TSTP Solution File: KLE106+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE106+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 12:20:01 EST 2010
% Result : Theorem 8.01s
% Output : CNFRefutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 23
% Syntax : Number of formulae : 177 ( 171 unt; 0 def)
% Number of atoms : 183 ( 181 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 0 |; 3 &)
% ( 0 <=>; 1 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 230 ( 14 sgn 79 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',left_distributivity) ).
fof(2,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',codomain4) ).
fof(3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',codomain3) ).
fof(5,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',codomain1) ).
fof(6,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',right_annihilation) ).
fof(7,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',multiplicative_right_identity) ).
fof(8,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',multiplicative_left_identity) ).
fof(9,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',backward_diamond) ).
fof(10,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',domain3) ).
fof(11,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',domain2) ).
fof(12,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',domain1) ).
fof(13,axiom,
! [X4] : c(X4) = antidomain(domain(X4)),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',complement) ).
fof(14,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',domain4) ).
fof(15,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',left_annihilation) ).
fof(16,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',additive_identity) ).
fof(17,axiom,
! [X4,X5] : backward_box(X4,X5) = c(backward_diamond(X4,c(X5))),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',backward_box) ).
fof(18,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',additive_idempotence) ).
fof(19,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',multiplicative_associativity) ).
fof(20,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',forward_diamond) ).
fof(21,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',additive_commutativity) ).
fof(22,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',additive_associativity) ).
fof(23,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',right_distributivity) ).
fof(24,conjecture,
! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),backward_box(X4,domain(X6))) = backward_box(X4,domain(X6)) ),
file('/tmp/tmpXYQjPE/sel_KLE106+1.p_1',goals) ).
fof(25,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),backward_box(X4,domain(X6))) = backward_box(X4,domain(X6)) ),
inference(assume_negation,[status(cth)],[24]) ).
fof(26,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(domain(X5),backward_box(X4,domain(X6))) = backward_box(X4,domain(X6))
=> addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(27,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(28,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X5] : codomain(X5) = coantidomain(coantidomain(X5)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(30,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[3]) ).
cnf(32,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[31]) ).
fof(35,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[5]) ).
cnf(36,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[6]) ).
cnf(38,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(40,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[8]) ).
cnf(42,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X6,X7] : backward_diamond(X6,X7) = codomain(multiplication(codomain(X7),X6)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(44,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[10]) ).
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)],[11]) ).
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,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[12]) ).
cnf(50,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[49]) ).
fof(51,plain,
! [X5] : c(X5) = antidomain(domain(X5)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(52,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[51]) ).
fof(53,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(54,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[53]) ).
fof(55,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[15]) ).
cnf(56,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[16]) ).
cnf(58,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[57]) ).
fof(59,plain,
! [X6,X7] : backward_box(X6,X7) = c(backward_diamond(X6,c(X7))),
inference(variable_rename,[status(thm)],[17]) ).
cnf(60,plain,
backward_box(X1,X2) = c(backward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[59]) ).
fof(61,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[18]) ).
cnf(62,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[19]) ).
cnf(64,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[63]) ).
fof(65,plain,
! [X6,X7] : forward_diamond(X6,X7) = domain(multiplication(X6,domain(X7))),
inference(variable_rename,[status(thm)],[20]) ).
cnf(66,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[65]) ).
fof(67,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[21]) ).
cnf(68,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[67]) ).
fof(69,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[22]) ).
cnf(70,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[69]) ).
fof(71,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[23]) ).
cnf(72,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[71]) ).
fof(73,negated_conjecture,
? [X4,X5,X6] :
( addition(domain(X5),backward_box(X4,domain(X6))) = backward_box(X4,domain(X6))
& addition(forward_diamond(X4,domain(X5)),domain(X6)) != domain(X6) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(74,negated_conjecture,
? [X7,X8,X9] :
( addition(domain(X8),backward_box(X7,domain(X9))) = backward_box(X7,domain(X9))
& addition(forward_diamond(X7,domain(X8)),domain(X9)) != domain(X9) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,negated_conjecture,
( addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) = backward_box(esk1_0,domain(esk3_0))
& addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0) ),
inference(skolemize,[status(esa)],[74]) ).
