TSTP Solution File: REL047+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL047+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:44:32 EDT 2023
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL047+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 19:41:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.56
% 0.19/0.56 % SZS status Theorem
% 0.19/0.56
% 0.19/0.59 % SZS output start Proof
% 0.19/0.59 Axiom 1 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.19/0.59 Axiom 2 (goals): join(x0, x2) = x2.
% 0.19/0.59 Axiom 3 (goals_1): join(x0, x1) = x1.
% 0.19/0.59 Axiom 4 (composition_identity): composition(X, one) = X.
% 0.19/0.59 Axiom 5 (converse_idempotence): converse(converse(X)) = X.
% 0.19/0.59 Axiom 6 (def_top): top = join(X, complement(X)).
% 0.19/0.59 Axiom 7 (def_zero): zero = meet(X, complement(X)).
% 0.19/0.59 Axiom 8 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.19/0.59 Axiom 9 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.19/0.59 Axiom 10 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.19/0.59 Axiom 11 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.19/0.59 Axiom 12 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.19/0.59 Axiom 13 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.19/0.59
% 0.19/0.59 Lemma 14: complement(top) = zero.
% 0.19/0.59 Proof:
% 0.19/0.59 complement(top)
% 0.19/0.59 = { by axiom 6 (def_top) }
% 0.19/0.59 complement(join(complement(X), complement(complement(X))))
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.59 meet(X, complement(X))
% 0.19/0.59 = { by axiom 7 (def_zero) R->L }
% 0.19/0.59 zero
% 0.19/0.59
% 0.19/0.59 Lemma 15: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.59 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.19/0.59 = { by axiom 13 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 16: join(zero, meet(X, X)) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 join(zero, meet(X, X))
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.59 join(zero, complement(join(complement(X), complement(X))))
% 0.19/0.59 = { by axiom 7 (def_zero) }
% 0.19/0.59 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.19/0.59 = { by lemma 15 }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 17: composition(converse(one), X) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 composition(converse(one), X)
% 0.19/0.59 = { by axiom 5 (converse_idempotence) R->L }
% 0.19/0.59 composition(converse(one), converse(converse(X)))
% 0.19/0.59 = { by axiom 9 (converse_multiplicativity) R->L }
% 0.19/0.59 converse(composition(converse(X), one))
% 0.19/0.59 = { by axiom 4 (composition_identity) }
% 0.19/0.59 converse(converse(X))
% 0.19/0.59 = { by axiom 5 (converse_idempotence) }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 18: join(complement(X), complement(X)) = complement(X).
% 0.19/0.59 Proof:
% 0.19/0.59 join(complement(X), complement(X))
% 0.19/0.59 = { by lemma 17 R->L }
% 0.19/0.59 join(complement(X), composition(converse(one), complement(X)))
% 0.19/0.59 = { by lemma 17 R->L }
% 0.19/0.59 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.19/0.59 = { by axiom 4 (composition_identity) R->L }
% 0.19/0.59 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.19/0.59 = { by axiom 10 (composition_associativity) R->L }
% 0.19/0.59 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.19/0.59 = { by lemma 17 }
% 0.19/0.59 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.19/0.59 = { by axiom 12 (converse_cancellativity) }
% 0.19/0.59 complement(X)
% 0.19/0.59
% 0.19/0.59 Lemma 19: join(zero, complement(complement(X))) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 join(zero, complement(complement(X)))
% 0.19/0.59 = { by axiom 7 (def_zero) }
% 0.19/0.59 join(meet(X, complement(X)), complement(complement(X)))
% 0.19/0.59 = { by lemma 18 R->L }
% 0.19/0.59 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.19/0.59 = { by lemma 15 }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 20: join(X, zero) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 join(X, zero)
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 join(zero, X)
% 0.19/0.59 = { by lemma 16 R->L }
% 0.19/0.59 join(zero, join(zero, meet(X, X)))
% 0.19/0.59 = { by axiom 8 (maddux2_join_associativity) }
% 0.19/0.59 join(join(zero, zero), meet(X, X))
% 0.19/0.59 = { by lemma 14 R->L }
% 0.19/0.59 join(join(zero, complement(top)), meet(X, X))
% 0.19/0.59 = { by lemma 14 R->L }
% 0.19/0.59 join(join(complement(top), complement(top)), meet(X, X))
% 0.19/0.59 = { by lemma 18 }
% 0.19/0.59 join(complement(top), meet(X, X))
% 0.19/0.59 = { by lemma 14 }
% 0.19/0.59 join(zero, meet(X, X))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) }
% 0.19/0.59 join(meet(X, X), zero)
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.59 join(complement(join(complement(X), complement(X))), zero)
% 0.19/0.59 = { by lemma 18 }
% 0.19/0.59 join(complement(complement(X)), zero)
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) }
% 0.19/0.59 join(zero, complement(complement(X)))
% 0.19/0.59 = { by lemma 19 }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 21: join(zero, X) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 join(zero, X)
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 join(X, zero)
% 0.19/0.59 = { by lemma 20 }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 22: join(X, join(Y, complement(X))) = join(Y, top).
