TSTP Solution File: REL041-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL041-2 : 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 : n027.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 13:44:27 EDT 2023
% Result : Unsatisfiable 4.30s 0.97s
% Output : Proof 4.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL041-2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 19:42:34 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.30/0.97 Command-line arguments: --ground-connectedness --complete-subsets
% 4.30/0.97
% 4.30/0.97 % SZS status Unsatisfiable
% 4.30/0.97
% 4.84/0.99 % SZS output start Proof
% 4.84/0.99 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 4.84/0.99 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 4.84/0.99 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 4.84/0.99 Axiom 4 (def_zero_13): zero = meet(X, complement(X)).
% 4.84/0.99 Axiom 5 (def_top_12): top = join(X, complement(X)).
% 4.84/0.99 Axiom 6 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 4.84/0.99 Axiom 7 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 4.84/0.99 Axiom 8 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 4.84/0.99 Axiom 9 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 4.84/0.99 Axiom 10 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 4.84/0.99 Axiom 11 (goals_17): join(composition(converse(sk1), sk1), one) = one.
% 4.84/0.99 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 4.84/0.99 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 4.84/0.99 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 4.84/0.99 Axiom 15 (modular_law_1_15): join(meet(composition(X, Y), Z), meet(composition(X, meet(Y, composition(converse(X), Z))), Z)) = meet(composition(X, meet(Y, composition(converse(X), Z))), Z).
% 4.84/0.99
% 4.84/0.99 Lemma 16: complement(top) = zero.
% 4.84/0.99 Proof:
% 4.84/0.99 complement(top)
% 4.84/0.99 = { by axiom 5 (def_top_12) }
% 4.84/0.99 complement(join(complement(X), complement(complement(X))))
% 4.84/0.99 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 4.84/0.99 meet(X, complement(X))
% 4.84/0.99 = { by axiom 4 (def_zero_13) R->L }
% 4.84/1.00 zero
% 4.84/1.00
% 4.84/1.00 Lemma 17: join(X, join(Y, complement(X))) = join(Y, top).
% 4.84/1.00 Proof:
% 4.84/1.00 join(X, join(Y, complement(X)))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(X, join(complement(X), Y))
% 4.84/1.00 = { by axiom 7 (maddux2_join_associativity_2) }
% 4.84/1.00 join(join(X, complement(X)), Y)
% 4.84/1.00 = { by axiom 5 (def_top_12) R->L }
% 4.84/1.00 join(top, Y)
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) }
% 4.84/1.00 join(Y, top)
% 4.84/1.00
% 4.84/1.00 Lemma 18: composition(converse(one), X) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 composition(converse(one), X)
% 4.84/1.00 = { by axiom 1 (converse_idempotence_8) R->L }
% 4.84/1.00 composition(converse(one), converse(converse(X)))
% 4.84/1.00 = { by axiom 8 (converse_multiplicativity_10) R->L }
% 4.84/1.00 converse(composition(converse(X), one))
% 4.84/1.00 = { by axiom 3 (composition_identity_6) }
% 4.84/1.00 converse(converse(X))
% 4.84/1.00 = { by axiom 1 (converse_idempotence_8) }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 19: composition(one, X) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 composition(one, X)
% 4.84/1.00 = { by lemma 18 R->L }
% 4.84/1.00 composition(converse(one), composition(one, X))
% 4.84/1.00 = { by axiom 9 (composition_associativity_5) }
% 4.84/1.00 composition(composition(converse(one), one), X)
% 4.84/1.00 = { by axiom 3 (composition_identity_6) }
% 4.84/1.00 composition(converse(one), X)
% 4.84/1.00 = { by lemma 18 }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 20: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 4.84/1.00 Proof:
% 4.84/1.00 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 4.84/1.00 = { by axiom 13 (converse_cancellativity_11) }
% 4.84/1.00 complement(X)
% 4.84/1.00
% 4.84/1.00 Lemma 21: join(complement(X), complement(X)) = complement(X).
% 4.84/1.00 Proof:
% 4.84/1.00 join(complement(X), complement(X))
% 4.84/1.00 = { by lemma 18 R->L }
% 4.84/1.00 join(complement(X), composition(converse(one), complement(X)))
% 4.84/1.00 = { by lemma 19 R->L }
% 4.84/1.00 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 4.84/1.00 = { by lemma 20 }
% 4.84/1.00 complement(X)
% 4.84/1.00
% 4.84/1.00 Lemma 22: join(top, complement(X)) = top.
