TSTP Solution File: KLE120+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE120+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 12:26:35 EST 2010
% Result : Theorem 1.35s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 128 ( 128 unt; 0 def)
% Number of atoms : 128 ( 125 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 169 ( 6 sgn 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',left_annihilation) ).
fof(3,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',multiplicative_left_identity) ).
fof(4,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmp3U2PCl/sel_KLE120+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/tmp3U2PCl/sel_KLE120+1.p_1',left_distributivity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',additive_commutativity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',additive_idempotence) ).
fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',multiplicative_associativity) ).
fof(9,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/tmp/tmp3U2PCl/sel_KLE120+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/tmp3U2PCl/sel_KLE120+1.p_1',codomain2) ).
fof(11,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',codomain1) ).
fof(12,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',additive_associativity) ).
fof(13,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',codomain4) ).
fof(14,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',backward_diamond) ).
fof(15,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',multiplicative_right_identity) ).
fof(16,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',domain3) ).
fof(18,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',right_distributivity) ).
fof(19,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',domain1) ).
fof(20,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',domain4) ).
fof(21,conjecture,
! [X4] : addition(backward_diamond(one,domain(X4)),domain(X4)) = domain(X4),
file('/tmp/tmp3U2PCl/sel_KLE120+1.p_1',goals) ).
fof(22,negated_conjecture,
~ ! [X4] : addition(backward_diamond(one,domain(X4)),domain(X4)) = domain(X4),
inference(assume_negation,[status(cth)],[21]) ).
fof(23,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[1]) ).
cnf(24,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(28,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(30,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(32,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(34,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(36,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(38,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[9]) ).
cnf(40,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,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(42,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[11]) ).
cnf(44,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[12]) ).
cnf(46,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X5] : codomain(X5) = coantidomain(coantidomain(X5)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(48,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[47]) ).
fof(49,plain,
! [X6,X7] : backward_diamond(X6,X7) = codomain(multiplication(codomain(X7),X6)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(50,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[49]) ).
fof(51,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[15]) ).
cnf(52,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[51]) ).
fof(53,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[16]) ).
cnf(54,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[53]) ).
fof(57,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[18]) ).
cnf(58,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[57]) ).
fof(59,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[19]) ).
cnf(60,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[59]) ).
fof(61,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[20]) ).
cnf(62,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,negated_conjecture,
? [X4] : addition(backward_diamond(one,domain(X4)),domain(X4)) != domain(X4),
inference(fof_nnf,[status(thm)],[22]) ).
fof(64,negated_conjecture,
? [X5] : addition(backward_diamond(one,domain(X5)),domain(X5)) != domain(X5),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,negated_conjecture,
addition(backward_diamond(one,domain(esk1_0)),domain(esk1_0)) != domain(esk1_0),
inference(skolemize,[status(esa)],[64]) ).
cnf(66,negated_conjecture,
addition(backward_diamond(one,domain(esk1_0)),domain(esk1_0)) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(67,plain,
coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[50,48,theory(equality)]),48,theory(equality)]),
[unfolding] ).
cnf(68,negated_conjecture,
addition(backward_diamond(one,antidomain(antidomain(esk1_0))),antidomain(antidomain(esk1_0))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[66,62,theory(equality)]),62,theory(equality)]),62,theory(equality)]),
[unfolding] ).
cnf(69,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),one))),antidomain(antidomain(esk1_0))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[68,67,theory(equality)]),
[unfolding] ).
cnf(70,plain,
zero = coantidomain(one),
inference(spm,[status(thm)],[28,44,theory(equality)]) ).
cnf(74,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[30,34,theory(equality)]) ).
cnf(78,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[40,34,theory(equality)]) ).
cnf(79,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[54,34,theory(equality)]) ).
cnf(88,plain,
multiplication(zero,X2) = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(spm,[status(thm)],[38,60,theory(equality)]) ).
cnf(99,plain,
zero = multiplication(antidomain(X1),multiplication(X1,X2)),
inference(rw,[status(thm)],[88,24,theory(equality)]) ).
cnf(103,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[46,36,theory(equality)]) ).
cnf(109,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[34,46,theory(equality)]) ).
cnf(128,plain,
addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(spm,[status(thm)],[58,44,theory(equality)]) ).
cnf(130,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[58,60,theory(equality)]) ).
cnf(148,plain,
multiplication(X1,X2) = multiplication(X1,addition(X2,coantidomain(X1))),
inference(rw,[status(thm)],[128,30,theory(equality)]) ).
cnf(149,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[130,30,theory(equality)]) ).
cnf(158,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[32,28,theory(equality)]) ).
cnf(166,plain,
addition(multiplication(X1,coantidomain(X2)),zero) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(spm,[status(thm)],[32,44,theory(equality)]) ).
cnf(168,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[32,60,theory(equality)]) ).
cnf(187,plain,
multiplication(X1,coantidomain(X2)) = multiplication(addition(X1,X2),coantidomain(X2)),
inference(rw,[status(thm)],[166,30,theory(equality)]) ).
cnf(188,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[168,30,theory(equality)]) ).
cnf(215,negated_conjecture,
addition(antidomain(antidomain(esk1_0)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(esk1_0))))))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[69,52,theory(equality)]),34,theory(equality)]) ).
cnf(235,plain,
addition(zero,coantidomain(zero)) = one,
inference(spm,[status(thm)],[78,70,theory(equality)]) ).
cnf(251,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[235,74,theory(equality)]) ).
cnf(389,plain,
addition(coantidomain(X1),one) = one,
inference(spm,[status(thm)],[103,78,theory(equality)]) ).
