TSTP Solution File: KLE105+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE105+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 12:19:51 EST 2010
% Result : Theorem 0s
% Output : CNFRefutation 0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 24
% Syntax : Number of formulae : 266 ( 261 unt; 0 def)
% Number of atoms : 271 ( 269 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 16 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 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 : 334 ( 26 sgn 80 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',left_distributivity) ).
fof(2,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',codomain4) ).
fof(3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',codomain3) ).
fof(4,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',codomain2) ).
fof(5,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',codomain1) ).
fof(6,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',right_annihilation) ).
fof(7,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',multiplicative_right_identity) ).
fof(8,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',multiplicative_left_identity) ).
fof(9,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',backward_diamond) ).
fof(10,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',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/tmpC1NAlF/sel_KLE105+1.p_2',domain2) ).
fof(12,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',domain1) ).
fof(13,axiom,
! [X4] : c(X4) = antidomain(domain(X4)),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',complement) ).
fof(14,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',domain4) ).
fof(15,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',left_annihilation) ).
fof(16,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',additive_identity) ).
fof(17,axiom,
! [X4,X5] : backward_box(X4,X5) = c(backward_diamond(X4,c(X5))),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',backward_box) ).
fof(18,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',additive_idempotence) ).
fof(19,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',multiplicative_associativity) ).
fof(20,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',forward_diamond) ).
fof(21,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',additive_commutativity) ).
fof(22,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',additive_associativity) ).
fof(23,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpC1NAlF/sel_KLE105+1.p_2',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/tmpC1NAlF/sel_KLE105+1.p_2',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,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(27,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X5] : codomain(X5) = coantidomain(coantidomain(X5)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(29,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[3]) ).
cnf(31,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,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)],[4]) ).
cnf(33,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[5]) ).
cnf(35,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[6]) ).
cnf(37,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(39,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[8]) ).
cnf(41,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X6,X7] : backward_diamond(X6,X7) = codomain(multiplication(codomain(X7),X6)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(43,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[10]) ).
cnf(45,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,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(47,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[12]) ).
cnf(49,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,plain,
! [X5] : c(X5) = antidomain(domain(X5)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(51,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(53,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[15]) ).
cnf(55,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[54]) ).
fof(56,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[16]) ).
cnf(57,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[56]) ).
fof(58,plain,
! [X6,X7] : backward_box(X6,X7) = c(backward_diamond(X6,c(X7))),
inference(variable_rename,[status(thm)],[17]) ).
cnf(59,plain,
backward_box(X1,X2) = c(backward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[58]) ).
fof(60,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[18]) ).
cnf(61,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[60]) ).
fof(62,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[19]) ).
cnf(63,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[62]) ).
fof(64,plain,
! [X6,X7] : forward_diamond(X6,X7) = domain(multiplication(X6,domain(X7))),
inference(variable_rename,[status(thm)],[20]) ).
cnf(65,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[64]) ).
fof(66,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[21]) ).
cnf(67,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[66]) ).
fof(68,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[22]) ).
cnf(69,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[68]) ).
fof(70,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[23]) ).
cnf(71,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[70]) ).
fof(72,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(fof_nnf,[status(thm)],[25]) ).
fof(73,negated_conjecture,
? [X7,X8,X9] :
( addition(forward_diamond(X7,domain(X8)),domain(X9)) = domain(X9)
& addition(domain(X8),backward_box(X7,domain(X9))) != backward_box(X7,domain(X9)) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,negated_conjecture,
( addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0)
& addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) != backward_box(esk1_0,domain(esk3_0)) ),
inference(skolemize,[status(esa)],[73]) ).
cnf(75,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)],[74]) ).
cnf(76,negated_conjecture,
addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0),
inference(split_conjunct,[status(thm)],[74]) ).
cnf(77,plain,
coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[43,29,theory(equality)]),29,theory(equality)]),
[unfolding] ).
cnf(78,plain,
antidomain(antidomain(antidomain(X1))) = c(X1),
inference(rw,[status(thm)],[51,53,theory(equality)]),
[unfolding] ).
cnf(79,plain,
antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))) = forward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[65,53,theory(equality)]),53,theory(equality)]),
[unfolding] ).
