TSTP Solution File: KLE035+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE035+2 : 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 11:58:06 EST 2010
% Result : Theorem 0.74s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 30 unt; 0 def)
% Number of atoms : 69 ( 28 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 43 ( 14 ~; 6 |; 20 &)
% ( 1 <=>; 2 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 34 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpp9_tzr/sel_KLE035+2.p_1',additive_identity) ).
fof(3,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpp9_tzr/sel_KLE035+2.p_1',left_distributivity) ).
fof(7,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpp9_tzr/sel_KLE035+2.p_1',multiplicative_associativity) ).
fof(9,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpp9_tzr/sel_KLE035+2.p_1',order) ).
fof(13,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpp9_tzr/sel_KLE035+2.p_1',right_distributivity) ).
fof(14,conjecture,
! [X4,X5,X6,X7] :
( ( test(X7)
& test(X6)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
file('/tmp/tmpp9_tzr/sel_KLE035+2.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X4,X5,X6,X7] :
( ( test(X7)
& test(X6)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
inference(assume_negation,[status(cth)],[14]) ).
fof(19,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(22,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[21]) ).
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,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(34,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[33]) ).
cnf(35,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(46,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(47,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,negated_conjecture,
? [X4,X5,X6,X7] :
( test(X7)
& test(X6)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X6,X5),c(X7)),zero)
& ~ leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(49,negated_conjecture,
? [X8,X9,X10,X11] :
( test(X11)
& test(X10)
& leq(multiplication(multiplication(X10,X8),c(X11)),zero)
& leq(multiplication(multiplication(X10,X9),c(X11)),zero)
& ~ leq(multiplication(multiplication(X10,addition(X8,X9)),c(X11)),zero) ),
inference(variable_rename,[status(thm)],[48]) ).
fof(50,negated_conjecture,
( test(esk4_0)
& test(esk3_0)
& leq(multiplication(multiplication(esk3_0,esk1_0),c(esk4_0)),zero)
& leq(multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)),zero)
& ~ leq(multiplication(multiplication(esk3_0,addition(esk1_0,esk2_0)),c(esk4_0)),zero) ),
inference(skolemize,[status(esa)],[49]) ).
cnf(51,negated_conjecture,
~ leq(multiplication(multiplication(esk3_0,addition(esk1_0,esk2_0)),c(esk4_0)),zero),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(52,negated_conjecture,
leq(multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)),zero),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(53,negated_conjecture,
leq(multiplication(multiplication(esk3_0,esk1_0),c(esk4_0)),zero),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(73,negated_conjecture,
leq(multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))),zero),
inference(rw,[status(thm)],[52,30,theory(equality)]) ).
cnf(74,negated_conjecture,
leq(multiplication(esk3_0,multiplication(esk1_0,c(esk4_0))),zero),
inference(rw,[status(thm)],[53,30,theory(equality)]) ).
cnf(75,negated_conjecture,
~ leq(multiplication(esk3_0,multiplication(addition(esk1_0,esk2_0),c(esk4_0))),zero),
inference(rw,[status(thm)],[51,30,theory(equality)]) ).
cnf(151,negated_conjecture,
addition(multiplication(esk3_0,multiplication(addition(esk1_0,esk2_0),c(esk4_0))),zero) != zero,
inference(spm,[status(thm)],[75,35,theory(equality)]) ).
cnf(152,negated_conjecture,
multiplication(esk3_0,multiplication(addition(esk1_0,esk2_0),c(esk4_0))) != zero,
inference(rw,[status(thm)],[151,20,theory(equality)]) ).
cnf(160,negated_conjecture,
addition(multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))),zero) = zero,
inference(spm,[status(thm)],[36,73,theory(equality)]) ).
cnf(161,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) = zero,
inference(rw,[status(thm)],[160,20,theory(equality)]) ).
cnf(164,negated_conjecture,
addition(multiplication(esk3_0,X1),zero) = multiplication(esk3_0,addition(X1,multiplication(esk2_0,c(esk4_0)))),
inference(spm,[status(thm)],[47,161,theory(equality)]) ).
cnf(171,negated_conjecture,
multiplication(esk3_0,X1) = multiplication(esk3_0,addition(X1,multiplication(esk2_0,c(esk4_0)))),
inference(rw,[status(thm)],[164,20,theory(equality)]) ).
cnf(176,negated_conjecture,
addition(multiplication(esk3_0,multiplication(esk1_0,c(esk4_0))),zero) = zero,
inference(spm,[status(thm)],[36,74,theory(equality)]) ).
cnf(177,negated_conjecture,
multiplication(esk3_0,multiplication(esk1_0,c(esk4_0))) = zero,
inference(rw,[status(thm)],[176,20,theory(equality)]) ).
cnf(789,negated_conjecture,
multiplication(esk3_0,multiplication(addition(X1,esk2_0),c(esk4_0))) = multiplication(esk3_0,multiplication(X1,c(esk4_0))),
inference(spm,[status(thm)],[171,22,theory(equality)]) ).
cnf(14332,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[152,789,theory(equality)]),177,theory(equality)]) ).
cnf(14333,negated_conjecture,
$false,
inference(cn,[status(thm)],[14332,theory(equality)]) ).
cnf(14334,negated_conjecture,
$false,
14333,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE035+2.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax, KLE001+2.ax]
% -running prover on /tmp/tmpp9_tzr/sel_KLE035+2.p_1 with time limit 29
% -prover status Theorem
% Problem KLE035+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE035+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE035+2.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
%
%------------------------------------------------------------------------------