TSTP Solution File: REL011+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL011+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 01:03:47 EST 2010
% Result : Theorem 0.81s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : None (Could not find formula named 3))
% Syntax : Number of formulae : 176
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',modular_law_2) ).
fof(2,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',modular_law_1) ).
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',converse_idempotence) ).
fof(5,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',composition_distributivity) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',maddux1_join_commutativity) ).
fof(8,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',composition_associativity) ).
fof(10,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',def_zero) ).
fof(11,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',converse_cancellativity) ).
fof(12,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',maddux4_definiton_of_meet) ).
fof(13,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',maddux2_join_associativity) ).
fof(14,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(15,conjecture,
! [X1,X2,X3] :
( meet(X1,composition(converse(X2),X3)) = zero
=> meet(composition(X2,X1),X3) = zero ),
file('/tmp/tmpho2Ehu/sel_REL011+2.p_1',goals) ).
fof(16,negated_conjecture,
~ ! [X1,X2,X3] :
( meet(X1,composition(converse(X2),X3)) = zero
=> meet(composition(X2,X1),X3) = zero ),
inference(assume_negation,[status(cth)],[15]) ).
fof(17,plain,
! [X4,X5,X6] : join(meet(composition(X4,X5),X6),meet(composition(meet(X4,composition(X6,converse(X5))),X5),X6)) = meet(composition(meet(X4,composition(X6,converse(X5))),X5),X6),
inference(variable_rename,[status(thm)],[1]) ).
cnf(18,plain,
join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5,X6] : join(meet(composition(X4,X5),X6),meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6)) = meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6),
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(22,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(24,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(26,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(28,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(30,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(32,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[31]) ).
fof(35,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(36,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[11]) ).
cnf(38,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[12]) ).
cnf(40,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[13]) ).
cnf(42,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[14]) ).
cnf(44,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,negated_conjecture,
? [X1,X2,X3] :
( meet(X1,composition(converse(X2),X3)) = zero
& meet(composition(X2,X1),X3) != zero ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(46,negated_conjecture,
? [X4,X5,X6] :
( meet(X4,composition(converse(X5),X6)) = zero
& meet(composition(X5,X4),X6) != zero ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,negated_conjecture,
( meet(esk1_0,composition(converse(esk2_0),esk3_0)) = zero
& meet(composition(esk2_0,esk1_0),esk3_0) != zero ),
inference(skolemize,[status(esa)],[46]) ).
cnf(48,negated_conjecture,
meet(composition(esk2_0,esk1_0),esk3_0) != zero,
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,negated_conjecture,
meet(esk1_0,composition(converse(esk2_0),esk3_0)) = zero,
inference(split_conjunct,[status(thm)],[47]) ).
cnf(50,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(rw,[status(thm)],[36,40,theory(equality)]),
[unfolding] ).
cnf(51,negated_conjecture,
complement(join(complement(esk1_0),complement(composition(converse(esk2_0),esk3_0)))) = zero,
inference(rw,[status(thm)],[49,40,theory(equality)]),
[unfolding] ).
cnf(52,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3)))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[20,40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),
[unfolding] ).
cnf(53,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3)))) = complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[18,40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),
[unfolding] ).
cnf(55,negated_conjecture,
complement(join(complement(composition(esk2_0,esk1_0)),complement(esk3_0))) != zero,
inference(rw,[status(thm)],[48,40,theory(equality)]),
[unfolding] ).
cnf(56,plain,
complement(join(zero,complement(zero))) = zero,
inference(spm,[status(thm)],[50,50,theory(equality)]) ).
cnf(58,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[22,24,theory(equality)]) ).
cnf(60,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[28,24,theory(equality)]) ).
cnf(61,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[28,24,theory(equality)]) ).
cnf(70,negated_conjecture,
complement(join(complement(esk3_0),complement(composition(esk2_0,esk1_0)))) != zero,
inference(rw,[status(thm)],[55,30,theory(equality)]) ).
cnf(71,plain,
join(converse(join(X1,X2)),X3) = join(converse(X1),join(converse(X2),X3)),
inference(spm,[status(thm)],[42,28,theory(equality)]) ).
cnf(73,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[30,42,theory(equality)]) ).
cnf(75,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[42,30,theory(equality)]) ).
