%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT252-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 11:44:38 AM UTC 2026
% Result : Unsatisfiable 31.20s 4.41s
% Output : Proof 31.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT252-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n015.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 14:11:45 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.20/4.41 Command-line arguments: --no-flatten-goal
% 31.20/4.41
% 31.20/4.41 % SZS status Unsatisfiable
% 31.20/4.41
% 31.20/4.44 % SZS output start Proof
% 31.20/4.44 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 31.20/4.44 Axiom 2 (complement_meet): meet(X, complement(X)) = zero.
% 31.20/4.44 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 31.20/4.44 Axiom 4 (idempotence_of_join): join(X, X) = X.
% 31.20/4.44 Axiom 5 (commutativity_of_join): join(X, Y) = join(Y, X).
% 31.20/4.44 Axiom 6 (complement_join): join(X, complement(X)) = one.
% 31.20/4.44 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 31.20/4.44 Axiom 8 (absorption1): meet(X, join(X, Y)) = X.
% 31.20/4.44 Axiom 9 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 31.20/4.44 Axiom 10 (absorption2): join(X, meet(X, Y)) = X.
% 31.20/4.44 Axiom 11 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 31.20/4.44 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 31.20/4.44 Axiom 13 (equation_H70): meet(X, join(Y, meet(Z, join(Y, W)))) = meet(X, join(Y, meet(Z, join(W, meet(Y, join(X, Z)))))).
% 31.20/4.44
% 31.20/4.44 Lemma 14: meet(X, one) = X.
% 31.20/4.44 Proof:
% 31.20/4.44 meet(X, one)
% 31.20/4.44 = { by axiom 6 (complement_join) R->L }
% 31.20/4.44 meet(X, join(X, complement(X)))
% 31.20/4.44 = { by axiom 8 (absorption1) }
% 31.20/4.44 X
% 31.20/4.44
% 31.20/4.44 Lemma 15: join(X, zero) = X.
% 31.20/4.44 Proof:
% 31.20/4.44 join(X, zero)
% 31.20/4.44 = { by axiom 2 (complement_meet) R->L }
% 31.20/4.44 join(X, meet(X, complement(X)))
% 31.20/4.44 = { by axiom 10 (absorption2) }
% 31.20/4.44 X
% 31.20/4.44
% 31.20/4.44 Lemma 16: join(X, meet(Y, X)) = X.
% 31.20/4.44 Proof:
% 31.20/4.44 join(X, meet(Y, X))
% 31.20/4.44 = { by axiom 1 (commutativity_of_meet) R->L }
% 31.20/4.44 join(X, meet(X, Y))
% 31.20/4.44 = { by axiom 10 (absorption2) }
% 31.20/4.44 X
% 31.20/4.45
% 31.20/4.45 Lemma 17: join(X, meet(Y, join(X, meet(Y, Z)))) = join(X, meet(Y, Z)).
% 31.20/4.45 Proof:
% 31.20/4.45 join(X, meet(Y, join(X, meet(Y, Z))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) R->L }
% 31.20/4.45 join(X, meet(Y, join(X, meet(Z, Y))))
% 31.20/4.45 = { by lemma 16 R->L }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(Z, meet(Y, join(X, meet(Z, Y))))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) R->L }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(Z, meet(Y, join(X, meet(Y, Z))))))
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) R->L }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(Z, meet(Y, join(meet(Y, Z), X)))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) R->L }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(meet(Y, join(meet(Y, Z), X)), Z)))
% 31.20/4.45 = { by axiom 9 (associativity_of_meet) }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(Y, meet(join(meet(Y, Z), X), Z))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(Y, meet(Z, join(meet(Y, Z), X)))))
% 31.20/4.45 = { by axiom 9 (associativity_of_meet) R->L }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(meet(Y, Z), join(meet(Y, Z), X))))
% 31.20/4.45 = { by axiom 8 (absorption1) }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(Y, Z)))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) }
% 31.20/4.45 join(X, join(meet(Y, join(X, meet(Z, Y))), meet(Z, Y)))
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) }
% 31.20/4.45 join(X, join(meet(Z, Y), meet(Y, join(X, meet(Z, Y)))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) }
% 31.20/4.45 join(X, join(meet(Z, Y), meet(Y, join(X, meet(Y, Z)))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) }
% 31.20/4.45 join(X, join(meet(Y, Z), meet(Y, join(X, meet(Y, Z)))))
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) R->L }
% 31.20/4.45 join(X, join(meet(Y, Z), meet(Y, join(meet(Y, Z), X))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) R->L }
% 31.20/4.45 join(X, join(meet(Y, Z), meet(join(meet(Y, Z), X), Y)))
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) R->L }
% 31.20/4.45 join(X, join(meet(join(meet(Y, Z), X), Y), meet(Y, Z)))
% 31.20/4.45 = { by axiom 11 (associativity_of_join) R->L }
% 31.20/4.45 join(join(X, meet(join(meet(Y, Z), X), Y)), meet(Y, Z))