% 4.84/1.00 Proof:
% 4.84/1.00 join(top, complement(X))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(complement(X), top)
% 4.84/1.00 = { by lemma 17 R->L }
% 4.84/1.00 join(X, join(complement(X), complement(X)))
% 4.84/1.00 = { by lemma 21 }
% 4.84/1.00 join(X, complement(X))
% 4.84/1.00 = { by axiom 5 (def_top_12) R->L }
% 4.84/1.00 top
% 4.84/1.00
% 4.84/1.00 Lemma 23: join(Y, top) = join(X, top).
% 4.84/1.00 Proof:
% 4.84/1.00 join(Y, top)
% 4.84/1.00 = { by lemma 22 R->L }
% 4.84/1.00 join(Y, join(top, complement(Y)))
% 4.84/1.00 = { by lemma 17 }
% 4.84/1.00 join(top, top)
% 4.84/1.00 = { by lemma 17 R->L }
% 4.84/1.00 join(X, join(top, complement(X)))
% 4.84/1.00 = { by lemma 22 }
% 4.84/1.00 join(X, top)
% 4.84/1.00
% 4.84/1.00 Lemma 24: join(X, top) = top.
% 4.84/1.00 Proof:
% 4.84/1.00 join(X, top)
% 4.84/1.00 = { by lemma 23 }
% 4.84/1.00 join(complement(Y), top)
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(top, complement(Y))
% 4.84/1.00 = { by lemma 22 }
% 4.84/1.00 top
% 4.84/1.00
% 4.84/1.00 Lemma 25: join(X, join(complement(X), Y)) = top.
% 4.84/1.00 Proof:
% 4.84/1.00 join(X, join(complement(X), Y))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(X, join(Y, complement(X)))
% 4.84/1.00 = { by lemma 17 }
% 4.84/1.00 join(Y, top)
% 4.84/1.00 = { by lemma 23 R->L }
% 4.84/1.00 join(Z, top)
% 4.84/1.00 = { by lemma 24 }
% 4.84/1.00 top
% 4.84/1.00
% 4.84/1.00 Lemma 26: join(X, converse(top)) = top.
% 4.84/1.00 Proof:
% 4.84/1.00 join(X, converse(top))
% 4.84/1.00 = { by axiom 5 (def_top_12) }
% 4.84/1.00 join(X, converse(join(converse(complement(X)), complement(converse(complement(X))))))
% 4.84/1.00 = { by axiom 6 (converse_additivity_9) }
% 4.84/1.00 join(X, join(converse(converse(complement(X))), converse(complement(converse(complement(X))))))
% 4.84/1.00 = { by axiom 1 (converse_idempotence_8) }
% 4.84/1.00 join(X, join(complement(X), converse(complement(converse(complement(X))))))
% 4.84/1.00 = { by lemma 25 }
% 4.84/1.00 top
% 4.84/1.00
% 4.84/1.00 Lemma 27: converse(top) = top.
% 4.84/1.00 Proof:
% 4.84/1.00 converse(top)
% 4.84/1.00 = { by lemma 24 R->L }
% 4.84/1.00 converse(join(X, top))
% 4.84/1.00 = { by axiom 6 (converse_additivity_9) }
% 4.84/1.00 join(converse(X), converse(top))
% 4.84/1.00 = { by lemma 26 }
% 4.84/1.00 top
% 4.84/1.00
% 4.84/1.00 Lemma 28: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 join(meet(X, Y), complement(join(complement(X), Y)))
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.00 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 4.84/1.00 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 29: join(zero, meet(X, X)) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 join(zero, meet(X, X))
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.00 join(zero, complement(join(complement(X), complement(X))))
% 4.84/1.00 = { by axiom 4 (def_zero_13) }
% 4.84/1.00 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 4.84/1.00 = { by lemma 28 }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 30: join(zero, join(X, complement(complement(Y)))) = join(X, Y).
