%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT237-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 9.29s 1.62s
% Output : Proof 9.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT237-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 14:08:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.29/1.62 Command-line arguments: --no-flatten-goal
% 9.29/1.62
% 9.29/1.62 % SZS status Unsatisfiable
% 9.29/1.62
% 9.29/1.63 % SZS output start Proof
% 9.29/1.63 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 9.29/1.63 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 9.29/1.63 Axiom 3 (complement_meet): meet(X, complement(X)) = zero.
% 9.29/1.63 Axiom 4 (prove_distributivity_hypothesis): meet(b, a) = a.
% 9.29/1.63 Axiom 5 (commutativity_of_join): join(X, Y) = join(Y, X).
% 9.29/1.63 Axiom 6 (complement_join): join(X, complement(X)) = one.
% 9.29/1.63 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 9.29/1.63 Axiom 8 (absorption1): meet(X, join(X, Y)) = X.
% 9.29/1.63 Axiom 9 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 9.29/1.63 Axiom 10 (absorption2): join(X, meet(X, Y)) = X.
% 9.29/1.63 Axiom 11 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 9.29/1.63 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 9.29/1.63 Axiom 13 (equation_H40): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(W, meet(Z, join(X, Y)))))).
% 9.29/1.63
% 9.29/1.63 Lemma 14: meet(X, one) = X.
% 9.29/1.63 Proof:
% 9.29/1.63 meet(X, one)
% 9.29/1.63 = { by axiom 6 (complement_join) R->L }
% 9.29/1.63 meet(X, join(X, complement(X)))
% 9.29/1.63 = { by axiom 8 (absorption1) }
% 9.29/1.63 X
% 9.29/1.63
% 9.29/1.63 Lemma 15: join(X, zero) = X.
% 9.29/1.63 Proof:
% 9.29/1.63 join(X, zero)
% 9.29/1.63 = { by axiom 3 (complement_meet) R->L }
% 9.29/1.63 join(X, meet(X, complement(X)))
% 9.29/1.63 = { by axiom 10 (absorption2) }
% 9.29/1.63 X
% 9.29/1.63
% 9.29/1.63 Lemma 16: join(X, meet(Y, X)) = X.
% 9.29/1.63 Proof:
% 9.29/1.63 join(X, meet(Y, X))
% 9.29/1.63 = { by axiom 2 (commutativity_of_meet) R->L }
% 9.29/1.63 join(X, meet(X, Y))
% 9.29/1.63 = { by axiom 10 (absorption2) }
% 9.29/1.64 X
% 9.29/1.64
% 9.29/1.64 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 9.29/1.64 Proof:
% 9.29/1.64 join(complement(b), complement(a))
% 9.29/1.64 = { by axiom 12 (meet_join_complement) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(b), complement(a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 5 (commutativity_of_join) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), complement(b))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by lemma 14 R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), one))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 6 (complement_join) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(a, complement(a))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 1 (idempotence_of_meet) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(meet(complement(b), complement(b)), join(a, complement(a))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 9 (associativity_of_meet) }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), meet(complement(b), join(a, complement(a)))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by lemma 16 R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(meet(complement(b), join(a, complement(a))), meet(a, meet(complement(b), join(a, complement(a)))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 2 (commutativity_of_meet) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(meet(complement(b), join(a, complement(a))), meet(a, meet(join(a, complement(a)), complement(b))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 9 (associativity_of_meet) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(meet(complement(b), join(a, complement(a))), meet(meet(a, join(a, complement(a))), complement(b)))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 8 (absorption1) }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(meet(complement(b), join(a, complement(a))), meet(a, complement(b)))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 5 (commutativity_of_join) }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(meet(a, complement(b)), meet(complement(b), join(a, complement(a))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 2 (commutativity_of_meet) }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(meet(complement(b), a), meet(complement(b), join(a, complement(a))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 13 (equation_H40) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(a, meet(complement(b), a))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by lemma 16 }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 2 (commutativity_of_meet) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(a, complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 4 (prove_distributivity_hypothesis) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(meet(b, a), complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 9 (associativity_of_meet) }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(b, meet(a, complement(b))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 2 (commutativity_of_meet) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(b, meet(complement(b), a)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 9 (associativity_of_meet) R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(meet(b, complement(b)), a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by axiom 3 (complement_meet) }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(zero, a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.64 = { by lemma 15 R->L }
% 9.29/1.64 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(zero, join(a, zero)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 5 (commutativity_of_join) }
% 9.29/1.65 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(zero, join(zero, a)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 8 (absorption1) }
% 9.29/1.65 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), zero)), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by lemma 15 }
% 9.29/1.65 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, complement(a)), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 3 (complement_meet) }
% 9.29/1.65 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 5 (commutativity_of_join) R->L }
% 9.29/1.65 ifeq(join(a, join(complement(a), complement(b))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 11 (associativity_of_join) R->L }
% 9.29/1.65 ifeq(join(join(a, complement(a)), complement(b)), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 6 (complement_join) }
% 9.29/1.65 ifeq(join(one, complement(b)), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by lemma 14 R->L }
% 9.29/1.65 ifeq(meet(join(one, complement(b)), one), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 2 (commutativity_of_meet) }
% 9.29/1.65 ifeq(meet(one, join(one, complement(b))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 8 (absorption1) }
% 9.29/1.65 ifeq(one, one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 7 (ifeq_axiom) }
% 9.29/1.65 ifeq(zero, zero, complement(a), join(complement(b), complement(a)))
% 9.29/1.65 = { by axiom 7 (ifeq_axiom) }
% 9.29/1.65 complement(a)
% 9.29/1.65 % SZS output end Proof
% 9.29/1.65
% 9.29/1.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------