TSTP Solution File: KLE034+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE034+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 11:56:49 EST 2010
% Result : Theorem 185.49s
% Output : CNFRefutation 185.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 41 unt; 0 def)
% Number of atoms : 152 ( 76 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 132 ( 47 ~; 40 |; 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 : 93 ( 3 sgn 54 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',multiplicative_left_identity) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',additive_identity) ).
fof(4,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',left_distributivity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',additive_commutativity) ).
fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',multiplicative_associativity) ).
fof(9,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',left_annihilation) ).
fof(10,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',order) ).
fof(12,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',test_3) ).
fof(13,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/tmp/tmpx8kCoS/sel_KLE034+2.p_4',test_2) ).
fof(19,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/tmpx8kCoS/sel_KLE034+2.p_4',goals) ).
fof(20,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)],[19]) ).
fof(24,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(25,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(27,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(29,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[28]) ).
fof(32,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[32]) ).
fof(36,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(37,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[9]) ).
cnf(39,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(41,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[40]) ).
cnf(42,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(47,plain,
! [X4,X5] :
( ~ test(X4)
| ( ( c(X4) != X5
| complement(X4,X5) )
& ( ~ complement(X4,X5)
| c(X4) = X5 ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(48,plain,
! [X6,X7] :
( ~ test(X6)
| ( ( c(X6) != X7
| complement(X6,X7) )
& ( ~ complement(X6,X7)
| c(X6) = X7 ) ) ),
inference(variable_rename,[status(thm)],[47]) ).
fof(49,plain,
! [X6,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(X6) ) ),
inference(distribute,[status(thm)],[48]) ).
cnf(51,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(52,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)],[13]) ).
fof(53,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)],[52]) ).
fof(54,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)],[53]) ).
cnf(56,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(75,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)],[20]) ).
fof(76,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)],[75]) ).
fof(77,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)],[76]) ).
cnf(78,negated_conjecture,
~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(79,negated_conjecture,
leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(80,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(83,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(97,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[27,33,theory(equality)]) ).
cnf(121,negated_conjecture,
leq(multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))),zero),
inference(rw,[status(thm)],[79,37,theory(equality)]) ).
cnf(122,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[80,37,theory(equality)]) ).
cnf(123,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)],[78,37,theory(equality)]),37,theory(equality)]),37,theory(equality)]) ).
cnf(135,plain,
( addition(X1,X2) = one
| c(X2) != X1
| ~ test(X2) ),
inference(spm,[status(thm)],[56,51,theory(equality)]) ).
cnf(235,negated_conjecture,
addition(multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))),zero) != zero,
inference(spm,[status(thm)],[123,42,theory(equality)]) ).
cnf(238,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))) != zero,
inference(rw,[status(thm)],[235,27,theory(equality)]) ).
cnf(240,negated_conjecture,
addition(multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))),zero) = zero,
inference(spm,[status(thm)],[43,121,theory(equality)]) ).
cnf(243,negated_conjecture,
multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))) = zero,
inference(rw,[status(thm)],[240,27,theory(equality)]) ).
cnf(247,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)],[29,243,theory(equality)]) ).
cnf(260,negated_conjecture,
addition(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero) = zero,
inference(spm,[status(thm)],[43,122,theory(equality)]) ).
cnf(264,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[260,27,theory(equality)]) ).
cnf(279,negated_conjecture,
multiplication(zero,X1) = multiplication(esk4_0,multiplication(multiplication(esk2_0,c(esk5_0)),X1)),
inference(spm,[status(thm)],[37,264,theory(equality)]) ).
cnf(287,negated_conjecture,
zero = multiplication(esk4_0,multiplication(multiplication(esk2_0,c(esk5_0)),X1)),
inference(rw,[status(thm)],[279,39,theory(equality)]) ).
cnf(288,negated_conjecture,
zero = multiplication(esk4_0,multiplication(esk2_0,multiplication(c(esk5_0),X1))),
inference(rw,[status(thm)],[287,37,theory(equality)]) ).
cnf(723,plain,
( addition(c(X1),X1) = one
| ~ test(X1) ),
inference(er,[status(thm)],[135,theory(equality)]) ).
cnf(730,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[723,33,theory(equality)]) ).
cnf(5653,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)],[247,97,theory(equality)]) ).
cnf(5683,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)],[5653,730,theory(equality)]) ).
cnf(5717,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)],[5683,25,theory(equality)]) ).
cnf(5718,negated_conjecture,
( multiplication(esk3_0,c(esk6_0)) = multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0)))
| $false ),
inference(rw,[status(thm)],[5717,83,theory(equality)]) ).
cnf(5719,negated_conjecture,
multiplication(esk3_0,c(esk6_0)) = multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0))),
inference(cn,[status(thm)],[5718,theory(equality)]) ).
cnf(26561,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))) = zero,
inference(spm,[status(thm)],[288,5719,theory(equality)]) ).
cnf(26617,negated_conjecture,
$false,
inference(sr,[status(thm)],[26561,238,theory(equality)]) ).
cnf(26618,negated_conjecture,
$false,
26617,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE034+2.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax, KLE001+2.ax]
% eprover: CPU time limit exceeded, terminating
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpx8kCoS/sel_KLE034+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpx8kCoS/sel_KLE034+2.p_2 with time limit 80
% -prover status ResourceOut
% --creating new selector for [KLE001+0.ax, KLE001+1.ax, KLE001+2.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpx8kCoS/sel_KLE034+2.p_3 with time limit 75
% -prover status ResourceOut
% --creating new selector for [KLE001+0.ax, KLE001+1.ax, KLE001+2.ax]
% -running prover on /tmp/tmpx8kCoS/sel_KLE034+2.p_4 with time limit 54
% -prover status Theorem
% Problem KLE034+2.p solved in phase 3.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE034+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE034+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
%
%------------------------------------------------------------------------------