% 0.19/0.59 Proof:
% 0.19/0.59 join(X, join(Y, complement(X)))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 join(X, join(complement(X), Y))
% 0.19/0.59 = { by axiom 8 (maddux2_join_associativity) }
% 0.19/0.59 join(join(X, complement(X)), Y)
% 0.19/0.59 = { by axiom 6 (def_top) R->L }
% 0.19/0.59 join(top, Y)
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) }
% 0.19/0.59 join(Y, top)
% 0.19/0.59
% 0.19/0.59 Lemma 23: join(x2, join(x0, X)) = join(X, x2).
% 0.19/0.59 Proof:
% 0.19/0.59 join(x2, join(x0, X))
% 0.19/0.59 = { by axiom 8 (maddux2_join_associativity) }
% 0.19/0.59 join(join(x2, x0), X)
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 join(join(x0, x2), X)
% 0.19/0.59 = { by axiom 2 (goals) }
% 0.19/0.59 join(x2, X)
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) }
% 0.19/0.59 join(X, x2)
% 0.19/0.59
% 0.19/0.59 Lemma 24: join(x0, top) = top.
% 0.19/0.59 Proof:
% 0.19/0.59 join(x0, top)
% 0.19/0.59 = { by lemma 22 R->L }
% 0.19/0.59 join(x2, join(x0, complement(x2)))
% 0.19/0.59 = { by lemma 23 }
% 0.19/0.59 join(complement(x2), x2)
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) }
% 0.19/0.59 join(x2, complement(x2))
% 0.19/0.59 = { by axiom 6 (def_top) R->L }
% 0.19/0.59 top
% 0.19/0.59
% 0.19/0.59 Lemma 25: complement(complement(X)) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 complement(complement(X))
% 0.19/0.59 = { by lemma 21 R->L }
% 0.19/0.59 join(zero, complement(complement(X)))
% 0.19/0.59 = { by lemma 19 }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 26: meet(Y, X) = meet(X, Y).
% 0.19/0.59 Proof:
% 0.19/0.59 meet(Y, X)
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.59 complement(join(complement(Y), complement(X)))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 complement(join(complement(X), complement(Y)))
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.59 meet(X, Y)
% 0.19/0.59
% 0.19/0.59 Lemma 27: complement(join(zero, complement(X))) = meet(X, top).
% 0.19/0.59 Proof:
% 0.19/0.59 complement(join(zero, complement(X)))
% 0.19/0.59 = { by lemma 14 R->L }
% 0.19/0.59 complement(join(complement(top), complement(X)))
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.59 meet(top, X)
% 0.19/0.59 = { by lemma 26 R->L }
% 0.19/0.59 meet(X, top)
% 0.19/0.59
% 0.19/0.59 Lemma 28: meet(X, top) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 meet(X, top)
% 0.19/0.59 = { by lemma 27 R->L }
% 0.19/0.59 complement(join(zero, complement(X)))
% 0.19/0.59 = { by lemma 21 }
% 0.19/0.59 complement(complement(X))
% 0.19/0.59 = { by lemma 25 }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 29: join(top, complement(X)) = top.