cnf(79,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[75,42,theory(equality)]) ).
cnf(90,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[38,30,theory(equality)]) ).
cnf(98,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[44,30,theory(equality)]) ).
cnf(100,plain,
join(zero,complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(spm,[status(thm)],[98,50,theory(equality)]) ).
cnf(102,plain,
join(complement(join(complement(X1),complement(X1))),zero) = X1,
inference(spm,[status(thm)],[98,50,theory(equality)]) ).
cnf(106,negated_conjecture,
join(complement(join(complement(esk1_0),composition(converse(esk2_0),esk3_0))),zero) = esk1_0,
inference(spm,[status(thm)],[98,51,theory(equality)]) ).
cnf(110,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[98,98,theory(equality)]) ).
cnf(111,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[98,30,theory(equality)]) ).
cnf(112,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[98,30,theory(equality)]) ).
cnf(116,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(rw,[status(thm)],[102,30,theory(equality)]) ).
cnf(118,negated_conjecture,
join(zero,complement(join(complement(esk1_0),composition(converse(esk2_0),esk3_0)))) = esk1_0,
inference(rw,[status(thm)],[106,30,theory(equality)]) ).
cnf(119,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[110,30,theory(equality)]) ).
cnf(120,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[52,30,theory(equality)]) ).
cnf(121,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),
inference(rw,[status(thm)],[120,30,theory(equality)]) ).
cnf(134,plain,
join(complement(complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))),complement(join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))))))) = join(complement(composition(X1,X2)),complement(X3)),
inference(spm,[status(thm)],[98,121,theory(equality)]) ).
cnf(149,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3))),
inference(rw,[status(thm)],[53,30,theory(equality)]) ).
cnf(150,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)))),
inference(rw,[status(thm)],[149,30,theory(equality)]) ).
cnf(206,plain,
join(zero,composition(converse(X1),complement(composition(X1,join(zero,complement(zero)))))) = zero,
inference(spm,[status(thm)],[90,56,theory(equality)]) ).
cnf(207,plain,
join(complement(join(zero,X1)),complement(join(zero,complement(X1)))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[98,56,theory(equality)]) ).
cnf(313,plain,
converse(join(X1,join(X2,converse(X3)))) = join(converse(join(X1,X2)),X3),
inference(spm,[status(thm)],[61,42,theory(equality)]) ).
cnf(345,plain,
join(zero,complement(join(zero,zero))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[116,50,theory(equality)]) ).
cnf(348,plain,
join(zero,complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[116,56,theory(equality)]) ).
cnf(377,plain,
join(zero,complement(join(zero,complement(complement(zero))))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[100,56,theory(equality)]) ).
cnf(400,plain,
converse(join(X3,join(converse(X1),X2))) = join(X1,converse(join(X2,X3))),
inference(spm,[status(thm)],[60,73,theory(equality)]) ).
cnf(880,plain,
join(zero,complement(zero)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[345,348,theory(equality)]) ).
cnf(1082,plain,
join(complement(join(zero,join(zero,complement(zero)))),complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[207,56,theory(equality)]) ).
cnf(1119,plain,
join(complement(join(zero,zero)),complement(join(zero,join(zero,complement(zero))))) = join(zero,complement(zero)),
inference(rw,[status(thm)],[1082,30,theory(equality)]) ).
cnf(1390,plain,
join(complement(join(complement(join(zero,zero)),join(zero,join(zero,complement(zero))))),complement(join(zero,complement(zero)))) = join(zero,zero),
inference(spm,[status(thm)],[98,1119,theory(equality)]) ).
cnf(1404,plain,
join(zero,complement(join(zero,join(zero,join(complement(zero),complement(zero)))))) = join(zero,zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1390,79,theory(equality)]),73,theory(equality)]),30,theory(equality)]),348,theory(equality)]),79,theory(equality)]),56,theory(equality)]),30,theory(equality)]) ).
cnf(2344,plain,
join(complement(X1),complement(join(complement(X2),join(complement(X1),complement(join(complement(X1),X2)))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[119,73,theory(equality)]),30,theory(equality)]) ).
cnf(2643,plain,
join(complement(join(complement(complement(X1)),X1)),complement(join(zero,complement(zero)))) = complement(X1),
inference(spm,[status(thm)],[112,880,theory(equality)]) ).
