TSTP Solution File: KLE088+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE088+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 12:13:53 EST 2010
% Result : Theorem 22.41s
% Output : CNFRefutation 22.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 18
% Syntax : Number of formulae : 301 ( 296 unt; 0 def)
% Number of atoms : 306 ( 304 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 404 ( 67 sgn 60 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',left_annihilation) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpX38QVk/sel_KLE088+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/tmpX38QVk/sel_KLE088+1.p_1',left_distributivity) ).
fof(5,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',additive_idempotence) ).
fof(7,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',multiplicative_associativity) ).
fof(8,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',codomain3) ).
fof(9,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',codomain2) ).
fof(10,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',codomain1) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',additive_associativity) ).
fof(12,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',multiplicative_right_identity) ).
fof(13,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmpX38QVk/sel_KLE088+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/tmpX38QVk/sel_KLE088+1.p_1',domain2) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',right_distributivity) ).
fof(16,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',domain1) ).
fof(17,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',multiplicative_left_identity) ).
fof(18,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',domain4) ).
fof(19,conjecture,
! [X4,X5] :
( multiplication(domain(X4),X5) = zero
=> addition(domain(X4),antidomain(X5)) = antidomain(X5) ),
file('/tmp/tmpX38QVk/sel_KLE088+1.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4,X5] :
( multiplication(domain(X4),X5) = zero
=> addition(domain(X4),antidomain(X5)) = antidomain(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(35,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[8]) ).
cnf(36,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X6,X7] : addition(coantidomain(multiplication(X6,X7)),coantidomain(multiplication(coantidomain(coantidomain(X6)),X7))) = coantidomain(multiplication(coantidomain(coantidomain(X6)),X7)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(38,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[10]) ).
cnf(40,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[39]) ).
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] :
( multiplication(domain(X4),X5) = zero
& addition(domain(X4),antidomain(X5)) != antidomain(X5) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(58,negated_conjecture,
? [X6,X7] :
( multiplication(domain(X6),X7) = zero
& addition(domain(X6),antidomain(X7)) != antidomain(X7) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,negated_conjecture,
( multiplication(domain(esk1_0),esk2_0) = zero
& addition(domain(esk1_0),antidomain(esk2_0)) != antidomain(esk2_0) ),
inference(skolemize,[status(esa)],[58]) ).
cnf(60,negated_conjecture,
addition(domain(esk1_0),antidomain(esk2_0)) != antidomain(esk2_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(61,negated_conjecture,
multiplication(domain(esk1_0),esk2_0) = zero,
inference(split_conjunct,[status(thm)],[59]) ).
cnf(62,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),esk2_0) = zero,
inference(rw,[status(thm)],[61,56,theory(equality)]),
[unfolding] ).
cnf(63,negated_conjecture,
addition(antidomain(antidomain(esk1_0)),antidomain(esk2_0)) != antidomain(esk2_0),
inference(rw,[status(thm)],[60,56,theory(equality)]),
[unfolding] ).
cnf(64,plain,
zero = coantidomain(one),
inference(spm,[status(thm)],[54,40,theory(equality)]) ).
cnf(65,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(72,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[46,30,theory(equality)]) ).
cnf(73,negated_conjecture,
addition(antidomain(esk2_0),antidomain(antidomain(esk1_0))) != antidomain(esk2_0),
inference(rw,[status(thm)],[63,30,theory(equality)]) ).
cnf(101,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[42,32,theory(equality)]) ).
cnf(102,plain,
addition(one,X2) = addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)),
inference(spm,[status(thm)],[42,72,theory(equality)]) ).
cnf(104,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[30,42,theory(equality)]) ).
cnf(106,plain,
addition(addition(X2,X1),X3) = addition(X1,addition(X2,X3)),
inference(spm,[status(thm)],[42,30,theory(equality)]) ).
cnf(111,plain,
addition(X2,addition(X1,X3)) = addition(X1,addition(X2,X3)),
inference(rw,[status(thm)],[106,42,theory(equality)]) ).
cnf(113,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[36,30,theory(equality)]) ).
cnf(120,negated_conjecture,
addition(zero,multiplication(antidomain(antidomain(esk1_0)),X1)) = multiplication(antidomain(antidomain(esk1_0)),addition(esk2_0,X1)),
inference(spm,[status(thm)],[50,62,theory(equality)]) ).
cnf(122,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[50,44,theory(equality)]) ).
cnf(127,plain,
addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(spm,[status(thm)],[50,40,theory(equality)]) ).
cnf(129,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[50,52,theory(equality)]) ).
cnf(148,plain,
multiplication(X1,X2) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[127,26,theory(equality)]) ).
cnf(149,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[129,26,theory(equality)]) ).
cnf(162,negated_conjecture,
addition(multiplication(X1,esk2_0),zero) = multiplication(addition(X1,antidomain(antidomain(esk1_0))),esk2_0),
inference(spm,[status(thm)],[28,62,theory(equality)]) ).
cnf(165,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[28,54,theory(equality)]) ).
cnf(167,plain,
addition(zero,multiplication(X2,coantidomain(X1))) = multiplication(addition(X1,X2),coantidomain(X1)),
inference(spm,[status(thm)],[28,40,theory(equality)]) ).
cnf(168,plain,
addition(multiplication(X1,coantidomain(X2)),zero) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(spm,[status(thm)],[28,40,theory(equality)]) ).
cnf(170,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[28,52,theory(equality)]) ).
cnf(184,negated_conjecture,
multiplication(X1,esk2_0) = multiplication(addition(X1,antidomain(antidomain(esk1_0))),esk2_0),
inference(rw,[status(thm)],[162,26,theory(equality)]) ).
cnf(190,plain,
multiplication(X1,coantidomain(X2)) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(rw,[status(thm)],[168,26,theory(equality)]) ).
cnf(191,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[170,26,theory(equality)]) ).
cnf(199,negated_conjecture,
addition(antidomain(zero),antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0))))) = antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0)))),
inference(spm,[status(thm)],[48,62,theory(equality)]) ).
