TSTP Solution File: KLE026+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE026+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 11:50:07 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 30 unt; 0 def)
% Number of atoms : 126 ( 62 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 109 ( 39 ~; 35 |; 28 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 55 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',multiplicative_left_identity) ).
fof(4,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',left_distributivity) ).
fof(5,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',additive_idempotence) ).
fof(7,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',multiplicative_associativity) ).
fof(9,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',additive_associativity) ).
fof(10,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',test_2) ).
fof(11,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',test_1) ).
fof(14,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',order) ).
fof(15,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
file('/tmp/tmp-8DO3D/sel_KLE026+1.p_1',goals) ).
fof(16,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
inference(assume_negation,[status(cth)],[15]) ).
fof(19,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(24,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(28,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[7]) ).
cnf(30,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[29]) ).
fof(33,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[9]) ).
cnf(34,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,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)],[10]) ).
fof(36,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)],[35]) ).
fof(37,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)],[36]) ).
cnf(39,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(42,plain,
! [X4] :
( ( ~ test(X4)
| ? [X5] : complement(X5,X4) )
& ( ! [X5] : ~ complement(X5,X4)
| test(X4) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(43,plain,
! [X6] :
( ( ~ test(X6)
| ? [X7] : complement(X7,X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X6] :
( ( ~ test(X6)
| complement(esk1_1(X6),X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(skolemize,[status(esa)],[43]) ).
fof(45,plain,
! [X6,X8] :
( ( ~ complement(X8,X6)
| test(X6) )
& ( ~ test(X6)
| complement(esk1_1(X6),X6) ) ),
inference(shift_quantors,[status(thm)],[44]) ).
cnf(46,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(52,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(53,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[52]) ).
cnf(54,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(56,negated_conjecture,
? [X4,X5,X6] :
( test(X5)
& test(X6)
& multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
& ~ leq(multiplication(X5,X4),multiplication(X4,X6)) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(57,negated_conjecture,
? [X7,X8,X9] :
( test(X8)
& test(X9)
& multiplication(X8,X7) = multiplication(multiplication(X8,X7),X9)
& ~ leq(multiplication(X8,X7),multiplication(X7,X9)) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0)
& ~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[57]) ).
cnf(59,negated_conjecture,
~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(62,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(71,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(spm,[status(thm)],[54,26,theory(equality)]) ).
cnf(76,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[39,46,theory(equality)]) ).
cnf(100,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk4_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[60,30,theory(equality)]) ).
cnf(114,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[34,28,theory(equality)]) ).
cnf(165,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[24,20,theory(equality)]) ).
cnf(479,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[114,76,theory(equality)]) ).
cnf(513,negated_conjecture,
addition(esk3_0,one) = one,
inference(spm,[status(thm)],[479,62,theory(equality)]) ).
cnf(517,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[513,26,theory(equality)]) ).
cnf(1133,plain,
( leq(multiplication(X1,X2),X2)
| multiplication(addition(one,X1),X2) != X2 ),
inference(spm,[status(thm)],[71,165,theory(equality)]) ).
cnf(1497,negated_conjecture,
( leq(multiplication(esk3_0,X1),X1)
| multiplication(one,X1) != X1 ),
inference(spm,[status(thm)],[1133,517,theory(equality)]) ).
cnf(1518,negated_conjecture,
( leq(multiplication(esk3_0,X1),X1)
| $false ),
inference(rw,[status(thm)],[1497,20,theory(equality)]) ).
cnf(1519,negated_conjecture,
leq(multiplication(esk3_0,X1),X1),
inference(cn,[status(thm)],[1518,theory(equality)]) ).
cnf(1534,negated_conjecture,
leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
inference(spm,[status(thm)],[1519,100,theory(equality)]) ).
cnf(1539,negated_conjecture,
$false,
inference(sr,[status(thm)],[1534,59,theory(equality)]) ).
cnf(1540,negated_conjecture,
$false,
1539,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE026+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmp-8DO3D/sel_KLE026+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE026+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE026+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE026+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
%
%------------------------------------------------------------------------------