cnf(2704,plain,
join(zero,complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2643,30,theory(equality)]),56,theory(equality)]),30,theory(equality)]) ).
cnf(2754,plain,
complement(zero) = join(zero,complement(zero)),
inference(rw,[status(thm)],[377,2704,theory(equality)]) ).
cnf(2755,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[100,2704,theory(equality)]) ).
cnf(2788,plain,
join(zero,complement(join(X1,X1))) = complement(X1),
inference(rw,[status(thm)],[2704,2755,theory(equality)]) ).
cnf(2805,plain,
join(complement(X1),X1) = join(zero,complement(zero)),
inference(rw,[status(thm)],[880,2755,theory(equality)]) ).
cnf(2806,plain,
join(X1,complement(X1)) = join(zero,complement(zero)),
inference(rw,[status(thm)],[2805,30,theory(equality)]) ).
cnf(2837,plain,
join(zero,composition(converse(X1),complement(composition(X1,complement(zero))))) = zero,
inference(rw,[status(thm)],[206,2754,theory(equality)]) ).
cnf(2893,plain,
join(X1,complement(X1)) = complement(zero),
inference(rw,[status(thm)],[2806,2754,theory(equality)]) ).
cnf(2894,plain,
join(complement(zero),X2) = join(X1,join(complement(X1),X2)),
inference(spm,[status(thm)],[42,2893,theory(equality)]) ).
cnf(2901,plain,
converse(complement(zero)) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[60,2893,theory(equality)]) ).
cnf(3155,plain,
join(zero,complement(join(complement(zero),complement(zero)))) = join(zero,zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1404,2894,theory(equality)]),2894,theory(equality)]) ).
cnf(3156,plain,
zero = join(zero,zero),
inference(rw,[status(thm)],[3155,116,theory(equality)]) ).
cnf(3204,plain,
join(zero,X1) = join(zero,join(zero,X1)),
inference(spm,[status(thm)],[42,3156,theory(equality)]) ).
cnf(3227,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[3204,2788,theory(equality)]) ).
cnf(3289,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[3227,2755,theory(equality)]) ).
cnf(3298,plain,
complement(join(X1,X1)) = complement(X1),
inference(rw,[status(thm)],[2788,3227,theory(equality)]) ).
cnf(3299,negated_conjecture,
complement(join(complement(esk1_0),composition(converse(esk2_0),esk3_0))) = esk1_0,
inference(rw,[status(thm)],[118,3227,theory(equality)]) ).
cnf(3306,plain,
converse(converse(X1)) = join(converse(zero),X1),
inference(spm,[status(thm)],[61,3289,theory(equality)]) ).
cnf(3314,plain,
X1 = join(X1,zero),
inference(spm,[status(thm)],[30,3289,theory(equality)]) ).
cnf(3338,plain,
X1 = join(converse(zero),X1),
inference(rw,[status(thm)],[3306,24,theory(equality)]) ).
cnf(3406,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[98,3298,theory(equality)]) ).
cnf(3454,plain,
X1 = join(X1,X1),
inference(rw,[status(thm)],[3406,98,theory(equality)]) ).
cnf(3496,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[42,3454,theory(equality)]) ).
cnf(3525,plain,
join(X1,complement(X1)) = join(complement(zero),complement(X1)),
inference(spm,[status(thm)],[2894,3454,theory(equality)]) ).
cnf(3583,plain,
complement(zero) = join(complement(zero),complement(X1)),
inference(rw,[status(thm)],[3525,2893,theory(equality)]) ).
cnf(3606,plain,
zero = converse(zero),
inference(spm,[status(thm)],[3314,3338,theory(equality)]) ).
cnf(3716,plain,
join(complement(zero),complement(join(complement(X1),complement(zero)))) = join(complement(zero),X1),
inference(spm,[status(thm)],[2344,3583,theory(equality)]) ).
cnf(3752,plain,
complement(zero) = join(complement(zero),X1),
inference(rw,[status(thm)],[3716,3583,theory(equality)]) ).
