%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE024+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 11:49:12 EST 2010
% Result : Theorem 0.71s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 103 ( 49 unt; 0 def)
% Number of atoms : 209 ( 117 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 178 ( 72 ~; 69 |; 29 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 143 ( 7 sgn 69 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',multiplicative_left_identity) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',additive_identity) ).
fof(4,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',left_distributivity) ).
fof(5,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',additive_associativity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',additive_commutativity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',additive_idempotence) ).
fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',multiplicative_associativity) ).
fof(9,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',left_annihilation) ).
fof(11,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',test_3) ).
fof(12,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',test_2) ).
fof(13,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',test_1) ).
fof(14,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',multiplicative_right_identity) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',right_distributivity) ).
fof(16,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = zero ) ),
file('/tmp/tmp9tbxl0/sel_KLE024+1.p_1',goals) ).
fof(17,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = zero ) ),
inference(assume_negation,[status(cth)],[16]) ).
fof(21,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(22,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(24,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(26,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[5]) ).
cnf(28,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
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)],[7]) ).
cnf(32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(34,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[9]) ).
cnf(36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[35]) ).
fof(40,plain,
! [X4,X5] :
( ~ test(X4)
| ( ( c(X4) != X5
| complement(X4,X5) )
& ( ~ complement(X4,X5)
| c(X4) = X5 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(41,plain,
! [X6,X7] :
( ~ test(X6)
| ( ( c(X6) != X7
| complement(X6,X7) )
& ( ~ complement(X6,X7)
| c(X6) = X7 ) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,plain,
! [X6,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(X6) ) ),
inference(distribute,[status(thm)],[41]) ).
cnf(44,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(45,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)],[12]) ).
fof(46,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)],[45]) ).
fof(47,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)],[46]) ).
cnf(49,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(50,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(51,plain,
( multiplication(X2,X1) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(52,plain,
! [X4] :
( ( ~ test(X4)
| ? [X5] : complement(X5,X4) )
& ( ! [X5] : ~ complement(X5,X4)
| test(X4) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(53,plain,
! [X6] :
( ( ~ test(X6)
| ? [X7] : complement(X7,X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(variable_rename,[status(thm)],[52]) ).
fof(54,plain,
! [X6] :
( ( ~ test(X6)
| complement(esk1_1(X6),X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(skolemize,[status(esa)],[53]) ).
fof(55,plain,
! [X6,X8] :
( ( ~ complement(X8,X6)
| test(X6) )
& ( ~ test(X6)
| complement(esk1_1(X6),X6) ) ),
inference(shift_quantors,[status(thm)],[54]) ).
cnf(57,plain,
( test(X1)
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(58,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[14]) ).
cnf(59,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[58]) ).
fof(60,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(61,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[60]) ).
fof(62,negated_conjecture,
? [X4,X5,X6] :
( test(X5)
& test(X6)
& addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
& multiplication(multiplication(X5,X4),c(X6)) != zero ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(63,negated_conjecture,
? [X7,X8,X9] :
( test(X8)
& test(X9)
& addition(multiplication(X7,c(X9)),multiplication(c(X8),X7)) = multiplication(c(X8),X7)
& multiplication(multiplication(X8,X7),c(X9)) != zero ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0)
& multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero ),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero,
inference(split_conjunct,[status(thm)],[64]) ).
cnf(66,negated_conjecture,
addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(68,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(69,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[24,30,theory(equality)]) ).
cnf(90,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[44,theory(equality)]) ).
cnf(100,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) != zero,
inference(rw,[status(thm)],[65,34,theory(equality)]) ).
cnf(114,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[28,32,theory(equality)]) ).
cnf(130,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[61,59,theory(equality)]) ).
cnf(206,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[57,90,theory(equality)]) ).
cnf(207,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[51,90,theory(equality)]) ).
cnf(208,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[50,90,theory(equality)]) ).
cnf(209,plain,
( addition(c(X1),X1) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[49,90,theory(equality)]) ).
cnf(210,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[209,30,theory(equality)]) ).
cnf(213,plain,
( multiplication(zero,X2) = multiplication(c(X1),multiplication(X1,X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[34,207,theory(equality)]) ).
cnf(217,plain,
( addition(multiplication(X1,X2),zero) = multiplication(addition(X1,c(X2)),X2)
| ~ test(X2) ),
inference(spm,[status(thm)],[26,207,theory(equality)]) ).
cnf(219,plain,
( zero = multiplication(c(X1),multiplication(X1,X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[213,36,theory(equality)]) ).
cnf(223,plain,
( multiplication(X1,X2) = multiplication(addition(X1,c(X2)),X2)
| ~ test(X2) ),
inference(rw,[status(thm)],[217,24,theory(equality)]) ).
cnf(232,plain,
( multiplication(zero,X2) = multiplication(X1,multiplication(c(X1),X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[34,208,theory(equality)]) ).
cnf(241,plain,
( zero = multiplication(X1,multiplication(c(X1),X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[232,36,theory(equality)]) ).
cnf(373,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[114,210,theory(equality)]) ).