cnf(203,plain,
addition(antidomain(zero),antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1)))))) = antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[48,40,theory(equality)]) ).
cnf(228,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)),
inference(spm,[status(thm)],[38,52,theory(equality)]) ).
cnf(239,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[72,65,theory(equality)]) ).
cnf(250,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[239,66,theory(equality)]) ).
cnf(259,plain,
addition(zero,coantidomain(zero)) = one,
inference(spm,[status(thm)],[113,64,theory(equality)]) ).
cnf(262,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[259,66,theory(equality)]) ).
cnf(370,plain,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[101,72,theory(equality)]) ).
cnf(374,plain,
addition(coantidomain(X1),one) = one,
inference(spm,[status(thm)],[101,113,theory(equality)]) ).
cnf(381,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[101,30,theory(equality)]) ).
cnf(385,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[370,30,theory(equality)]) ).
cnf(391,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[374,30,theory(equality)]) ).
cnf(412,negated_conjecture,
multiplication(one,esk2_0) = multiplication(antidomain(esk1_0),esk2_0),
inference(spm,[status(thm)],[184,72,theory(equality)]) ).
cnf(425,negated_conjecture,
esk2_0 = multiplication(antidomain(esk1_0),esk2_0),
inference(rw,[status(thm)],[412,54,theory(equality)]) ).
cnf(553,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)],[191,48,theory(equality)]) ).
cnf(560,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[191,30,theory(equality)]) ).
cnf(572,plain,
zero = multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))),
inference(rw,[status(thm)],[553,52,theory(equality)]) ).
cnf(685,plain,
multiplication(coantidomain(X1),one) = multiplication(coantidomain(X1),coantidomain(X1)),
inference(spm,[status(thm)],[148,113,theory(equality)]) ).
cnf(702,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[148,30,theory(equality)]) ).
cnf(709,plain,
coantidomain(X1) = multiplication(coantidomain(X1),coantidomain(X1)),
inference(rw,[status(thm)],[685,44,theory(equality)]) ).
cnf(731,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[560,72,theory(equality)]) ).
cnf(752,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[731,54,theory(equality)]) ).
cnf(769,plain,
addition(X1,multiplication(antidomain(antidomain(X1)),X2)) = multiplication(antidomain(antidomain(X1)),addition(X1,X2)),
inference(spm,[status(thm)],[50,752,theory(equality)]) ).
cnf(886,plain,
addition(multiplication(coantidomain(X1),X2),coantidomain(X1)) = multiplication(coantidomain(X1),addition(X2,coantidomain(X1))),
inference(spm,[status(thm)],[50,709,theory(equality)]) ).
cnf(897,plain,
addition(coantidomain(X1),multiplication(coantidomain(X1),X2)) = multiplication(coantidomain(X1),addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[886,30,theory(equality)]) ).
cnf(941,plain,
multiplication(antidomain(antidomain(antidomain(X1))),one) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(spm,[status(thm)],[149,72,theory(equality)]) ).
cnf(943,plain,
multiplication(antidomain(X1),addition(X2,addition(X3,X1))) = multiplication(antidomain(X1),addition(X2,X3)),
inference(spm,[status(thm)],[149,42,theory(equality)]) ).
cnf(951,plain,
addition(antidomain(multiplication(antidomain(X1),X2)),antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X2,X1)))))) = antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X2,X1))))),
inference(spm,[status(thm)],[48,149,theory(equality)]) ).
cnf(959,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,X2)) = multiplication(antidomain(addition(X1,X2)),X1),
inference(spm,[status(thm)],[149,101,theory(equality)]) ).
cnf(960,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,X2)) = multiplication(antidomain(addition(X1,X2)),X2),
inference(spm,[status(thm)],[149,381,theory(equality)]) ).
cnf(962,plain,
multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),addition(one,X2)) = multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)),
inference(spm,[status(thm)],[149,102,theory(equality)]) ).
cnf(963,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[149,30,theory(equality)]) ).
cnf(965,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(rw,[status(thm)],[941,44,theory(equality)]) ).
cnf(966,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[965,752,theory(equality)]) ).
cnf(982,plain,
zero = multiplication(antidomain(addition(X1,X2)),X1),
inference(rw,[status(thm)],[959,52,theory(equality)]) ).
cnf(983,plain,
zero = multiplication(antidomain(addition(X1,X2)),X2),
inference(rw,[status(thm)],[960,52,theory(equality)]) ).
cnf(984,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
inference(spm,[status(thm)],[52,966,theory(equality)]) ).
cnf(1023,plain,
addition(zero,multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),addition(antidomain(antidomain(X1)),X2)),
inference(spm,[status(thm)],[50,984,theory(equality)]) ).
cnf(1037,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[1023,66,theory(equality)]) ).
cnf(1054,plain,
zero = antidomain(addition(one,X1)),
inference(spm,[status(thm)],[44,982,theory(equality)]) ).
cnf(1056,plain,
multiplication(zero,X3) = multiplication(antidomain(addition(X1,X2)),multiplication(X1,X3)),
inference(spm,[status(thm)],[34,982,theory(equality)]) ).
cnf(1062,plain,
addition(zero,multiplication(X3,X1)) = multiplication(addition(antidomain(addition(X1,X2)),X3),X1),
inference(spm,[status(thm)],[28,982,theory(equality)]) ).
cnf(1064,plain,
multiplication(antidomain(multiplication(addition(X1,X3),X2)),multiplication(X1,X2)) = zero,
inference(spm,[status(thm)],[982,28,theory(equality)]) ).
cnf(1065,plain,
addition(antidomain(zero),antidomain(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1))))) = antidomain(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[48,982,theory(equality)]) ).
cnf(1083,plain,
zero = multiplication(antidomain(addition(X1,X2)),multiplication(X1,X3)),
inference(rw,[status(thm)],[1056,22,theory(equality)]) ).
