%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT218-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 11:44:33 AM UTC 2026
% Result : Unsatisfiable 78.69s 10.44s
% Output : Proof 79.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT218-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n019.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 14:06:33 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 78.69/10.44 Command-line arguments: --flatten-regeneralise
% 78.69/10.44
% 78.69/10.44 % SZS status Unsatisfiable
% 78.69/10.45
% 78.69/10.49 % SZS output start Proof
% 78.69/10.49 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 78.69/10.49 Axiom 2 (complement_meet): meet(X, complement(X)) = zero.
% 78.69/10.49 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 78.69/10.49 Axiom 4 (idempotence_of_join): join(X, X) = X.
% 78.69/10.49 Axiom 5 (commutativity_of_join): join(X, Y) = join(Y, X).
% 78.69/10.49 Axiom 6 (complement_join): join(X, complement(X)) = one.
% 78.69/10.49 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 78.69/10.49 Axiom 8 (absorption1): meet(X, join(X, Y)) = X.
% 78.69/10.49 Axiom 9 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 78.69/10.49 Axiom 10 (absorption2): join(X, meet(X, Y)) = X.
% 78.69/10.49 Axiom 11 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 78.69/10.49 Axiom 12 (equation_H1): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(X, meet(Z, W))))).
% 78.69/10.49 Axiom 13 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 78.69/10.49
% 78.69/10.49 Lemma 14: meet(X, one) = X.
% 78.69/10.49 Proof:
% 78.69/10.49 meet(X, one)
% 78.69/10.49 = { by axiom 6 (complement_join) R->L }
% 78.69/10.49 meet(X, join(X, complement(X)))
% 78.69/10.49 = { by axiom 8 (absorption1) }
% 78.69/10.49 X
% 78.69/10.49
% 78.69/10.49 Lemma 15: join(X, zero) = X.
% 78.69/10.49 Proof:
% 78.69/10.49 join(X, zero)
% 78.69/10.49 = { by axiom 2 (complement_meet) R->L }
% 78.69/10.49 join(X, meet(X, complement(X)))
% 78.69/10.49 = { by axiom 10 (absorption2) }
% 78.69/10.49 X
% 78.69/10.49
% 78.69/10.49 Lemma 16: meet(complement(X), X) = zero.
% 78.69/10.49 Proof:
% 78.69/10.49 meet(complement(X), X)
% 78.69/10.49 = { by axiom 1 (commutativity_of_meet) R->L }
% 78.69/10.49 meet(X, complement(X))
% 78.69/10.49 = { by axiom 2 (complement_meet) }
% 78.69/10.49 zero
% 78.69/10.49
% 78.69/10.49 Lemma 17: join(complement(X), X) = one.
% 78.69/10.49 Proof:
% 78.69/10.49 join(complement(X), X)
% 78.69/10.49 = { by axiom 5 (commutativity_of_join) R->L }
% 78.69/10.49 join(X, complement(X))
% 78.69/10.49 = { by axiom 6 (complement_join) }
% 78.69/10.49 one
% 78.69/10.49
% 78.69/10.49 Lemma 18: join(X, meet(Y, X)) = X.
% 78.69/10.49 Proof:
% 78.69/10.49 join(X, meet(Y, X))
% 78.69/10.49 = { by axiom 1 (commutativity_of_meet) R->L }
% 78.69/10.49 join(X, meet(X, Y))
% 78.69/10.49 = { by axiom 10 (absorption2) }
% 78.69/10.49 X
% 78.69/10.49
% 78.69/10.49 Lemma 19: join(join(X, complement(Y)), Y) = one.
