%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT213-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:44:33 AM UTC 2026
% Result : Unsatisfiable 47.39s 6.56s
% Output : Proof 48.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT213-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 % Computer : n010.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8046.5625MB
% 0.13/0.44 % OS : Linux 6.8.0-71-generic
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Sun Sep 27 14:06:16 UTC 2026
% 0.13/0.44 % CPUTime :
% 0.13/0.44 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.39/6.56 Command-line arguments: --no-flatten-goal
% 47.39/6.56
% 47.39/6.56 % SZS status Unsatisfiable
% 47.39/6.56
% 48.19/6.66 % SZS output start Proof
% 48.19/6.66 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 48.19/6.66 Axiom 2 (complement_join): join(X, complement(X)) = one.
% 48.19/6.66 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 48.19/6.66 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 48.19/6.66 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 48.19/6.66 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 48.19/6.66 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 48.19/6.66 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 48.19/6.66 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 48.19/6.66 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 48.19/6.66 Axiom 11 (equation_H76): meet(X, join(Y, meet(Z, join(Y, W)))) = meet(X, join(Y, meet(Z, join(W, meet(X, Y))))).
% 48.19/6.66 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 48.19/6.66
% 48.19/6.66 Lemma 13: meet(X, one) = X.
% 48.19/6.66 Proof:
% 48.19/6.66 meet(X, one)
% 48.19/6.66 = { by axiom 2 (complement_join) R->L }
% 48.19/6.66 meet(X, join(X, complement(X)))
% 48.19/6.66 = { by axiom 9 (absorption1) }
% 48.19/6.66 X
% 48.19/6.66
% 48.19/6.66 Lemma 14: join(X, zero) = X.
% 48.19/6.66 Proof:
% 48.19/6.66 join(X, zero)
% 48.19/6.66 = { by axiom 5 (complement_meet) R->L }
% 48.19/6.66 join(X, meet(X, complement(X)))
% 48.19/6.66 = { by axiom 7 (absorption2) }
% 48.19/6.66 X
% 48.19/6.66
% 48.19/6.66 Lemma 15: join(zero, X) = X.
% 48.19/6.66 Proof:
% 48.19/6.66 join(zero, X)
% 48.19/6.66 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.66 join(X, zero)
% 48.19/6.66 = { by lemma 14 }
% 48.19/6.66 X
% 48.19/6.66
% 48.19/6.66 Lemma 16: meet(X, zero) = zero.
% 48.19/6.66 Proof:
% 48.19/6.66 meet(X, zero)
% 48.19/6.66 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.66 meet(zero, X)
% 48.19/6.66 = { by lemma 15 R->L }
% 48.19/6.66 join(zero, meet(zero, X))
% 48.19/6.66 = { by axiom 7 (absorption2) }
% 48.19/6.66 zero
% 48.19/6.66
% 48.19/6.66 Lemma 17: meet(X, join(complement(X), meet(X, Y))) = meet(X, join(Y, complement(X))).
% 48.19/6.66 Proof:
% 48.19/6.66 meet(X, join(complement(X), meet(X, Y)))
% 48.19/6.66 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.66 meet(X, join(complement(X), meet(Y, X)))
% 48.19/6.66 = { by axiom 7 (absorption2) R->L }
% 48.19/6.66 meet(X, join(complement(X), meet(Y, join(X, meet(X, complement(X))))))
% 48.19/6.66 = { by axiom 11 (equation_H76) R->L }
% 48.19/6.66 meet(X, join(complement(X), meet(Y, join(complement(X), X))))
% 48.19/6.66 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.66 meet(X, join(complement(X), meet(Y, join(X, complement(X)))))
% 48.19/6.66 = { by axiom 2 (complement_join) }
% 48.19/6.66 meet(X, join(complement(X), meet(Y, one)))
% 48.19/6.66 = { by lemma 13 }
% 48.19/6.66 meet(X, join(complement(X), Y))
% 48.19/6.66 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.66 meet(X, join(Y, complement(X)))
% 48.19/6.66
% 48.19/6.66 Lemma 18: meet(X, join(complement(X), meet(Y, X))) = meet(X, join(Y, complement(X))).
