TSTP Solution File: KLE009+2 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE009+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 11:39:29 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 24 unt; 0 def)
% Number of atoms : 112 ( 63 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 115 ( 51 ~; 37 |; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpf333T9/sel_KLE009+2.p_1',additive_associativity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpf333T9/sel_KLE009+2.p_1',additive_commutativity) ).
fof(11,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmpf333T9/sel_KLE009+2.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/tmpf333T9/sel_KLE009+2.p_1',test_2) ).
fof(14,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpf333T9/sel_KLE009+2.p_1',multiplicative_right_identity) ).
fof(17,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpf333T9/sel_KLE009+2.p_1',right_distributivity) ).
fof(18,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
file('/tmp/tmpf333T9/sel_KLE009+2.p_1',goals) ).
fof(19,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
inference(assume_negation,[status(cth)],[18]) ).
fof(29,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[5]) ).
cnf(30,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(32,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[31]) ).
fof(42,plain,
! [X4,X5] :
( ~ test(X4)
| ( ( c(X4) != X5
| complement(X4,X5) )
& ( ~ complement(X4,X5)
| c(X4) = X5 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(43,plain,
! [X6,X7] :
( ~ test(X6)
| ( ( c(X6) != X7
| complement(X6,X7) )
& ( ~ complement(X6,X7)
| c(X6) = X7 ) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X6,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(X6) ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(46,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(47,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(48,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)],[47]) ).
fof(49,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)],[48]) ).
cnf(51,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(60,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[14]) ).
cnf(61,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[60]) ).
fof(68,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[17]) ).
cnf(69,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[68]) ).
fof(70,negated_conjecture,
? [X4,X5] :
( test(X5)
& test(X4)
& one != addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(71,negated_conjecture,
? [X6,X7] :
( test(X7)
& test(X6)
& one != addition(addition(addition(multiplication(X6,X7),multiplication(X6,c(X7))),multiplication(c(X6),X7)),multiplication(c(X6),c(X7))) ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& one != addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))) ),
inference(skolemize,[status(esa)],[71]) ).
cnf(73,negated_conjecture,
one != addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(75,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(87,plain,
( addition(X1,X2) = one
| c(X2) != X1
| ~ test(X2) ),
inference(spm,[status(thm)],[51,46,theory(equality)]) ).
cnf(115,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[32,30,theory(equality)]) ).
cnf(200,negated_conjecture,
addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[73,69,theory(equality)]),32,theory(equality)]),30,theory(equality)]) ).
cnf(298,plain,
( addition(c(X1),X1) = one
| ~ test(X1) ),
inference(er,[status(thm)],[87,theory(equality)]) ).
cnf(301,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[298,32,theory(equality)]) ).
cnf(305,negated_conjecture,
( addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,one),multiplication(c(esk2_0),c(esk3_0)))) != one
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[200,301,theory(equality)]) ).
cnf(310,negated_conjecture,
( addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))) != one
| ~ test(esk3_0) ),
inference(rw,[status(thm)],[305,61,theory(equality)]) ).
cnf(311,negated_conjecture,
( addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))) != one
| $false ),
inference(rw,[status(thm)],[310,75,theory(equality)]) ).
cnf(312,negated_conjecture,
addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))) != one,
inference(cn,[status(thm)],[311,theory(equality)]) ).
cnf(888,negated_conjecture,
addition(esk2_0,multiplication(c(esk2_0),addition(esk3_0,c(esk3_0)))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[312,115,theory(equality)]),69,theory(equality)]),32,theory(equality)]) ).
cnf(940,negated_conjecture,
( addition(esk2_0,multiplication(c(esk2_0),one)) != one
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[888,301,theory(equality)]) ).
cnf(943,negated_conjecture,
( addition(esk2_0,c(esk2_0)) != one
| ~ test(esk3_0) ),
inference(rw,[status(thm)],[940,61,theory(equality)]) ).
cnf(944,negated_conjecture,
( addition(esk2_0,c(esk2_0)) != one
| $false ),
inference(rw,[status(thm)],[943,75,theory(equality)]) ).
cnf(945,negated_conjecture,
addition(esk2_0,c(esk2_0)) != one,
inference(cn,[status(thm)],[944,theory(equality)]) ).
cnf(950,negated_conjecture,
~ test(esk2_0),
inference(spm,[status(thm)],[945,301,theory(equality)]) ).
cnf(952,negated_conjecture,
$false,
inference(rw,[status(thm)],[950,74,theory(equality)]) ).
cnf(953,negated_conjecture,
$false,
inference(cn,[status(thm)],[952,theory(equality)]) ).
cnf(954,negated_conjecture,
$false,
953,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE009+2.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax, KLE001+2.ax]
% -running prover on /tmp/tmpf333T9/sel_KLE009+2.p_1 with time limit 29
% -prover status Theorem
% Problem KLE009+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE009+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE009+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
%
%------------------------------------------------------------------------------