% 78.69/10.49 Proof:
% 78.69/10.49 join(join(X, complement(Y)), Y)
% 78.69/10.49 = { by axiom 5 (commutativity_of_join) R->L }
% 78.69/10.49 join(Y, join(X, complement(Y)))
% 78.69/10.49 = { by axiom 13 (meet_join_complement) R->L }
% 78.69/10.49 join(ifeq(join(complement(Y), Y), one, ifeq(meet(complement(Y), Y), zero, complement(complement(Y)), Y), Y), join(X, complement(Y)))
% 78.69/10.49 = { by lemma 17 }
% 78.69/10.49 join(ifeq(one, one, ifeq(meet(complement(Y), Y), zero, complement(complement(Y)), Y), Y), join(X, complement(Y)))
% 78.69/10.49 = { by axiom 7 (ifeq_axiom) }
% 78.69/10.49 join(ifeq(meet(complement(Y), Y), zero, complement(complement(Y)), Y), join(X, complement(Y)))
% 78.69/10.49 = { by lemma 16 }
% 78.69/10.49 join(ifeq(zero, zero, complement(complement(Y)), Y), join(X, complement(Y)))
% 78.69/10.49 = { by axiom 7 (ifeq_axiom) }
% 78.69/10.49 join(complement(complement(Y)), join(X, complement(Y)))
% 78.69/10.49 = { by axiom 5 (commutativity_of_join) R->L }
% 78.69/10.49 join(join(X, complement(Y)), complement(complement(Y)))
% 78.69/10.49 = { by axiom 11 (associativity_of_join) }
% 78.69/10.49 join(X, join(complement(Y), complement(complement(Y))))
% 78.69/10.49 = { by axiom 5 (commutativity_of_join) }
% 78.69/10.49 join(X, join(complement(complement(Y)), complement(Y)))
% 78.69/10.49 = { by lemma 17 }
% 78.69/10.49 join(X, one)
% 78.69/10.49 = { by axiom 5 (commutativity_of_join) R->L }
% 78.69/10.49 join(one, X)
% 78.69/10.49 = { by lemma 14 R->L }
% 78.69/10.50 meet(join(one, X), one)
% 78.69/10.50 = { by axiom 1 (commutativity_of_meet) }
% 78.69/10.50 meet(one, join(one, X))
% 78.69/10.50 = { by axiom 8 (absorption1) }
% 78.69/10.50 one
% 78.69/10.50
% 78.69/10.50 Lemma 20: meet(X, complement(join(Y, complement(X)))) = complement(join(Y, complement(X))).
% 78.69/10.50 Proof:
% 78.69/10.50 meet(X, complement(join(Y, complement(X))))
% 78.69/10.50 = { by axiom 13 (meet_join_complement) R->L }
% 78.69/10.50 ifeq(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by lemma 18 R->L }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by axiom 1 (commutativity_of_meet) R->L }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), meet(complement(join(Y, complement(X))), X)))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by lemma 15 R->L }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), meet(complement(join(Y, complement(X))), join(X, zero))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by lemma 16 R->L }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), meet(complement(join(Y, complement(X))), join(X, meet(complement(join(Y, complement(X))), join(Y, complement(X)))))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by axiom 12 (equation_H1) R->L }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), meet(complement(join(Y, complement(X))), join(X, join(Y, complement(X))))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by axiom 5 (commutativity_of_join) }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), meet(complement(join(Y, complement(X))), join(join(Y, complement(X)), X))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by lemma 19 }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), meet(complement(join(Y, complement(X))), one)))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by lemma 14 }
% 78.69/10.50 ifeq(join(join(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X)))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 78.69/10.50 = { by axiom 11 (associativity_of_join) }
% 78.69/10.51 ifeq(join(join(Y, complement(X)), join(meet(X, complement(join(Y, complement(X)))), meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X))))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 5 (commutativity_of_join) R->L }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), join(meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 8 (absorption1) R->L }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), join(meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X))))), meet(X, meet(complement(join(Y, complement(X))), join(complement(join(Y, complement(X))), join(Y, complement(X))))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 5 (commutativity_of_join) }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), join(meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X))))), meet(X, meet(complement(join(Y, complement(X))), join(join(Y, complement(X)), complement(join(Y, complement(X)))))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 