%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE084+1 : 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 12:13:00 EST 2010
% Result : Theorem 7.70s
% Output : CNFRefutation 7.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 93 ( 93 unt; 0 def)
% Number of atoms : 93 ( 90 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 154 ( 14 sgn 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',left_annihilation) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpTpUuZh/sel_KLE084+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/tmpTpUuZh/sel_KLE084+1.p_1',left_distributivity) ).
fof(5,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',additive_idempotence) ).
fof(7,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',multiplicative_associativity) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',additive_associativity) ).
fof(12,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',multiplicative_right_identity) ).
fof(13,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',domain3) ).
fof(14,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',domain2) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',right_distributivity) ).
fof(16,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',domain1) ).
fof(17,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',multiplicative_left_identity) ).
fof(18,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',domain4) ).
fof(19,conjecture,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/tmp/tmpTpUuZh/sel_KLE084+1.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
inference(assume_negation,[status(cth)],[19]) ).
fof(21,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[1]) ).
cnf(22,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[21]) ).
fof(25,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(28,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(30,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[7]) ).
cnf(34,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[33]) ).
fof(41,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[11]) ).
cnf(42,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[12]) ).
cnf(44,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[13]) ).
cnf(46,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X6,X7] : addition(antidomain(multiplication(X6,X7)),antidomain(multiplication(X6,antidomain(antidomain(X7))))) = antidomain(multiplication(X6,antidomain(antidomain(X7)))),
inference(variable_rename,[status(thm)],[14]) ).
cnf(48,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[47]) ).
fof(49,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(50,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[49]) ).
fof(51,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[16]) ).
cnf(52,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[51]) ).
fof(53,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[17]) ).
cnf(54,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[53]) ).
fof(55,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[18]) ).
cnf(56,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,negated_conjecture,
? [X4,X5] : domain(multiplication(X4,X5)) != domain(multiplication(X4,domain(X5))),
inference(fof_nnf,[status(thm)],[20]) ).
fof(58,negated_conjecture,
? [X6,X7] : domain(multiplication(X6,X7)) != domain(multiplication(X6,domain(X7))),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,negated_conjecture,
domain(multiplication(esk1_0,esk2_0)) != domain(multiplication(esk1_0,domain(esk2_0))),
inference(skolemize,[status(esa)],[58]) ).
cnf(60,negated_conjecture,
domain(multiplication(esk1_0,esk2_0)) != domain(multiplication(esk1_0,domain(esk2_0))),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(61,negated_conjecture,
antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) != antidomain(antidomain(multiplication(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[60,56,theory(equality)]),56,theory(equality)]),56,theory(equality)]),
[unfolding] ).
cnf(62,plain,
zero = antidomain(one),
inference(spm,[status(thm)],[44,52,theory(equality)]) ).
cnf(66,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[26,30,theory(equality)]) ).
cnf(70,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[46,30,theory(equality)]) ).
cnf(77,plain,
multiplication(zero,X2) = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(spm,[status(thm)],[34,52,theory(equality)]) ).
cnf(89,plain,
zero = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(rw,[status(thm)],[77,22,theory(equality)]) ).
cnf(104,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[50,52,theory(equality)]) ).
cnf(123,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[104,26,theory(equality)]) ).
cnf(141,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[28,52,theory(equality)]) ).
cnf(161,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[141,26,theory(equality)]) ).
cnf(189,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[42,32,theory(equality)]) ).
cnf(226,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[70,62,theory(equality)]) ).
cnf(272,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[226,66,theory(equality)]) ).
cnf(384,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),multiplication(X1,antidomain(antidomain(X2)))) = multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))),
inference(spm,[status(thm)],[161,48,theory(equality)]) ).
cnf(392,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[161,30,theory(equality)]) ).
cnf(404,plain,
zero = multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))),
inference(rw,[status(thm)],[384,52,theory(equality)]) ).
cnf(433,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[392,70,theory(equality)]) ).
cnf(453,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[433,54,theory(equality)]) ).
cnf(467,plain,
multiplication(X1,X2) = multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)),
inference(spm,[status(thm)],[34,453,theory(equality)]) ).
cnf(700,plain,
multiplication(antidomain(antidomain(multiplication(X1,X2))),multiplication(X1,multiplication(X2,X3))) = multiplication(X1,multiplication(X2,X3)),
inference(spm,[status(thm)],[467,34,theory(equality)]) ).