cnf(80,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)],[76,53,theory(equality)]),53,theory(equality)]),53,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)],[75,53,theory(equality)]),53,theory(equality)]),53,theory(equality)]),
[unfolding] ).
cnf(82,plain,
antidomain(antidomain(antidomain(backward_diamond(X1,antidomain(antidomain(antidomain(X2))))))) = backward_box(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[59,78,theory(equality)]),78,theory(equality)]),
[unfolding] ).
cnf(83,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)],[81,82,theory(equality)]),82,theory(equality)]),
[unfolding] ).
cnf(84,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)],[80,79,theory(equality)]),
[unfolding] ).
cnf(85,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)],[83,77,theory(equality)]),77,theory(equality)]),
[unfolding] ).
cnf(86,plain,
zero = coantidomain(one),
inference(spm,[status(thm)],[41,35,theory(equality)]) ).
cnf(87,plain,
zero = antidomain(one),
inference(spm,[status(thm)],[39,49,theory(equality)]) ).
cnf(90,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[57,67,theory(equality)]) ).
cnf(94,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[31,67,theory(equality)]) ).
cnf(95,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[45,67,theory(equality)]) ).
cnf(97,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[69,61,theory(equality)]) ).
cnf(100,plain,
addition(one,X2) = addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)),
inference(spm,[status(thm)],[69,94,theory(equality)]) ).
cnf(101,plain,
addition(one,X2) = addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)),
inference(spm,[status(thm)],[69,95,theory(equality)]) ).
cnf(119,plain,
multiplication(zero,X2) = multiplication(X1,multiplication(coantidomain(X1),X2)),
inference(spm,[status(thm)],[63,35,theory(equality)]) ).
cnf(130,plain,
zero = multiplication(X1,multiplication(coantidomain(X1),X2)),
inference(rw,[status(thm)],[119,55,theory(equality)]) ).
cnf(134,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)],[84,67,theory(equality)]) ).
cnf(137,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[71,39,theory(equality)]) ).
cnf(146,plain,
addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(spm,[status(thm)],[71,35,theory(equality)]) ).
cnf(147,plain,
addition(zero,multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),addition(X1,X2)),
inference(spm,[status(thm)],[71,49,theory(equality)]) ).
cnf(148,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[71,49,theory(equality)]) ).
cnf(166,plain,
multiplication(X1,X2) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[146,57,theory(equality)]) ).
cnf(167,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[148,57,theory(equality)]) ).
cnf(177,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[27,41,theory(equality)]) ).
cnf(184,plain,
addition(multiplication(X1,coantidomain(X2)),zero) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(spm,[status(thm)],[27,35,theory(equality)]) ).
cnf(186,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[27,49,theory(equality)]) ).
cnf(205,plain,
multiplication(X1,coantidomain(X2)) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(rw,[status(thm)],[184,57,theory(equality)]) ).
cnf(206,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[186,57,theory(equality)]) ).
cnf(233,plain,
addition(coantidomain(X1),coantidomain(multiplication(coantidomain(coantidomain(X1)),one))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),one)),
inference(spm,[status(thm)],[33,39,theory(equality)]) ).
cnf(241,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)),
inference(spm,[status(thm)],[33,49,theory(equality)]) ).
cnf(243,plain,
addition(coantidomain(multiplication(X1,multiplication(X2,X3))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3)),
inference(spm,[status(thm)],[33,63,theory(equality)]) ).
cnf(244,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),one)),
inference(rw,[status(thm)],[233,39,theory(equality)]) ).
cnf(245,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[244,39,theory(equality)]) ).
cnf(252,plain,
addition(zero,coantidomain(zero)) = one,
inference(spm,[status(thm)],[94,86,theory(equality)]) ).
cnf(257,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[95,87,theory(equality)]) ).
cnf(268,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[252,90,theory(equality)]) ).
cnf(276,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[257,90,theory(equality)]) ).
cnf(294,plain,
addition(antidomain(zero),antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))))) = antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))),
inference(spm,[status(thm)],[47,130,theory(equality)]) ).
cnf(310,plain,
addition(one,antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))))) = antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))),
inference(rw,[status(thm)],[294,276,theory(equality)]) ).
cnf(358,plain,
addition(coantidomain(X1),one) = one,
inference(spm,[status(thm)],[97,94,theory(equality)]) ).
cnf(359,plain,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[97,95,theory(equality)]) ).