cnf(390,plain,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[103,79,theory(equality)]) ).
cnf(404,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[389,34,theory(equality)]) ).
cnf(405,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[390,34,theory(equality)]) ).
cnf(567,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[148,34,theory(equality)]) ).
cnf(629,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[188,34,theory(equality)]) ).
cnf(892,plain,
multiplication(X1,one) = multiplication(X1,coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[567,78,theory(equality)]) ).
cnf(915,plain,
X1 = multiplication(X1,coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[892,52,theory(equality)]) ).
cnf(992,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[629,79,theory(equality)]) ).
cnf(1013,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[992,28,theory(equality)]) ).
cnf(1034,plain,
addition(X1,one) = addition(antidomain(antidomain(X2)),addition(X1,antidomain(X2))),
inference(spm,[status(thm)],[109,79,theory(equality)]) ).
cnf(1130,plain,
addition(X1,one) = addition(antidomain(X2),addition(antidomain(antidomain(X2)),X1)),
inference(rw,[status(thm)],[1034,109,theory(equality)]) ).
cnf(1195,plain,
multiplication(antidomain(antidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[99,1013,theory(equality)]) ).
cnf(1423,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)],[42,1195,theory(equality)]) ).
cnf(1439,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1423,251,theory(equality)]),404,theory(equality)]) ).
cnf(1792,plain,
multiplication(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1),one) = zero,
inference(spm,[status(thm)],[44,1439,theory(equality)]) ).
cnf(1815,plain,
multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1792,38,theory(equality)]),52,theory(equality)]) ).
cnf(1912,plain,
addition(coantidomain(coantidomain(X1)),X1) = multiplication(addition(one,X1),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[158,915,theory(equality)]) ).
cnf(1955,plain,
addition(X1,coantidomain(coantidomain(X1))) = multiplication(addition(one,X1),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[1912,34,theory(equality)]) ).
cnf(2411,plain,
multiplication(antidomain(antidomain(antidomain(X1))),one) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(spm,[status(thm)],[149,79,theory(equality)]) ).
cnf(2455,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(rw,[status(thm)],[2411,52,theory(equality)]) ).
cnf(2456,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[2455,1013,theory(equality)]) ).
cnf(2517,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[1815,2456,theory(equality)]) ).
cnf(2623,plain,
addition(zero,multiplication(X2,X1)) = multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1),
inference(spm,[status(thm)],[32,2517,theory(equality)]) ).
cnf(2645,plain,
multiplication(X2,X1) = multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1),
inference(rw,[status(thm)],[2623,74,theory(equality)]) ).
cnf(3205,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(X1)))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[187,78,theory(equality)]) ).
cnf(3254,plain,
coantidomain(coantidomain(coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[3205,28,theory(equality)]) ).
cnf(3255,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[3254,915,theory(equality)]) ).
cnf(3330,negated_conjecture,
addition(antidomain(antidomain(esk1_0)),coantidomain(coantidomain(antidomain(antidomain(esk1_0))))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[215,3255,theory(equality)]) ).
cnf(40434,plain,
multiplication(one,coantidomain(coantidomain(antidomain(X1)))) = addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))),
inference(spm,[status(thm)],[1955,405,theory(equality)]) ).
cnf(40531,plain,
coantidomain(coantidomain(antidomain(X1))) = addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))),
inference(rw,[status(thm)],[40434,28,theory(equality)]) ).
cnf(41339,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1))))) = addition(coantidomain(coantidomain(antidomain(antidomain(X1)))),one),
inference(spm,[status(thm)],[1130,40531,theory(equality)]) ).
cnf(41362,negated_conjecture,
coantidomain(coantidomain(antidomain(antidomain(esk1_0)))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[3330,40531,theory(equality)]) ).
cnf(41418,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[41339,34,theory(equality)]),404,theory(equality)]) ).
cnf(41452,plain,
addition(antidomain(antidomain(X1)),coantidomain(coantidomain(antidomain(X1)))) = one,
inference(spm,[status(thm)],[41418,2456,theory(equality)]) ).
cnf(41898,plain,
multiplication(coantidomain(antidomain(X1)),one) = multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))),
inference(spm,[status(thm)],[148,41452,theory(equality)]) ).
cnf(41973,plain,
coantidomain(antidomain(X1)) = multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))),
inference(rw,[status(thm)],[41898,52,theory(equality)]) ).
cnf(44953,plain,
multiplication(one,X1) = multiplication(coantidomain(coantidomain(coantidomain(antidomain(X1)))),X1),
inference(spm,[status(thm)],[2645,78,theory(equality)]) ).
cnf(45070,plain,
X1 = multiplication(coantidomain(coantidomain(coantidomain(antidomain(X1)))),X1),
inference(rw,[status(thm)],[44953,28,theory(equality)]) ).
cnf(45071,plain,
X1 = multiplication(coantidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[45070,3255,theory(equality)]) ).
cnf(45180,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[45071,2456,theory(equality)]) ).
cnf(45273,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[45180,41973,theory(equality)]) ).
cnf(45535,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[41362,45273,theory(equality)]),2456,theory(equality)]),45273,theory(equality)]) ).
cnf(45536,negated_conjecture,
$false,
inference(cn,[status(thm)],[45535,theory(equality)]) ).
cnf(45537,negated_conjecture,
$false,
45536,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE120+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax, KLE001+6.ax]
% -running prover on /tmp/tmp3U2PCl/sel_KLE120+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE120+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE120+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE120+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
%
%------------------------------------------------------------------------------