cnf(1087,plain,
multiplication(X3,X1) = multiplication(addition(antidomain(addition(X1,X2)),X3),X1),
inference(rw,[status(thm)],[1062,66,theory(equality)]) ).
cnf(1089,plain,
one = antidomain(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1065,250,theory(equality)]),385,theory(equality)]) ).
cnf(1103,plain,
addition(antidomain(multiplication(X1,addition(one,X2))),antidomain(multiplication(X1,antidomain(zero)))) = antidomain(multiplication(X1,antidomain(zero))),
inference(spm,[status(thm)],[48,1054,theory(equality)]) ).
cnf(1125,plain,
addition(antidomain(X1),antidomain(multiplication(X1,addition(one,X2)))) = antidomain(multiplication(X1,antidomain(zero))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1103,250,theory(equality)]),44,theory(equality)]),30,theory(equality)]) ).
cnf(1126,plain,
addition(antidomain(X1),antidomain(multiplication(X1,addition(one,X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1125,250,theory(equality)]),44,theory(equality)]) ).
cnf(1233,plain,
addition(antidomain(X1),addition(X2,addition(X3,antidomain(antidomain(X1))))) = addition(one,addition(X2,X3)),
inference(spm,[status(thm)],[102,104,theory(equality)]) ).
cnf(1306,plain,
multiplication(zero,X3) = multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)),
inference(spm,[status(thm)],[34,983,theory(equality)]) ).
cnf(1310,plain,
addition(multiplication(antidomain(addition(X1,X2)),X3),zero) = multiplication(antidomain(addition(X1,X2)),addition(X3,X2)),
inference(spm,[status(thm)],[50,983,theory(equality)]) ).
cnf(1338,plain,
zero = multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)),
inference(rw,[status(thm)],[1306,22,theory(equality)]) ).
cnf(1341,plain,
multiplication(antidomain(addition(X1,X2)),X3) = multiplication(antidomain(addition(X1,X2)),addition(X3,X2)),
inference(rw,[status(thm)],[1310,26,theory(equality)]) ).
cnf(1523,plain,
addition(X1,one) = addition(one,addition(X1,antidomain(X2))),
inference(spm,[status(thm)],[111,385,theory(equality)]) ).
cnf(1830,plain,
multiplication(antidomain(coantidomain(X1)),one) = multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[963,113,theory(equality)]) ).
cnf(1834,plain,
addition(multiplication(antidomain(X1),X2),multiplication(X3,addition(X1,X2))) = multiplication(addition(antidomain(X1),X3),addition(X1,X2)),
inference(spm,[status(thm)],[28,963,theory(equality)]) ).
cnf(1837,plain,
addition(antidomain(multiplication(antidomain(X1),X2)),antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X1,X2)))))) = antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X1,X2))))),
inference(spm,[status(thm)],[48,963,theory(equality)]) ).
cnf(1866,plain,
antidomain(coantidomain(X1)) = multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[1830,44,theory(equality)]) ).
cnf(1985,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),X1) = multiplication(antidomain(antidomain(esk1_0)),addition(esk2_0,X1)),
inference(rw,[status(thm)],[120,66,theory(equality)]) ).
cnf(2119,negated_conjecture,
multiplication(antidomain(addition(antidomain(esk1_0),X1)),esk2_0) = zero,
inference(spm,[status(thm)],[1083,425,theory(equality)]) ).
cnf(2224,negated_conjecture,
multiplication(antidomain(addition(X1,antidomain(esk1_0))),esk2_0) = zero,
inference(spm,[status(thm)],[2119,381,theory(equality)]) ).
cnf(2259,negated_conjecture,
multiplication(zero,X2) = multiplication(antidomain(addition(X1,antidomain(esk1_0))),multiplication(esk2_0,X2)),
inference(spm,[status(thm)],[34,2224,theory(equality)]) ).
cnf(2277,negated_conjecture,
zero = multiplication(antidomain(addition(X1,antidomain(esk1_0))),multiplication(esk2_0,X2)),
inference(rw,[status(thm)],[2259,22,theory(equality)]) ).
cnf(2778,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[702,113,theory(equality)]) ).
cnf(2813,plain,
X1 = multiplication(X1,coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[2778,44,theory(equality)]) ).
cnf(2845,plain,
addition(multiplication(X1,addition(one,X2)),X3) = addition(X1,addition(multiplication(X1,X2),X3)),
inference(spm,[status(thm)],[42,122,theory(equality)]) ).
cnf(2857,plain,
addition(addition(X1,antidomain(X2)),multiplication(X1,X2)) = multiplication(addition(X1,antidomain(X2)),addition(one,X2)),
inference(spm,[status(thm)],[122,191,theory(equality)]) ).
cnf(2865,plain,
addition(antidomain(antidomain(X1)),X1) = multiplication(antidomain(antidomain(X1)),addition(one,X1)),
inference(spm,[status(thm)],[122,752,theory(equality)]) ).
cnf(2935,plain,
addition(X1,addition(antidomain(X2),multiplication(X1,X2))) = multiplication(addition(X1,antidomain(X2)),addition(one,X2)),
inference(rw,[status(thm)],[2857,42,theory(equality)]) ).
cnf(2945,plain,
addition(X1,antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(X1)),addition(one,X1)),
inference(rw,[status(thm)],[2865,30,theory(equality)]) ).
cnf(3441,plain,
addition(addition(X1,coantidomain(X2)),multiplication(X2,X1)) = multiplication(addition(one,X2),addition(X1,coantidomain(X2))),
inference(spm,[status(thm)],[165,148,theory(equality)]) ).
cnf(3448,plain,
addition(addition(X1,X2),multiplication(antidomain(X2),X1)) = multiplication(addition(one,antidomain(X2)),addition(X1,X2)),
inference(spm,[status(thm)],[165,149,theory(equality)]) ).
cnf(3538,plain,
addition(X1,addition(coantidomain(X2),multiplication(X2,X1))) = multiplication(addition(one,X2),addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[3441,42,theory(equality)]) ).