% 0.19/0.59 Proof:
% 0.19/0.59 join(top, complement(X))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 join(complement(X), top)
% 0.19/0.59 = { by lemma 22 R->L }
% 0.19/0.59 join(X, join(complement(X), complement(X)))
% 0.19/0.59 = { by lemma 18 }
% 0.19/0.59 join(X, complement(X))
% 0.19/0.59 = { by axiom 6 (def_top) R->L }
% 0.19/0.59 top
% 0.19/0.59
% 0.19/0.59 Lemma 30: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 0.19/0.59 Proof:
% 0.19/0.59 meet(X, join(complement(Y), complement(Z)))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 meet(X, join(complement(Z), complement(Y)))
% 0.19/0.59 = { by lemma 26 }
% 0.19/0.59 meet(join(complement(Z), complement(Y)), X)
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.59 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 0.19/0.59 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.59 complement(join(meet(Z, Y), complement(X)))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) }
% 0.19/0.59 complement(join(complement(X), meet(Z, Y)))
% 0.19/0.59 = { by lemma 26 R->L }
% 0.19/0.59 complement(join(complement(X), meet(Y, Z)))
% 0.19/0.59
% 0.19/0.59 Lemma 31: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 0.19/0.59 Proof:
% 0.19/0.59 complement(join(X, complement(Y)))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 complement(join(complement(Y), X))
% 0.19/0.59 = { by lemma 28 R->L }
% 0.19/0.59 complement(join(complement(Y), meet(X, top)))
% 0.19/0.59 = { by lemma 26 R->L }
% 0.19/0.59 complement(join(complement(Y), meet(top, X)))
% 0.19/0.59 = { by lemma 30 R->L }
% 0.19/0.59 meet(Y, join(complement(top), complement(X)))
% 0.19/0.59 = { by lemma 14 }
% 0.19/0.59 meet(Y, join(zero, complement(X)))
% 0.19/0.59 = { by lemma 21 }
% 0.19/0.59 meet(Y, complement(X))
% 0.19/0.59
% 0.19/0.59 Lemma 32: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 0.19/0.59 Proof:
% 0.19/0.59 complement(meet(complement(X), Y))
% 0.19/0.59 = { by lemma 26 }
% 0.19/0.59 complement(meet(Y, complement(X)))
% 0.19/0.59 = { by lemma 21 R->L }
% 0.19/0.59 complement(join(zero, meet(Y, complement(X))))
% 0.19/0.59 = { by lemma 31 R->L }
% 0.19/0.59 complement(join(zero, complement(join(X, complement(Y)))))
% 0.19/0.59 = { by lemma 27 }
% 0.19/0.59 meet(join(X, complement(Y)), top)
% 0.19/0.59 = { by lemma 28 }
% 0.19/0.59 join(X, complement(Y))
% 0.19/0.59
% 0.19/0.59 Lemma 33: meet(X, join(X, complement(Y))) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 meet(X, join(X, complement(Y)))
% 0.19/0.59 = { by lemma 20 R->L }
% 0.19/0.59 join(meet(X, join(X, complement(Y))), zero)
% 0.19/0.59 = { by lemma 14 R->L }
% 0.19/0.59 join(meet(X, join(X, complement(Y))), complement(top))
% 0.19/0.59 = { by lemma 32 R->L }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(top))
% 0.19/0.59 = { by lemma 24 R->L }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(x0, top)))
% 0.19/0.59 = { by lemma 29 R->L }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(x0, join(top, complement(x0)))))
% 0.19/0.59 = { by lemma 22 }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(top, top)))
% 0.19/0.59 = { by lemma 22 R->L }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(Y), join(top, complement(complement(Y))))))
% 0.19/0.59 = { by lemma 29 }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(Y), top)))
% 0.19/0.59 = { by lemma 22 R->L }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(complement(Y), complement(complement(X))))))
% 0.19/0.59 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(complement(complement(X)), complement(Y)))))
% 0.19/0.59 = { by lemma 16 R->L }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(zero, meet(join(complement(complement(X)), complement(Y)), join(complement(complement(X)), complement(Y)))))))
% 0.19/0.59 = { by lemma 30 }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(zero, complement(join(complement(join(complement(complement(X)), complement(Y))), meet(complement(X), Y)))))))
% 0.19/0.59 = { by lemma 21 }
% 0.19/0.59 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(complement(join(complement(complement(X)), complement(Y))), meet(complement(X), Y))))))
% 0.19/0.60 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(complement(X), Y), meet(complement(X), Y))))))
% 0.19/0.60 = { by lemma 26 }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), meet(complement(X), Y))))))
% 0.19/0.60 = { by lemma 26 }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), meet(Y, complement(X)))))))
% 0.19/0.60 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), complement(join(complement(Y), complement(complement(X)))))))))
% 0.19/0.60 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(complement(join(complement(Y), complement(complement(X)))), complement(join(complement(Y), complement(complement(X)))))))))
% 0.19/0.60 = { by lemma 18 }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(complement(join(complement(Y), complement(complement(X))))))))
% 0.19/0.60 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(Y, complement(X))))))
% 0.19/0.60 = { by lemma 26 R->L }
% 0.19/0.60 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(complement(X), Y)))))
% 0.19/0.60 = { by lemma 15 }
% 0.19/0.60 X
% 0.19/0.60
% 0.19/0.60 Lemma 34: join(X, meet(X, Y)) = X.