% 48.19/6.66 Proof:
% 48.19/6.66 meet(X, join(complement(X), meet(Y, X)))
% 48.19/6.66 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.66 meet(X, join(complement(X), meet(X, Y)))
% 48.19/6.66 = { by lemma 17 }
% 48.19/6.66 meet(X, join(Y, complement(X)))
% 48.19/6.66
% 48.19/6.66 Lemma 19: join(X, join(Y, complement(X))) = one.
% 48.19/6.66 Proof:
% 48.19/6.66 join(X, join(Y, complement(X)))
% 48.19/6.66 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.66 join(X, join(complement(X), Y))
% 48.19/6.66 = { by axiom 8 (associativity_of_join) R->L }
% 48.19/6.66 join(join(X, complement(X)), Y)
% 48.19/6.66 = { by axiom 2 (complement_join) }
% 48.19/6.66 join(one, Y)
% 48.19/6.66 = { by lemma 13 R->L }
% 48.19/6.66 join(one, meet(Y, one))
% 48.19/6.66 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.66 join(one, meet(one, Y))
% 48.19/6.66 = { by axiom 7 (absorption2) }
% 48.19/6.66 one
% 48.19/6.66
% 48.19/6.66 Lemma 20: join(X, complement(complement(X))) = complement(complement(X)).
% 48.19/6.66 Proof:
% 48.19/6.66 join(X, complement(complement(X)))
% 48.19/6.66 = { by axiom 12 (meet_join_complement) R->L }
% 48.19/6.66 ifeq(join(complement(X), join(X, complement(complement(X)))), one, ifeq(meet(complement(X), join(X, complement(complement(X)))), zero, complement(complement(X)), join(X, complement(complement(X)))), join(X, complement(complement(X))))
% 48.19/6.66 = { by lemma 18 R->L }
% 48.19/6.66 ifeq(join(complement(X), join(X, complement(complement(X)))), one, ifeq(meet(complement(X), join(complement(complement(X)), meet(X, complement(X)))), zero, complement(complement(X)), join(X, complement(complement(X)))), join(X, complement(complement(X))))
% 48.19/6.66 = { by axiom 5 (complement_meet) }
% 48.19/6.66 ifeq(join(complement(X), join(X, complement(complement(X)))), one, ifeq(meet(complement(X), join(complement(complement(X)), zero)), zero, complement(complement(X)), join(X, complement(complement(X)))), join(X, complement(complement(X))))
% 48.19/6.67 = { by lemma 14 }
% 48.19/6.67 ifeq(join(complement(X), join(X, complement(complement(X)))), one, ifeq(meet(complement(X), complement(complement(X))), zero, complement(complement(X)), join(X, complement(complement(X)))), join(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 5 (complement_meet) }
% 48.19/6.67 ifeq(join(complement(X), join(X, complement(complement(X)))), one, ifeq(zero, zero, complement(complement(X)), join(X, complement(complement(X)))), join(X, complement(complement(X))))
% 48.19/6.67 = { by lemma 19 }
% 48.19/6.67 ifeq(one, one, ifeq(zero, zero, complement(complement(X)), join(X, complement(complement(X)))), join(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 6 (ifeq_axiom) }
% 48.19/6.67 ifeq(zero, zero, complement(complement(X)), join(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 6 (ifeq_axiom) }
% 48.19/6.67 complement(complement(X))
% 48.19/6.67
% 48.19/6.67 Lemma 21: meet(X, complement(complement(X))) = X.
% 48.19/6.67 Proof:
% 48.19/6.67 meet(X, complement(complement(X)))
% 48.19/6.67 = { by lemma 20 R->L }
% 48.19/6.67 meet(X, join(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 9 (absorption1) }
% 48.19/6.67 X
% 48.19/6.67
% 48.19/6.67 Lemma 22: complement(complement(X)) = X.
