TSTP Solution File: KLE091+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE091+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 12:14:20 EST 2010
% Result : Theorem 0.87s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 20
% Syntax : Number of formulae : 184 ( 184 unt; 0 def)
% Number of atoms : 184 ( 181 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 229 ( 8 sgn 62 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',left_annihilation) ).
fof(2,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',right_annihilation) ).
fof(3,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',multiplicative_left_identity) ).
fof(4,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',additive_identity) ).
fof(5,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',left_distributivity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',additive_commutativity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',additive_idempotence) ).
fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',multiplicative_associativity) ).
fof(9,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',codomain3) ).
fof(10,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',codomain2) ).
fof(11,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',codomain1) ).
fof(12,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',additive_associativity) ).
fof(13,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',codomain4) ).
fof(14,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',multiplicative_right_identity) ).
fof(15,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',domain3) ).
fof(16,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',domain2) ).
fof(17,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',right_distributivity) ).
fof(18,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',domain1) ).
fof(19,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',domain4) ).
fof(20,conjecture,
! [X4] : domain(codomain(X4)) = codomain(X4),
file('/tmp/tmpryDlOD/sel_KLE091+1.p_1',goals) ).
fof(21,negated_conjecture,
~ ! [X4] : domain(codomain(X4)) = codomain(X4),
inference(assume_negation,[status(cth)],[20]) ).
fof(22,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[1]) ).
cnf(23,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[2]) ).
cnf(25,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(27,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(29,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(31,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(35,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(37,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[9]) ).
cnf(39,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,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)],[10]) ).
cnf(41,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[11]) ).
cnf(43,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[12]) ).
cnf(45,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,plain,
! [X5] : codomain(X5) = coantidomain(coantidomain(X5)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(47,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[14]) ).
cnf(49,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[15]) ).
cnf(51,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,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)],[16]) ).
cnf(53,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[17]) ).
cnf(55,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[54]) ).
fof(56,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[18]) ).
cnf(57,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[56]) ).
fof(58,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[19]) ).
cnf(59,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[58]) ).
fof(60,negated_conjecture,
? [X4] : domain(codomain(X4)) != codomain(X4),
inference(fof_nnf,[status(thm)],[21]) ).
fof(61,negated_conjecture,
? [X5] : domain(codomain(X5)) != codomain(X5),
inference(variable_rename,[status(thm)],[60]) ).
fof(62,negated_conjecture,
domain(codomain(esk1_0)) != codomain(esk1_0),
inference(skolemize,[status(esa)],[61]) ).
cnf(63,negated_conjecture,
domain(codomain(esk1_0)) != codomain(esk1_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(64,negated_conjecture,
domain(coantidomain(coantidomain(esk1_0))) != coantidomain(coantidomain(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[63,47,theory(equality)]),47,theory(equality)]),
[unfolding] ).
cnf(65,negated_conjecture,
antidomain(antidomain(coantidomain(coantidomain(esk1_0)))) != coantidomain(coantidomain(esk1_0)),
inference(rw,[status(thm)],[64,59,theory(equality)]),
[unfolding] ).
cnf(66,plain,
zero = coantidomain(one),
inference(spm,[status(thm)],[27,43,theory(equality)]) ).
cnf(67,plain,
zero = antidomain(one),
inference(spm,[status(thm)],[49,57,theory(equality)]) ).
cnf(70,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[29,33,theory(equality)]) ).
cnf(74,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[39,33,theory(equality)]) ).
cnf(75,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[51,33,theory(equality)]) ).
cnf(84,plain,
multiplication(zero,X2) = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(spm,[status(thm)],[37,57,theory(equality)]) ).
cnf(95,plain,
zero = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(rw,[status(thm)],[84,23,theory(equality)]) ).
cnf(99,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[45,35,theory(equality)]) ).
cnf(102,plain,
addition(one,X2) = addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)),
inference(spm,[status(thm)],[45,74,theory(equality)]) ).
cnf(103,plain,
addition(one,X2) = addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)),
inference(spm,[status(thm)],[45,75,theory(equality)]) ).