% 4.84/1.00 Proof:
% 4.84/1.00 join(zero, join(X, complement(complement(Y))))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(zero, join(complement(complement(Y)), X))
% 4.84/1.00 = { by lemma 21 R->L }
% 4.84/1.00 join(zero, join(complement(join(complement(Y), complement(Y))), X))
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 4.84/1.00 join(zero, join(meet(Y, Y), X))
% 4.84/1.00 = { by axiom 7 (maddux2_join_associativity_2) }
% 4.84/1.00 join(join(zero, meet(Y, Y)), X)
% 4.84/1.00 = { by lemma 29 }
% 4.84/1.00 join(Y, X)
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) }
% 4.84/1.00 join(X, Y)
% 4.84/1.00
% 4.84/1.00 Lemma 31: join(zero, complement(complement(X))) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 join(zero, complement(complement(X)))
% 4.84/1.00 = { by axiom 4 (def_zero_13) }
% 4.84/1.00 join(meet(X, complement(X)), complement(complement(X)))
% 4.84/1.00 = { by lemma 21 R->L }
% 4.84/1.00 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 4.84/1.00 = { by lemma 28 }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 32: join(zero, complement(X)) = complement(X).
% 4.84/1.00 Proof:
% 4.84/1.00 join(zero, complement(X))
% 4.84/1.00 = { by lemma 31 R->L }
% 4.84/1.00 join(zero, join(zero, complement(complement(complement(X)))))
% 4.84/1.00 = { by lemma 21 R->L }
% 4.84/1.00 join(zero, join(zero, join(complement(complement(complement(X))), complement(complement(complement(X))))))
% 4.84/1.00 = { by lemma 30 }
% 4.84/1.00 join(zero, join(complement(complement(complement(X))), complement(X)))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) }
% 4.84/1.00 join(zero, join(complement(X), complement(complement(complement(X)))))
% 4.84/1.00 = { by lemma 30 }
% 4.84/1.00 join(complement(X), complement(X))
% 4.84/1.00 = { by lemma 21 }
% 4.84/1.00 complement(X)
% 4.84/1.00
% 4.84/1.00 Lemma 33: join(X, zero) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 join(X, zero)
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(zero, X)
% 4.84/1.00 = { by lemma 30 R->L }
% 4.84/1.00 join(zero, join(zero, complement(complement(X))))
% 4.84/1.00 = { by lemma 32 }
% 4.84/1.00 join(zero, complement(complement(X)))
% 4.84/1.00 = { by lemma 31 }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 34: join(top, X) = top.
% 4.84/1.00 Proof:
% 4.84/1.00 join(top, X)
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(X, top)
% 4.84/1.00 = { by lemma 23 R->L }
% 4.84/1.00 join(Y, top)
% 4.84/1.00 = { by lemma 24 }
% 4.84/1.00 top
% 4.84/1.00
% 4.84/1.00 Lemma 35: join(zero, X) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 join(zero, X)
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(X, zero)
% 4.84/1.00 = { by lemma 33 }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 36: meet(Y, X) = meet(X, Y).
% 4.84/1.00 Proof:
% 4.84/1.00 meet(Y, X)
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.00 complement(join(complement(Y), complement(X)))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 complement(join(complement(X), complement(Y)))
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 4.84/1.00 meet(X, Y)
% 4.84/1.00
% 4.84/1.00 Lemma 37: complement(join(zero, complement(X))) = meet(X, top).
% 4.84/1.00 Proof:
% 4.84/1.00 complement(join(zero, complement(X)))
% 4.84/1.00 = { by lemma 16 R->L }
% 4.84/1.00 complement(join(complement(top), complement(X)))
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 4.84/1.00 meet(top, X)
% 4.84/1.00 = { by lemma 36 R->L }
% 4.84/1.00 meet(X, top)
% 4.84/1.00
% 4.84/1.00 Lemma 38: join(X, complement(zero)) = top.
% 4.84/1.00 Proof:
% 4.84/1.00 join(X, complement(zero))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(complement(zero), X)
% 4.84/1.00 = { by lemma 30 R->L }
% 4.84/1.00 join(zero, join(complement(zero), complement(complement(X))))
% 4.84/1.00 = { by lemma 25 }
% 4.84/1.00 top
% 4.84/1.00
% 4.84/1.00 Lemma 39: meet(X, zero) = zero.