cnf(374,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[97,67,theory(equality)]) ).
cnf(378,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[358,67,theory(equality)]) ).
cnf(379,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[359,67,theory(equality)]) ).
cnf(594,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[166,67,theory(equality)]) ).
cnf(656,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[206,67,theory(equality)]) ).
cnf(794,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[594,94,theory(equality)]) ).
cnf(817,plain,
X1 = multiplication(X1,coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[794,39,theory(equality)]) ).
cnf(834,plain,
multiplication(X1,X2) = multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)),
inference(spm,[status(thm)],[63,817,theory(equality)]) ).
cnf(862,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[656,95,theory(equality)]) ).
cnf(884,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[862,41,theory(equality)]) ).
cnf(899,plain,
multiplication(X1,X2) = multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)),
inference(spm,[status(thm)],[63,884,theory(equality)]) ).
cnf(1281,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),
inference(spm,[status(thm)],[166,245,theory(equality)]) ).
cnf(1293,plain,
zero = multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),
inference(rw,[status(thm)],[1281,35,theory(equality)]) ).
cnf(1300,plain,
addition(antidomain(zero),antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))))) = antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[47,1293,theory(equality)]) ).
cnf(1313,plain,
one = antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1300,276,theory(equality)]),379,theory(equality)]) ).
cnf(1323,plain,
multiplication(antidomain(antidomain(antidomain(X1))),one) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(spm,[status(thm)],[167,95,theory(equality)]) ).
cnf(1340,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,X2)) = multiplication(antidomain(addition(X1,X2)),X2),
inference(spm,[status(thm)],[167,374,theory(equality)]) ).
cnf(1357,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(rw,[status(thm)],[1323,39,theory(equality)]) ).
cnf(1358,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[1357,884,theory(equality)]) ).
cnf(1373,plain,
zero = multiplication(antidomain(addition(X1,X2)),X2),
inference(rw,[status(thm)],[1340,49,theory(equality)]) ).
cnf(1413,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[134,1358,theory(equality)]) ).
cnf(1414,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)],[85,1358,theory(equality)]),1358,theory(equality)]),1358,theory(equality)]) ).
cnf(1415,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)],[1414,1358,theory(equality)]),1358,theory(equality)]),1358,theory(equality)]) ).
cnf(1686,plain,
multiplication(zero,X3) = multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)),
inference(spm,[status(thm)],[63,1373,theory(equality)]) ).
cnf(1725,plain,
zero = multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)),
inference(rw,[status(thm)],[1686,55,theory(equality)]) ).
cnf(1967,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[205,94,theory(equality)]) ).
cnf(1996,plain,
multiplication(addition(X2,X1),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(spm,[status(thm)],[205,67,theory(equality)]) ).
cnf(2002,plain,
coantidomain(coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[1967,41,theory(equality)]) ).
cnf(2003,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[2002,817,theory(equality)]) ).
cnf(2468,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X1,X2)),
inference(rw,[status(thm)],[147,90,theory(equality)]) ).
cnf(2470,plain,
multiplication(antidomain(coantidomain(X1)),one) = multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[2468,94,theory(equality)]) ).
cnf(2508,plain,
antidomain(coantidomain(X1)) = multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[2470,39,theory(equality)]) ).
cnf(2741,plain,
multiplication(one,coantidomain(antidomain(X1))) = multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))),
inference(spm,[status(thm)],[1996,95,theory(equality)]) ).
cnf(2783,plain,
coantidomain(antidomain(X1)) = multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[2741,41,theory(equality)]) ).
cnf(2976,plain,
addition(addition(X1,coantidomain(X2)),multiplication(X2,X1)) = multiplication(addition(one,X2),addition(X1,coantidomain(X2))),
inference(spm,[status(thm)],[177,166,theory(equality)]) ).
cnf(3039,plain,
addition(X1,addition(coantidomain(X2),multiplication(X2,X1))) = multiplication(addition(one,X2),addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[2976,69,theory(equality)]) ).
cnf(3187,plain,
addition(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = multiplication(addition(one,antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[177,2508,theory(equality)]) ).
cnf(3208,plain,
addition(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = multiplication(addition(one,antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[3187,67,theory(equality)]) ).
