TSTP Solution File: KLE141+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE141+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 12:36:05 EST 2010
% Result : Theorem 2.37s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 75 ( 58 unt; 0 def)
% Number of atoms : 96 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 16 |; 2 &)
% ( 1 <=>; 2 =>; 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 : 111 ( 12 sgn 54 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',multiplicative_left_identity) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',additive_identity) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',additive_commutativity) ).
fof(5,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',isolation) ).
fof(6,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',multiplicative_right_identity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',idempotence) ).
fof(8,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',star_induction2) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',additive_associativity) ).
fof(12,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',infty_coinduction) ).
fof(14,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',distributivity1) ).
fof(15,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',star_unfold1) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',order) ).
fof(19,conjecture,
! [X4] : multiplication(strong_iteration(one),X4) = strong_iteration(one),
file('/tmp/tmp6t9Icu/sel_KLE141+1.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4] : multiplication(strong_iteration(one),X4) = strong_iteration(one),
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(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(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(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(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(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(62,negated_conjecture,
? [X4] : multiplication(strong_iteration(one),X4) != strong_iteration(one),
inference(fof_nnf,[status(thm)],[20]) ).
fof(63,negated_conjecture,
? [X5] : multiplication(strong_iteration(one),X5) != strong_iteration(one),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
multiplication(strong_iteration(one),esk1_0) != strong_iteration(one),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
multiplication(strong_iteration(one),esk1_0) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,plain,
leq(X1,X1),
inference(spm,[status(thm)],[56,34,theory(equality)]) ).
cnf(68,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[26,28,theory(equality)]) ).
cnf(91,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[44,34,theory(equality)]) ).
cnf(123,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[51,32,theory(equality)]) ).
cnf(179,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[47,24,theory(equality)]) ).
cnf(189,plain,
( leq(multiplication(X1,star(X2)),one)
| ~ leq(addition(X2,X1),one) ),
inference(spm,[status(thm)],[37,24,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(960,plain,
multiplication(addition(X1,X2),addition(one,X3)) = addition(X1,addition(X2,multiplication(addition(X1,X2),X3))),
inference(spm,[status(thm)],[44,123,theory(equality)]) ).
cnf(1155,plain,
( leq(multiplication(X1,star(X1)),one)
| ~ leq(X1,one) ),
inference(spm,[status(thm)],[189,34,theory(equality)]) ).
cnf(1185,plain,
leq(multiplication(one,star(one)),one),
inference(spm,[status(thm)],[1155,67,theory(equality)]) ).
cnf(1187,plain,
leq(star(one),one),
inference(rw,[status(thm)],[1185,24,theory(equality)]) ).
cnf(1189,plain,
addition(star(one),one) = one,
inference(spm,[status(thm)],[57,1187,theory(equality)]) ).
cnf(1191,plain,
star(one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1189,28,theory(equality)]),242,theory(equality)]) ).
cnf(1194,plain,
addition(one,multiplication(strong_iteration(one),zero)) = strong_iteration(one),
inference(spm,[status(thm)],[30,1191,theory(equality)]) ).
cnf(7850,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| $false ),
inference(rw,[status(thm)],[179,252,theory(equality)]) ).
cnf(7851,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[7850,theory(equality)]) ).
cnf(7852,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[7851,32,theory(equality)]) ).
cnf(7854,plain,
addition(X1,multiplication(strong_iteration(one),X2)) = multiplication(strong_iteration(one),X2),
inference(spm,[status(thm)],[57,7851,theory(equality)]) ).
cnf(7865,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[57,7852,theory(equality)]) ).
cnf(7941,plain,
strong_iteration(one) = addition(strong_iteration(one),X1),
inference(spm,[status(thm)],[28,7865,theory(equality)]) ).
cnf(8073,plain,
strong_iteration(one) = multiplication(strong_iteration(one),addition(one,X1)),
inference(spm,[status(thm)],[123,7941,theory(equality)]) ).
cnf(61726,plain,
addition(one,addition(multiplication(strong_iteration(one),zero),multiplication(strong_iteration(one),X1))) = multiplication(strong_iteration(one),addition(one,X1)),
inference(spm,[status(thm)],[960,1194,theory(equality)]) ).
cnf(62197,plain,
addition(one,multiplication(strong_iteration(one),X1)) = multiplication(strong_iteration(one),addition(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[61726,51,theory(equality)]),68,theory(equality)]) ).
cnf(62198,plain,
addition(one,multiplication(strong_iteration(one),X1)) = strong_iteration(one),
inference(rw,[status(thm)],[62197,8073,theory(equality)]) ).
cnf(76867,plain,
multiplication(strong_iteration(one),X1) = strong_iteration(one),
inference(rw,[status(thm)],[62198,7854,theory(equality)]) ).
cnf(77613,negated_conjecture,
$false,
inference(rw,[status(thm)],[65,76867,theory(equality)]) ).
cnf(77614,negated_conjecture,
$false,
inference(cn,[status(thm)],[77613,theory(equality)]) ).
cnf(77615,negated_conjecture,
$false,
77614,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE141+1.p
% --creating new selector for [KLE004+0.ax]
% -running prover on /tmp/tmp6t9Icu/sel_KLE141+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE141+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE141+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE141+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
%
%------------------------------------------------------------------------------