% 4.84/1.00 Proof:
% 4.84/1.00 meet(X, zero)
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.00 complement(join(complement(X), complement(zero)))
% 4.84/1.00 = { by lemma 38 }
% 4.84/1.00 complement(top)
% 4.84/1.00 = { by lemma 16 }
% 4.84/1.00 zero
% 4.84/1.00
% 4.84/1.00 Lemma 40: meet(X, top) = X.
% 4.84/1.00 Proof:
% 4.84/1.00 meet(X, top)
% 4.84/1.00 = { by lemma 37 R->L }
% 4.84/1.00 complement(join(zero, complement(X)))
% 4.84/1.00 = { by lemma 32 R->L }
% 4.84/1.00 join(zero, complement(join(zero, complement(X))))
% 4.84/1.00 = { by lemma 37 }
% 4.84/1.00 join(zero, meet(X, top))
% 4.84/1.00 = { by lemma 38 R->L }
% 4.84/1.00 join(zero, meet(X, join(complement(zero), complement(zero))))
% 4.84/1.00 = { by lemma 21 }
% 4.84/1.00 join(zero, meet(X, complement(zero)))
% 4.84/1.00 = { by lemma 39 R->L }
% 4.84/1.00 join(meet(X, zero), meet(X, complement(zero)))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 join(meet(X, complement(zero)), meet(X, zero))
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.00 join(meet(X, complement(zero)), complement(join(complement(X), complement(zero))))
% 4.84/1.00 = { by lemma 28 }
% 4.84/1.00 X
% 4.84/1.00
% 4.84/1.00 Lemma 41: meet(zero, X) = zero.
% 4.84/1.00 Proof:
% 4.84/1.00 meet(zero, X)
% 4.84/1.00 = { by lemma 36 }
% 4.84/1.00 meet(X, zero)
% 4.84/1.00 = { by lemma 39 }
% 4.84/1.00 zero
% 4.84/1.00
% 4.84/1.00 Lemma 42: composition(top, zero) = zero.
% 4.84/1.00 Proof:
% 4.84/1.00 composition(top, zero)
% 4.84/1.00 = { by lemma 27 R->L }
% 4.84/1.00 composition(converse(top), zero)
% 4.84/1.00 = { by lemma 35 R->L }
% 4.84/1.00 join(zero, composition(converse(top), zero))
% 4.84/1.00 = { by lemma 16 R->L }
% 4.84/1.00 join(complement(top), composition(converse(top), zero))
% 4.84/1.00 = { by lemma 16 R->L }
% 4.84/1.00 join(complement(top), composition(converse(top), complement(top)))
% 4.84/1.00 = { by lemma 34 R->L }
% 4.84/1.00 join(complement(top), composition(converse(top), complement(join(top, composition(top, top)))))
% 4.84/1.00 = { by lemma 27 R->L }
% 4.84/1.00 join(complement(top), composition(converse(top), complement(join(top, composition(converse(top), top)))))
% 4.84/1.00 = { by lemma 19 R->L }
% 4.84/1.00 join(complement(top), composition(converse(top), complement(join(composition(one, top), composition(converse(top), top)))))
% 4.84/1.00 = { by axiom 12 (composition_distributivity_7) R->L }
% 4.84/1.00 join(complement(top), composition(converse(top), complement(composition(join(one, converse(top)), top))))
% 4.84/1.00 = { by lemma 26 }
% 4.84/1.00 join(complement(top), composition(converse(top), complement(composition(top, top))))
% 4.84/1.00 = { by lemma 20 }
% 4.84/1.00 complement(top)
% 4.84/1.00 = { by lemma 16 }
% 4.84/1.00 zero
% 4.84/1.00
% 4.84/1.00 Lemma 43: composition(X, zero) = zero.