cnf(3209,plain,
addition(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3208,379,theory(equality)]),41,theory(equality)]) ).
cnf(3225,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = multiplication(antidomain(antidomain(X1)),addition(one,coantidomain(antidomain(X1)))),
inference(spm,[status(thm)],[137,2783,theory(equality)]) ).
cnf(3245,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3225,378,theory(equality)]),39,theory(equality)]) ).
cnf(3361,plain,
multiplication(coantidomain(X1),coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),antidomain(coantidomain(X1))),
inference(spm,[status(thm)],[166,3209,theory(equality)]) ).
cnf(3384,plain,
zero = multiplication(coantidomain(X1),antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[3361,35,theory(equality)]) ).
cnf(3424,plain,
multiplication(X1,zero) = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[834,3384,theory(equality)]) ).
cnf(3453,plain,
zero = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[3424,37,theory(equality)]) ).
cnf(3458,plain,
addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[71,3453,theory(equality)]) ).
cnf(3484,plain,
multiplication(X1,X2) = multiplication(X1,addition(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[3458,90,theory(equality)]) ).
cnf(3709,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = antidomain(X1),
inference(spm,[status(thm)],[3245,1358,theory(equality)]) ).
cnf(3809,plain,
multiplication(antidomain(X1),X1) = multiplication(coantidomain(antidomain(antidomain(X1))),X1),
inference(spm,[status(thm)],[656,3709,theory(equality)]) ).
cnf(3833,plain,
zero = multiplication(coantidomain(antidomain(antidomain(X1))),X1),
inference(rw,[status(thm)],[3809,49,theory(equality)]) ).
cnf(3853,plain,
addition(zero,multiplication(X2,X1)) = multiplication(addition(coantidomain(antidomain(antidomain(X1))),X2),X1),
inference(spm,[status(thm)],[27,3833,theory(equality)]) ).
cnf(3878,plain,
multiplication(X2,X1) = multiplication(addition(coantidomain(antidomain(antidomain(X1))),X2),X1),
inference(rw,[status(thm)],[3853,90,theory(equality)]) ).
cnf(5351,plain,
multiplication(antidomain(addition(X1,antidomain(antidomain(X2)))),X2) = zero,
inference(spm,[status(thm)],[1725,884,theory(equality)]) ).
cnf(6940,plain,
multiplication(one,multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))) = zero,
inference(spm,[status(thm)],[49,1313,theory(equality)]) ).
cnf(6977,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[6940,41,theory(equality)]) ).
cnf(7042,plain,
multiplication(X1,zero) = multiplication(X1,antidomain(antidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[834,6977,theory(equality)]) ).
cnf(7084,plain,
zero = multiplication(X1,antidomain(antidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[7042,37,theory(equality)]) ).
cnf(7098,plain,
addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[71,7084,theory(equality)]) ).
cnf(7136,plain,
multiplication(X1,X2) = multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[7098,90,theory(equality)]) ).
cnf(8700,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(esk3_0))),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) = zero,
inference(spm,[status(thm)],[5351,1413,theory(equality)]) ).
cnf(8748,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) = zero,
inference(rw,[status(thm)],[8700,1358,theory(equality)]) ).
cnf(8775,negated_conjecture,
multiplication(zero,X1) = multiplication(antidomain(esk3_0),multiplication(multiplication(esk1_0,antidomain(antidomain(esk2_0))),X1)),
inference(spm,[status(thm)],[63,8748,theory(equality)]) ).
cnf(8801,negated_conjecture,
zero = multiplication(antidomain(esk3_0),multiplication(multiplication(esk1_0,antidomain(antidomain(esk2_0))),X1)),
inference(rw,[status(thm)],[8775,55,theory(equality)]) ).
cnf(8802,negated_conjecture,
zero = multiplication(antidomain(esk3_0),multiplication(esk1_0,multiplication(antidomain(antidomain(esk2_0)),X1))),
inference(rw,[status(thm)],[8801,63,theory(equality)]) ).
cnf(10147,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,esk2_0)) = zero,
inference(spm,[status(thm)],[8802,884,theory(equality)]) ).
cnf(12796,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[241,268,theory(equality)]),378,theory(equality)]) ).
cnf(12799,plain,
multiplication(multiplication(coantidomain(coantidomain(antidomain(X1))),X1),one) = zero,
inference(spm,[status(thm)],[35,12796,theory(equality)]) ).