cnf(3547,plain,
addition(X1,addition(X2,multiplication(antidomain(X2),X1))) = multiplication(addition(one,antidomain(X2)),addition(X1,X2)),
inference(rw,[status(thm)],[3448,42,theory(equality)]) ).
cnf(3548,plain,
addition(X1,addition(X2,multiplication(antidomain(X2),X1))) = addition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3547,385,theory(equality)]),54,theory(equality)]) ).
cnf(4773,plain,
multiplication(X2,coantidomain(X1)) = multiplication(addition(X1,X2),coantidomain(X1)),
inference(rw,[status(thm)],[167,66,theory(equality)]) ).
cnf(4775,plain,
multiplication(one,coantidomain(antidomain(X1))) = multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))),
inference(spm,[status(thm)],[4773,72,theory(equality)]) ).
cnf(4826,plain,
coantidomain(antidomain(X1)) = multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[4775,54,theory(equality)]) ).
cnf(5204,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[190,113,theory(equality)]) ).
cnf(5253,plain,
coantidomain(coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[5204,54,theory(equality)]) ).
cnf(5254,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[5253,2813,theory(equality)]) ).
cnf(8047,negated_conjecture,
one = antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[199,250,theory(equality)]),385,theory(equality)]) ).
cnf(8048,negated_conjecture,
multiplication(one,multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0)))) = zero,
inference(spm,[status(thm)],[52,8047,theory(equality)]) ).
cnf(8071,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[8048,54,theory(equality)]) ).
cnf(8329,plain,
one = antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[203,250,theory(equality)]),385,theory(equality)]) ).
cnf(8332,plain,
multiplication(one,multiplication(X1,antidomain(antidomain(coantidomain(X1))))) = zero,
inference(spm,[status(thm)],[52,8329,theory(equality)]) ).
cnf(8366,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[8332,54,theory(equality)]) ).
cnf(8403,plain,
addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[50,8366,theory(equality)]) ).
cnf(8450,plain,
multiplication(X1,X2) = multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[8403,66,theory(equality)]) ).
cnf(11784,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(addition(X1,X2))),X1),
inference(spm,[status(thm)],[1087,72,theory(equality)]) ).
cnf(11881,plain,
X1 = multiplication(antidomain(antidomain(addition(X1,X2))),X1),
inference(rw,[status(thm)],[11784,54,theory(equality)]) ).
cnf(11988,plain,
multiplication(antidomain(antidomain(multiplication(X1,addition(one,X2)))),X1) = X1,
inference(spm,[status(thm)],[11881,122,theory(equality)]) ).
cnf(12025,plain,
multiplication(antidomain(antidomain(addition(X2,addition(X3,X1)))),X1) = X1,
inference(spm,[status(thm)],[11881,104,theory(equality)]) ).
cnf(13118,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[228,262,theory(equality)]),391,theory(equality)]) ).
cnf(13121,plain,
multiplication(multiplication(coantidomain(coantidomain(antidomain(X1))),X1),one) = zero,
inference(spm,[status(thm)],[40,13118,theory(equality)]) ).
cnf(13157,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[13121,34,theory(equality)]),44,theory(equality)]) ).
cnf(20498,plain,
multiplication(one,multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1)))) = zero,
inference(spm,[status(thm)],[52,1089,theory(equality)]) ).
cnf(20599,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[20498,54,theory(equality)]) ).
cnf(20828,plain,
multiplication(antidomain(addition(X2,X1)),antidomain(antidomain(X1))) = zero,
inference(spm,[status(thm)],[20599,381,theory(equality)]) ).
cnf(20999,plain,
multiplication(zero,X3) = multiplication(antidomain(addition(X1,X2)),multiplication(antidomain(antidomain(X2)),X3)),
inference(spm,[status(thm)],[34,20828,theory(equality)]) ).
cnf(21100,plain,
zero = multiplication(antidomain(addition(X1,X2)),multiplication(antidomain(antidomain(X2)),X3)),
inference(rw,[status(thm)],[20999,22,theory(equality)]) ).
cnf(31313,plain,
multiplication(antidomain(zero),multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(multiplication(X2,X3))))) = zero,
inference(spm,[status(thm)],[572,1338,theory(equality)]) ).
cnf(31344,negated_conjecture,
multiplication(antidomain(zero),multiplication(antidomain(addition(X1,antidomain(esk1_0))),antidomain(antidomain(multiplication(esk2_0,X2))))) = zero,
inference(spm,[status(thm)],[572,2277,theory(equality)]) ).
cnf(31583,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(multiplication(X2,X3)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[31313,250,theory(equality)]),54,theory(equality)]) ).
cnf(31606,negated_conjecture,
multiplication(antidomain(addition(X1,antidomain(esk1_0))),antidomain(antidomain(multiplication(esk2_0,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[31344,250,theory(equality)]),54,theory(equality)]) ).
cnf(35551,plain,
multiplication(antidomain(multiplication(one,X2)),multiplication(coantidomain(X1),X2)) = zero,
inference(spm,[status(thm)],[1064,113,theory(equality)]) ).
cnf(35884,plain,
multiplication(antidomain(X2),multiplication(coantidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[35551,54,theory(equality)]) ).
cnf(55686,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = multiplication(antidomain(antidomain(X1)),addition(one,coantidomain(antidomain(X1)))),
inference(spm,[status(thm)],[122,4826,theory(equality)]) ).
cnf(55768,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[55686,391,theory(equality)]),44,theory(equality)]) ).
cnf(104124,negated_conjecture,
addition(esk1_0,zero) = multiplication(antidomain(antidomain(esk1_0)),addition(esk1_0,antidomain(antidomain(esk2_0)))),
inference(spm,[status(thm)],[769,8071,theory(equality)]) ).
cnf(104478,negated_conjecture,
esk1_0 = multiplication(antidomain(antidomain(esk1_0)),addition(esk1_0,antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[104124,26,theory(equality)]) ).