cnf(76,negated_conjecture,
addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(77,negated_conjecture,
addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) = backward_box(esk1_0,domain(esk3_0)),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(78,plain,
coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[44,30,theory(equality)]),30,theory(equality)]),
[unfolding] ).
cnf(79,plain,
antidomain(antidomain(antidomain(X1))) = c(X1),
inference(rw,[status(thm)],[52,54,theory(equality)]),
[unfolding] ).
cnf(80,plain,
antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))) = forward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[66,54,theory(equality)]),54,theory(equality)]),
[unfolding] ).
cnf(81,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),backward_box(esk1_0,antidomain(antidomain(esk3_0)))) = backward_box(esk1_0,antidomain(antidomain(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[77,54,theory(equality)]),54,theory(equality)]),54,theory(equality)]),
[unfolding] ).
cnf(82,negated_conjecture,
addition(forward_diamond(esk1_0,antidomain(antidomain(esk2_0))),antidomain(antidomain(esk3_0))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[76,54,theory(equality)]),54,theory(equality)]),54,theory(equality)]),
[unfolding] ).
cnf(83,plain,
antidomain(antidomain(antidomain(backward_diamond(X1,antidomain(antidomain(antidomain(X2))))))) = backward_box(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[60,79,theory(equality)]),79,theory(equality)]),
[unfolding] ).
cnf(84,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(backward_diamond(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))) = antidomain(antidomain(antidomain(backward_diamond(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[81,83,theory(equality)]),83,theory(equality)]),
[unfolding] ).
cnf(85,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[82,80,theory(equality)]),
[unfolding] ).
cnf(86,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0))))))) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[84,78,theory(equality)]),78,theory(equality)]),
[unfolding] ).
cnf(88,plain,
zero = antidomain(one),
inference(spm,[status(thm)],[40,50,theory(equality)]) ).
cnf(91,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[58,68,theory(equality)]) ).
cnf(95,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[32,68,theory(equality)]) ).
cnf(96,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[46,68,theory(equality)]) ).
cnf(98,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[70,62,theory(equality)]) ).
cnf(102,plain,
addition(one,X2) = addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)),
inference(spm,[status(thm)],[70,96,theory(equality)]) ).
cnf(106,plain,
addition(addition(X2,X1),X3) = addition(X1,addition(X2,X3)),
inference(spm,[status(thm)],[70,68,theory(equality)]) ).
cnf(111,plain,
addition(X2,addition(X1,X3)) = addition(X1,addition(X2,X3)),
inference(rw,[status(thm)],[106,70,theory(equality)]) ).
cnf(136,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[72,40,theory(equality)]) ).
cnf(145,plain,
addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(spm,[status(thm)],[72,36,theory(equality)]) ).
cnf(146,plain,
addition(zero,multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),addition(X1,X2)),
inference(spm,[status(thm)],[72,50,theory(equality)]) ).
cnf(147,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[72,50,theory(equality)]) ).
cnf(165,plain,
multiplication(X1,X2) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[145,58,theory(equality)]) ).
cnf(166,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[147,58,theory(equality)]) ).
cnf(176,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[28,42,theory(equality)]) ).
cnf(185,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[28,50,theory(equality)]) ).
cnf(205,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[185,58,theory(equality)]) ).
cnf(232,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[85,68,theory(equality)]) ).
cnf(258,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[96,88,theory(equality)]) ).
cnf(277,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[258,91,theory(equality)]) ).
cnf(360,plain,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[98,96,theory(equality)]) ).
cnf(380,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[360,68,theory(equality)]) ).
cnf(595,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[165,68,theory(equality)]) ).
cnf(658,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[205,68,theory(equality)]) ).
cnf(796,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[595,95,theory(equality)]) ).
cnf(819,plain,
X1 = multiplication(X1,coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[796,40,theory(equality)]) ).
