%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE009+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 11:39:33 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : None (Could not find formula named the)
% Syntax : Number of formulae : 62
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpffAlb_/sel_KLE009+3.p_1',additive_associativity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpffAlb_/sel_KLE009+3.p_1',additive_commutativity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpffAlb_/sel_KLE009+3.p_1',additive_idempotence) ).
fof(11,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmpffAlb_/sel_KLE009+3.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/tmpffAlb_/sel_KLE009+3.p_1',test_2) ).
fof(14,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpffAlb_/sel_KLE009+3.p_1',multiplicative_right_identity) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpffAlb_/sel_KLE009+3.p_1',right_distributivity) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpffAlb_/sel_KLE009+3.p_1',order) ).
fof(17,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
file('/tmp/tmpffAlb_/sel_KLE009+3.p_1',goals) ).
fof(18,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[17]) ).
fof(28,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[5]) ).
cnf(29,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[28]) ).
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(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(59,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[14]) ).
cnf(60,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[59]) ).
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]) ).
fof(67,negated_conjecture,
? [X4,X5] :
( test(X5)
& test(X4)
& ( ~ leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
| ~ leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(68,negated_conjecture,
? [X6,X7] :
( test(X7)
& test(X6)
& ( ~ leq(one,addition(addition(addition(multiplication(X6,X7),multiplication(X6,c(X7))),multiplication(c(X6),X7)),multiplication(c(X6),c(X7))))
| ~ leq(addition(addition(addition(multiplication(X6,X7),multiplication(X6,c(X7))),multiplication(c(X6),X7)),multiplication(c(X6),c(X7))),one) ) ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(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))))
| ~ leq(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))),one) ) ),
inference(skolemize,[status(esa)],[68]) ).
cnf(70,negated_conjecture,
( ~ leq(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))),one)
| ~ leq(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)],[69]) ).
cnf(71,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(72,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(84,negated_conjecture,
( complement(esk2_0,X1)
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[45,71,theory(equality)]) ).
cnf(85,negated_conjecture,
( complement(esk3_0,X1)
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[45,72,theory(equality)]) ).
cnf(107,plain,
addition(X1,addition(X2,addition(X1,X2))) = addition(X1,X2),
inference(spm,[status(thm)],[33,29,theory(equality)]) ).
cnf(110,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[31,29,theory(equality)]) ).
cnf(187,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))))
| ~ leq(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))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[70,62,theory(equality)]),31,theory(equality)]),29,theory(equality)]) ).
cnf(188,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))))
| ~ leq(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)],[187,62,theory(equality)]),31,theory(equality)]),29,theory(equality)]) ).
cnf(189,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))))
| addition(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) != one ),
inference(spm,[status(thm)],[188,65,theory(equality)]) ).
cnf(190,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))))
| addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),addition(one,multiplication(c(esk2_0),c(esk3_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[189,29,theory(equality)]),29,theory(equality)]),31,theory(equality)]) ).
cnf(198,negated_conjecture,
( addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),addition(one,multiplication(c(esk2_0),c(esk3_0))))) != one
| addition(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0))))) != addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))) ),
inference(spm,[status(thm)],[190,65,theory(equality)]) ).
cnf(200,negated_conjecture,
( addition(X1,esk2_0) = one
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[50,84,theory(equality)]) ).
cnf(207,negated_conjecture,
addition(c(esk2_0),esk2_0) = one,
inference(er,[status(thm)],[200,theory(equality)]) ).
cnf(208,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[207,31,theory(equality)]) ).
cnf(225,negated_conjecture,
( addition(X1,esk3_0) = one
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[50,85,theory(equality)]) ).
cnf(313,negated_conjecture,
addition(c(esk3_0),esk3_0) = one,
inference(er,[status(thm)],[225,theory(equality)]) ).
cnf(314,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[313,31,theory(equality)]) ).
cnf(316,negated_conjecture,
( addition(one,addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))))) != addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0))))
| addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),addition(one,multiplication(c(esk2_0),c(esk3_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[198,314,theory(equality)]),60,theory(equality)]) ).
cnf(317,negated_conjecture,
( addition(one,addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))))) != addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))))
| addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),addition(one,multiplication(c(esk2_0),c(esk3_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[316,314,theory(equality)]),60,theory(equality)]) ).
cnf(318,negated_conjecture,
( addition(one,addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))))) != addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))))
| addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,addition(one,multiplication(c(esk2_0),c(esk3_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[317,314,theory(equality)]),60,theory(equality)]) ).
cnf(400,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),one)) = one,
inference(spm,[status(thm)],[107,208,theory(equality)]) ).
cnf(420,negated_conjecture,
addition(esk2_0,addition(one,c(esk2_0))) = one,
inference(rw,[status(thm)],[400,31,theory(equality)]) ).
cnf(554,negated_conjecture,
( one != addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))))
| addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,addition(one,multiplication(c(esk2_0),c(esk3_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[318,110,theory(equality)]),62,theory(equality)]),31,theory(equality)]),314,theory(equality)]),60,theory(equality)]),208,theory(equality)]),33,theory(equality)]) ).
cnf(555,negated_conjecture,
( $false
| addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,addition(one,multiplication(c(esk2_0),c(esk3_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[554,110,theory(equality)]),62,theory(equality)]),31,theory(equality)]),314,theory(equality)]),60,theory(equality)]),208,theory(equality)]) ).
cnf(556,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[555,110,theory(equality)]),29,theory(equality)]),62,theory(equality)]),31,theory(equality)]),314,theory(equality)]),60,theory(equality)]),420,theory(equality)]) ).
cnf(557,negated_conjecture,
$false,
inference(cn,[status(thm)],[556,theory(equality)]) ).
cnf(558,negated_conjecture,
$false,
557,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE009+3.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpffAlb_/sel_KLE009+3.p_1 with time limit 29
% -prover status Theorem
% Problem KLE009+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE009+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE009+3.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
%
%------------------------------------------------------------------------------