1 (commutativity_of_meet) }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), join(meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X))))), meet(X, meet(join(join(Y, complement(X)), complement(join(Y, complement(X)))), complement(join(Y, complement(X))))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 9 (associativity_of_meet) R->L }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), join(meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X))))), meet(meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X))))), complement(join(Y, complement(X)))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 10 (absorption2) }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), meet(X, join(join(Y, complement(X)), complement(join(Y, complement(X)))))), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 6 (complement_join) }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), meet(X, one)), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by lemma 14 }
% 79.52/10.51 ifeq(join(join(Y, complement(X)), X), one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by lemma 19 }
% 79.52/10.51 ifeq(one, one, ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X))))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 7 (ifeq_axiom) }
% 79.52/10.51 ifeq(meet(join(Y, complement(X)), meet(X, complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 1 (commutativity_of_meet) R->L }
% 79.52/10.51 ifeq(meet(join(Y, complement(X)), meet(complement(join(Y, complement(X))), X)), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 9 (associativity_of_meet) R->L }
% 79.52/10.51 ifeq(meet(meet(join(Y, complement(X)), complement(join(Y, complement(X)))), X), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 1 (commutativity_of_meet) }
% 79.52/10.51 ifeq(meet(X, meet(join(Y, complement(X)), complement(join(Y, complement(X))))), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 2 (complement_meet) }
% 79.52/10.51 ifeq(meet(X, zero), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 1 (commutativity_of_meet) R->L }
% 79.52/10.51 ifeq(meet(zero, X), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by lemma 15 R->L }
% 79.52/10.51 ifeq(meet(zero, join(X, zero)), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 5 (commutativity_of_join) }
% 79.52/10.51 ifeq(meet(zero, join(zero, X)), zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 8 (absorption1) }
% 79.52/10.51 ifeq(zero, zero, complement(join(Y, complement(X))), meet(X, complement(join(Y, complement(X)))))
% 79.52/10.51 = { by axiom 7 (ifeq_axiom) }
% 79.52/10.51 complement(join(Y, complement(X)))
% 79.52/10.52
% 79.52/10.52 Lemma 21: join(b, complement(join(X, complement(a)))) = b.
% 79.52/10.52 Proof:
% 79.52/10.52 join(b, complement(join(X, complement(a))))
% 79.52/10.52 = { by lemma 20 R->L }
% 79.52/10.52 join(b, meet(a, complement(join(X, complement(a)))))
% 79.52/10.52 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 79.52/10.52 join(b, meet(meet(b, a), complement(join(X, complement(a)))))
% 79.52/10.52 = { by axiom 9 (associativity_of_meet) }
% 79.52/10.52 join(b, meet(b, meet(a, complement(join(X, complement(a))))))
% 79.52/10.52 = { by axiom 1 (commutativity_of_meet) }
% 79.52/10.52 join(b, meet(b, meet(complement(join(X, complement(a))), a)))
% 79.52/10.52 = { by axiom 10 (absorption2) }
% 79.52/10.52 b
% 79.52/10.52
% 79.52/10.52 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 79.52/10.52 Proof:
% 79.52/10.52 join(complement(b), complement(a))
% 79.52/10.52 = { by axiom 5 (commutativity_of_join) R->L }
% 79.52/10.52 join(complement(a), complement(b))
% 79.52/10.52 = { by lemma 21 R->L }
% 79.52/10.52 join(complement(a), complement(join(b, complement(join(complement(a), complement(a))))))
% 79.52/10.52 = { by lemma 20 R->L }
% 79.52/10.52 join(complement(a), meet(join(complement(a), complement(a)), complement(join(b, complement(join(complement(a), complement(a)))))))
% 79.52/10.52 = { by lemma 21 }
% 79.52/10.52 join(complement(a), meet(join(complement(a), complement(a)), complement(b)))
% 79.52/10.52 = { by axiom 1 (commutativity_of_meet) }
% 79.52/10.52 join(complement(a), meet(complement(b), join(complement(a), complement(a))))
% 79.52/10.52 = { by axiom 4 (idempotence_of_join) }
% 79.52/10.52 join(complement(a), meet(complement(b), complement(a)))
% 79.52/10.52 = { by lemma 18 }
% 79.52/10.52 complement(a)
% 79.52/10.52 % SZS output end Proof
% 79.52/10.52
% 79.52/10.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------