TSTP Solution File: KLE092+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE092+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 12:14:25 EST 2010
% Result : Theorem 0.82s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 19
% Syntax : Number of formulae : 180 ( 180 unt; 0 def)
% Number of atoms : 180 ( 177 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 226 ( 8 sgn 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',left_annihilation) ).
fof(2,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',right_annihilation) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpNSVB-h/sel_KLE092+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/tmpNSVB-h/sel_KLE092+1.p_1',left_distributivity) ).
fof(5,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',additive_idempotence) ).
fof(7,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',multiplicative_associativity) ).
fof(8,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/tmp/tmpNSVB-h/sel_KLE092+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/tmpNSVB-h/sel_KLE092+1.p_1',codomain2) ).
fof(10,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',codomain1) ).
fof(11,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',additive_associativity) ).
fof(12,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',multiplicative_right_identity) ).
fof(13,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmpNSVB-h/sel_KLE092+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/tmpNSVB-h/sel_KLE092+1.p_1',domain2) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',right_distributivity) ).
fof(16,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',domain1) ).
fof(17,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',multiplicative_left_identity) ).
fof(18,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',domain4) ).
fof(19,conjecture,
! [X4] : domain(coantidomain(X4)) = coantidomain(X4),
file('/tmp/tmpNSVB-h/sel_KLE092+1.p_1',goals) ).
fof(20,negated_conjecture,
~ ! [X4] : domain(coantidomain(X4)) = coantidomain(X4),
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(23,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[2]) ).
cnf(24,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[23]) ).
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] : domain(coantidomain(X4)) != coantidomain(X4),
inference(fof_nnf,[status(thm)],[20]) ).
fof(58,negated_conjecture,
? [X5] : domain(coantidomain(X5)) != coantidomain(X5),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,negated_conjecture,
domain(coantidomain(esk1_0)) != coantidomain(esk1_0),
inference(skolemize,[status(esa)],[58]) ).
cnf(60,negated_conjecture,
domain(coantidomain(esk1_0)) != coantidomain(esk1_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(61,negated_conjecture,
antidomain(antidomain(coantidomain(esk1_0))) != coantidomain(esk1_0),
inference(rw,[status(thm)],[60,56,theory(equality)]),
[unfolding] ).
cnf(62,plain,
zero = coantidomain(one),
inference(spm,[status(thm)],[54,40,theory(equality)]) ).
cnf(63,plain,
zero = antidomain(one),
inference(spm,[status(thm)],[44,52,theory(equality)]) ).
cnf(66,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[26,30,theory(equality)]) ).
cnf(70,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[36,30,theory(equality)]) ).
cnf(71,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[46,30,theory(equality)]) ).
cnf(80,plain,
multiplication(zero,X2) = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(spm,[status(thm)],[34,52,theory(equality)]) ).
cnf(91,plain,
zero = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(rw,[status(thm)],[80,22,theory(equality)]) ).
cnf(95,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[42,32,theory(equality)]) ).
cnf(98,plain,
addition(one,X2) = addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)),
inference(spm,[status(thm)],[42,70,theory(equality)]) ).
cnf(99,plain,
addition(one,X2) = addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)),
inference(spm,[status(thm)],[42,71,theory(equality)]) ).
cnf(111,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[50,44,theory(equality)]) ).
cnf(120,plain,
addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(spm,[status(thm)],[50,40,theory(equality)]) ).
cnf(122,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[50,52,theory(equality)]) ).
cnf(140,plain,
multiplication(X1,X2) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[120,26,theory(equality)]) ).
cnf(141,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[122,26,theory(equality)]) ).
cnf(151,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[28,54,theory(equality)]) ).
cnf(158,plain,
addition(multiplication(X1,coantidomain(X2)),zero) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(spm,[status(thm)],[28,40,theory(equality)]) ).
cnf(160,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[28,52,theory(equality)]) ).