% 0.19/0.60 Proof:
% 0.19/0.60 join(X, meet(X, Y))
% 0.19/0.60 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.60 join(X, complement(join(complement(X), complement(Y))))
% 0.19/0.60 = { by lemma 32 R->L }
% 0.19/0.60 complement(meet(complement(X), join(complement(X), complement(Y))))
% 0.19/0.60 = { by lemma 33 }
% 0.19/0.60 complement(complement(X))
% 0.19/0.60 = { by lemma 25 }
% 0.19/0.60 X
% 0.19/0.60
% 0.19/0.60 Lemma 35: complement(join(complement(X), Y)) = meet(X, complement(Y)).
% 0.19/0.60 Proof:
% 0.19/0.60 complement(join(complement(X), Y))
% 0.19/0.60 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.60 complement(join(Y, complement(X)))
% 0.19/0.60 = { by lemma 31 }
% 0.19/0.60 meet(X, complement(Y))
% 0.19/0.60
% 0.19/0.60 Lemma 36: meet(X, join(Y, X)) = X.
% 0.19/0.60 Proof:
% 0.19/0.60 meet(X, join(Y, X))
% 0.19/0.60 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.60 meet(X, join(X, Y))
% 0.19/0.60 = { by lemma 28 R->L }
% 0.19/0.60 meet(X, join(X, meet(Y, top)))
% 0.19/0.60 = { by lemma 27 R->L }
% 0.19/0.60 meet(X, join(X, complement(join(zero, complement(Y)))))
% 0.19/0.60 = { by lemma 33 }
% 0.19/0.60 X
% 0.19/0.60
% 0.19/0.60 Goal 1 (goals_2): join(x0, meet(x1, x2)) = meet(x1, x2).
% 0.19/0.60 Proof:
% 0.19/0.60 join(x0, meet(x1, x2))
% 0.19/0.60 = { by lemma 36 R->L }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), join(x2, join(x0, meet(x1, x2))))
% 0.19/0.60 = { by lemma 23 }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), join(meet(x1, x2), x2))
% 0.19/0.60 = { by axiom 1 (maddux1_join_commutativity) }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), join(x2, meet(x1, x2)))
% 0.19/0.60 = { by lemma 26 R->L }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), join(x2, meet(x2, x1)))
% 0.19/0.60 = { by lemma 34 }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), x2)
% 0.19/0.60 = { by lemma 26 R->L }
% 0.19/0.60 meet(x2, join(x0, meet(x1, x2)))
% 0.19/0.60 = { by lemma 36 R->L }
% 0.19/0.60 meet(x2, meet(join(x0, meet(x1, x2)), join(x1, join(x0, meet(x1, x2)))))
% 0.19/0.60 = { by axiom 8 (maddux2_join_associativity) }
% 0.19/0.60 meet(x2, meet(join(x0, meet(x1, x2)), join(join(x1, x0), meet(x1, x2))))
% 0.19/0.60 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.19/0.60 meet(x2, meet(join(x0, meet(x1, x2)), join(join(x0, x1), meet(x1, x2))))
% 0.19/0.60 = { by axiom 3 (goals_1) }
% 0.19/0.60 meet(x2, meet(join(x0, meet(x1, x2)), join(x1, meet(x1, x2))))
% 0.19/0.60 = { by lemma 34 }
% 0.19/0.60 meet(x2, meet(join(x0, meet(x1, x2)), x1))
% 0.19/0.60 = { by lemma 26 R->L }
% 0.19/0.60 meet(x2, meet(x1, join(x0, meet(x1, x2))))
% 0.19/0.60 = { by lemma 28 R->L }
% 0.19/0.60 meet(meet(x2, top), meet(x1, join(x0, meet(x1, x2))))
% 0.19/0.60 = { by lemma 27 R->L }
% 0.19/0.60 meet(complement(join(zero, complement(x2))), meet(x1, join(x0, meet(x1, x2))))
% 0.19/0.60 = { by lemma 26 }
% 0.19/0.60 meet(complement(join(zero, complement(x2))), meet(join(x0, meet(x1, x2)), x1))
% 0.19/0.60 = { by lemma 26 }
% 0.19/0.60 meet(meet(join(x0, meet(x1, x2)), x1), complement(join(zero, complement(x2))))
