TSTP Solution File: KLE035+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE035+1 : 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 11:57:06 EST 2010
% Result : Theorem 22.94s
% Output : CNFRefutation 22.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 41 unt; 0 def)
% Number of atoms : 80 ( 40 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 : 6 ( 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 : 72 ( 0 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpTkKqmG/sel_KLE035+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/tmpTkKqmG/sel_KLE035+1.p_1',left_distributivity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',additive_commutativity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',additive_idempotence) ).
fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',multiplicative_associativity) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',right_distributivity) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpTkKqmG/sel_KLE035+1.p_1',order) ).
fof(17,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/tmpTkKqmG/sel_KLE035+1.p_1',goals) ).
fof(18,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)],[17]) ).
fof(24,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(25,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(27,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(30,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(33,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(35,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[34]) ).
fof(61,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(62,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(64,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[63]) ).
cnf(65,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(66,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(67,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)],[18]) ).
fof(68,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)],[67]) ).
fof(69,negated_conjecture,
( test(esk5_0)
& test(esk4_0)
& leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
& leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero)
& ~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero) ),
inference(skolemize,[status(esa)],[68]) ).
cnf(70,negated_conjecture,
~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(71,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(72,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(75,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[25,31,theory(equality)]) ).
cnf(111,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[71,35,theory(equality)]) ).
cnf(112,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[72,35,theory(equality)]) ).
cnf(113,negated_conjecture,
~ leq(multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),zero),
inference(rw,[status(thm)],[70,35,theory(equality)]) ).
cnf(207,negated_conjecture,
addition(multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),zero) != zero,
inference(spm,[status(thm)],[113,65,theory(equality)]) ).
cnf(210,negated_conjecture,
multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))) != zero,
inference(rw,[status(thm)],[207,25,theory(equality)]) ).
cnf(223,negated_conjecture,
addition(multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))),zero) = zero,
inference(spm,[status(thm)],[66,111,theory(equality)]) ).
cnf(226,negated_conjecture,
multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[223,25,theory(equality)]) ).
cnf(228,negated_conjecture,
addition(zero,multiplication(esk4_0,X1)) = multiplication(esk4_0,addition(multiplication(esk3_0,c(esk5_0)),X1)),
inference(spm,[status(thm)],[62,226,theory(equality)]) ).
cnf(236,negated_conjecture,
multiplication(esk4_0,X1) = multiplication(esk4_0,addition(multiplication(esk3_0,c(esk5_0)),X1)),
inference(rw,[status(thm)],[228,75,theory(equality)]) ).
cnf(245,negated_conjecture,
addition(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero) = zero,
inference(spm,[status(thm)],[66,112,theory(equality)]) ).
cnf(249,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[245,25,theory(equality)]) ).
cnf(264,negated_conjecture,
addition(multiplication(esk4_0,X1),zero) = multiplication(esk4_0,addition(X1,multiplication(esk2_0,c(esk5_0)))),
inference(spm,[status(thm)],[62,249,theory(equality)]) ).
cnf(273,negated_conjecture,
multiplication(esk4_0,X1) = multiplication(esk4_0,addition(X1,multiplication(esk2_0,c(esk5_0)))),
inference(rw,[status(thm)],[264,25,theory(equality)]) ).
cnf(5201,negated_conjecture,
addition(multiplication(esk4_0,X1),multiplication(X2,addition(multiplication(esk3_0,c(esk5_0)),X1))) = multiplication(addition(esk4_0,X2),addition(multiplication(esk3_0,c(esk5_0)),X1)),
inference(spm,[status(thm)],[27,236,theory(equality)]) ).
cnf(580719,negated_conjecture,
addition(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),multiplication(esk4_0,multiplication(esk3_0,c(esk5_0)))) = multiplication(addition(esk4_0,esk4_0),addition(multiplication(esk3_0,c(esk5_0)),multiplication(esk2_0,c(esk5_0)))),
inference(spm,[status(thm)],[5201,273,theory(equality)]) ).
cnf(581338,negated_conjecture,
zero = multiplication(addition(esk4_0,esk4_0),addition(multiplication(esk3_0,c(esk5_0)),multiplication(esk2_0,c(esk5_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[580719,249,theory(equality)]),226,theory(equality)]),25,theory(equality)]) ).
cnf(581339,negated_conjecture,
zero = multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[581338,33,theory(equality)]),27,theory(equality)]),31,theory(equality)]) ).
cnf(581340,negated_conjecture,
$false,
inference(sr,[status(thm)],[581339,210,theory(equality)]) ).
cnf(581341,negated_conjecture,
$false,
581340,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE035+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpTkKqmG/sel_KLE035+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE035+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE035+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE035+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
%
%------------------------------------------------------------------------------