cnf(115,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[55,49,theory(equality)]) ).
cnf(124,plain,
addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(spm,[status(thm)],[55,43,theory(equality)]) ).
cnf(126,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[55,57,theory(equality)]) ).
cnf(144,plain,
multiplication(X1,X2) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[124,29,theory(equality)]) ).
cnf(145,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[126,29,theory(equality)]) ).
cnf(155,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[31,27,theory(equality)]) ).
cnf(162,plain,
addition(multiplication(X1,coantidomain(X2)),zero) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(spm,[status(thm)],[31,43,theory(equality)]) ).
cnf(164,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[31,57,theory(equality)]) ).
cnf(183,plain,
multiplication(X1,coantidomain(X2)) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(rw,[status(thm)],[162,29,theory(equality)]) ).
cnf(184,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[164,29,theory(equality)]) ).
cnf(190,plain,
addition(antidomain(X1),antidomain(multiplication(one,antidomain(antidomain(X1))))) = antidomain(multiplication(one,antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[53,27,theory(equality)]) ).
cnf(201,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(multiplication(one,antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[190,27,theory(equality)]) ).
cnf(202,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[201,27,theory(equality)]) ).
cnf(211,plain,
addition(coantidomain(X1),coantidomain(multiplication(coantidomain(coantidomain(X1)),one))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),one)),
inference(spm,[status(thm)],[41,49,theory(equality)]) ).
cnf(222,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),one)),
inference(rw,[status(thm)],[211,49,theory(equality)]) ).
cnf(223,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[222,49,theory(equality)]) ).
cnf(230,plain,
addition(zero,coantidomain(zero)) = one,
inference(spm,[status(thm)],[74,66,theory(equality)]) ).
cnf(235,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[75,67,theory(equality)]) ).
cnf(246,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[230,70,theory(equality)]) ).
cnf(254,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[235,70,theory(equality)]) ).
cnf(391,plain,
addition(coantidomain(X1),one) = one,
inference(spm,[status(thm)],[99,74,theory(equality)]) ).
cnf(392,plain,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[99,75,theory(equality)]) ).
cnf(407,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[391,33,theory(equality)]) ).
cnf(408,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[392,33,theory(equality)]) ).
cnf(568,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),
inference(spm,[status(thm)],[144,223,theory(equality)]) ).
cnf(569,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[144,33,theory(equality)]) ).
cnf(592,plain,
zero = multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),
inference(rw,[status(thm)],[568,43,theory(equality)]) ).
cnf(619,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)],[53,592,theory(equality)]) ).
cnf(632,plain,
one = antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[619,254,theory(equality)]),408,theory(equality)]) ).
cnf(641,plain,
multiplication(one,multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))) = zero,
inference(spm,[status(thm)],[57,632,theory(equality)]) ).
cnf(651,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[641,27,theory(equality)]) ).
cnf(714,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[184,33,theory(equality)]) ).
cnf(825,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[569,74,theory(equality)]) ).
cnf(849,plain,
X1 = multiplication(X1,coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[825,49,theory(equality)]) ).
cnf(867,plain,
multiplication(X1,X2) = multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)),
inference(spm,[status(thm)],[37,849,theory(equality)]) ).
cnf(999,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = addition(one,antidomain(antidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[103,202,theory(equality)]) ).
cnf(1018,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = one,
inference(rw,[status(thm)],[999,408,theory(equality)]) ).
cnf(1057,plain,
multiplication(one,antidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),antidomain(antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[184,1018,theory(equality)]) ).
cnf(1063,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(X1),antidomain(antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[1057,27,theory(equality)]) ).
cnf(1070,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[714,75,theory(equality)]) ).
cnf(1092,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[1070,27,theory(equality)]) ).
cnf(1118,plain,
multiplication(antidomain(antidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[95,1092,theory(equality)]) ).
cnf(1136,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1)),
inference(spm,[status(thm)],[41,1118,theory(equality)]) ).
cnf(1151,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1136,246,theory(equality)]),407,theory(equality)]) ).