cnf(387,negated_conjecture,
addition(esk3_0,one) = one,
inference(spm,[status(thm)],[373,68,theory(equality)]) ).
cnf(391,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[387,30,theory(equality)]) ).
cnf(584,plain,
( addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,multiplication(c(X1),X3)))
| ~ test(X1) ),
inference(spm,[status(thm)],[61,241,theory(equality)]) ).
cnf(603,plain,
( multiplication(X1,X2) = multiplication(X1,addition(X2,multiplication(c(X1),X3)))
| ~ test(X1) ),
inference(rw,[status(thm)],[584,24,theory(equality)]) ).
cnf(1522,plain,
( multiplication(one,X1) = multiplication(X1,X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[223,210,theory(equality)]) ).
cnf(1542,plain,
( X1 = multiplication(X1,X1)
| ~ test(X1) ),
inference(rw,[status(thm)],[1522,22,theory(equality)]) ).
cnf(1547,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[1542,68,theory(equality)]) ).
cnf(1560,negated_conjecture,
( multiplication(c(esk3_0),esk3_0) = zero
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[219,1547,theory(equality)]) ).
cnf(1568,negated_conjecture,
( multiplication(c(esk3_0),esk3_0) = zero
| $false ),
inference(rw,[status(thm)],[1560,68,theory(equality)]) ).
cnf(1569,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(cn,[status(thm)],[1568,theory(equality)]) ).
cnf(1595,negated_conjecture,
addition(zero,multiplication(X1,esk3_0)) = multiplication(addition(c(esk3_0),X1),esk3_0),
inference(spm,[status(thm)],[26,1569,theory(equality)]) ).
cnf(1607,negated_conjecture,
multiplication(X1,esk3_0) = multiplication(addition(c(esk3_0),X1),esk3_0),
inference(rw,[status(thm)],[1595,69,theory(equality)]) ).
cnf(2027,negated_conjecture,
( multiplication(one,esk3_0) = multiplication(c(c(esk3_0)),esk3_0)
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[1607,210,theory(equality)]) ).
cnf(2049,negated_conjecture,
( esk3_0 = multiplication(c(c(esk3_0)),esk3_0)
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[2027,22,theory(equality)]) ).
cnf(2141,negated_conjecture,
( addition(c(c(esk3_0)),esk3_0) = multiplication(c(c(esk3_0)),addition(one,esk3_0))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[130,2049,theory(equality)]) ).
cnf(2153,negated_conjecture,
( addition(esk3_0,c(c(esk3_0))) = multiplication(c(c(esk3_0)),addition(one,esk3_0))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[2141,30,theory(equality)]) ).
cnf(2154,negated_conjecture,
( addition(esk3_0,c(c(esk3_0))) = c(c(esk3_0))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2153,391,theory(equality)]),59,theory(equality)]) ).
cnf(2225,negated_conjecture,
( multiplication(c(c(esk3_0)),c(esk3_0)) = multiplication(esk3_0,c(esk3_0))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[223,2154,theory(equality)]) ).
cnf(3564,negated_conjecture,
( multiplication(esk3_0,c(esk3_0)) = zero
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[207,2225,theory(equality)]) ).
cnf(3588,negated_conjecture,
( multiplication(esk3_0,c(esk3_0)) = zero
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[3564,206,theory(equality)]) ).
cnf(3591,negated_conjecture,
( multiplication(esk3_0,c(esk3_0)) = zero
| $false ),
inference(rw,[status(thm)],[3588,68,theory(equality)]) ).
cnf(3592,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(cn,[status(thm)],[3591,theory(equality)]) ).
cnf(3593,negated_conjecture,
multiplication(zero,X1) = multiplication(esk3_0,multiplication(c(esk3_0),X1)),
inference(spm,[status(thm)],[34,3592,theory(equality)]) ).
cnf(3616,negated_conjecture,
zero = multiplication(esk3_0,multiplication(c(esk3_0),X1)),
inference(rw,[status(thm)],[3593,36,theory(equality)]) ).
cnf(14662,negated_conjecture,
( multiplication(esk3_0,multiplication(c(esk3_0),esk2_0)) = multiplication(esk3_0,multiplication(esk2_0,c(esk4_0)))
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[603,66,theory(equality)]) ).
cnf(14785,negated_conjecture,
( zero = multiplication(esk3_0,multiplication(esk2_0,c(esk4_0)))
| ~ test(esk3_0) ),
inference(rw,[status(thm)],[14662,3616,theory(equality)]) ).
cnf(14786,negated_conjecture,
( zero = multiplication(esk3_0,multiplication(esk2_0,c(esk4_0)))
| $false ),
inference(rw,[status(thm)],[14785,68,theory(equality)]) ).
cnf(14787,negated_conjecture,
zero = multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))),
inference(cn,[status(thm)],[14786,theory(equality)]) ).
cnf(14788,negated_conjecture,
$false,
inference(sr,[status(thm)],[14787,100,theory(equality)]) ).
cnf(14789,negated_conjecture,
$false,
14788,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE024+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmp9tbxl0/sel_KLE024+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE024+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE024+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE024+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
%
%------------------------------------------------------------------------------