% 4.84/1.00 Proof:
% 4.84/1.00 composition(X, zero)
% 4.84/1.00 = { by lemma 35 R->L }
% 4.84/1.00 join(zero, composition(X, zero))
% 4.84/1.00 = { by lemma 42 R->L }
% 4.84/1.00 join(composition(top, zero), composition(X, zero))
% 4.84/1.00 = { by axiom 12 (composition_distributivity_7) R->L }
% 4.84/1.00 composition(join(top, X), zero)
% 4.84/1.00 = { by lemma 34 }
% 4.84/1.00 composition(top, zero)
% 4.84/1.00 = { by lemma 42 }
% 4.84/1.00 zero
% 4.84/1.00
% 4.84/1.00 Lemma 44: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 4.84/1.00 Proof:
% 4.84/1.00 meet(X, join(complement(Y), complement(Z)))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.00 meet(X, join(complement(Z), complement(Y)))
% 4.84/1.00 = { by lemma 36 }
% 4.84/1.00 meet(join(complement(Z), complement(Y)), X)
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.00 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 4.84/1.00 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 4.84/1.00 complement(join(meet(Z, Y), complement(X)))
% 4.84/1.00 = { by axiom 2 (maddux1_join_commutativity_1) }
% 4.84/1.00 complement(join(complement(X), meet(Z, Y)))
% 4.84/1.00 = { by lemma 36 R->L }
% 4.84/1.01 complement(join(complement(X), meet(Y, Z)))
% 4.84/1.01
% 4.84/1.01 Lemma 45: meet(complement(X), composition(converse(sk1), composition(sk1, X))) = zero.
% 4.84/1.01 Proof:
% 4.84/1.01 meet(complement(X), composition(converse(sk1), composition(sk1, X)))
% 4.84/1.01 = { by lemma 36 }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(X))
% 4.84/1.01 = { by lemma 19 R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(composition(one, X)))
% 4.84/1.01 = { by axiom 11 (goals_17) R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(composition(join(composition(converse(sk1), sk1), one), X)))
% 4.84/1.01 = { by axiom 12 (composition_distributivity_7) }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(composition(composition(converse(sk1), sk1), X), composition(one, X))))
% 4.84/1.01 = { by axiom 9 (composition_associativity_5) R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(composition(converse(sk1), composition(sk1, X)), composition(one, X))))
% 4.84/1.01 = { by axiom 2 (maddux1_join_commutativity_1) }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(composition(one, X), composition(converse(sk1), composition(sk1, X)))))
% 4.84/1.01 = { by lemma 19 }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(X, composition(converse(sk1), composition(sk1, X)))))
% 4.84/1.01 = { by lemma 40 R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(X, meet(composition(converse(sk1), composition(sk1, X)), top))))
% 4.84/1.01 = { by lemma 37 R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(X, complement(join(zero, complement(composition(converse(sk1), composition(sk1, X))))))))
% 4.84/1.01 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(complement(join(zero, complement(composition(converse(sk1), composition(sk1, X))))), X)))
% 4.84/1.01 = { by lemma 40 R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(complement(join(zero, complement(composition(converse(sk1), composition(sk1, X))))), meet(X, top))))
% 4.84/1.01 = { by lemma 36 R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), complement(join(complement(join(zero, complement(composition(converse(sk1), composition(sk1, X))))), meet(top, X))))
% 4.84/1.01 = { by lemma 44 R->L }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), meet(join(zero, complement(composition(converse(sk1), composition(sk1, X)))), join(complement(top), complement(X))))
% 4.84/1.01 = { by lemma 16 }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), meet(join(zero, complement(composition(converse(sk1), composition(sk1, X)))), join(zero, complement(X))))
% 4.84/1.01 = { by lemma 32 }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), meet(join(zero, complement(composition(converse(sk1), composition(sk1, X)))), complement(X)))
% 4.84/1.01 = { by lemma 32 }
% 4.84/1.01 meet(composition(converse(sk1), composition(sk1, X)), meet(complement(composition(converse(sk1), composition(sk1, X))), complement(X)))
% 4.84/1.01 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(meet(complement(composition(converse(sk1), composition(sk1, X))), complement(X)))))
% 4.84/1.01 = { by lemma 36 }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(meet(complement(X), complement(composition(converse(sk1), composition(sk1, X)))))))
% 4.84/1.01 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(complement(join(complement(complement(X)), complement(complement(composition(converse(sk1), composition(sk1, X)))))))))
