TSTP Solution File: LAT224-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT224-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n024.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 06:27:50 EDT 2023
% Result : Unsatisfiable 34.31s 4.89s
% Output : Proof 34.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : LAT224-10 : TPTP v8.1.2. Released v7.3.0.
% 0.05/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 07:58:54 EDT 2023
% 0.11/0.33 % CPUTime :
% 34.31/4.89 Command-line arguments: --no-flatten-goal
% 34.31/4.89
% 34.31/4.89 % SZS status Unsatisfiable
% 34.31/4.89
% 34.97/4.93 % SZS output start Proof
% 34.97/4.93 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 34.97/4.93 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 34.97/4.93 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 34.97/4.93 Axiom 4 (complement_join): join(X, complement(X)) = one.
% 34.97/4.93 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 34.97/4.93 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 34.97/4.93 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 34.97/4.93 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 34.97/4.93 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 34.97/4.93 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 34.97/4.93 Axiom 11 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 34.97/4.93 Axiom 12 (equation_H8): meet(X, join(Y, meet(X, Z))) = join(meet(X, Y), meet(X, join(Y, meet(Z, join(X, meet(Y, Z)))))).
% 34.97/4.93
% 34.97/4.93 Lemma 13: meet(X, one) = X.
% 34.97/4.93 Proof:
% 34.97/4.93 meet(X, one)
% 34.97/4.93 = { by axiom 4 (complement_join) R->L }
% 34.97/4.93 meet(X, join(X, complement(X)))
% 34.97/4.93 = { by axiom 9 (absorption1) }
% 34.97/4.93 X
% 34.97/4.93
% 34.97/4.93 Lemma 14: meet(one, X) = X.
% 34.97/4.93 Proof:
% 34.97/4.93 meet(one, X)
% 34.97/4.93 = { by axiom 2 (commutativity_of_meet) R->L }
% 34.97/4.93 meet(X, one)
% 34.97/4.93 = { by lemma 13 }
% 34.97/4.93 X
% 34.97/4.93
% 34.97/4.93 Lemma 15: join(X, one) = one.
% 34.97/4.93 Proof:
% 34.97/4.93 join(X, one)
% 34.97/4.93 = { by axiom 1 (commutativity_of_join) R->L }
% 34.97/4.93 join(one, X)
% 34.97/4.93 = { by lemma 14 R->L }
% 34.97/4.93 join(one, meet(one, X))
% 34.97/4.93 = { by axiom 7 (absorption2) }
% 34.97/4.93 one
% 34.97/4.93
% 34.97/4.93 Lemma 16: join(X, meet(Y, X)) = X.
% 34.97/4.93 Proof:
% 34.97/4.93 join(X, meet(Y, X))
% 34.97/4.93 = { by axiom 2 (commutativity_of_meet) R->L }
% 34.97/4.93 join(X, meet(X, Y))
% 34.97/4.93 = { by axiom 7 (absorption2) }
% 34.97/4.93 X
% 34.97/4.93
% 34.97/4.93 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 34.97/4.93 Proof:
% 34.97/4.93 join(complement(b), complement(a))
% 34.97/4.93 = { by axiom 1 (commutativity_of_join) R->L }
% 34.97/4.93 join(complement(a), complement(b))
% 34.97/4.93 = { by axiom 6 (ifeq_axiom) R->L }
% 34.97/4.93 join(complement(a), ifeq(zero, zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 5 (complement_meet) R->L }
% 34.97/4.93 join(complement(a), ifeq(meet(meet(b, complement(a)), complement(meet(b, complement(a)))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 10 (associativity_of_meet) }
% 34.97/4.93 join(complement(a), ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 6 (ifeq_axiom) R->L }
% 34.97/4.93 join(complement(a), ifeq(one, one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by lemma 15 R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, one), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 4 (complement_join) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, join(meet(b, complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 8 (associativity_of_join) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(join(b, meet(b, complement(a))), complement(meet(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 7 (absorption2) }
% 34.97/4.93 join(complement(a), ifeq(join(b, complement(meet(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by lemma 14 R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(one, complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by lemma 15 R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(join(b, one), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 4 (complement_join) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(join(b, join(a, complement(a))), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 8 (associativity_of_join) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(join(join(b, a), complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(join(join(b, meet(b, a)), complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 7 (absorption2) }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(join(b, complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 1 (commutativity_of_join) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(join(complement(a), b), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 2 (commutativity_of_meet) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(complement(meet(b, complement(a))), join(complement(a), b))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 1 (commutativity_of_join) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, meet(complement(meet(b, complement(a))), join(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by lemma 16 R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), meet(complement(meet(b, complement(a))), join(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 2 (commutativity_of_meet) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), meet(join(b, complement(a)), complement(meet(b, complement(a))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.93 = { by axiom 10 (associativity_of_meet) R->L }
% 34.97/4.93 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(meet(complement(a), join(b, complement(a))), complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 2 (commutativity_of_meet) }
% 34.97/4.94 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), meet(complement(a), join(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 1 (commutativity_of_join) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), meet(complement(a), join(complement(a), b))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 9 (absorption1) }
% 34.97/4.94 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 2 (commutativity_of_meet) }
% 34.97/4.94 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 1 (commutativity_of_join) }
% 34.97/4.94 join(complement(a), ifeq(join(b, join(meet(complement(a), complement(meet(b, complement(a)))), meet(complement(meet(b, complement(a))), join(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 2 (commutativity_of_meet) }
% 34.97/4.94 join(complement(a), ifeq(join(b, join(meet(complement(a), complement(meet(b, complement(a)))), meet(join(b, complement(a)), complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 8 (associativity_of_join) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(join(b, complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 2 (commutativity_of_meet) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by lemma 13 R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), one)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 4 (complement_join) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(meet(b, complement(a)), complement(meet(b, complement(a)))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 1 (commutativity_of_join) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by lemma 16 R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), join(meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a)))))), meet(b, meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a))))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 2 (commutativity_of_meet) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), join(meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a)))))), meet(b, meet(join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a))))), complement(meet(b, complement(a))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 10 (associativity_of_meet) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), join(meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a)))))), meet(meet(b, join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a)))))), complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 9 (absorption1) }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), join(meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a)))))), meet(b, complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 1 (commutativity_of_join) }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), join(meet(b, complement(meet(b, complement(a)))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a)))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 2 (commutativity_of_meet) }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), join(meet(complement(meet(b, complement(a))), b), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a)))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 12 (equation_H8) R->L }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(meet(b, complement(a))), complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 2 (commutativity_of_meet) }
% 34.97/4.94 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), complement(meet(b, complement(a))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by lemma 16 }
% 34.97/4.94 join(complement(a), ifeq(join(b, meet(complement(a), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 34.97/4.94 = { by axiom 11 (meet_join_complement) }
% 34.97/4.94 join(complement(a), meet(complement(a), complement(meet(b, complement(a)))))
% 34.97/4.94 = { by axiom 7 (absorption2) }
% 34.97/4.94 complement(a)
% 34.97/4.94 % SZS output end Proof
% 34.97/4.94
% 34.97/4.94 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------