cnf(12856,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[12799,63,theory(equality)]),39,theory(equality)]) ).
cnf(13693,negated_conjecture,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0)),
inference(spm,[status(thm)],[243,10147,theory(equality)]) ).
cnf(14051,negated_conjecture,
one = coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[13693,268,theory(equality)]),378,theory(equality)]) ).
cnf(14107,negated_conjecture,
multiplication(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0),one) = zero,
inference(spm,[status(thm)],[35,14051,theory(equality)]) ).
cnf(14156,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[14107,63,theory(equality)]),39,theory(equality)]) ).
cnf(17580,plain,
one = antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))),
inference(rw,[status(thm)],[310,379,theory(equality)]) ).
cnf(17586,plain,
multiplication(one,multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))) = zero,
inference(spm,[status(thm)],[49,17580,theory(equality)]) ).
cnf(17690,plain,
multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))) = zero,
inference(rw,[status(thm)],[17586,41,theory(equality)]) ).
cnf(18806,plain,
addition(zero,multiplication(X1,X3)) = multiplication(X1,addition(antidomain(antidomain(multiplication(coantidomain(X1),X2))),X3)),
inference(spm,[status(thm)],[71,17690,theory(equality)]) ).
cnf(18931,plain,
multiplication(X1,X3) = multiplication(X1,addition(antidomain(antidomain(multiplication(coantidomain(X1),X2))),X3)),
inference(rw,[status(thm)],[18806,90,theory(equality)]) ).
cnf(35675,plain,
multiplication(X1,one) = multiplication(X1,antidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[3484,95,theory(equality)]) ).
cnf(35791,plain,
X1 = multiplication(X1,antidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[35675,39,theory(equality)]) ).
cnf(35908,plain,
multiplication(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(spm,[status(thm)],[35791,2003,theory(equality)]) ).
cnf(36082,plain,
addition(antidomain(antidomain(coantidomain(X1))),coantidomain(X1)) = multiplication(addition(one,coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[177,35908,theory(equality)]) ).
cnf(36154,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = multiplication(addition(one,coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[36082,67,theory(equality)]) ).
cnf(36155,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[36154,378,theory(equality)]),41,theory(equality)]) ).
cnf(36966,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = addition(one,antidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[100,36155,theory(equality)]) ).
cnf(37035,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[36966,379,theory(equality)]) ).
cnf(37101,plain,
multiplication(one,antidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[206,37035,theory(equality)]) ).
cnf(37109,plain,
addition(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))) = one,
inference(spm,[status(thm)],[37035,2003,theory(equality)]) ).
cnf(37178,plain,
antidomain(coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[37101,41,theory(equality)]) ).
cnf(37189,plain,
addition(antidomain(antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[37109,67,theory(equality)]) ).
cnf(37259,plain,
multiplication(one,antidomain(coantidomain(X1))) = multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))),
inference(spm,[status(thm)],[656,37189,theory(equality)]) ).
cnf(37334,plain,
antidomain(coantidomain(X1)) = multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[37259,41,theory(equality)]) ).
cnf(40159,plain,
multiplication(one,X1) = multiplication(coantidomain(coantidomain(antidomain(antidomain(X1)))),X1),
inference(spm,[status(thm)],[3878,94,theory(equality)]) ).
cnf(40260,plain,
X1 = multiplication(coantidomain(coantidomain(antidomain(antidomain(X1)))),X1),
inference(rw,[status(thm)],[40159,41,theory(equality)]) ).
cnf(40349,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(X1)) = antidomain(X1),
inference(spm,[status(thm)],[40260,1358,theory(equality)]) ).
cnf(40491,plain,
addition(coantidomain(coantidomain(antidomain(X1))),antidomain(X1)) = multiplication(coantidomain(coantidomain(antidomain(X1))),addition(one,antidomain(X1))),
inference(spm,[status(thm)],[137,40349,theory(equality)]) ).
cnf(40559,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = multiplication(coantidomain(coantidomain(antidomain(X1))),addition(one,antidomain(X1))),
inference(rw,[status(thm)],[40491,67,theory(equality)]) ).
cnf(40560,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[40559,379,theory(equality)]),39,theory(equality)]) ).