cnf(3779,negated_conjecture,
join(complement(esk1_0),complement(join(complement(composition(converse(esk2_0),esk3_0)),join(complement(esk1_0),esk1_0)))) = join(complement(esk1_0),composition(converse(esk2_0),esk3_0)),
inference(spm,[status(thm)],[2344,3299,theory(equality)]) ).
cnf(3799,negated_conjecture,
complement(esk1_0) = join(complement(esk1_0),composition(converse(esk2_0),esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3779,30,theory(equality)]),2893,theory(equality)]),30,theory(equality)]),3583,theory(equality)]),2755,theory(equality)]),30,theory(equality)]),3289,theory(equality)]) ).
cnf(3808,plain,
composition(converse(X1),complement(composition(X1,complement(zero)))) = zero,
inference(rw,[status(thm)],[2837,3289,theory(equality)]) ).
cnf(3904,plain,
complement(zero) = converse(complement(zero)),
inference(spm,[status(thm)],[2901,3752,theory(equality)]) ).
cnf(3906,plain,
complement(zero) = join(X1,complement(zero)),
inference(spm,[status(thm)],[30,3752,theory(equality)]) ).
cnf(3995,plain,
composition(complement(zero),complement(composition(complement(zero),complement(zero)))) = zero,
inference(spm,[status(thm)],[3808,3904,theory(equality)]) ).
cnf(3996,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(rw,[status(thm)],[2901,3904,theory(equality)]) ).
cnf(4105,plain,
converse(join(X1,complement(zero))) = join(converse(join(X1,X2)),complement(converse(X2))),
inference(spm,[status(thm)],[313,3996,theory(equality)]) ).
cnf(4111,plain,
converse(join(X1,complement(zero))) = join(X2,converse(join(converse(complement(converse(converse(X2)))),X1))),
inference(spm,[status(thm)],[400,3996,theory(equality)]) ).
cnf(4137,plain,
complement(zero) = join(converse(join(X1,X2)),complement(converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4105,3906,theory(equality)]),3904,theory(equality)]) ).
cnf(4138,plain,
complement(zero) = join(complement(converse(X2)),converse(join(X1,X2))),
inference(rw,[status(thm)],[4137,30,theory(equality)]) ).
cnf(4145,plain,
complement(zero) = join(X2,converse(join(converse(complement(converse(converse(X2)))),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4111,3906,theory(equality)]),3904,theory(equality)]) ).
cnf(4146,plain,
complement(zero) = join(X2,join(complement(X2),converse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4145,24,theory(equality)]),60,theory(equality)]) ).
cnf(4948,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[3496,98,theory(equality)]) ).
cnf(4978,plain,
join(complement(join(X1,complement(X2))),X2) = X2,
inference(spm,[status(thm)],[3496,111,theory(equality)]) ).
cnf(5022,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[4948,30,theory(equality)]) ).
cnf(5059,plain,
join(X2,complement(join(X1,complement(X2)))) = X2,
inference(rw,[status(thm)],[4978,30,theory(equality)]) ).
cnf(5373,plain,
join(zero,composition(X1,complement(composition(complement(zero),complement(zero))))) = composition(join(complement(zero),X1),complement(composition(complement(zero),complement(zero)))),
inference(spm,[status(thm)],[26,3995,theory(equality)]) ).
cnf(5397,plain,
composition(X1,complement(composition(complement(zero),complement(zero)))) = composition(join(complement(zero),X1),complement(composition(complement(zero),complement(zero)))),
inference(rw,[status(thm)],[5373,3289,theory(equality)]) ).
cnf(5398,plain,
composition(X1,complement(composition(complement(zero),complement(zero)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5397,3752,theory(equality)]),3995,theory(equality)]) ).
cnf(5441,plain,
zero = composition(X1,composition(X2,complement(composition(complement(zero),complement(zero))))),
inference(spm,[status(thm)],[32,5398,theory(equality)]) ).
cnf(5478,plain,
zero = composition(X1,zero),
inference(rw,[status(thm)],[5441,5398,theory(equality)]) ).
cnf(5550,plain,
converse(zero) = composition(converse(zero),X1),
inference(spm,[status(thm)],[58,5478,theory(equality)]) ).
cnf(5595,plain,
zero = composition(converse(zero),X1),
inference(rw,[status(thm)],[5550,3606,theory(equality)]) ).