cnf(108655,plain,
multiplication(coantidomain(X1),addition(one,X2)) = multiplication(coantidomain(X1),addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[897,122,theory(equality)]) ).
cnf(108753,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = multiplication(coantidomain(antidomain(X1)),addition(one,antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[108655,55768,theory(equality)]) ).
cnf(108882,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[108753,385,theory(equality)]),44,theory(equality)]) ).
cnf(134769,negated_conjecture,
multiplication(antidomain(addition(antidomain(antidomain(antidomain(multiplication(esk2_0,X1)))),antidomain(esk1_0))),addition(one,antidomain(esk1_0))) = zero,
inference(spm,[status(thm)],[31606,962,theory(equality)]) ).
cnf(135031,negated_conjecture,
antidomain(addition(antidomain(esk1_0),antidomain(multiplication(esk2_0,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[134769,966,theory(equality)]),30,theory(equality)]),385,theory(equality)]),44,theory(equality)]) ).
cnf(135063,negated_conjecture,
antidomain(addition(antidomain(esk1_0),antidomain(esk2_0))) = zero,
inference(spm,[status(thm)],[135031,44,theory(equality)]) ).
cnf(135283,negated_conjecture,
antidomain(addition(antidomain(esk2_0),antidomain(esk1_0))) = zero,
inference(rw,[status(thm)],[135063,30,theory(equality)]) ).
cnf(135704,negated_conjecture,
addition(antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0))),antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(zero)))) = antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(zero))),
inference(spm,[status(thm)],[951,135283,theory(equality)]) ).
cnf(135909,negated_conjecture,
addition(antidomain(esk1_0),antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)))) = antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(zero))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[135704,250,theory(equality)]),44,theory(equality)]),966,theory(equality)]),30,theory(equality)]) ).
cnf(135910,negated_conjecture,
addition(antidomain(esk1_0),antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)))) = antidomain(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[135909,250,theory(equality)]),44,theory(equality)]),966,theory(equality)]) ).
cnf(174543,plain,
antidomain(addition(antidomain(antidomain(X1)),X2)) = multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[962,1341,theory(equality)]),44,theory(equality)]) ).
cnf(176246,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)],[165,174543,theory(equality)]) ).
cnf(176344,plain,
antidomain(addition(antidomain(antidomain(antidomain(multiplication(X1,X2)))),X1)) = zero,
inference(spm,[status(thm)],[31583,174543,theory(equality)]) ).
cnf(176473,plain,
addition(antidomain(X1),antidomain(addition(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[176246,385,theory(equality)]),54,theory(equality)]) ).
cnf(176555,plain,
antidomain(addition(X1,antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[176344,966,theory(equality)]),30,theory(equality)]) ).
cnf(203283,plain,
addition(antidomain(X1),antidomain(addition(X2,antidomain(antidomain(X1))))) = antidomain(X1),
inference(spm,[status(thm)],[176473,381,theory(equality)]) ).
cnf(234216,plain,
addition(multiplication(antidomain(X1),X2),addition(X1,X2)) = multiplication(addition(antidomain(X1),one),addition(X1,X2)),
inference(spm,[status(thm)],[1834,54,theory(equality)]) ).
cnf(234680,negated_conjecture,
addition(multiplication(antidomain(esk1_0),antidomain(antidomain(esk2_0))),esk1_0) = multiplication(addition(antidomain(esk1_0),antidomain(antidomain(esk1_0))),addition(esk1_0,antidomain(antidomain(esk2_0)))),
inference(spm,[status(thm)],[1834,104478,theory(equality)]) ).
cnf(234949,plain,
addition(X2,X1) = multiplication(addition(antidomain(X1),one),addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[234216,104,theory(equality)]),30,theory(equality)]),3548,theory(equality)]) ).
cnf(234950,plain,
addition(X2,X1) = addition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[234949,30,theory(equality)]),385,theory(equality)]),54,theory(equality)]) ).
cnf(235533,negated_conjecture,
addition(esk1_0,multiplication(antidomain(esk1_0),antidomain(antidomain(esk2_0)))) = multiplication(addition(antidomain(esk1_0),antidomain(antidomain(esk1_0))),addition(esk1_0,antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[234680,30,theory(equality)]) ).
cnf(235534,negated_conjecture,
addition(esk1_0,multiplication(antidomain(esk1_0),antidomain(antidomain(esk2_0)))) = addition(esk1_0,antidomain(antidomain(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[235533,72,theory(equality)]),54,theory(equality)]) ).
cnf(240113,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(antidomain(multiplication(X1,addition(one,X2)))),antidomain(antidomain(addition(antidomain(multiplication(X1,addition(one,X2))),X1)))))) = antidomain(multiplication(antidomain(antidomain(multiplication(X1,addition(one,X2)))),antidomain(antidomain(addition(antidomain(multiplication(X1,addition(one,X2))),X1))))),
inference(spm,[status(thm)],[1837,11988,theory(equality)]) ).
cnf(240909,plain,
antidomain(X1) = antidomain(multiplication(antidomain(antidomain(multiplication(X1,addition(one,X2)))),antidomain(antidomain(addition(antidomain(multiplication(X1,addition(one,X2))),X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[240113,30,theory(equality)]),176555,theory(equality)]),250,theory(equality)]),44,theory(equality)]),966,theory(equality)]),1126,theory(equality)]) ).
cnf(240910,plain,
antidomain(X1) = antidomain(multiplication(X1,addition(one,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[240909,30,theory(equality)]),176555,theory(equality)]),250,theory(equality)]),44,theory(equality)]),966,theory(equality)]) ).
cnf(281105,plain,
multiplication(X1,one) = multiplication(X1,antidomain(antidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[8450,72,theory(equality)]) ).
cnf(281427,plain,
X1 = multiplication(X1,antidomain(antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[281105,44,theory(equality)]) ).