% 0.19/0.60 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.60 meet(complement(join(complement(join(x0, meet(x1, x2))), complement(x1))), complement(join(zero, complement(x2))))
% 0.19/0.60 = { by lemma 26 }
% 0.19/0.60 meet(complement(join(zero, complement(x2))), complement(join(complement(join(x0, meet(x1, x2))), complement(x1))))
% 0.19/0.60 = { by lemma 21 R->L }
% 0.19/0.60 meet(join(zero, complement(join(zero, complement(x2)))), complement(join(complement(join(x0, meet(x1, x2))), complement(x1))))
% 0.19/0.60 = { by lemma 31 R->L }
% 0.19/0.60 complement(join(join(complement(join(x0, meet(x1, x2))), complement(x1)), complement(join(zero, complement(join(zero, complement(x2)))))))
% 0.19/0.60 = { by lemma 27 }
% 0.19/0.60 complement(join(join(complement(join(x0, meet(x1, x2))), complement(x1)), meet(join(zero, complement(x2)), top)))
% 0.19/0.60 = { by lemma 28 }
% 0.19/0.60 complement(join(join(complement(join(x0, meet(x1, x2))), complement(x1)), join(zero, complement(x2))))
% 0.19/0.60 = { by axiom 8 (maddux2_join_associativity) R->L }
% 0.19/0.60 complement(join(complement(join(x0, meet(x1, x2))), join(complement(x1), join(zero, complement(x2)))))
% 0.19/0.60 = { by lemma 35 }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), complement(join(complement(x1), join(zero, complement(x2)))))
% 0.19/0.60 = { by lemma 35 }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), meet(x1, complement(join(zero, complement(x2)))))
% 0.19/0.60 = { by lemma 27 }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), meet(x1, meet(x2, top)))
% 0.19/0.60 = { by lemma 28 }
% 0.19/0.60 meet(join(x0, meet(x1, x2)), meet(x1, x2))
% 0.19/0.60 = { by lemma 26 }
% 0.19/0.60 meet(meet(x1, x2), join(x0, meet(x1, x2)))
% 0.19/0.60 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.60 complement(join(complement(meet(x1, x2)), complement(join(x0, meet(x1, x2)))))
% 0.19/0.60 = { by lemma 21 R->L }
% 0.19/0.60 join(zero, complement(join(complement(meet(x1, x2)), complement(join(x0, meet(x1, x2))))))
% 0.19/0.60 = { by lemma 14 R->L }
% 0.19/0.60 join(complement(top), complement(join(complement(meet(x1, x2)), complement(join(x0, meet(x1, x2))))))
% 0.19/0.60 = { by lemma 24 R->L }
% 0.19/0.60 join(complement(join(x0, top)), complement(join(complement(meet(x1, x2)), complement(join(x0, meet(x1, x2))))))
% 0.19/0.60 = { by axiom 6 (def_top) }
% 0.19/0.60 join(complement(join(x0, join(meet(x1, x2), complement(meet(x1, x2))))), complement(join(complement(meet(x1, x2)), complement(join(x0, meet(x1, x2))))))
% 0.19/0.60 = { by axiom 8 (maddux2_join_associativity) }
% 0.19/0.60 join(complement(join(join(x0, meet(x1, x2)), complement(meet(x1, x2)))), complement(join(complement(meet(x1, x2)), complement(join(x0, meet(x1, x2))))))
% 0.19/0.60 = { by lemma 31 }
% 0.19/0.60 join(meet(meet(x1, x2), complement(join(x0, meet(x1, x2)))), complement(join(complement(meet(x1, x2)), complement(join(x0, meet(x1, x2))))))
% 0.19/0.60 = { by lemma 15 }
% 0.19/0.60 meet(x1, x2)
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60
% 0.19/0.60 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------