cnf(41259,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1))))) = addition(one,coantidomain(coantidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[101,40560,theory(equality)]) ).
cnf(41334,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1))))) = one,
inference(rw,[status(thm)],[41259,378,theory(equality)]) ).
cnf(41410,plain,
addition(antidomain(antidomain(X1)),coantidomain(coantidomain(antidomain(X1)))) = one,
inference(spm,[status(thm)],[41334,1358,theory(equality)]) ).
cnf(41583,plain,
multiplication(coantidomain(antidomain(X1)),one) = multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))),
inference(spm,[status(thm)],[166,41410,theory(equality)]) ).
cnf(41662,plain,
coantidomain(antidomain(X1)) = multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))),
inference(rw,[status(thm)],[41583,39,theory(equality)]) ).
cnf(44309,plain,
multiplication(X1,one) = multiplication(X1,antidomain(antidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[7136,95,theory(equality)]) ).
cnf(44434,plain,
X1 = multiplication(X1,antidomain(antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[44309,39,theory(equality)]) ).
cnf(44435,plain,
X1 = multiplication(X1,antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[44434,1358,theory(equality)]) ).
cnf(44563,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[44435,2003,theory(equality)]) ).
cnf(44639,plain,
coantidomain(X1) = antidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[37178,44435,theory(equality)]) ).
cnf(44657,plain,
antidomain(coantidomain(X1)) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[44563,37334,theory(equality)]) ).
cnf(44827,negated_conjecture,
multiplication(antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0) = zero,
inference(rw,[status(thm)],[14156,44657,theory(equality)]) ).
cnf(44833,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[12856,44657,theory(equality)]) ).
cnf(44875,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(coantidomain(multiplication(antidomain(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)],[1415,44657,theory(equality)]),44657,theory(equality)]) ).
cnf(44876,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) != antidomain(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(esk3_0))),esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[44875,44657,theory(equality)]),44657,theory(equality)]) ).
cnf(44911,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[44639,44657,theory(equality)]) ).
cnf(45253,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(coantidomain(antidomain(esk3_0))),esk1_0))) != antidomain(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(esk3_0))),esk1_0)))),
inference(rw,[status(thm)],[44876,44911,theory(equality)]) ).
cnf(45254,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(coantidomain(antidomain(esk3_0))),esk1_0))) != coantidomain(multiplication(antidomain(coantidomain(antidomain(esk3_0))),esk1_0)),
inference(rw,[status(thm)],[45253,44911,theory(equality)]) ).
cnf(45483,negated_conjecture,
addition(zero,multiplication(X1,esk2_0)) = multiplication(addition(antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),X1),esk2_0),
inference(spm,[status(thm)],[27,44827,theory(equality)]) ).
cnf(45525,negated_conjecture,
multiplication(X1,esk2_0) = multiplication(addition(antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),X1),esk2_0),
inference(rw,[status(thm)],[45483,90,theory(equality)]) ).
cnf(45575,plain,
addition(zero,multiplication(X2,X1)) = multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1),
inference(spm,[status(thm)],[27,44833,theory(equality)]) ).
cnf(45647,plain,
multiplication(X2,X1) = multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1),
inference(rw,[status(thm)],[45575,90,theory(equality)]) ).
cnf(63485,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(coantidomain(antidomain(X1)))),X1),
inference(spm,[status(thm)],[45647,95,theory(equality)]) ).
cnf(63613,plain,
X1 = multiplication(antidomain(antidomain(coantidomain(antidomain(X1)))),X1),
inference(rw,[status(thm)],[63485,41,theory(equality)]) ).
cnf(63614,plain,
X1 = multiplication(coantidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[63613,44911,theory(equality)]) ).
cnf(63738,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[63614,1358,theory(equality)]) ).
cnf(63834,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[63738,41662,theory(equality)]) ).
cnf(64080,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) != coantidomain(multiplication(antidomain(coantidomain(antidomain(esk3_0))),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[45254,63834,theory(equality)]),1358,theory(equality)]) ).
cnf(64081,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) != coantidomain(multiplication(antidomain(esk3_0),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[64080,63834,theory(equality)]),1358,theory(equality)]) ).