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) }
% 31.20/4.45 join(meet(Y, Z), join(X, meet(join(meet(Y, Z), X), Y)))
% 31.20/4.45 = { by axiom 11 (associativity_of_join) R->L }
% 31.20/4.45 join(join(meet(Y, Z), X), meet(join(meet(Y, Z), X), Y))
% 31.20/4.45 = { by axiom 10 (absorption2) }
% 31.20/4.45 join(meet(Y, Z), X)
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) }
% 31.20/4.45 join(X, meet(Y, Z))
% 31.20/4.45
% 31.20/4.45 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 31.20/4.45 Proof:
% 31.20/4.45 join(complement(b), complement(a))
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) R->L }
% 31.20/4.45 join(complement(a), complement(b))
% 31.20/4.45 = { by axiom 7 (ifeq_axiom) R->L }
% 31.20/4.45 join(complement(a), ifeq(zero, zero, complement(b), meet(complement(b), complement(a))))
% 31.20/4.45 = { by axiom 8 (absorption1) R->L }
% 31.20/4.45 join(complement(a), ifeq(meet(zero, join(zero, complement(a))), zero, complement(b), meet(complement(b), complement(a))))
% 31.20/4.45 = { by axiom 5 (commutativity_of_join) R->L }
% 31.20/4.45 join(complement(a), ifeq(meet(zero, join(complement(a), zero)), zero, complement(b), meet(complement(b), complement(a))))
% 31.20/4.45 = { by lemma 15 }
% 31.20/4.45 join(complement(a), ifeq(meet(zero, complement(a)), zero, complement(b), meet(complement(b), complement(a))))
% 31.20/4.45 = { by axiom 2 (complement_meet) R->L }
% 31.20/4.45 join(complement(a), ifeq(meet(meet(b, complement(b)), complement(a)), zero, complement(b), meet(complement(b), complement(a))))
% 31.20/4.45 = { by axiom 9 (associativity_of_meet) }
% 31.20/4.45 join(complement(a), ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))))
% 31.20/4.45 = { by axiom 7 (ifeq_axiom) R->L }
% 31.20/4.45 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))))
% 31.20/4.45 = { by axiom 6 (complement_join) R->L }
% 31.20/4.45 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))))
% 31.20/4.45 = { by lemma 14 R->L }
% 31.20/4.45 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))))
% 31.20/4.45 = { by axiom 8 (absorption1) R->L }
% 31.20/4.45 join(complement(a), ifeq(join(b, meet(complement(b), meet(one, 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))))
% 31.20/4.45 = { by axiom 1 (commutativity_of_meet) R->L }
% 31.20/4.45 join(complement(a), ifeq(join(b, meet(complement(b), meet(join(one, b), one))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 31.20/4.46 = { by lemma 14 }
% 31.20/4.46 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))))
% 31.20/4.46 = { by axiom 5 (commutativity_of_join) }
% 31.20/4.46 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))))
% 31.20/4.46 = { by axiom 6 (complement_join) R->L }
% 31.20/4.46 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))))
% 31.20/4.46 = { by axiom 11 (associativity_of_join) R->L }
% 31.20/4.46 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))))
% 31.20/4.46 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 31.20/4.46 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))))
% 31.20/4.46 = { by axiom 10 (absorption2) }
% 31.20/4.46 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))))
% 31.20/4.46 = { by lemma 17 R->L }
% 31.20/4.46 join(complement(a), ifeq(join(b, meet(complement(b), 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))))
% 31.20/4.46 = { by axiom 13 (equation_H70) }
% 31.20/4.46 join(complement(a), ifeq(join(b, meet(complement(b), join(b, meet(complement(b), join(complement(a), meet(b, 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))))
% 31.20/4.46 = { by lemma 17 }
% 31.20/4.46 join(complement(a), ifeq(join(b, meet(complement(b), join(complement(a), meet(b, 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))))
% 31.20/4.46 = { by axiom 4 (idempotence_of_join) }
% 31.20/4.46 join(complement(a), ifeq(join(b, meet(complement(b), join(complement(a), meet(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))))
% 31.20/4.46 = { by axiom 2 (complement_meet) }
% 31.20/4.46 join(complement(a), ifeq(join(b, meet(complement(b), join(complement(a), zero))), one, ifeq(meet(b, meet(complement(b), complement(a))), zero, complement(b), meet(complement(b), complement(a))), meet(complement(b), complement(a))))
% 31.20/4.46 = { by lemma 15 }
% 31.20/4.46 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))))
% 31.20/4.46 = { by axiom 12 (meet_join_complement) }
% 31.20/4.46 join(complement(a), meet(complement(b), complement(a)))
% 31.20/4.46 = { by lemma 16 }
% 31.20/4.46 complement(a)
% 31.20/4.46 % SZS output end Proof
% 31.20/4.46
% 31.20/4.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------