%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT244-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 173.27s 22.34s
% Output : Proof 173.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT244-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n013.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sun Sep 27 14:07:36 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 173.27/22.34 Command-line arguments: --no-flatten-goal
% 173.27/22.34
% 173.27/22.34 % SZS status Unsatisfiable
% 173.27/22.34
% 173.27/22.34 % SZS output start Proof
% 173.27/22.34 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 173.27/22.34 Axiom 2 (complement_meet): meet(X, complement(X)) = zero.
% 173.27/22.34 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 173.27/22.34 Axiom 4 (idempotence_of_join): join(X, X) = X.
% 173.27/22.34 Axiom 5 (commutativity_of_join): join(X, Y) = join(Y, X).
% 173.27/22.34 Axiom 6 (complement_join): join(X, complement(X)) = one.
% 173.27/22.34 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 173.27/22.34 Axiom 8 (absorption1): meet(X, join(X, Y)) = X.
% 173.27/22.34 Axiom 9 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 173.27/22.34 Axiom 10 (absorption2): join(X, meet(X, Y)) = X.
% 173.27/22.34 Axiom 11 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 173.27/22.34 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 173.27/22.34 Axiom 13 (equation_H58): meet(X, join(Y, Z)) = meet(X, join(Y, meet(join(X, Y), join(Z, meet(X, Y))))).
% 173.27/22.34
% 173.27/22.34 Lemma 14: join(X, zero) = X.
% 173.27/22.34 Proof:
% 173.27/22.34 join(X, zero)
% 173.27/22.34 = { by axiom 2 (complement_meet) R->L }
% 173.27/22.34 join(X, meet(X, complement(X)))
% 173.27/22.34 = { by axiom 10 (absorption2) }
% 173.27/22.35 X
% 173.27/22.35
% 173.27/22.35 Lemma 15: meet(a, complement(b)) = zero.
% 173.27/22.35 Proof:
% 173.27/22.35 meet(a, complement(b))
% 173.27/22.35 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 173.27/22.35 meet(meet(b, a), complement(b))
% 173.27/22.35 = { by axiom 9 (associativity_of_meet) }
% 173.27/22.35 meet(b, meet(a, complement(b)))
% 173.27/22.35 = { by axiom 1 (commutativity_of_meet) R->L }
% 173.27/22.35 meet(b, meet(complement(b), a))
% 173.27/22.35 = { by axiom 9 (associativity_of_meet) R->L }
% 173.27/22.35 meet(meet(b, complement(b)), a)
% 173.27/22.35 = { by axiom 2 (complement_meet) }
% 173.27/22.35 meet(zero, a)
% 173.27/22.35 = { by lemma 14 R->L }
% 173.27/22.35 meet(zero, join(a, zero))
% 173.27/22.35 = { by axiom 5 (commutativity_of_join) }
% 173.27/22.35 meet(zero, join(zero, a))
% 173.27/22.35 = { by axiom 8 (absorption1) }
% 173.27/22.35 zero
% 173.27/22.35
% 173.27/22.35 Lemma 16: join(complement(b), complement(join(a, complement(b)))) = complement(a).
% 173.27/22.35 Proof:
% 173.27/22.35 join(complement(b), complement(join(a, complement(b))))
% 173.27/22.35 = { by axiom 12 (meet_join_complement) R->L }
% 173.27/22.35 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)))))
% 173.27/22.35 = { by axiom 13 (equation_H58) }
% 173.27/22.35 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(b), meet(join(a, complement(b)), join(complement(join(a, complement(b))), meet(a, complement(b)))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 173.27/22.35 = { by lemma 15 }
% 173.27/22.35 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(b), meet(join(a, complement(b)), 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)))))
% 173.27/22.35 = { by lemma 14 }
% 173.27/22.35 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)))))
% 173.27/22.35 = { by axiom 2 (complement_meet) }
% 173.27/22.35 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)))))
% 173.27/22.35 = { by lemma 14 }
% 173.27/22.35 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)))))
% 173.27/22.35 = { by lemma 15 }
% 173.27/22.35 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)))))
% 173.27/22.35 = { by axiom 11 (associativity_of_join) R->L }
% 173.27/22.35 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)))))
% 173.27/22.35 = { by axiom 6 (complement_join) }
% 173.27/22.35 ifeq(one, one, ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 173.27/22.35 = { by axiom 7 (ifeq_axiom) }
% 173.27/22.35 ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b)))))
% 173.27/22.35 = { by axiom 7 (ifeq_axiom) }
% 173.27/22.35 complement(a)
% 173.27/22.35
% 173.27/22.35 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 173.27/22.35 Proof:
% 173.27/22.35 join(complement(b), complement(a))
% 173.27/22.35 = { by lemma 16 R->L }
% 173.27/22.35 join(complement(b), join(complement(b), complement(join(a, complement(b)))))
% 173.27/22.35 = { by axiom 11 (associativity_of_join) R->L }
% 173.27/22.35 join(join(complement(b), complement(b)), complement(join(a, complement(b))))
% 173.27/22.35 = { by axiom 4 (idempotence_of_join) }
% 173.27/22.35 join(complement(b), complement(join(a, complement(b))))
% 173.27/22.35 = { by lemma 16 }
% 173.27/22.35 complement(a)
% 173.27/22.35 % SZS output end Proof
% 173.27/22.35
% 173.27/22.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------