cnf(1150,plain,
multiplication(antidomain(antidomain(antidomain(X1))),one) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(spm,[status(thm)],[123,70,theory(equality)]) ).
cnf(1170,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,X2)) = multiplication(antidomain(addition(X1,X2)),X1),
inference(spm,[status(thm)],[123,189,theory(equality)]) ).
cnf(1183,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(rw,[status(thm)],[1150,44,theory(equality)]) ).
cnf(1184,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[1183,453,theory(equality)]) ).
cnf(1201,plain,
zero = multiplication(antidomain(addition(X1,X2)),X1),
inference(rw,[status(thm)],[1170,52,theory(equality)]) ).
cnf(1388,plain,
addition(zero,multiplication(X3,X1)) = multiplication(addition(antidomain(addition(X1,X2)),X3),X1),
inference(spm,[status(thm)],[28,1201,theory(equality)]) ).
cnf(1420,plain,
multiplication(X3,X1) = multiplication(addition(antidomain(addition(X1,X2)),X3),X1),
inference(rw,[status(thm)],[1388,66,theory(equality)]) ).
cnf(1863,plain,
multiplication(antidomain(zero),multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2))))) = zero,
inference(spm,[status(thm)],[404,89,theory(equality)]) ).
cnf(1921,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1863,272,theory(equality)]),54,theory(equality)]) ).
cnf(2005,plain,
addition(zero,multiplication(antidomain(X1),X3)) = multiplication(antidomain(X1),addition(antidomain(antidomain(multiplication(X1,X2))),X3)),
inference(spm,[status(thm)],[50,1921,theory(equality)]) ).
cnf(2055,plain,
multiplication(antidomain(X1),X3) = multiplication(antidomain(X1),addition(antidomain(antidomain(multiplication(X1,X2))),X3)),
inference(rw,[status(thm)],[2005,66,theory(equality)]) ).
cnf(18016,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(addition(X1,X2))),X1),
inference(spm,[status(thm)],[1420,70,theory(equality)]) ).
cnf(18130,plain,
X1 = multiplication(antidomain(antidomain(addition(X1,X2))),X1),
inference(rw,[status(thm)],[18016,54,theory(equality)]) ).
cnf(18207,plain,
multiplication(antidomain(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2)))))),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(spm,[status(thm)],[18130,48,theory(equality)]) ).
cnf(18309,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[18207,1184,theory(equality)]) ).
cnf(100006,plain,
multiplication(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[700,453,theory(equality)]) ).
cnf(281509,plain,
multiplication(antidomain(X1),one) = multiplication(antidomain(X1),antidomain(antidomain(antidomain(multiplication(X1,X2))))),
inference(spm,[status(thm)],[2055,70,theory(equality)]) ).
cnf(282137,plain,
antidomain(X1) = multiplication(antidomain(X1),antidomain(antidomain(antidomain(multiplication(X1,X2))))),
inference(rw,[status(thm)],[281509,44,theory(equality)]) ).
cnf(282138,plain,
antidomain(X1) = multiplication(antidomain(X1),antidomain(multiplication(X1,X2))),
inference(rw,[status(thm)],[282137,1184,theory(equality)]) ).
cnf(283056,plain,
multiplication(antidomain(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2)))))),antidomain(multiplication(X1,X2))) = antidomain(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2)))))),
inference(spm,[status(thm)],[282138,100006,theory(equality)]) ).
cnf(283621,plain,
antidomain(multiplication(X1,X2)) = antidomain(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[283056,1184,theory(equality)]),18309,theory(equality)]) ).
cnf(283622,plain,
antidomain(multiplication(X1,X2)) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(rw,[status(thm)],[283621,1184,theory(equality)]) ).
cnf(284366,negated_conjecture,
$false,
inference(rw,[status(thm)],[61,283622,theory(equality)]) ).
cnf(284367,negated_conjecture,
$false,
inference(cn,[status(thm)],[284366,theory(equality)]) ).
cnf(284368,negated_conjecture,
$false,
284367,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE084+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax]
% -running prover on /tmp/tmpTpUuZh/sel_KLE084+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE084+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE084+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE084+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
%
%------------------------------------------------------------------------------