cnf(5596,plain,
zero = composition(zero,X1),
inference(rw,[status(thm)],[5595,3606,theory(equality)]) ).
cnf(6260,plain,
join(complement(join(join(X1,complement(complement(X2))),complement(X2))),complement(complement(X2))) = X2,
inference(spm,[status(thm)],[111,5059,theory(equality)]) ).
cnf(6312,plain,
complement(complement(X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6260,42,theory(equality)]),30,theory(equality)]),2893,theory(equality)]),3906,theory(equality)]),2755,theory(equality)]),3289,theory(equality)]) ).
cnf(6371,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[5022,6312,theory(equality)]) ).
cnf(6372,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[5059,6312,theory(equality)]) ).
cnf(6682,plain,
join(complement(X3),join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(join(complement(X3),join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))))) = join(complement(composition(X1,X2)),complement(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[134,2755,theory(equality)]),2755,theory(equality)]),79,theory(equality)]),42,theory(equality)]) ).
cnf(7062,plain,
join(X1,join(converse(X2),complement(X1))) = complement(zero),
inference(spm,[status(thm)],[4146,30,theory(equality)]) ).
cnf(7997,plain,
join(X1,join(X2,complement(X1))) = complement(zero),
inference(spm,[status(thm)],[7062,24,theory(equality)]) ).
cnf(8110,plain,
complement(zero) = join(converse(join(X1,X2)),complement(converse(X1))),
inference(spm,[status(thm)],[71,7997,theory(equality)]) ).
cnf(8172,plain,
complement(zero) = join(complement(converse(X1)),converse(join(X1,X2))),
inference(rw,[status(thm)],[8110,30,theory(equality)]) ).
cnf(10054,negated_conjecture,
join(complement(converse(composition(converse(esk2_0),esk3_0))),converse(complement(esk1_0))) = complement(zero),
inference(spm,[status(thm)],[4138,3799,theory(equality)]) ).
cnf(10147,negated_conjecture,
join(converse(complement(esk1_0)),complement(composition(converse(esk3_0),esk2_0))) = complement(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[10054,58,theory(equality)]),30,theory(equality)]) ).
cnf(10342,negated_conjecture,
converse(complement(zero)) = join(complement(esk1_0),converse(complement(composition(converse(esk3_0),esk2_0)))),
inference(spm,[status(thm)],[60,10147,theory(equality)]) ).
cnf(10361,negated_conjecture,
complement(zero) = join(complement(esk1_0),converse(complement(composition(converse(esk3_0),esk2_0)))),
inference(rw,[status(thm)],[10342,3904,theory(equality)]) ).
cnf(10384,negated_conjecture,
join(complement(complement(zero)),complement(join(complement(esk1_0),complement(converse(complement(composition(converse(esk3_0),esk2_0))))))) = esk1_0,
inference(spm,[status(thm)],[98,10361,theory(equality)]) ).
cnf(10406,negated_conjecture,
complement(join(complement(esk1_0),complement(converse(complement(composition(converse(esk3_0),esk2_0)))))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[10384,2755,theory(equality)]),3289,theory(equality)]) ).
cnf(10451,negated_conjecture,
join(esk1_0,complement(join(complement(X1),join(esk1_0,complement(join(esk1_0,X1)))))) = join(esk1_0,X1),
inference(spm,[status(thm)],[2344,10406,theory(equality)]) ).
cnf(10453,negated_conjecture,
join(complement(esk1_0),complement(join(complement(complement(converse(complement(composition(converse(esk3_0),esk2_0))))),join(complement(esk1_0),esk1_0)))) = join(complement(esk1_0),complement(converse(complement(composition(converse(esk3_0),esk2_0))))),
inference(spm,[status(thm)],[2344,10406,theory(equality)]) ).
cnf(10504,negated_conjecture,
join(esk1_0,complement(join(esk1_0,complement(X1)))) = join(esk1_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[10451,79,theory(equality)]),6372,theory(equality)]) ).
cnf(10505,negated_conjecture,
complement(esk1_0) = join(complement(esk1_0),complement(converse(complement(composition(converse(esk3_0),esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[10453,6312,theory(equality)]),30,theory(equality)]),2893,theory(equality)]),3906,theory(equality)]),2755,theory(equality)]),30,theory(equality)]),3289,theory(equality)]) ).