cnf(836,plain,
multiplication(X1,X2) = multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)),
inference(spm,[status(thm)],[64,819,theory(equality)]) ).
cnf(864,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[658,96,theory(equality)]) ).
cnf(885,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[864,42,theory(equality)]) ).
cnf(1323,plain,
multiplication(antidomain(antidomain(antidomain(X1))),one) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(spm,[status(thm)],[166,96,theory(equality)]) ).
cnf(1340,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,X2)) = multiplication(antidomain(addition(X1,X2)),X1),
inference(spm,[status(thm)],[166,98,theory(equality)]) ).
cnf(1347,plain,
multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),addition(one,X2)) = multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)),
inference(spm,[status(thm)],[166,102,theory(equality)]) ).
cnf(1355,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,addition(X3,X2))) = multiplication(antidomain(addition(X1,X2)),X3),
inference(spm,[status(thm)],[166,111,theory(equality)]) ).
cnf(1358,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(rw,[status(thm)],[1323,40,theory(equality)]) ).
cnf(1359,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[1358,885,theory(equality)]) ).
cnf(1374,plain,
zero = multiplication(antidomain(addition(X1,X2)),X1),
inference(rw,[status(thm)],[1340,50,theory(equality)]) ).
cnf(1415,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[86,1359,theory(equality)]),1359,theory(equality)]),1359,theory(equality)]) ).
cnf(1416,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) = antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1415,1359,theory(equality)]),1359,theory(equality)]),1359,theory(equality)]) ).
cnf(1417,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[232,1359,theory(equality)]) ).
cnf(1441,plain,
addition(zero,multiplication(antidomain(addition(X1,X2)),X3)) = multiplication(antidomain(addition(X1,X2)),addition(X1,X3)),
inference(spm,[status(thm)],[72,1374,theory(equality)]) ).
cnf(1444,plain,
addition(zero,multiplication(X3,X1)) = multiplication(addition(antidomain(addition(X1,X2)),X3),X1),
inference(spm,[status(thm)],[28,1374,theory(equality)]) ).
cnf(1474,plain,
multiplication(antidomain(addition(X1,X2)),X3) = multiplication(antidomain(addition(X1,X2)),addition(X1,X3)),
inference(rw,[status(thm)],[1441,91,theory(equality)]) ).
cnf(1476,plain,
multiplication(X3,X1) = multiplication(addition(antidomain(addition(X1,X2)),X3),X1),
inference(rw,[status(thm)],[1444,91,theory(equality)]) ).
cnf(1582,negated_conjecture,
addition(antidomain(esk2_0),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) = addition(one,antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))),
inference(spm,[status(thm)],[102,1416,theory(equality)]) ).
cnf(1592,negated_conjecture,
addition(antidomain(esk2_0),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) = one,
inference(rw,[status(thm)],[1582,380,theory(equality)]) ).
cnf(2472,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X1,X2)),
inference(rw,[status(thm)],[146,91,theory(equality)]) ).
cnf(2474,plain,
multiplication(antidomain(coantidomain(X1)),one) = multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[2472,95,theory(equality)]) ).
cnf(2511,plain,
antidomain(coantidomain(X1)) = multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[2474,40,theory(equality)]) ).
cnf(3032,plain,
addition(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = multiplication(addition(one,antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[176,2511,theory(equality)]) ).
cnf(3097,plain,
addition(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = multiplication(addition(one,antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[3032,68,theory(equality)]) ).
cnf(3098,plain,
addition(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3097,380,theory(equality)]),42,theory(equality)]) ).
cnf(3491,plain,
multiplication(coantidomain(X1),coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),antidomain(coantidomain(X1))),
inference(spm,[status(thm)],[165,3098,theory(equality)]) ).
cnf(3514,plain,
zero = multiplication(coantidomain(X1),antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[3491,36,theory(equality)]) ).
cnf(3554,plain,
multiplication(X1,zero) = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[836,3514,theory(equality)]) ).
cnf(3583,plain,
zero = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[3554,38,theory(equality)]) ).