cnf(281428,plain,
X1 = multiplication(X1,antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[281427,966,theory(equality)]) ).
cnf(281828,plain,
multiplication(antidomain(antidomain(coantidomain(coantidomain(X1)))),coantidomain(X1)) = zero,
inference(spm,[status(thm)],[35884,281428,theory(equality)]) ).
cnf(286444,plain,
addition(coantidomain(coantidomain(X1)),zero) = multiplication(antidomain(antidomain(coantidomain(coantidomain(X1)))),addition(coantidomain(coantidomain(X1)),coantidomain(X1))),
inference(spm,[status(thm)],[769,281828,theory(equality)]) ).
cnf(286590,plain,
coantidomain(coantidomain(X1)) = multiplication(antidomain(antidomain(coantidomain(coantidomain(X1)))),addition(coantidomain(coantidomain(X1)),coantidomain(X1))),
inference(rw,[status(thm)],[286444,26,theory(equality)]) ).
cnf(286591,plain,
coantidomain(coantidomain(X1)) = antidomain(antidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[286590,30,theory(equality)]),113,theory(equality)]),44,theory(equality)]) ).
cnf(289395,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(spm,[status(thm)],[286591,5254,theory(equality)]) ).
cnf(291686,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[4826,289395,theory(equality)]) ).
cnf(291946,plain,
antidomain(coantidomain(X1)) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[291686,1866,theory(equality)]) ).
cnf(292195,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[13157,291946,theory(equality)]) ).
cnf(292444,plain,
addition(zero,multiplication(X2,X1)) = multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1),
inference(spm,[status(thm)],[28,292195,theory(equality)]) ).
cnf(292694,plain,
multiplication(X2,X1) = multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1),
inference(rw,[status(thm)],[292444,66,theory(equality)]) ).
cnf(437949,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(coantidomain(antidomain(X1)))),X1),
inference(spm,[status(thm)],[292694,72,theory(equality)]) ).
cnf(438334,plain,
X1 = multiplication(antidomain(antidomain(coantidomain(antidomain(X1)))),X1),
inference(rw,[status(thm)],[437949,54,theory(equality)]) ).
cnf(438335,plain,
X1 = multiplication(coantidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[438334,289395,theory(equality)]) ).
cnf(438694,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[438335,966,theory(equality)]) ).
cnf(438999,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[438694,108882,theory(equality)]) ).
cnf(444568,plain,
antidomain(addition(X1,antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(spm,[status(thm)],[240910,2945,theory(equality)]) ).
cnf(444960,plain,
antidomain(addition(X1,antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[444568,966,theory(equality)]) ).
cnf(462390,plain,
addition(multiplication(X1,one),X3) = addition(X1,addition(multiplication(X1,antidomain(X2)),X3)),
inference(spm,[status(thm)],[2845,385,theory(equality)]) ).
cnf(463767,plain,
antidomain(addition(X1,addition(multiplication(X1,X2),antidomain(antidomain(multiplication(X1,addition(one,X2))))))) = antidomain(multiplication(X1,addition(one,X2))),
inference(spm,[status(thm)],[444960,2845,theory(equality)]) ).
cnf(463887,plain,
addition(X1,X3) = addition(X1,addition(multiplication(X1,antidomain(X2)),X3)),
inference(rw,[status(thm)],[462390,44,theory(equality)]) ).
cnf(464949,plain,
antidomain(addition(X1,addition(multiplication(X1,X2),antidomain(antidomain(X1))))) = antidomain(multiplication(X1,addition(one,X2))),
inference(rw,[status(thm)],[463767,240910,theory(equality)]) ).
cnf(464950,plain,
antidomain(addition(X1,addition(multiplication(X1,X2),antidomain(antidomain(X1))))) = antidomain(X1),
inference(rw,[status(thm)],[464949,240910,theory(equality)]) ).
cnf(465736,plain,
addition(X1,addition(X3,multiplication(X1,antidomain(X2)))) = addition(X1,X3),
inference(spm,[status(thm)],[463887,234950,theory(equality)]) ).
cnf(474083,negated_conjecture,
addition(antidomain(esk1_0),addition(esk1_0,antidomain(antidomain(esk2_0)))) = addition(antidomain(esk1_0),esk1_0),
inference(spm,[status(thm)],[465736,235534,theory(equality)]) ).
cnf(474805,negated_conjecture,
addition(esk1_0,addition(antidomain(esk1_0),antidomain(antidomain(esk2_0)))) = addition(antidomain(esk1_0),esk1_0),
inference(rw,[status(thm)],[474083,111,theory(equality)]) ).
cnf(474806,negated_conjecture,
addition(esk1_0,addition(antidomain(esk1_0),antidomain(antidomain(esk2_0)))) = addition(esk1_0,antidomain(esk1_0)),
inference(rw,[status(thm)],[474805,30,theory(equality)]) ).
cnf(477915,negated_conjecture,
addition(antidomain(esk2_0),addition(esk1_0,antidomain(esk1_0))) = addition(one,addition(esk1_0,antidomain(esk1_0))),
inference(spm,[status(thm)],[1233,474806,theory(equality)]) ).
cnf(478102,negated_conjecture,
addition(esk1_0,addition(antidomain(esk2_0),antidomain(esk1_0))) = addition(one,addition(esk1_0,antidomain(esk1_0))),
inference(rw,[status(thm)],[477915,111,theory(equality)]) ).
cnf(478103,negated_conjecture,
addition(esk1_0,addition(antidomain(esk2_0),antidomain(esk1_0))) = addition(one,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[478102,1523,theory(equality)]),30,theory(equality)]) ).
cnf(478285,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),addition(one,esk1_0)) = multiplication(antidomain(antidomain(esk1_0)),addition(esk1_0,antidomain(esk2_0))),
inference(spm,[status(thm)],[943,478103,theory(equality)]) ).