cnf(1706,plain,
multiplication(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1),one) = zero,
inference(spm,[status(thm)],[43,1151,theory(equality)]) ).
cnf(1731,plain,
multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1706,37,theory(equality)]),49,theory(equality)]) ).
cnf(1834,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),addition(one,antidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[115,1063,theory(equality)]) ).
cnf(1896,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(X1),addition(one,antidomain(antidomain(antidomain(X1))))),
inference(rw,[status(thm)],[1834,202,theory(equality)]) ).
cnf(1897,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1896,408,theory(equality)]),49,theory(equality)]) ).
cnf(1922,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[1731,1897,theory(equality)]) ).
cnf(1961,plain,
addition(zero,multiplication(X2,X1)) = multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1),
inference(spm,[status(thm)],[31,1922,theory(equality)]) ).
cnf(1978,plain,
multiplication(X2,X1) = multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1),
inference(rw,[status(thm)],[1961,70,theory(equality)]) ).
cnf(2570,plain,
multiplication(antidomain(coantidomain(coantidomain(X1))),one) = multiplication(antidomain(coantidomain(coantidomain(X1))),coantidomain(X1)),
inference(spm,[status(thm)],[145,74,theory(equality)]) ).
cnf(2614,plain,
antidomain(coantidomain(coantidomain(X1))) = multiplication(antidomain(coantidomain(coantidomain(X1))),coantidomain(X1)),
inference(rw,[status(thm)],[2570,49,theory(equality)]) ).
cnf(2952,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[183,74,theory(equality)]) ).
cnf(2953,plain,
multiplication(one,coantidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[183,75,theory(equality)]) ).
cnf(2988,plain,
coantidomain(coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[2952,27,theory(equality)]) ).
cnf(2989,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[2988,849,theory(equality)]) ).
cnf(2990,plain,
coantidomain(antidomain(antidomain(X1))) = multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[2953,27,theory(equality)]) ).
cnf(3144,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),addition(one,coantidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[115,2990,theory(equality)]) ).
cnf(3158,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3144,407,theory(equality)]),49,theory(equality)]) ).
cnf(3574,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[3158,1897,theory(equality)]) ).
cnf(3597,plain,
addition(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[3574,33,theory(equality)]) ).
cnf(4199,plain,
addition(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = multiplication(addition(one,antidomain(coantidomain(coantidomain(X1)))),coantidomain(X1)),
inference(spm,[status(thm)],[155,2614,theory(equality)]) ).
cnf(4277,plain,
addition(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4199,408,theory(equality)]),27,theory(equality)]) ).
cnf(4309,plain,
multiplication(X1,coantidomain(X1)) = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[569,4277,theory(equality)]) ).
cnf(4332,plain,
zero = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[4309,43,theory(equality)]) ).
cnf(4348,plain,
addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[55,4332,theory(equality)]) ).
cnf(4373,plain,
multiplication(X1,X2) = multiplication(X1,addition(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[4348,70,theory(equality)]) ).
cnf(6964,plain,
multiplication(X1,zero) = multiplication(X1,antidomain(antidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[867,651,theory(equality)]) ).
cnf(7038,plain,
zero = multiplication(X1,antidomain(antidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[6964,25,theory(equality)]) ).
cnf(7095,plain,
multiplication(zero,X2) = multiplication(X1,multiplication(antidomain(antidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[37,7038,theory(equality)]) ).
cnf(7135,plain,
zero = multiplication(X1,multiplication(antidomain(antidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[7095,23,theory(equality)]) ).
cnf(7593,plain,
multiplication(X1,coantidomain(antidomain(antidomain(antidomain(coantidomain(X1)))))) = zero,
inference(spm,[status(thm)],[7135,2990,theory(equality)]) ).
cnf(7662,plain,
multiplication(X1,coantidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[7593,1897,theory(equality)]) ).
cnf(7703,plain,
addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(coantidomain(antidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[55,7662,theory(equality)]) ).
cnf(7741,plain,
multiplication(X1,X2) = multiplication(X1,addition(coantidomain(antidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[7703,70,theory(equality)]) ).