cnf(3586,plain,
multiplication(zero,X2) = multiplication(X1,multiplication(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[64,3583,theory(equality)]) ).
cnf(3613,plain,
zero = multiplication(X1,multiplication(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[3586,56,theory(equality)]) ).
cnf(15125,negated_conjecture,
multiplication(one,esk2_0) = multiplication(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0)))),esk2_0),
inference(spm,[status(thm)],[658,1592,theory(equality)]) ).
cnf(15157,negated_conjecture,
esk2_0 = multiplication(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0)))),esk2_0),
inference(rw,[status(thm)],[15125,42,theory(equality)]) ).
cnf(15210,negated_conjecture,
multiplication(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0),esk2_0) = zero,
inference(spm,[status(thm)],[3613,15157,theory(equality)]) ).
cnf(15233,negated_conjecture,
multiplication(coantidomain(coantidomain(antidomain(esk3_0))),multiplication(esk1_0,esk2_0)) = zero,
inference(rw,[status(thm)],[15210,64,theory(equality)]) ).
cnf(15460,negated_conjecture,
multiplication(antidomain(esk3_0),zero) = multiplication(antidomain(esk3_0),multiplication(esk1_0,esk2_0)),
inference(spm,[status(thm)],[836,15233,theory(equality)]) ).
cnf(15506,negated_conjecture,
zero = multiplication(antidomain(esk3_0),multiplication(esk1_0,esk2_0)),
inference(rw,[status(thm)],[15460,38,theory(equality)]) ).
cnf(15541,negated_conjecture,
addition(antidomain(zero),antidomain(multiplication(antidomain(esk3_0),antidomain(antidomain(multiplication(esk1_0,esk2_0)))))) = antidomain(multiplication(antidomain(esk3_0),antidomain(antidomain(multiplication(esk1_0,esk2_0))))),
inference(spm,[status(thm)],[48,15506,theory(equality)]) ).
cnf(15578,negated_conjecture,
one = antidomain(multiplication(antidomain(esk3_0),antidomain(antidomain(multiplication(esk1_0,esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[15541,277,theory(equality)]),380,theory(equality)]) ).
cnf(15748,negated_conjecture,
multiplication(one,multiplication(antidomain(esk3_0),antidomain(antidomain(multiplication(esk1_0,esk2_0))))) = zero,
inference(spm,[status(thm)],[50,15578,theory(equality)]) ).
cnf(15792,negated_conjecture,
multiplication(antidomain(esk3_0),antidomain(antidomain(multiplication(esk1_0,esk2_0)))) = zero,
inference(rw,[status(thm)],[15748,42,theory(equality)]) ).
cnf(15847,negated_conjecture,
addition(zero,multiplication(antidomain(esk3_0),X1)) = multiplication(antidomain(esk3_0),addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),X1)),
inference(spm,[status(thm)],[72,15792,theory(equality)]) ).
cnf(15884,negated_conjecture,
multiplication(antidomain(esk3_0),X1) = multiplication(antidomain(esk3_0),addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),X1)),
inference(rw,[status(thm)],[15847,91,theory(equality)]) ).
cnf(18762,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(addition(X1,X2))),X1),
inference(spm,[status(thm)],[1476,96,theory(equality)]) ).
cnf(18875,plain,
X1 = multiplication(antidomain(antidomain(addition(X1,X2))),X1),
inference(rw,[status(thm)],[18762,42,theory(equality)]) ).
cnf(18951,plain,
multiplication(X1,X3) = multiplication(antidomain(antidomain(addition(X1,X2))),multiplication(X1,X3)),
inference(spm,[status(thm)],[64,18875,theory(equality)]) ).
cnf(172171,plain,
multiplication(antidomain(addition(X1,X2)),addition(X3,X2)) = multiplication(antidomain(addition(X1,X2)),X3),
inference(rw,[status(thm)],[1355,1474,theory(equality)]) ).