cnf(478484,negated_conjecture,
addition(esk1_0,antidomain(antidomain(esk1_0))) = multiplication(antidomain(antidomain(esk1_0)),addition(esk1_0,antidomain(esk2_0))),
inference(rw,[status(thm)],[478285,2945,theory(equality)]) ).
cnf(480486,negated_conjecture,
addition(addition(esk1_0,antidomain(esk2_0)),addition(esk1_0,antidomain(antidomain(esk1_0)))) = multiplication(addition(one,antidomain(antidomain(esk1_0))),addition(esk1_0,antidomain(esk2_0))),
inference(spm,[status(thm)],[165,478484,theory(equality)]) ).
cnf(480641,negated_conjecture,
addition(esk1_0,addition(antidomain(esk2_0),antidomain(antidomain(esk1_0)))) = multiplication(addition(one,antidomain(antidomain(esk1_0))),addition(esk1_0,antidomain(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[480486,42,theory(equality)]),111,theory(equality)]),101,theory(equality)]) ).
cnf(480642,negated_conjecture,
addition(esk1_0,addition(antidomain(esk2_0),antidomain(antidomain(esk1_0)))) = addition(esk1_0,antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[480641,385,theory(equality)]),54,theory(equality)]) ).
cnf(480806,negated_conjecture,
multiplication(antidomain(antidomain(addition(esk1_0,antidomain(esk2_0)))),antidomain(antidomain(esk1_0))) = antidomain(antidomain(esk1_0)),
inference(spm,[status(thm)],[12025,480642,theory(equality)]) ).
cnf(481258,negated_conjecture,
addition(antidomain(antidomain(addition(esk1_0,antidomain(esk2_0)))),addition(antidomain(antidomain(antidomain(esk1_0))),antidomain(antidomain(esk1_0)))) = multiplication(addition(antidomain(antidomain(addition(esk1_0,antidomain(esk2_0)))),antidomain(antidomain(antidomain(esk1_0)))),addition(one,antidomain(antidomain(esk1_0)))),
inference(spm,[status(thm)],[2935,480806,theory(equality)]) ).
cnf(481401,negated_conjecture,
one = multiplication(addition(antidomain(antidomain(addition(esk1_0,antidomain(esk2_0)))),antidomain(antidomain(antidomain(esk1_0)))),addition(one,antidomain(antidomain(esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[481258,966,theory(equality)]),72,theory(equality)]),234950,theory(equality)]),385,theory(equality)]) ).
cnf(481402,negated_conjecture,
one = addition(antidomain(esk1_0),antidomain(antidomain(addition(esk1_0,antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[481401,966,theory(equality)]),234950,theory(equality)]),385,theory(equality)]),44,theory(equality)]) ).
cnf(481895,negated_conjecture,
multiplication(one,antidomain(addition(esk1_0,antidomain(esk2_0)))) = multiplication(antidomain(esk1_0),antidomain(addition(esk1_0,antidomain(esk2_0)))),
inference(spm,[status(thm)],[191,481402,theory(equality)]) ).
cnf(482127,negated_conjecture,
antidomain(addition(esk1_0,antidomain(esk2_0))) = multiplication(antidomain(esk1_0),antidomain(addition(esk1_0,antidomain(esk2_0)))),
inference(rw,[status(thm)],[481895,54,theory(equality)]) ).
cnf(482413,negated_conjecture,
addition(antidomain(esk1_0),antidomain(addition(esk1_0,antidomain(esk2_0)))) = multiplication(antidomain(esk1_0),addition(one,antidomain(addition(esk1_0,antidomain(esk2_0))))),
inference(spm,[status(thm)],[122,482127,theory(equality)]) ).
cnf(482546,negated_conjecture,
addition(antidomain(esk1_0),antidomain(addition(esk1_0,antidomain(esk2_0)))) = antidomain(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[482413,385,theory(equality)]),44,theory(equality)]) ).
cnf(557219,plain,
addition(antidomain(X1),addition(coantidomain(antidomain(addition(antidomain(antidomain(X1)),X2))),antidomain(addition(antidomain(antidomain(X1)),X2)))) = multiplication(addition(one,antidomain(addition(antidomain(antidomain(X1)),X2))),addition(antidomain(X1),coantidomain(antidomain(addition(antidomain(antidomain(X1)),X2))))),
inference(spm,[status(thm)],[3538,174543,theory(equality)]) ).
cnf(558330,plain,
one = multiplication(addition(one,antidomain(addition(antidomain(antidomain(X1)),X2))),addition(antidomain(X1),coantidomain(antidomain(addition(antidomain(antidomain(X1)),X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[557219,438999,theory(equality)]),30,theory(equality)]),72,theory(equality)]),30,theory(equality)]),385,theory(equality)]) ).
cnf(558331,plain,
one = addition(antidomain(X1),antidomain(antidomain(addition(antidomain(antidomain(X1)),X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[558330,385,theory(equality)]),438999,theory(equality)]),54,theory(equality)]) ).
cnf(655723,plain,
multiplication(antidomain(X1),one) = multiplication(antidomain(X1),antidomain(antidomain(addition(antidomain(antidomain(antidomain(X1))),X2)))),
inference(spm,[status(thm)],[1037,558331,theory(equality)]) ).
cnf(656314,plain,
antidomain(X1) = multiplication(antidomain(X1),antidomain(antidomain(addition(antidomain(antidomain(antidomain(X1))),X2)))),
inference(rw,[status(thm)],[655723,44,theory(equality)]) ).
cnf(656315,plain,
antidomain(X1) = multiplication(antidomain(X1),antidomain(antidomain(addition(antidomain(X1),X2)))),
inference(rw,[status(thm)],[656314,966,theory(equality)]) ).
cnf(657684,plain,
multiplication(antidomain(X1),antidomain(antidomain(addition(X2,antidomain(X1))))) = antidomain(X1),
inference(spm,[status(thm)],[656315,381,theory(equality)]) ).
