%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT246-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 11:44:37 AM UTC 2026
% Result : Unsatisfiable 150.44s 19.46s
% Output : Proof 151.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT246-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 14:08:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 150.44/19.46 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 150.44/19.46
% 150.44/19.46 % SZS status Unsatisfiable
% 150.44/19.46
% 150.44/19.48 % SZS output start Proof
% 150.44/19.48 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 150.44/19.49 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 150.44/19.49 Axiom 3 (complement_join): join(X, complement(X)) = one.
% 150.44/19.49 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 150.44/19.49 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 150.44/19.49 Axiom 6 (prove_distributivity_hypothesis): meet(b, a) = a.
% 150.44/19.49 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 150.44/19.49 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 150.44/19.49 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 150.44/19.49 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 150.44/19.49 Axiom 11 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 150.44/19.49 Axiom 12 (equation_H60): meet(X, meet(join(Y, Z), join(Y, W))) = meet(X, join(Y, meet(join(Y, Z), join(W, meet(X, Y))))).
% 150.44/19.49 Axiom 13 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 150.44/19.49
% 150.44/19.49 Lemma 14: join(X, zero) = X.
% 150.44/19.49 Proof:
% 150.44/19.49 join(X, zero)
% 150.44/19.49 = { by axiom 5 (complement_meet) R->L }
% 150.44/19.49 join(X, meet(X, complement(X)))
% 150.44/19.49 = { by axiom 7 (absorption2) }
% 150.44/19.49 X
% 150.44/19.49
% 150.44/19.49 Lemma 15: meet(a, meet(b, X)) = meet(X, a).
% 150.44/19.49 Proof:
% 150.44/19.49 meet(a, meet(b, X))
% 150.44/19.49 = { by axiom 10 (associativity_of_meet) R->L }
% 150.44/19.49 meet(meet(a, b), X)
% 150.44/19.49 = { by axiom 4 (commutativity_of_meet) R->L }
% 150.44/19.49 meet(meet(b, a), X)
% 150.44/19.49 = { by axiom 6 (prove_distributivity_hypothesis) }
% 150.44/19.49 meet(a, X)
% 150.44/19.49 = { by axiom 4 (commutativity_of_meet) }
% 150.44/19.49 meet(X, a)
% 150.44/19.49
% 150.44/19.49 Lemma 16: join(complement(b), complement(join(a, complement(b)))) = complement(a).
% 150.44/19.49 Proof:
% 150.44/19.49 join(complement(b), complement(join(a, complement(b))))
% 150.44/19.49 = { by axiom 13 (meet_join_complement) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(b), complement(join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 2 (commutativity_of_join) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(join(a, complement(b))), complement(b))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 9 (absorption1) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(a, complement(b))), join(complement(join(a, complement(b))), complement(b))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 4 (commutativity_of_meet) }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(join(complement(join(a, complement(b))), complement(b)), meet(a, join(a, complement(b)))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 4 (commutativity_of_meet) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(join(complement(join(a, complement(b))), complement(b)), meet(join(a, complement(b)), a)), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 10 (associativity_of_meet) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(join(complement(join(a, complement(b))), complement(b)), join(a, complement(b))), a), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by lemma 15 R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, meet(join(complement(join(a, complement(b))), complement(b)), join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 2 (commutativity_of_join) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, meet(join(complement(join(a, complement(b))), complement(b)), join(complement(b), a)))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 2 (commutativity_of_join) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, meet(join(complement(b), complement(join(a, complement(b)))), join(complement(b), a)))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 4 (commutativity_of_meet) R->L }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, meet(join(complement(b), a), join(complement(b), complement(join(a, complement(b))))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.49 = { by axiom 12 (equation_H60) }
% 150.44/19.49 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, join(complement(b), meet(join(complement(b), a), join(complement(join(a, complement(b))), meet(b, complement(b))))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 5 (complement_meet) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, join(complement(b), meet(join(complement(b), a), join(complement(join(a, complement(b))), zero))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by lemma 14 }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, join(complement(b), meet(join(complement(b), a), complement(join(a, complement(b))))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 4 (commutativity_of_meet) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, join(complement(b), meet(complement(join(a, complement(b))), join(complement(b), a))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 2 (commutativity_of_join) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, join(complement(b), meet(complement(join(a, complement(b))), join(a, complement(b)))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by lemma 15 }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(join(complement(b), meet(complement(join(a, complement(b))), join(a, complement(b)))), a), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 4 (commutativity_of_meet) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(b), meet(complement(join(a, complement(b))), join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 4 (commutativity_of_meet) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(b), meet(join(a, complement(b)), complement(join(a, complement(b)))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 5 (complement_meet) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(b), zero)), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by lemma 14 }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, complement(b)), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 4 (commutativity_of_meet) R->L }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(complement(b), a), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by lemma 15 R->L }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(b, complement(b))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 5 (complement_meet) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, zero), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 4 (commutativity_of_meet) R->L }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(zero, a), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by lemma 14 R->L }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(join(meet(zero, a), zero), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 2 (commutativity_of_join) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(join(zero, meet(zero, a)), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 7 (absorption2) }
% 150.44/19.50 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 8 (associativity_of_join) R->L }
% 150.44/19.50 ifeq(join(join(a, complement(b)), complement(join(a, complement(b)))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 150.44/19.50 = { by axiom 3 (complement_join) }
% 150.44/19.50 ifeq(one, one, ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 151.26/19.50 = { by axiom 11 (ifeq_axiom) }
% 151.26/19.50 ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b)))))
% 151.26/19.50 = { by axiom 11 (ifeq_axiom) }
% 151.26/19.50 complement(a)
% 151.26/19.50
% 151.26/19.50 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 151.26/19.50 Proof:
% 151.26/19.50 join(complement(b), complement(a))
% 151.26/19.50 = { by lemma 16 R->L }
% 151.26/19.50 join(complement(b), join(complement(b), complement(join(a, complement(b)))))
% 151.26/19.50 = { by axiom 8 (associativity_of_join) R->L }
% 151.26/19.50 join(join(complement(b), complement(b)), complement(join(a, complement(b))))
% 151.26/19.50 = { by axiom 1 (idempotence_of_join) }
% 151.26/19.50 join(complement(b), complement(join(a, complement(b))))
% 151.26/19.50 = { by lemma 16 }
% 151.26/19.50 complement(a)
% 151.26/19.50 % SZS output end Proof
% 151.26/19.50
% 151.26/19.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------