TSTP Solution File: KLE048+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE048+1 : 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 12:04:42 EST 2010
% Result : Theorem 0.37s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 50 unt; 0 def)
% Number of atoms : 152 ( 66 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 114 ( 46 ~; 42 |; 20 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 11 sgn 54 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',right_annihilation) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_identity) ).
fof(5,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_idempotence) ).
fof(7,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',star_induction_right) ).
fof(9,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',order) ).
fof(10,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',additive_associativity) ).
fof(11,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',test_2) ).
fof(12,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',test_1) ).
fof(14,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',star_unfold_right) ).
fof(18,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',multiplicative_left_identity) ).
fof(19,conjecture,
! [X4] :
( test(X4)
=> star(X4) = one ),
file('/tmp/tmps5mfKk/sel_KLE048+1.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4] :
( test(X4)
=> star(X4) = one ),
inference(assume_negation,[status(cth)],[19]) ).
fof(21,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[1]) ).
cnf(22,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[21]) ).
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(29,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(30,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X1,X2,X3] :
( ~ leq(addition(multiplication(X1,X2),X3),X1)
| leq(multiplication(X3,star(X2)),X1) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(34,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X4,X5),X6),X4)
| leq(multiplication(X6,star(X5)),X4) ),
inference(variable_rename,[status(thm)],[33]) ).
cnf(35,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(38,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(39,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(41,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(42,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[10]) ).
cnf(43,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X4,X5] :
( ( ~ complement(X5,X4)
| ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) )
& ( multiplication(X4,X5) != zero
| multiplication(X5,X4) != zero
| addition(X4,X5) != one
| complement(X5,X4) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(45,plain,
! [X6,X7] :
( ( ~ complement(X7,X6)
| ( multiplication(X6,X7) = zero
& multiplication(X7,X6) = zero
& addition(X6,X7) = one ) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| addition(X6,X7) != one
| complement(X7,X6) ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X6,X7] :
( ( multiplication(X6,X7) = zero
| ~ complement(X7,X6) )
& ( multiplication(X7,X6) = zero
| ~ complement(X7,X6) )
& ( addition(X6,X7) = one
| ~ complement(X7,X6) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| addition(X6,X7) != one
| complement(X7,X6) ) ),
inference(distribute,[status(thm)],[45]) ).
cnf(48,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(51,plain,
! [X4] :
( ( ~ test(X4)
| ? [X5] : complement(X5,X4) )
& ( ! [X5] : ~ complement(X5,X4)
| test(X4) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(52,plain,
! [X6] :
( ( ~ test(X6)
| ? [X7] : complement(X7,X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X6] :
( ( ~ test(X6)
| complement(esk1_1(X6),X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(skolemize,[status(esa)],[52]) ).
fof(54,plain,
! [X6,X8] :
( ( ~ complement(X8,X6)
| test(X6) )
& ( ~ test(X6)
| complement(esk1_1(X6),X6) ) ),
inference(shift_quantors,[status(thm)],[53]) ).
cnf(55,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(59,plain,
! [X2] : leq(addition(one,multiplication(X2,star(X2))),star(X2)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(60,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[59]) ).
fof(68,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[18]) ).
cnf(69,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[68]) ).
fof(70,negated_conjecture,
? [X4] :
( test(X4)
& star(X4) != one ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(71,negated_conjecture,
? [X5] :
( test(X5)
& star(X5) != one ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,negated_conjecture,
( test(esk2_0)
& star(esk2_0) != one ),
inference(skolemize,[status(esa)],[71]) ).
cnf(73,negated_conjecture,
star(esk2_0) != one,
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(76,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[26,30,theory(equality)]) ).
cnf(83,plain,
leq(X1,X1),
inference(spm,[status(thm)],[40,32,theory(equality)]) ).
cnf(88,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[48,55,theory(equality)]) ).
cnf(91,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(spm,[status(thm)],[41,60,theory(equality)]) ).
cnf(93,plain,
addition(star(X1),addition(one,multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[91,30,theory(equality)]) ).
cnf(134,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[43,32,theory(equality)]) ).
cnf(146,plain,
( leq(multiplication(X1,star(zero)),X2)
| ~ leq(addition(zero,X1),X2) ),
inference(spm,[status(thm)],[35,22,theory(equality)]) ).