% 48.19/6.67 Proof:
% 48.19/6.67 complement(complement(X))
% 48.19/6.67 = { by axiom 6 (ifeq_axiom) R->L }
% 48.19/6.67 ifeq(one, one, complement(complement(X)), X)
% 48.19/6.67 = { by axiom 2 (complement_join) R->L }
% 48.19/6.67 ifeq(join(X, complement(X)), one, complement(complement(X)), X)
% 48.19/6.67 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.67 ifeq(join(complement(X), X), one, complement(complement(X)), X)
% 48.19/6.67 = { by lemma 21 R->L }
% 48.19/6.67 ifeq(join(complement(X), X), one, complement(complement(X)), meet(X, complement(complement(X))))
% 48.19/6.67 = { by lemma 21 R->L }
% 48.19/6.67 ifeq(join(complement(X), meet(X, complement(complement(X)))), one, complement(complement(X)), meet(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 6 (ifeq_axiom) R->L }
% 48.19/6.67 ifeq(join(complement(X), meet(X, complement(complement(X)))), one, ifeq(zero, zero, complement(complement(X)), meet(X, complement(complement(X)))), meet(X, complement(complement(X))))
% 48.19/6.67 = { by lemma 16 R->L }
% 48.19/6.67 ifeq(join(complement(X), meet(X, complement(complement(X)))), one, ifeq(meet(X, zero), zero, complement(complement(X)), meet(X, complement(complement(X)))), meet(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.67 ifeq(join(complement(X), meet(X, complement(complement(X)))), one, ifeq(meet(zero, X), zero, complement(complement(X)), meet(X, complement(complement(X)))), meet(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 5 (complement_meet) R->L }
% 48.19/6.67 ifeq(join(complement(X), meet(X, complement(complement(X)))), one, ifeq(meet(meet(complement(X), complement(complement(X))), X), zero, complement(complement(X)), meet(X, complement(complement(X)))), meet(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 10 (associativity_of_meet) }
% 48.19/6.67 ifeq(join(complement(X), meet(X, complement(complement(X)))), one, ifeq(meet(complement(X), meet(complement(complement(X)), X)), zero, complement(complement(X)), meet(X, complement(complement(X)))), meet(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.67 ifeq(join(complement(X), meet(X, complement(complement(X)))), one, ifeq(meet(complement(X), meet(X, complement(complement(X)))), zero, complement(complement(X)), meet(X, complement(complement(X)))), meet(X, complement(complement(X))))
% 48.19/6.67 = { by axiom 12 (meet_join_complement) }
% 48.19/6.67 meet(X, complement(complement(X)))
% 48.19/6.67 = { by lemma 21 }
% 48.19/6.67 X
% 48.19/6.67
% 48.19/6.67 Lemma 23: meet(X, join(Y, X)) = X.
% 48.19/6.67 Proof:
% 48.19/6.67 meet(X, join(Y, X))
% 48.19/6.67 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.67 meet(X, join(X, Y))
% 48.19/6.67 = { by axiom 9 (absorption1) }
% 48.19/6.67 X
% 48.19/6.67
% 48.19/6.67 Lemma 24: meet(X, complement(join(X, Y))) = zero.
% 48.19/6.67 Proof:
% 48.19/6.67 meet(X, complement(join(X, Y)))
% 48.19/6.67 = { by axiom 9 (absorption1) R->L }
% 48.19/6.67 meet(meet(X, join(X, Y)), complement(join(X, Y)))
% 48.19/6.67 = { by axiom 10 (associativity_of_meet) }
% 48.19/6.67 meet(X, meet(join(X, Y), complement(join(X, Y))))
% 48.19/6.67 = { by axiom 5 (complement_meet) }
% 48.19/6.67 meet(X, zero)
% 48.19/6.67 = { by lemma 16 }
% 48.19/6.67 zero
% 48.19/6.67
% 48.19/6.67 Lemma 25: join(X, join(complement(X), Y)) = one.
% 48.19/6.67 Proof:
% 48.19/6.67 join(X, join(complement(X), Y))
% 48.19/6.67 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.67 join(X, join(Y, complement(X)))
% 48.19/6.67 = { by lemma 19 }
% 48.19/6.67 one
% 48.19/6.67
% 48.19/6.67 Lemma 26: join(X, meet(complement(X), Y)) = join(X, Y).
