TSTP Solution File: KLE027+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE027+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 11:50:31 EST 2010
% Result : Theorem 0.61s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 28 unt; 0 def)
% Number of atoms : 133 ( 75 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 123 ( 51 ~; 45 |; 22 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 108 ( 4 sgn 54 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpdwAP0L/sel_KLE027+1.p_1',multiplicative_left_identity) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpdwAP0L/sel_KLE027+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/tmpdwAP0L/sel_KLE027+1.p_1',left_distributivity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpdwAP0L/sel_KLE027+1.p_1',additive_commutativity) ).
fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpdwAP0L/sel_KLE027+1.p_1',multiplicative_associativity) ).
fof(9,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpdwAP0L/sel_KLE027+1.p_1',left_annihilation) ).
fof(11,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmpdwAP0L/sel_KLE027+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/tmpdwAP0L/sel_KLE027+1.p_1',test_2) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpdwAP0L/sel_KLE027+1.p_1',right_distributivity) ).
fof(16,conjecture,
! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X8) )
=> addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)) = addition(multiplication(X7,X4),multiplication(c(X7),X6)) ),
file('/tmp/tmpdwAP0L/sel_KLE027+1.p_1',goals) ).
fof(17,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X8) )
=> addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)) = addition(multiplication(X7,X4),multiplication(c(X7),X6)) ),
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(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(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(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,X7,X8] :
( test(X7)
& test(X8)
& addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)) != addition(multiplication(X7,X4),multiplication(c(X7),X6)) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(63,negated_conjecture,
? [X9,X10,X11,X12,X13] :
( test(X12)
& test(X13)
& addition(multiplication(X12,addition(multiplication(X12,X9),multiplication(c(X12),X10))),multiplication(c(X12),X11)) != addition(multiplication(X12,X9),multiplication(c(X12),X11)) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
( test(esk5_0)
& test(esk6_0)
& addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)) != addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)) ),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)) != addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(75,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[44,theory(equality)]) ).
cnf(180,negated_conjecture,
addition(multiplication(c(esk5_0),esk4_0),multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0)))) != addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),
inference(rw,[status(thm)],[65,30,theory(equality)]) ).
cnf(194,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[51,75,theory(equality)]) ).
cnf(195,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[50,75,theory(equality)]) ).
cnf(196,plain,
( addition(c(X1),X1) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[49,75,theory(equality)]) ).
cnf(197,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[196,30,theory(equality)]) ).
cnf(216,plain,
( addition(multiplication(X1,X2),zero) = multiplication(addition(X1,c(X2)),X2)
| ~ test(X2) ),
inference(spm,[status(thm)],[26,194,theory(equality)]) ).
cnf(222,plain,
( multiplication(X1,X2) = multiplication(addition(X1,c(X2)),X2)
| ~ test(X2) ),
inference(rw,[status(thm)],[216,24,theory(equality)]) ).
cnf(231,plain,
( multiplication(zero,X2) = multiplication(X1,multiplication(c(X1),X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[34,195,theory(equality)]) ).
cnf(240,plain,
( zero = multiplication(X1,multiplication(c(X1),X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[231,36,theory(equality)]) ).
cnf(516,plain,
( addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,multiplication(c(X1),X3)))
| ~ test(X1) ),
inference(spm,[status(thm)],[61,240,theory(equality)]) ).
cnf(535,plain,
( multiplication(X1,X2) = multiplication(X1,addition(X2,multiplication(c(X1),X3)))
| ~ test(X1) ),
inference(rw,[status(thm)],[516,24,theory(equality)]) ).
cnf(1134,plain,
( multiplication(one,X1) = multiplication(X1,X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[222,197,theory(equality)]) ).
cnf(1152,plain,
( X1 = multiplication(X1,X1)
| ~ test(X1) ),
inference(rw,[status(thm)],[1134,22,theory(equality)]) ).
cnf(1157,negated_conjecture,
multiplication(esk5_0,esk5_0) = esk5_0,
inference(spm,[status(thm)],[1152,67,theory(equality)]) ).
cnf(1162,negated_conjecture,
multiplication(esk5_0,X1) = multiplication(esk5_0,multiplication(esk5_0,X1)),
inference(spm,[status(thm)],[34,1157,theory(equality)]) ).
cnf(14739,negated_conjecture,
( addition(multiplication(c(esk5_0),esk4_0),multiplication(esk5_0,multiplication(esk5_0,esk2_0))) != addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0))
| ~ test(esk5_0) ),
inference(spm,[status(thm)],[180,535,theory(equality)]) ).
cnf(14905,negated_conjecture,
( $false
| ~ test(esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[14739,1162,theory(equality)]),30,theory(equality)]) ).
cnf(14906,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[14905,67,theory(equality)]) ).
cnf(14907,negated_conjecture,
$false,
inference(cn,[status(thm)],[14906,theory(equality)]) ).
cnf(14908,negated_conjecture,
$false,
14907,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE027+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpdwAP0L/sel_KLE027+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE027+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE027+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE027+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
%
%------------------------------------------------------------------------------