cnf(150,plain,
( leq(multiplication(X1,star(X2)),one)
| ~ leq(addition(X2,X1),one) ),
inference(spm,[status(thm)],[35,69,theory(equality)]) ).
cnf(265,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[40,134,theory(equality)]) ).
cnf(286,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[265,30,theory(equality)]) ).
cnf(328,plain,
leq(X1,addition(X2,addition(X3,X1))),
inference(spm,[status(thm)],[286,43,theory(equality)]) ).
cnf(391,plain,
leq(X1,addition(X2,addition(X1,X3))),
inference(spm,[status(thm)],[328,30,theory(equality)]) ).
cnf(535,plain,
( leq(X1,one)
| ~ test(X1) ),
inference(spm,[status(thm)],[265,88,theory(equality)]) ).
cnf(567,negated_conjecture,
leq(esk2_0,one),
inference(spm,[status(thm)],[535,74,theory(equality)]) ).
cnf(572,negated_conjecture,
addition(esk2_0,one) = one,
inference(spm,[status(thm)],[41,567,theory(equality)]) ).
cnf(573,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[572,30,theory(equality)]) ).
cnf(585,plain,
leq(one,star(X1)),
inference(spm,[status(thm)],[391,93,theory(equality)]) ).
cnf(608,negated_conjecture,
leq(esk2_0,addition(X1,one)),
inference(spm,[status(thm)],[328,573,theory(equality)]) ).
cnf(619,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[41,585,theory(equality)]) ).
cnf(639,negated_conjecture,
leq(esk2_0,addition(one,X1)),
inference(spm,[status(thm)],[608,30,theory(equality)]) ).
cnf(675,negated_conjecture,
leq(esk2_0,star(X1)),
inference(spm,[status(thm)],[639,619,theory(equality)]) ).
cnf(686,negated_conjecture,
addition(esk2_0,star(X1)) = star(X1),
inference(spm,[status(thm)],[41,675,theory(equality)]) ).
cnf(1523,plain,
( leq(multiplication(X1,star(zero)),X2)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[146,76,theory(equality)]) ).
cnf(1526,plain,
leq(multiplication(X1,star(zero)),X1),
inference(spm,[status(thm)],[1523,83,theory(equality)]) ).
cnf(1599,plain,
leq(star(zero),one),
inference(spm,[status(thm)],[1526,69,theory(equality)]) ).
cnf(1612,plain,
addition(star(zero),one) = one,
inference(spm,[status(thm)],[41,1599,theory(equality)]) ).
cnf(1614,plain,
star(zero) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1612,30,theory(equality)]),619,theory(equality)]) ).
cnf(1677,negated_conjecture,
( leq(multiplication(star(X1),star(esk2_0)),one)
| ~ leq(star(X1),one) ),
inference(spm,[status(thm)],[150,686,theory(equality)]) ).
cnf(6528,negated_conjecture,
( leq(multiplication(one,star(esk2_0)),one)
| ~ leq(one,one) ),
inference(spm,[status(thm)],[1677,1614,theory(equality)]) ).
cnf(6530,negated_conjecture,
( leq(star(esk2_0),one)
| ~ leq(one,one) ),
inference(rw,[status(thm)],[6528,69,theory(equality)]) ).
cnf(6531,negated_conjecture,
( leq(star(esk2_0),one)
| $false ),
inference(rw,[status(thm)],[6530,83,theory(equality)]) ).
cnf(6532,negated_conjecture,
leq(star(esk2_0),one),
inference(cn,[status(thm)],[6531,theory(equality)]) ).
cnf(6536,negated_conjecture,
addition(star(esk2_0),one) = one,
inference(spm,[status(thm)],[41,6532,theory(equality)]) ).
cnf(6540,negated_conjecture,
star(esk2_0) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6536,30,theory(equality)]),619,theory(equality)]) ).
cnf(6541,negated_conjecture,
$false,
inference(sr,[status(thm)],[6540,73,theory(equality)]) ).
cnf(6542,negated_conjecture,
$false,
6541,
[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/KLE048+1.p
% --creating new selector for [KLE002+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmps5mfKk/sel_KLE048+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE048+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE048+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE048+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
%
%------------------------------------------------------------------------------