% 48.19/6.67 Proof:
% 48.19/6.67 join(X, meet(complement(X), Y))
% 48.19/6.67 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.67 join(X, meet(Y, complement(X)))
% 48.19/6.67 = { by lemma 22 R->L }
% 48.19/6.67 complement(complement(join(X, meet(Y, complement(X)))))
% 48.19/6.67 = { by axiom 6 (ifeq_axiom) R->L }
% 48.19/6.67 ifeq(zero, zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.67 = { by axiom 6 (ifeq_axiom) R->L }
% 48.19/6.67 ifeq(one, one, ifeq(zero, zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.67 = { by lemma 25 R->L }
% 48.19/6.67 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(zero, zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.67 = { by axiom 5 (complement_meet) R->L }
% 48.19/6.67 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), complement(complement(join(X, meet(Y, complement(X)))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.67 = { by lemma 14 R->L }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), zero)), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by axiom 5 (complement_meet) R->L }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(meet(Y, complement(join(X, meet(Y, complement(X))))), complement(meet(Y, complement(join(X, meet(Y, complement(X))))))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by axiom 10 (associativity_of_meet) }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, meet(complement(join(X, meet(Y, complement(X)))), complement(meet(Y, complement(join(X, meet(Y, complement(X)))))))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, meet(complement(meet(Y, complement(join(X, meet(Y, complement(X)))))), complement(join(X, meet(Y, complement(X)))))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by axiom 10 (associativity_of_meet) R->L }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(meet(Y, complement(meet(Y, complement(join(X, meet(Y, complement(X))))))), complement(join(X, meet(Y, complement(X))))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by lemma 18 }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(meet(Y, complement(meet(Y, complement(join(X, meet(Y, complement(X))))))), complement(complement(join(X, meet(Y, complement(X))))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, complement(join(X, meet(Y, complement(X))))))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.68 ifeq(join(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), one, ifeq(meet(complement(join(X, meet(Y, complement(X)))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), zero, complement(complement(join(X, meet(Y, complement(X))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))), join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y)))))
% 48.19/6.68 = { by axiom 12 (meet_join_complement) }
% 48.19/6.68 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(join(X, meet(Y, complement(X)))), Y))))
% 48.19/6.68 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.68 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, complement(join(X, meet(Y, complement(X))))))))
% 48.19/6.68 = { by lemma 23 R->L }
% 48.19/6.68 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), join(complement(X), complement(join(X, meet(Y, complement(X))))))))))
% 48.19/6.68 = { by axiom 12 (meet_join_complement) R->L }
% 48.19/6.68 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(join(X, join(complement(X), complement(join(X, meet(Y, complement(X)))))), one, ifeq(meet(X, join(complement(X), complement(join(X, meet(Y, complement(X)))))), zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.68 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.68 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(join(X, join(complement(X), complement(join(X, meet(Y, complement(X)))))), one, ifeq(meet(X, join(complement(join(X, meet(Y, complement(X)))), complement(X))), zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.69 = { by lemma 17 R->L }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(join(X, join(complement(X), complement(join(X, meet(Y, complement(X)))))), one, ifeq(meet(X, join(complement(X), meet(X, complement(join(X, meet(Y, complement(X))))))), zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.69 = { by lemma 24 }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(join(X, join(complement(X), complement(join(X, meet(Y, complement(X)))))), one, ifeq(meet(X, join(complement(X), zero)), zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.69 = { by lemma 14 }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(join(X, join(complement(X), complement(join(X, meet(Y, complement(X)))))), one, ifeq(meet(X, complement(X)), zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.69 = { by axiom 5 (complement_meet) }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(join(X, join(complement(X), complement(join(X, meet(Y, complement(X)))))), one, ifeq(zero, zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.69 = { by lemma 25 }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(one, one, ifeq(zero, zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.69 = { by axiom 6 (ifeq_axiom) }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), ifeq(zero, zero, complement(X), join(complement(X), complement(join(X, meet(Y, complement(X)))))))))))
% 48.19/6.69 = { by axiom 6 (ifeq_axiom) }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(X, meet(Y, complement(X)))), complement(X))))))
% 48.19/6.69 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(X), complement(join(X, meet(Y, complement(X)))))))))
% 48.19/6.69 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(X), complement(join(X, meet(complement(X), Y))))))))
% 48.19/6.69 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(X), complement(join(meet(complement(X), Y), X)))))))
% 48.19/6.69 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(Y, meet(complement(join(meet(complement(X), Y), X)), complement(X))))))
% 48.19/6.69 = { by axiom 10 (associativity_of_meet) R->L }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(meet(Y, complement(join(meet(complement(X), Y), X))), complement(X)))))
% 48.19/6.69 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(complement(X), meet(Y, complement(join(meet(complement(X), Y), X)))))))
% 48.19/6.69 = { by axiom 10 (associativity_of_meet) R->L }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(meet(meet(complement(X), Y), complement(join(meet(complement(X), Y), X))))))
% 48.19/6.69 = { by lemma 24 }
% 48.19/6.69 join(complement(complement(join(X, meet(Y, complement(X))))), meet(Y, complement(zero)))
% 48.19/6.69 = { by lemma 22 }
% 48.19/6.69 join(join(X, meet(Y, complement(X))), meet(Y, complement(zero)))
% 48.19/6.69 = { by axiom 8 (associativity_of_join) }
% 48.19/6.69 join(X, join(meet(Y, complement(X)), meet(Y, complement(zero))))
% 48.19/6.69 = { by lemma 15 R->L }
% 48.19/6.69 join(X, join(meet(Y, complement(X)), meet(Y, join(zero, complement(zero)))))
% 48.19/6.69 = { by axiom 2 (complement_join) }
% 48.19/6.69 join(X, join(meet(Y, complement(X)), meet(Y, one)))
% 48.19/6.69 = { by lemma 13 }
% 48.19/6.69 join(X, join(meet(Y, complement(X)), Y))
% 48.19/6.69 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.69 join(X, join(Y, meet(Y, complement(X))))
% 48.19/6.69 = { by axiom 7 (absorption2) }
% 48.19/6.69 join(X, Y)
% 48.19/6.69
% 48.19/6.69 Lemma 27: join(X, join(complement(complement(X)), Y)) = join(Y, complement(complement(X))).
% 48.19/6.69 Proof:
% 48.19/6.69 join(X, join(complement(complement(X)), Y))
% 48.19/6.69 = { by axiom 8 (associativity_of_join) R->L }
% 48.19/6.69 join(join(X, complement(complement(X))), Y)
% 48.19/6.69 = { by lemma 20 }
% 48.19/6.69 join(complement(complement(X)), Y)
% 48.19/6.69 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.69 join(Y, complement(complement(X)))
% 48.19/6.69
% 48.19/6.69 Lemma 28: meet(X, join(Y, meet(X, Z))) = meet(X, join(Y, Z)).
% 48.19/6.69 Proof:
% 48.19/6.69 meet(X, join(Y, meet(X, Z)))
% 48.19/6.69 = { by lemma 23 R->L }
% 48.19/6.69 meet(X, meet(join(Y, meet(X, Z)), join(Z, join(Y, meet(X, Z)))))
% 48.19/6.69 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.69 meet(X, meet(join(Y, meet(X, Z)), join(join(Y, meet(X, Z)), Z)))
% 48.19/6.69 = { by axiom 8 (associativity_of_join) }
% 48.19/6.69 meet(X, meet(join(Y, meet(X, Z)), join(Y, join(meet(X, Z), Z))))
% 48.19/6.69 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.70 meet(X, meet(join(Y, meet(X, Z)), join(Y, join(Z, meet(X, Z)))))
% 48.19/6.70 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.70 meet(X, meet(join(Y, meet(X, Z)), join(Y, join(Z, meet(Z, X)))))
% 48.19/6.70 = { by axiom 7 (absorption2) }
