equality)]) ).
cnf(2204,plain,
leq(addition(X1,one),star(X1)),
inference(spm,[status(thm)],[2188,22,theory(equality)]) ).
cnf(2224,plain,
addition(addition(X1,one),star(X1)) = star(X1),
inference(spm,[status(thm)],[31,2204,theory(equality)]) ).
cnf(2229,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2224,33,theory(equality)]),1803,theory(equality)]) ).
cnf(2251,plain,
addition(X1,star(X2)) = addition(X2,addition(X1,star(X2))),
inference(spm,[status(thm)],[77,2229,theory(equality)]) ).
cnf(2714,plain,
leq(multiplication(X1,X2),multiplication(X1,star(X2))),
inference(spm,[status(thm)],[191,2229,theory(equality)]) ).
cnf(7866,plain,
leq(multiplication(X1,addition(one,X1)),multiplication(addition(one,X1),star(X1))),
inference(spm,[status(thm)],[2714,806,theory(equality)]) ).
cnf(7894,plain,
leq(multiplication(X1,addition(one,X1)),star(X1)),
inference(rw,[status(thm)],[7866,1852,theory(equality)]) ).
cnf(7939,plain,
addition(multiplication(X1,addition(one,X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[31,7894,theory(equality)]) ).
cnf(7955,plain,
addition(star(X1),multiplication(X1,addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[7939,22,theory(equality)]) ).
cnf(24238,plain,
star(X1) = addition(X1,addition(multiplication(X1,X1),star(X1))),
inference(spm,[status(thm)],[514,7955,theory(equality)]) ).
cnf(24385,plain,
star(X1) = addition(multiplication(X1,X1),star(X1)),
inference(rw,[status(thm)],[24238,2251,theory(equality)]) ).
cnf(24423,plain,
leq(multiplication(X1,X1),star(X1)),
inference(spm,[status(thm)],[175,24385,theory(equality)]) ).
cnf(24639,negated_conjecture,
$false,
inference(rw,[status(thm)],[47,24423,theory(equality)]) ).
cnf(24640,negated_conjecture,
$false,
inference(cn,[status(thm)],[24639,theory(equality)]) ).
cnf(24641,negated_conjecture,
$false,
24640,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE170+1.002.p
% --creating new selector for [KLE002+0.ax]
% -running prover on /tmp/tmp0haApJ/sel_KLE170+1.002.p_1 with time limit 29
% -prover status Theorem
% Problem KLE170+1.002.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE170+1.002.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE170+1.002.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
%
%------------------------------------------------------------------------------