cnf(179,plain,
multiplication(X1,coantidomain(X2)) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(rw,[status(thm)],[158,26,theory(equality)]) ).
cnf(180,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[160,26,theory(equality)]) ).
cnf(186,plain,
addition(antidomain(X1),antidomain(multiplication(one,antidomain(antidomain(X1))))) = antidomain(multiplication(one,antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[48,54,theory(equality)]) ).
cnf(197,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(multiplication(one,antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[186,54,theory(equality)]) ).
cnf(198,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[197,54,theory(equality)]) ).
cnf(207,plain,
addition(coantidomain(X1),coantidomain(multiplication(coantidomain(coantidomain(X1)),one))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),one)),
inference(spm,[status(thm)],[38,44,theory(equality)]) ).
cnf(218,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),one)),
inference(rw,[status(thm)],[207,44,theory(equality)]) ).
cnf(219,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[218,44,theory(equality)]) ).
cnf(226,plain,
addition(zero,coantidomain(zero)) = one,
inference(spm,[status(thm)],[70,62,theory(equality)]) ).
cnf(231,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[71,63,theory(equality)]) ).
cnf(242,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[226,66,theory(equality)]) ).
cnf(250,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[231,66,theory(equality)]) ).
cnf(387,plain,
addition(coantidomain(X1),one) = one,
inference(spm,[status(thm)],[95,70,theory(equality)]) ).
cnf(388,plain,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[95,71,theory(equality)]) ).
cnf(403,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[387,30,theory(equality)]) ).
cnf(404,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[388,30,theory(equality)]) ).
cnf(564,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),
inference(spm,[status(thm)],[140,219,theory(equality)]) ).
cnf(565,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[140,30,theory(equality)]) ).
cnf(588,plain,
zero = multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),
inference(rw,[status(thm)],[564,40,theory(equality)]) ).
cnf(615,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)],[48,588,theory(equality)]) ).
cnf(628,plain,
one = antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[615,250,theory(equality)]),404,theory(equality)]) ).
cnf(637,plain,
multiplication(one,multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))) = zero,
inference(spm,[status(thm)],[52,628,theory(equality)]) ).
cnf(647,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[637,54,theory(equality)]) ).
cnf(710,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[180,30,theory(equality)]) ).
cnf(821,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[565,70,theory(equality)]) ).
cnf(845,plain,
X1 = multiplication(X1,coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[821,44,theory(equality)]) ).
cnf(863,plain,
multiplication(X1,X2) = multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)),
inference(spm,[status(thm)],[34,845,theory(equality)]) ).
cnf(995,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = addition(one,antidomain(antidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[99,198,theory(equality)]) ).
cnf(1014,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = one,
inference(rw,[status(thm)],[995,404,theory(equality)]) ).
cnf(1053,plain,
multiplication(one,antidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),antidomain(antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[180,1014,theory(equality)]) ).
cnf(1059,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(X1),antidomain(antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[1053,54,theory(equality)]) ).
cnf(1066,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[710,71,theory(equality)]) ).
cnf(1088,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[1066,54,theory(equality)]) ).
cnf(1114,plain,
multiplication(antidomain(antidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[91,1088,theory(equality)]) ).
cnf(1132,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)],[38,1114,theory(equality)]) ).
cnf(1147,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1132,242,theory(equality)]),403,theory(equality)]) ).
cnf(1702,plain,
multiplication(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1),one) = zero,
inference(spm,[status(thm)],[40,1147,theory(equality)]) ).
cnf(1727,plain,
multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1702,34,theory(equality)]),44,theory(equality)]) ).
cnf(1830,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),addition(one,antidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[111,1059,theory(equality)]) ).
cnf(1892,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(X1),addition(one,antidomain(antidomain(antidomain(X1))))),
inference(rw,[status(thm)],[1830,198,theory(equality)]) ).
cnf(1893,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1892,404,theory(equality)]),44,theory(equality)]) ).
cnf(1918,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[1727,1893,theory(equality)]) ).
