TSTP Solution File: KLE034+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE034+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 11:56:34 EST 2010
% Result : Theorem 0.36s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 41 unt; 0 def)
% Number of atoms : 151 ( 74 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 130 ( 46 ~; 39 |; 39 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 92 ( 3 sgn 54 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpWjN67I/sel_KLE034+1.p_1',multiplicative_left_identity) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpWjN67I/sel_KLE034+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/tmpWjN67I/sel_KLE034+1.p_1',left_distributivity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpWjN67I/sel_KLE034+1.p_1',additive_commutativity) ).
fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpWjN67I/sel_KLE034+1.p_1',multiplicative_associativity) ).
fof(9,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpWjN67I/sel_KLE034+1.p_1',left_annihilation) ).
fof(11,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmpWjN67I/sel_KLE034+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/tmpWjN67I/sel_KLE034+1.p_1',test_2) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpWjN67I/sel_KLE034+1.p_1',order) ).
fof(17,conjecture,
! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X6)
& test(X8)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X7,X5),c(X8)),zero) )
=> leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
file('/tmp/tmpWjN67I/sel_KLE034+1.p_1',goals) ).
fof(18,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X6)
& test(X8)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X7,X5),c(X8)),zero) )
=> leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
inference(assume_negation,[status(cth)],[17]) ).
fof(22,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(23,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[22]) ).
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(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(36,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[9]) ).
cnf(37,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[36]) ).
fof(41,plain,
! [X4,X5] :
( ~ test(X4)
| ( ( c(X4) != X5
| complement(X4,X5) )
& ( ~ complement(X4,X5)
| c(X4) = X5 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(42,plain,
! [X6,X7] :
( ~ test(X6)
| ( ( c(X6) != X7
| complement(X6,X7) )
& ( ~ complement(X6,X7)
| c(X6) = X7 ) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X6,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(X6) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(45,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(46,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(47,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)],[46]) ).
fof(48,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)],[47]) ).
cnf(50,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
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,X8] :
( test(X7)
& test(X6)
& test(X8)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X7,X5),c(X8)),zero)
& ~ leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(68,negated_conjecture,
? [X9,X10,X11,X12,X13] :
( test(X12)
& test(X11)
& test(X13)
& leq(multiplication(multiplication(X11,X9),c(X12)),zero)
& leq(multiplication(multiplication(X12,X10),c(X13)),zero)
& ~ leq(multiplication(multiplication(multiplication(X11,X9),X10),c(X13)),zero) ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,negated_conjecture,
( test(esk5_0)
& test(esk4_0)
& test(esk6_0)
& leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
& leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero)
& ~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero) ),
inference(skolemize,[status(esa)],[68]) ).
cnf(70,negated_conjecture,
~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(71,negated_conjecture,
leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_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,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(89,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[25,31,theory(equality)]) ).
cnf(96,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[45,theory(equality)]) ).
cnf(111,negated_conjecture,
leq(multiplication(esk5_0,multiplication(esk3_0,c(esk6_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(esk2_0,multiplication(esk3_0,c(esk6_0)))),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[70,35,theory(equality)]),35,theory(equality)]),35,theory(equality)]) ).
cnf(208,negated_conjecture,
addition(multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))),zero) != zero,
inference(spm,[status(thm)],[113,65,theory(equality)]) ).
cnf(211,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))) != zero,
inference(rw,[status(thm)],[208,25,theory(equality)]) ).
cnf(223,negated_conjecture,
addition(multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))),zero) = zero,
inference(spm,[status(thm)],[66,111,theory(equality)]) ).
cnf(226,negated_conjecture,
multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))) = zero,
inference(rw,[status(thm)],[223,25,theory(equality)]) ).
cnf(230,negated_conjecture,
addition(zero,multiplication(X1,multiplication(esk3_0,c(esk6_0)))) = multiplication(addition(esk5_0,X1),multiplication(esk3_0,c(esk6_0))),
inference(spm,[status(thm)],[27,226,theory(equality)]) ).
cnf(238,negated_conjecture,
multiplication(X1,multiplication(esk3_0,c(esk6_0))) = multiplication(addition(esk5_0,X1),multiplication(esk3_0,c(esk6_0))),
inference(rw,[status(thm)],[230,89,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(262,negated_conjecture,
multiplication(zero,X1) = multiplication(esk4_0,multiplication(multiplication(esk2_0,c(esk5_0)),X1)),
inference(spm,[status(thm)],[35,249,theory(equality)]) ).
cnf(270,negated_conjecture,
zero = multiplication(esk4_0,multiplication(multiplication(esk2_0,c(esk5_0)),X1)),
inference(rw,[status(thm)],[262,37,theory(equality)]) ).
cnf(271,negated_conjecture,
zero = multiplication(esk4_0,multiplication(esk2_0,multiplication(c(esk5_0),X1))),
inference(rw,[status(thm)],[270,35,theory(equality)]) ).
cnf(283,plain,
( addition(c(X1),X1) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[50,96,theory(equality)]) ).
cnf(284,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[283,31,theory(equality)]) ).
cnf(4688,negated_conjecture,
( multiplication(one,multiplication(esk3_0,c(esk6_0))) = multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0)))
| ~ test(esk5_0) ),
inference(spm,[status(thm)],[238,284,theory(equality)]) ).
cnf(4722,negated_conjecture,
( multiplication(esk3_0,c(esk6_0)) = multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0)))
| ~ test(esk5_0) ),
inference(rw,[status(thm)],[4688,23,theory(equality)]) ).
cnf(4723,negated_conjecture,
( multiplication(esk3_0,c(esk6_0)) = multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0)))
| $false ),
inference(rw,[status(thm)],[4722,75,theory(equality)]) ).
cnf(4724,negated_conjecture,
multiplication(esk3_0,c(esk6_0)) = multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0))),
inference(cn,[status(thm)],[4723,theory(equality)]) ).
cnf(4749,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))) = zero,
inference(spm,[status(thm)],[271,4724,theory(equality)]) ).
cnf(4776,negated_conjecture,
$false,
inference(sr,[status(thm)],[4749,211,theory(equality)]) ).
cnf(4777,negated_conjecture,
$false,
4776,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE034+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpWjN67I/sel_KLE034+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE034+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE034+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE034+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
%
%------------------------------------------------------------------------------