% 48.19/6.70 meet(X, meet(join(Y, meet(X, Z)), join(Y, Z)))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.70 meet(X, meet(join(Y, meet(X, Z)), join(Z, Y)))
% 48.19/6.70 = { by axiom 4 (commutativity_of_meet) }
% 48.19/6.70 meet(X, meet(join(Z, Y), join(Y, meet(X, Z))))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.70 meet(X, meet(join(Y, Z), join(Y, meet(X, Z))))
% 48.19/6.70 = { by axiom 10 (associativity_of_meet) R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(X, Z)))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(meet(X, Z), Y))
% 48.19/6.70 = { by lemma 22 R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(meet(X, Z), complement(complement(Y))))
% 48.19/6.70 = { by lemma 27 R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, join(complement(complement(Y)), meet(X, Z))))
% 48.19/6.70 = { by lemma 26 R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(complement(Y), join(complement(complement(Y)), meet(X, Z)))))
% 48.19/6.70 = { by lemma 14 R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(complement(Y), join(complement(complement(Y)), meet(X, join(Z, zero))))))
% 48.19/6.70 = { by axiom 5 (complement_meet) R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(complement(Y), join(complement(complement(Y)), meet(X, join(Z, meet(complement(Y), complement(complement(Y)))))))))
% 48.19/6.70 = { by axiom 11 (equation_H76) R->L }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(complement(Y), join(complement(complement(Y)), meet(X, join(complement(complement(Y)), Z))))))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(complement(Y), join(complement(complement(Y)), meet(X, join(Z, complement(complement(Y))))))))
% 48.19/6.70 = { by lemma 26 }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, join(complement(complement(Y)), meet(X, join(Z, complement(complement(Y)))))))
% 48.19/6.70 = { by lemma 27 }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(meet(X, join(Z, complement(complement(Y)))), complement(complement(Y))))
% 48.19/6.70 = { by lemma 22 }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(meet(X, join(Z, complement(complement(Y)))), Y))
% 48.19/6.70 = { by lemma 22 }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(meet(X, join(Z, Y)), Y))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(X, join(Z, Y))))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.70 meet(meet(X, join(Y, Z)), join(Y, meet(X, join(Y, Z))))
% 48.19/6.70 = { by lemma 23 }
% 48.19/6.70 meet(X, join(Y, Z))
% 48.19/6.70
% 48.19/6.70 Lemma 29: meet(X, join(meet(X, Y), meet(X, Z))) = join(meet(X, Y), meet(X, Z)).
% 48.19/6.70 Proof:
% 48.19/6.70 meet(X, join(meet(X, Y), meet(X, Z)))
% 48.19/6.70 = { by axiom 7 (absorption2) R->L }
% 48.19/6.70 meet(join(X, meet(X, Y)), join(meet(X, Y), meet(X, Z)))
% 48.19/6.70 = { by axiom 4 (commutativity_of_meet) R->L }
% 48.19/6.70 meet(join(meet(X, Y), meet(X, Z)), join(X, meet(X, Y)))
% 48.19/6.70 = { by axiom 7 (absorption2) R->L }
% 48.19/6.70 meet(join(meet(X, Y), meet(X, Z)), join(join(X, meet(X, Z)), meet(X, Y)))
% 48.19/6.70 = { by axiom 8 (associativity_of_join) }
% 48.19/6.70 meet(join(meet(X, Y), meet(X, Z)), join(X, join(meet(X, Z), meet(X, Y))))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) }
% 48.19/6.70 meet(join(meet(X, Y), meet(X, Z)), join(X, join(meet(X, Y), meet(X, Z))))
% 48.19/6.70 = { by lemma 23 }
% 48.19/6.70 join(meet(X, Y), meet(X, Z))
% 48.19/6.70
% 48.19/6.70 Goal 1 (prove_distributivity): meet(a, join(b, c)) = join(meet(a, b), meet(a, c)).
% 48.19/6.70 Proof:
% 48.19/6.70 meet(a, join(b, c))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.70 meet(a, join(c, b))
% 48.19/6.70 = { by lemma 28 R->L }
% 48.19/6.70 meet(a, join(c, meet(a, b)))
% 48.19/6.70 = { by axiom 1 (commutativity_of_join) R->L }
% 48.19/6.70 meet(a, join(meet(a, b), c))
% 48.19/6.70 = { by axiom 3 (idempotence_of_meet) R->L }
% 48.19/6.70 meet(meet(a, a), join(meet(a, b), c))
% 48.19/6.70 = { by axiom 10 (associativity_of_meet) }
% 48.19/6.70 meet(a, meet(a, join(meet(a, b), c)))
% 48.19/6.70 = { by lemma 28 R->L }
% 48.19/6.70 meet(a, meet(a, join(meet(a, b), meet(a, c))))
% 48.19/6.70 = { by lemma 29 }
% 48.19/6.70 meet(a, join(meet(a, b), meet(a, c)))
% 48.19/6.70 = { by lemma 29 }
% 48.19/6.70 join(meet(a, b), meet(a, c))
% 48.19/6.70 % SZS output end Proof
% 48.19/6.70
% 48.19/6.70 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------