cnf(19314,plain,
multiplication(one,X1) = multiplication(coantidomain(coantidomain(coantidomain(antidomain(X1)))),X1),
inference(spm,[status(thm)],[1978,74,theory(equality)]) ).
cnf(19382,plain,
X1 = multiplication(coantidomain(coantidomain(coantidomain(antidomain(X1)))),X1),
inference(rw,[status(thm)],[19314,27,theory(equality)]) ).
cnf(19383,plain,
X1 = multiplication(coantidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[19382,2989,theory(equality)]) ).
cnf(19450,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[19383,1897,theory(equality)]) ).
cnf(20093,plain,
addition(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = multiplication(coantidomain(antidomain(X1)),addition(one,antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[115,19450,theory(equality)]) ).
cnf(20146,plain,
antidomain(antidomain(X1)) = multiplication(coantidomain(antidomain(X1)),addition(one,antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[20093,3597,theory(equality)]) ).
cnf(20147,plain,
antidomain(antidomain(X1)) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[20146,408,theory(equality)]),49,theory(equality)]) ).
cnf(20269,plain,
multiplication(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[2990,20147,theory(equality)]) ).
cnf(20270,plain,
multiplication(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[20269,20147,theory(equality)]) ).
cnf(20271,plain,
antidomain(X1) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[20270,849,theory(equality)]) ).
cnf(20284,plain,
addition(antidomain(X1),coantidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[75,20147,theory(equality)]) ).
cnf(20285,negated_conjecture,
coantidomain(antidomain(coantidomain(coantidomain(esk1_0)))) != coantidomain(coantidomain(esk1_0)),
inference(rw,[status(thm)],[65,20147,theory(equality)]) ).
cnf(22301,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[4373,20284,theory(equality)]) ).
cnf(22368,plain,
X1 = multiplication(X1,coantidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[22301,49,theory(equality)]) ).
cnf(22388,plain,
multiplication(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(spm,[status(thm)],[22368,2989,theory(equality)]) ).
cnf(22498,plain,
addition(coantidomain(antidomain(coantidomain(X1))),coantidomain(X1)) = multiplication(addition(one,coantidomain(X1)),coantidomain(antidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[155,22388,theory(equality)]) ).
cnf(22545,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = multiplication(addition(one,coantidomain(X1)),coantidomain(antidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[22498,33,theory(equality)]) ).
cnf(22546,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = coantidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[22545,407,theory(equality)]),27,theory(equality)]) ).
cnf(22580,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(coantidomain(X1))))) = addition(one,coantidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[102,22546,theory(equality)]) ).
cnf(22625,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[22580,407,theory(equality)]) ).
cnf(22680,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(antidomain(coantidomain(X1)))) = one,
inference(spm,[status(thm)],[22625,2989,theory(equality)]) ).
cnf(22777,plain,
multiplication(one,coantidomain(coantidomain(antidomain(coantidomain(X1))))) = multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[183,22680,theory(equality)]) ).
cnf(22828,plain,
antidomain(coantidomain(X1)) = multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[22777,20271,theory(equality)]),27,theory(equality)]) ).
cnf(22829,plain,
antidomain(coantidomain(X1)) = multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[22828,20271,theory(equality)]) ).
cnf(26893,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[7741,74,theory(equality)]) ).
cnf(26977,plain,
X1 = multiplication(X1,coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[26893,49,theory(equality)]) ).
cnf(26978,plain,
X1 = multiplication(X1,antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[26977,20271,theory(equality)]) ).
cnf(27065,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[26978,2989,theory(equality)]) ).
cnf(27130,plain,
antidomain(coantidomain(X1)) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[27065,22829,theory(equality)]) ).
cnf(27300,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[20285,27130,theory(equality)]),2989,theory(equality)]) ).
cnf(27301,negated_conjecture,
$false,
inference(cn,[status(thm)],[27300,theory(equality)]) ).
cnf(27302,negated_conjecture,
$false,
27301,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE091+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax]
% -running prover on /tmp/tmpryDlOD/sel_KLE091+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE091+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE091+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE091+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
%
%------------------------------------------------------------------------------