cnf(1957,plain,
addition(zero,multiplication(X2,X1)) = multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1),
inference(spm,[status(thm)],[28,1918,theory(equality)]) ).
cnf(1974,plain,
multiplication(X2,X1) = multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1),
inference(rw,[status(thm)],[1957,66,theory(equality)]) ).
cnf(2566,plain,
multiplication(antidomain(coantidomain(coantidomain(X1))),one) = multiplication(antidomain(coantidomain(coantidomain(X1))),coantidomain(X1)),
inference(spm,[status(thm)],[141,70,theory(equality)]) ).
cnf(2610,plain,
antidomain(coantidomain(coantidomain(X1))) = multiplication(antidomain(coantidomain(coantidomain(X1))),coantidomain(X1)),
inference(rw,[status(thm)],[2566,44,theory(equality)]) ).
cnf(2948,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[179,70,theory(equality)]) ).
cnf(2949,plain,
multiplication(one,coantidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[179,71,theory(equality)]) ).
cnf(2984,plain,
coantidomain(coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[2948,54,theory(equality)]) ).
cnf(2985,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[2984,845,theory(equality)]) ).
cnf(2986,plain,
coantidomain(antidomain(antidomain(X1))) = multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[2949,54,theory(equality)]) ).
cnf(3140,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),addition(one,coantidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[111,2986,theory(equality)]) ).
cnf(3154,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3140,403,theory(equality)]),44,theory(equality)]) ).
cnf(3570,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[3154,1893,theory(equality)]) ).
cnf(3593,plain,
addition(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[3570,30,theory(equality)]) ).
cnf(4195,plain,
addition(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = multiplication(addition(one,antidomain(coantidomain(coantidomain(X1)))),coantidomain(X1)),
inference(spm,[status(thm)],[151,2610,theory(equality)]) ).
cnf(4273,plain,
addition(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4195,404,theory(equality)]),54,theory(equality)]) ).
cnf(4305,plain,
multiplication(X1,coantidomain(X1)) = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[565,4273,theory(equality)]) ).
cnf(4328,plain,
zero = multiplication(X1,antidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[4305,40,theory(equality)]) ).
cnf(4344,plain,
addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[50,4328,theory(equality)]) ).
cnf(4369,plain,
multiplication(X1,X2) = multiplication(X1,addition(antidomain(coantidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[4344,66,theory(equality)]) ).
cnf(6960,plain,
multiplication(X1,zero) = multiplication(X1,antidomain(antidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[863,647,theory(equality)]) ).
cnf(7034,plain,
zero = multiplication(X1,antidomain(antidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[6960,24,theory(equality)]) ).
cnf(7091,plain,
multiplication(zero,X2) = multiplication(X1,multiplication(antidomain(antidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[34,7034,theory(equality)]) ).
cnf(7131,plain,
zero = multiplication(X1,multiplication(antidomain(antidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[7091,22,theory(equality)]) ).
cnf(7589,plain,
multiplication(X1,coantidomain(antidomain(antidomain(antidomain(coantidomain(X1)))))) = zero,
inference(spm,[status(thm)],[7131,2986,theory(equality)]) ).
cnf(7658,plain,
multiplication(X1,coantidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[7589,1893,theory(equality)]) ).
cnf(7699,plain,
addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(coantidomain(antidomain(coantidomain(X1))),X2)),
inference(spm,[status(thm)],[50,7658,theory(equality)]) ).
cnf(7737,plain,
multiplication(X1,X2) = multiplication(X1,addition(coantidomain(antidomain(coantidomain(X1))),X2)),
inference(rw,[status(thm)],[7699,66,theory(equality)]) ).
cnf(19308,plain,
multiplication(one,X1) = multiplication(coantidomain(coantidomain(coantidomain(antidomain(X1)))),X1),
inference(spm,[status(thm)],[1974,70,theory(equality)]) ).