cnf(173523,negated_conjecture,
multiplication(antidomain(esk3_0),one) = multiplication(antidomain(esk3_0),antidomain(antidomain(antidomain(multiplication(esk1_0,esk2_0))))),
inference(spm,[status(thm)],[15884,96,theory(equality)]) ).
cnf(173663,negated_conjecture,
antidomain(esk3_0) = multiplication(antidomain(esk3_0),antidomain(antidomain(antidomain(multiplication(esk1_0,esk2_0))))),
inference(rw,[status(thm)],[173523,40,theory(equality)]) ).
cnf(173664,negated_conjecture,
antidomain(esk3_0) = multiplication(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0))),
inference(rw,[status(thm)],[173663,1359,theory(equality)]) ).
cnf(174058,plain,
antidomain(addition(antidomain(antidomain(X1)),X2)) = multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1347,172171,theory(equality)]),40,theory(equality)]) ).
cnf(174782,negated_conjecture,
addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(esk3_0)) = multiplication(addition(one,antidomain(esk3_0)),antidomain(multiplication(esk1_0,esk2_0))),
inference(spm,[status(thm)],[176,173664,theory(equality)]) ).
cnf(174872,negated_conjecture,
addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0))) = multiplication(addition(one,antidomain(esk3_0)),antidomain(multiplication(esk1_0,esk2_0))),
inference(rw,[status(thm)],[174782,68,theory(equality)]) ).
cnf(174873,negated_conjecture,
addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0))) = antidomain(multiplication(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[174872,380,theory(equality)]),42,theory(equality)]) ).
cnf(175200,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(multiplication(esk1_0,esk2_0)))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(spm,[status(thm)],[18875,174873,theory(equality)]) ).
cnf(175317,negated_conjecture,
multiplication(antidomain(multiplication(esk1_0,esk2_0)),antidomain(esk3_0)) = antidomain(esk3_0),
inference(rw,[status(thm)],[175200,1359,theory(equality)]) ).
cnf(175461,negated_conjecture,
multiplication(antidomain(antidomain(addition(antidomain(multiplication(esk1_0,esk2_0)),X1))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(spm,[status(thm)],[18951,175317,theory(equality)]) ).
cnf(176138,plain,
addition(antidomain(X1),antidomain(addition(antidomain(antidomain(X1)),X2))) = multiplication(addition(one,antidomain(addition(antidomain(antidomain(X1)),X2))),antidomain(X1)),
inference(spm,[status(thm)],[176,174058,theory(equality)]) ).
cnf(176308,plain,
addition(antidomain(X1),antidomain(addition(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[176138,380,theory(equality)]),42,theory(equality)]) ).
cnf(178620,plain,
addition(antidomain(antidomain(X1)),antidomain(addition(antidomain(X1),X2))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[176308,1359,theory(equality)]) ).
cnf(248050,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(spm,[status(thm)],[175461,48,theory(equality)]) ).
cnf(248233,negated_conjecture,
multiplication(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(rw,[status(thm)],[248050,1359,theory(equality)]) ).
cnf(248395,negated_conjecture,
addition(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))),antidomain(esk3_0)) = multiplication(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))),addition(one,antidomain(esk3_0))),
inference(spm,[status(thm)],[136,248233,theory(equality)]) ).
cnf(248505,negated_conjecture,
addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) = multiplication(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))),addition(one,antidomain(esk3_0))),
inference(rw,[status(thm)],[248395,68,theory(equality)]) ).
cnf(248506,negated_conjecture,
addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) = antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[248505,380,theory(equality)]),40,theory(equality)]) ).
cnf(259712,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(esk3_0)),
inference(spm,[status(thm)],[178620,248506,theory(equality)]) ).
cnf(260050,negated_conjecture,
$false,
inference(sr,[status(thm)],[259712,1417,theory(equality)]) ).
cnf(260051,negated_conjecture,
$false,
260050,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE106+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax, KLE001+6.ax]
% -running prover on /tmp/tmpXYQjPE/sel_KLE106+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE106+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE106+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE106+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
%
%------------------------------------------------------------------------------