cnf(10732,negated_conjecture,
join(complement(join(esk1_0,X1)),complement(join(complement(join(esk1_0,complement(X1))),complement(esk1_0)))) = join(esk1_0,complement(X1)),
inference(spm,[status(thm)],[111,10504,theory(equality)]) ).
cnf(10757,negated_conjecture,
join(esk1_0,complement(join(esk1_0,X1))) = join(esk1_0,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[10732,30,theory(equality)]),6371,theory(equality)]),6312,theory(equality)]),30,theory(equality)]) ).
cnf(14044,negated_conjecture,
join(complement(complement(esk1_0)),complement(join(complement(converse(complement(composition(converse(esk3_0),esk2_0)))),complement(complement(esk1_0))))) = converse(complement(composition(converse(esk3_0),esk2_0))),
inference(spm,[status(thm)],[111,10505,theory(equality)]) ).
cnf(14076,negated_conjecture,
join(esk1_0,converse(complement(composition(converse(esk3_0),esk2_0)))) = converse(complement(composition(converse(esk3_0),esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[14044,6312,theory(equality)]),6312,theory(equality)]),30,theory(equality)]),10757,theory(equality)]),6312,theory(equality)]) ).
cnf(17382,negated_conjecture,
join(complement(converse(esk1_0)),converse(converse(complement(composition(converse(esk3_0),esk2_0))))) = complement(zero),
inference(spm,[status(thm)],[8172,14076,theory(equality)]) ).
cnf(17402,negated_conjecture,
join(complement(converse(esk1_0)),complement(composition(converse(esk3_0),esk2_0))) = complement(zero),
inference(rw,[status(thm)],[17382,24,theory(equality)]) ).
cnf(17695,negated_conjecture,
join(complement(esk2_0),join(complement(composition(esk3_0,complement(complement(zero)))),complement(join(complement(esk2_0),join(complement(join(complement(composition(esk3_0,converse(esk1_0))),complement(esk2_0))),complement(composition(esk3_0,complement(complement(zero))))))))) = join(complement(composition(esk3_0,converse(esk1_0))),complement(esk2_0)),
inference(spm,[status(thm)],[6682,17402,theory(equality)]) ).
cnf(17753,negated_conjecture,
complement(zero) = join(complement(composition(esk3_0,converse(esk1_0))),complement(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[17695,2755,theory(equality)]),5478,theory(equality)]),30,theory(equality)]),2755,theory(equality)]),5478,theory(equality)]),3906,theory(equality)]),3906,theory(equality)]),2755,theory(equality)]),30,theory(equality)]),2893,theory(equality)]),3906,theory(equality)]) ).
cnf(17754,negated_conjecture,
complement(zero) = join(complement(esk2_0),complement(composition(esk3_0,converse(esk1_0)))),
inference(rw,[status(thm)],[17753,30,theory(equality)]) ).
cnf(17806,negated_conjecture,
join(complement(join(complement(composition(esk2_0,esk1_0)),complement(esk3_0))),complement(join(complement(esk3_0),complement(composition(complement(complement(zero)),esk1_0))))) = complement(join(complement(esk3_0),complement(composition(complement(complement(zero)),esk1_0)))),
inference(spm,[status(thm)],[150,17754,theory(equality)]) ).
cnf(17851,negated_conjecture,
complement(join(complement(esk3_0),complement(composition(esk2_0,esk1_0)))) = complement(join(complement(esk3_0),complement(composition(complement(complement(zero)),esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[17806,30,theory(equality)]),2755,theory(equality)]),5596,theory(equality)]),3906,theory(equality)]),2755,theory(equality)]),3314,theory(equality)]) ).
cnf(17852,negated_conjecture,
complement(join(complement(esk3_0),complement(composition(esk2_0,esk1_0)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[17851,2755,theory(equality)]),5596,theory(equality)]),3906,theory(equality)]),2755,theory(equality)]) ).
cnf(17853,negated_conjecture,
$false,
inference(sr,[status(thm)],[17852,70,theory(equality)]) ).
cnf(17854,negated_conjecture,
$false,
17853,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL011+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpho2Ehu/sel_REL011+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL011+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL011+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL011+2.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
%
%------------------------------------------------------------------------------