cnf(19376,plain,
X1 = multiplication(coantidomain(coantidomain(coantidomain(antidomain(X1)))),X1),
inference(rw,[status(thm)],[19308,54,theory(equality)]) ).
cnf(19377,plain,
X1 = multiplication(coantidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[19376,2985,theory(equality)]) ).
cnf(19444,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[19377,1893,theory(equality)]) ).
cnf(20087,plain,
addition(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = multiplication(coantidomain(antidomain(X1)),addition(one,antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[111,19444,theory(equality)]) ).
cnf(20140,plain,
antidomain(antidomain(X1)) = multiplication(coantidomain(antidomain(X1)),addition(one,antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[20087,3593,theory(equality)]) ).
cnf(20141,plain,
antidomain(antidomain(X1)) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[20140,404,theory(equality)]),44,theory(equality)]) ).
cnf(20263,plain,
multiplication(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[2986,20141,theory(equality)]) ).
cnf(20264,plain,
multiplication(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[20263,20141,theory(equality)]) ).
cnf(20265,plain,
antidomain(X1) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[20264,845,theory(equality)]) ).
cnf(20278,plain,
addition(antidomain(X1),coantidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[71,20141,theory(equality)]) ).
cnf(20279,negated_conjecture,
coantidomain(antidomain(coantidomain(esk1_0))) != coantidomain(esk1_0),
inference(rw,[status(thm)],[61,20141,theory(equality)]) ).
cnf(22295,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[4369,20278,theory(equality)]) ).
cnf(22362,plain,
X1 = multiplication(X1,coantidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[22295,44,theory(equality)]) ).
cnf(22382,plain,
multiplication(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(spm,[status(thm)],[22362,2985,theory(equality)]) ).
cnf(22492,plain,
addition(coantidomain(antidomain(coantidomain(X1))),coantidomain(X1)) = multiplication(addition(one,coantidomain(X1)),coantidomain(antidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[151,22382,theory(equality)]) ).
cnf(22539,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = multiplication(addition(one,coantidomain(X1)),coantidomain(antidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[22492,30,theory(equality)]) ).
cnf(22540,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = coantidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[22539,403,theory(equality)]),54,theory(equality)]) ).
cnf(22574,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(coantidomain(X1))))) = addition(one,coantidomain(antidomain(coantidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[98,22540,theory(equality)]) ).
cnf(22619,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[22574,403,theory(equality)]) ).
cnf(22674,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(antidomain(coantidomain(X1)))) = one,
inference(spm,[status(thm)],[22619,2985,theory(equality)]) ).
cnf(22771,plain,
multiplication(one,coantidomain(coantidomain(antidomain(coantidomain(X1))))) = multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[179,22674,theory(equality)]) ).
cnf(22822,plain,
antidomain(coantidomain(X1)) = multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[22771,20265,theory(equality)]),54,theory(equality)]) ).
cnf(22823,plain,
antidomain(coantidomain(X1)) = multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[22822,20265,theory(equality)]) ).
cnf(26887,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(spm,[status(thm)],[7737,70,theory(equality)]) ).
cnf(26971,plain,
X1 = multiplication(X1,coantidomain(coantidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[26887,44,theory(equality)]) ).
cnf(26972,plain,
X1 = multiplication(X1,antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[26971,20265,theory(equality)]) ).
cnf(27059,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[26972,2985,theory(equality)]) ).
cnf(27124,plain,
antidomain(coantidomain(X1)) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[27059,22823,theory(equality)]) ).
cnf(27294,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[20279,27124,theory(equality)]),2985,theory(equality)]) ).
cnf(27295,negated_conjecture,
$false,
inference(cn,[status(thm)],[27294,theory(equality)]) ).
cnf(27296,negated_conjecture,
$false,
27295,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE092+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax]
% -running prover on /tmp/tmpNSVB-h/sel_KLE092+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE092+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE092+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE092+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
%
%------------------------------------------------------------------------------