cnf(78341,negated_conjecture,
multiplication(one,esk2_0) = multiplication(antidomain(antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),esk2_0),
inference(spm,[status(thm)],[45525,95,theory(equality)]) ).
cnf(78424,negated_conjecture,
esk2_0 = multiplication(antidomain(antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),esk2_0),
inference(rw,[status(thm)],[78341,41,theory(equality)]) ).
cnf(78425,negated_conjecture,
esk2_0 = multiplication(coantidomain(multiplication(antidomain(esk3_0),esk1_0)),esk2_0),
inference(rw,[status(thm)],[78424,44911,theory(equality)]) ).
cnf(1662786,plain,
multiplication(X1,one) = multiplication(X1,antidomain(antidomain(antidomain(multiplication(coantidomain(X1),X2))))),
inference(spm,[status(thm)],[18931,95,theory(equality)]) ).
cnf(1663924,plain,
X1 = multiplication(X1,antidomain(antidomain(antidomain(multiplication(coantidomain(X1),X2))))),
inference(rw,[status(thm)],[1662786,39,theory(equality)]) ).
cnf(1663925,plain,
X1 = multiplication(X1,antidomain(multiplication(coantidomain(X1),X2))),
inference(rw,[status(thm)],[1663924,1358,theory(equality)]) ).
cnf(1665125,plain,
multiplication(antidomain(X1),antidomain(multiplication(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(spm,[status(thm)],[1663925,63834,theory(equality)]) ).
cnf(1705604,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(spm,[status(thm)],[1665125,899,theory(equality)]) ).
cnf(1710626,plain,
addition(antidomain(multiplication(X1,X2)),addition(coantidomain(antidomain(X1)),antidomain(X1))) = multiplication(addition(one,antidomain(X1)),addition(antidomain(multiplication(X1,X2)),coantidomain(antidomain(X1)))),
inference(spm,[status(thm)],[3039,1705604,theory(equality)]) ).
cnf(1712213,plain,
one = multiplication(addition(one,antidomain(X1)),addition(antidomain(multiplication(X1,X2)),coantidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1710626,67,theory(equality)]),63834,theory(equality)]),95,theory(equality)]),67,theory(equality)]),379,theory(equality)]) ).
cnf(1712214,plain,
one = addition(antidomain(antidomain(X1)),antidomain(multiplication(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1712213,379,theory(equality)]),63834,theory(equality)]),67,theory(equality)]),41,theory(equality)]) ).
cnf(1723479,negated_conjecture,
addition(antidomain(antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),antidomain(esk2_0)) = one,
inference(spm,[status(thm)],[1712214,78425,theory(equality)]) ).
cnf(1725159,negated_conjecture,
addition(antidomain(esk2_0),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1723479,44911,theory(equality)]),67,theory(equality)]) ).
cnf(1726633,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),one) = multiplication(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))),
inference(spm,[status(thm)],[2468,1725159,theory(equality)]) ).
cnf(1727123,negated_conjecture,
antidomain(antidomain(esk2_0)) = multiplication(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))),
inference(rw,[status(thm)],[1726633,39,theory(equality)]) ).
cnf(1765300,negated_conjecture,
addition(coantidomain(multiplication(antidomain(esk3_0),esk1_0)),antidomain(antidomain(esk2_0))) = multiplication(addition(one,antidomain(antidomain(esk2_0))),coantidomain(multiplication(antidomain(esk3_0),esk1_0))),
inference(spm,[status(thm)],[177,1727123,theory(equality)]) ).
cnf(1765689,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) = multiplication(addition(one,antidomain(antidomain(esk2_0))),coantidomain(multiplication(antidomain(esk3_0),esk1_0))),
inference(rw,[status(thm)],[1765300,67,theory(equality)]) ).
cnf(1765690,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) = coantidomain(multiplication(antidomain(esk3_0),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1765689,379,theory(equality)]),41,theory(equality)]) ).
cnf(1765691,negated_conjecture,
$false,
inference(sr,[status(thm)],[1765690,64081,theory(equality)]) ).
cnf(1765692,negated_conjecture,
$false,
1765691,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE105+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax, KLE001+6.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpC1NAlF/sel_KLE105+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpC1NAlF/sel_KLE105+1.p_2 with time limit 81
% -prover status Theorem
% Problem KLE105+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE105+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE105+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
%
%------------------------------------------------------------------------------