% 4.84/1.01 = { by lemma 21 R->L }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(join(complement(join(complement(complement(X)), complement(complement(composition(converse(sk1), composition(sk1, X)))))), complement(join(complement(complement(X)), complement(complement(composition(converse(sk1), composition(sk1, X))))))))))
% 4.84/1.01 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(join(meet(complement(X), complement(composition(converse(sk1), composition(sk1, X)))), complement(join(complement(complement(X)), complement(complement(composition(converse(sk1), composition(sk1, X))))))))))
% 4.84/1.01 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(join(meet(complement(X), complement(composition(converse(sk1), composition(sk1, X)))), meet(complement(X), complement(composition(converse(sk1), composition(sk1, X))))))))
% 4.84/1.01 = { by lemma 36 R->L }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(join(meet(complement(X), complement(composition(converse(sk1), composition(sk1, X)))), meet(complement(composition(converse(sk1), composition(sk1, X))), complement(X))))))
% 4.84/1.01 = { by lemma 36 R->L }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(join(meet(complement(composition(converse(sk1), composition(sk1, X))), complement(X)), meet(complement(composition(converse(sk1), composition(sk1, X))), complement(X))))))
% 4.84/1.01 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), complement(join(complement(join(complement(complement(composition(converse(sk1), composition(sk1, X)))), complement(complement(X)))), meet(complement(composition(converse(sk1), composition(sk1, X))), complement(X))))))
% 4.84/1.01 = { by lemma 32 R->L }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), join(zero, complement(join(complement(join(complement(complement(composition(converse(sk1), composition(sk1, X)))), complement(complement(X)))), meet(complement(composition(converse(sk1), composition(sk1, X))), complement(X)))))))
% 4.84/1.01 = { by lemma 44 R->L }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), join(zero, meet(join(complement(complement(composition(converse(sk1), composition(sk1, X)))), complement(complement(X))), join(complement(complement(composition(converse(sk1), composition(sk1, X)))), complement(complement(X)))))))
% 4.84/1.01 = { by lemma 29 }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), join(complement(complement(composition(converse(sk1), composition(sk1, X)))), complement(complement(X)))))
% 4.84/1.01 = { by axiom 2 (maddux1_join_commutativity_1) }
% 4.84/1.01 complement(join(complement(composition(converse(sk1), composition(sk1, X))), join(complement(complement(X)), complement(complement(composition(converse(sk1), composition(sk1, X)))))))
% 4.84/1.01 = { by lemma 17 }
% 4.84/1.01 complement(join(complement(complement(X)), top))
% 4.84/1.01 = { by lemma 24 }
% 4.84/1.01 complement(top)
% 4.84/1.01 = { by lemma 16 }
% 4.84/1.01 zero
% 4.84/1.01
% 4.84/1.01 Goal 1 (goals_18): meet(composition(sk1, sk2), composition(sk1, complement(sk2))) = zero.
% 4.84/1.01 Proof:
% 4.84/1.01 meet(composition(sk1, sk2), composition(sk1, complement(sk2)))
% 4.84/1.01 = { by lemma 33 R->L }
% 4.84/1.01 join(meet(composition(sk1, sk2), composition(sk1, complement(sk2))), zero)
% 4.84/1.01 = { by lemma 41 R->L }
% 4.84/1.01 join(meet(composition(sk1, sk2), composition(sk1, complement(sk2))), meet(zero, composition(sk1, sk2)))
% 4.84/1.01 = { by lemma 43 R->L }
% 4.84/1.01 join(meet(composition(sk1, sk2), composition(sk1, complement(sk2))), meet(composition(sk1, zero), composition(sk1, sk2)))
% 4.84/1.01 = { by lemma 36 R->L }
% 4.84/1.01 join(meet(composition(sk1, complement(sk2)), composition(sk1, sk2)), meet(composition(sk1, zero), composition(sk1, sk2)))
% 4.84/1.01 = { by lemma 45 R->L }
% 4.84/1.01 join(meet(composition(sk1, complement(sk2)), composition(sk1, sk2)), meet(composition(sk1, meet(complement(sk2), composition(converse(sk1), composition(sk1, sk2)))), composition(sk1, sk2)))
% 4.84/1.01 = { by axiom 15 (modular_law_1_15) }
% 4.84/1.01 meet(composition(sk1, meet(complement(sk2), composition(converse(sk1), composition(sk1, sk2)))), composition(sk1, sk2))
% 4.84/1.01 = { by lemma 45 }
% 4.84/1.01 meet(composition(sk1, zero), composition(sk1, sk2))
% 4.84/1.01 = { by lemma 43 }
% 4.84/1.01 meet(zero, composition(sk1, sk2))
% 4.84/1.01 = { by lemma 41 }
% 4.84/1.01 zero
% 4.84/1.01 % SZS output end Proof
% 4.84/1.01
% 4.84/1.01 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------