%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT239-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 11:44:36 AM UTC 2026
% Result : Unsatisfiable 53.99s 7.32s
% Output : Proof 53.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT239-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n016.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 14:12:46 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.99/7.32 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 53.99/7.32
% 53.99/7.32 % SZS status Unsatisfiable
% 53.99/7.32
% 53.99/7.35 % SZS output start Proof
% 53.99/7.35 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 53.99/7.35 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 53.99/7.35 Axiom 3 (complement_join): join(X, complement(X)) = one.
% 53.99/7.35 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 53.99/7.35 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 53.99/7.35 Axiom 6 (prove_distributivity_hypothesis): meet(b, a) = a.
% 53.99/7.35 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 53.99/7.35 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 53.99/7.35 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 53.99/7.35 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 53.99/7.35 Axiom 11 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 53.99/7.35 Axiom 12 (equation_H49): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, join(meet(X, Z), meet(Z, join(Y, W))))).
% 53.99/7.35 Axiom 13 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 53.99/7.35
% 53.99/7.35 Lemma 14: meet(X, one) = X.
% 53.99/7.35 Proof:
% 53.99/7.35 meet(X, one)
% 53.99/7.35 = { by axiom 3 (complement_join) R->L }
% 53.99/7.35 meet(X, join(X, complement(X)))
% 53.99/7.35 = { by axiom 9 (absorption1) }
% 53.99/7.35 X
% 53.99/7.36
% 53.99/7.36 Lemma 15: join(X, meet(Y, X)) = X.
% 53.99/7.36 Proof:
% 53.99/7.36 join(X, meet(Y, X))
% 53.99/7.36 = { by axiom 4 (commutativity_of_meet) R->L }
% 53.99/7.36 join(X, meet(X, Y))
% 53.99/7.36 = { by axiom 7 (absorption2) }
% 53.99/7.36 X
% 53.99/7.36
% 53.99/7.36 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 53.99/7.36 Proof:
% 53.99/7.36 join(complement(b), complement(a))
% 53.99/7.36 = { by axiom 2 (commutativity_of_join) R->L }
% 53.99/7.36 join(complement(a), complement(b))
% 53.99/7.36 = { by axiom 11 (ifeq_axiom) R->L }
% 53.99/7.36 join(complement(a), ifeq(zero, zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 7 (absorption2) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(zero, meet(zero, complement(a))), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 2 (commutativity_of_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(meet(zero, complement(a)), zero), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 5 (complement_meet) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(meet(zero, complement(a)), meet(meet(zero, complement(a)), complement(meet(zero, complement(a))))), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 7 (absorption2) }
% 53.99/7.36 join(complement(a), ifeq(meet(zero, complement(a)), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 4 (commutativity_of_meet) }
% 53.99/7.36 join(complement(a), ifeq(meet(complement(a), zero), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 5 (complement_meet) R->L }
% 53.99/7.36 join(complement(a), ifeq(meet(complement(a), meet(b, complement(b))), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 4 (commutativity_of_meet) R->L }
% 53.99/7.36 join(complement(a), ifeq(meet(meet(b, complement(b)), complement(a)), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 10 (associativity_of_meet) }
% 53.99/7.36 join(complement(a), ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 11 (ifeq_axiom) R->L }
% 53.99/7.36 join(complement(a), ifeq(one, one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 3 (complement_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, complement(b)), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by lemma 14 R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), one)), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 7 (absorption2) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(one, meet(one, b)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 4 (commutativity_of_meet) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(one, meet(b, one)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by lemma 14 }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(one, b))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 2 (commutativity_of_join) }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(b, one))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 3 (complement_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(b, join(a, complement(a))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 2 (commutativity_of_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(b, join(complement(a), a)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 8 (associativity_of_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(join(b, complement(a)), a))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 2 (commutativity_of_join) }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(a, join(b, complement(a))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 8 (associativity_of_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(join(a, b), complement(a)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 2 (commutativity_of_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(join(b, a), complement(a)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 6 (prove_distributivity_hypothesis) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(join(b, meet(b, a)), complement(a)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 4 (commutativity_of_meet) }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(join(b, meet(a, b)), complement(a)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by lemma 15 }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(b, complement(a)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by axiom 2 (commutativity_of_join) R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, meet(complement(b), join(complement(a), b))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.36 = { by lemma 15 R->L }
% 53.99/7.36 join(complement(a), ifeq(join(b, join(meet(complement(b), join(complement(a), b)), meet(complement(a), meet(complement(b), join(complement(a), b))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 4 (commutativity_of_meet) R->L }
% 53.99/7.37 join(complement(a), ifeq(join(b, join(meet(complement(b), join(complement(a), b)), meet(complement(a), meet(join(complement(a), b), complement(b))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 10 (associativity_of_meet) R->L }
% 53.99/7.37 join(complement(a), ifeq(join(b, join(meet(complement(b), join(complement(a), b)), meet(meet(complement(a), join(complement(a), b)), complement(b)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 9 (absorption1) }
% 53.99/7.37 join(complement(a), ifeq(join(b, join(meet(complement(b), join(complement(a), b)), meet(complement(a), complement(b)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 2 (commutativity_of_join) }
% 53.99/7.37 join(complement(a), ifeq(join(b, join(meet(complement(a), complement(b)), meet(complement(b), join(complement(a), b)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 8 (associativity_of_join) R->L }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(complement(a), b))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 2 (commutativity_of_join) R->L }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(b, complement(a)))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by lemma 15 R->L }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(b, join(complement(a), meet(complement(b), complement(a)))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 2 (commutativity_of_join) R->L }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(b, join(meet(complement(b), complement(a)), complement(a))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by lemma 14 R->L }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(b, join(meet(complement(b), complement(a)), meet(complement(a), one))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 3 (complement_join) R->L }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(b, join(meet(complement(b), complement(a)), meet(complement(a), join(b, complement(b))))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 12 (equation_H49) R->L }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(b, meet(complement(a), join(complement(b), complement(b)))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 1 (idempotence_of_join) }
% 53.99/7.37 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(b))), meet(complement(b), join(b, meet(complement(a), complement(b))))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by lemma 15 }
% 53.99/7.37 join(complement(a), ifeq(join(b, meet(complement(a), complement(b))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 4 (commutativity_of_meet) }
% 53.99/7.37 join(complement(a), ifeq(join(b, meet(complement(b), complement(a))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 53.99/7.37 = { by axiom 13 (meet_join_complement) }
% 53.99/7.37 join(complement(a), meet(complement(b), complement(a)))
% 53.99/7.37 = { by lemma 15 }
% 53.99/7.37 complement(a)
% 53.99/7.37 % SZS output end Proof
% 53.99/7.37
% 53.99/7.37 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------