cnf(659109,plain,
addition(antidomain(antidomain(addition(X1,antidomain(X2)))),addition(coantidomain(antidomain(X2)),antidomain(X2))) = multiplication(addition(one,antidomain(X2)),addition(antidomain(antidomain(addition(X1,antidomain(X2)))),coantidomain(antidomain(X2)))),
inference(spm,[status(thm)],[3538,657684,theory(equality)]) ).
cnf(659553,plain,
one = multiplication(addition(one,antidomain(X2)),addition(antidomain(antidomain(addition(X1,antidomain(X2)))),coantidomain(antidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[659109,234950,theory(equality)]),438999,theory(equality)]),72,theory(equality)]),234950,theory(equality)]),385,theory(equality)]) ).
cnf(659554,plain,
one = addition(antidomain(antidomain(X2)),antidomain(antidomain(addition(X1,antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[659553,385,theory(equality)]),438999,theory(equality)]),234950,theory(equality)]),54,theory(equality)]) ).
cnf(670625,negated_conjecture,
addition(antidomain(antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)))),antidomain(antidomain(antidomain(esk1_0)))) = one,
inference(spm,[status(thm)],[659554,135910,theory(equality)]) ).
cnf(671139,negated_conjecture,
addition(antidomain(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[670625,966,theory(equality)]),30,theory(equality)]) ).
cnf(671509,negated_conjecture,
multiplication(one,esk1_0) = multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)))),esk1_0),
inference(spm,[status(thm)],[560,671139,theory(equality)]) ).
cnf(671772,negated_conjecture,
esk1_0 = multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)))),esk1_0),
inference(rw,[status(thm)],[671509,54,theory(equality)]) ).
cnf(672140,negated_conjecture,
multiplication(antidomain(addition(X1,multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)))),esk1_0) = zero,
inference(spm,[status(thm)],[21100,671772,theory(equality)]) ).
cnf(678418,negated_conjecture,
multiplication(antidomain(multiplication(addition(one,antidomain(antidomain(esk1_0))),antidomain(esk2_0))),esk1_0) = zero,
inference(spm,[status(thm)],[672140,165,theory(equality)]) ).
cnf(678610,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),esk1_0) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[678418,385,theory(equality)]),54,theory(equality)]) ).
cnf(678879,negated_conjecture,
addition(esk2_0,zero) = multiplication(antidomain(antidomain(esk2_0)),addition(esk2_0,esk1_0)),
inference(spm,[status(thm)],[769,678610,theory(equality)]) ).
cnf(679078,negated_conjecture,
esk2_0 = multiplication(antidomain(antidomain(esk2_0)),addition(esk2_0,esk1_0)),
inference(rw,[status(thm)],[678879,26,theory(equality)]) ).
cnf(682673,negated_conjecture,
addition(multiplication(antidomain(esk2_0),esk1_0),esk2_0) = multiplication(addition(antidomain(esk2_0),antidomain(antidomain(esk2_0))),addition(esk2_0,esk1_0)),
inference(spm,[status(thm)],[1834,679078,theory(equality)]) ).
cnf(682888,negated_conjecture,
addition(esk2_0,multiplication(antidomain(esk2_0),esk1_0)) = multiplication(addition(antidomain(esk2_0),antidomain(antidomain(esk2_0))),addition(esk2_0,esk1_0)),
inference(rw,[status(thm)],[682673,234950,theory(equality)]) ).
cnf(682889,negated_conjecture,
addition(esk2_0,multiplication(antidomain(esk2_0),esk1_0)) = addition(esk2_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[682888,72,theory(equality)]),54,theory(equality)]) ).
cnf(683003,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),addition(esk2_0,esk1_0)) = multiplication(antidomain(antidomain(esk1_0)),multiplication(antidomain(esk2_0),esk1_0)),
inference(spm,[status(thm)],[1985,682889,theory(equality)]) ).
cnf(683215,negated_conjecture,
esk1_0 = multiplication(antidomain(antidomain(esk1_0)),multiplication(antidomain(esk2_0),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[683003,1985,theory(equality)]),752,theory(equality)]) ).
cnf(683954,negated_conjecture,
addition(multiplication(antidomain(esk2_0),esk1_0),esk1_0) = multiplication(addition(one,antidomain(antidomain(esk1_0))),multiplication(antidomain(esk2_0),esk1_0)),
inference(spm,[status(thm)],[165,683215,theory(equality)]) ).
cnf(684151,negated_conjecture,
esk1_0 = multiplication(addition(one,antidomain(antidomain(esk1_0))),multiplication(antidomain(esk2_0),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[683954,30,theory(equality)]),165,theory(equality)]),385,theory(equality)]),54,theory(equality)]) ).
cnf(684152,negated_conjecture,
esk1_0 = multiplication(antidomain(esk2_0),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[684151,385,theory(equality)]),54,theory(equality)]) ).
cnf(684442,negated_conjecture,
antidomain(addition(antidomain(esk2_0),addition(esk1_0,antidomain(antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(esk2_0)),
inference(spm,[status(thm)],[464950,684152,theory(equality)]) ).
cnf(684565,negated_conjecture,
antidomain(addition(esk1_0,antidomain(esk2_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[684442,966,theory(equality)]),381,theory(equality)]) ).
cnf(684918,negated_conjecture,
addition(antidomain(esk1_0),antidomain(antidomain(esk2_0))) = antidomain(esk1_0),
inference(rw,[status(thm)],[482546,684565,theory(equality)]) ).
cnf(685930,negated_conjecture,
addition(antidomain(esk2_0),antidomain(antidomain(esk1_0))) = antidomain(esk2_0),
inference(spm,[status(thm)],[203283,684918,theory(equality)]) ).
cnf(686181,negated_conjecture,
$false,
inference(sr,[status(thm)],[685930,73,theory(equality)]) ).
cnf(686182,negated_conjecture,
$false,
686181,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE088+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax]
% -running prover on /tmp/tmpX38QVk/sel_KLE088+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE088+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE088+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE088+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
%
%------------------------------------------------------------------------------