%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT242-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 66.74s 8.95s
% Output : Proof 66.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT242-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 14:05:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.74/8.95 Command-line arguments: --no-flatten-goal
% 66.74/8.95
% 66.74/8.95 % SZS status Unsatisfiable
% 66.74/8.95
% 66.74/9.00 % SZS output start Proof
% 66.74/9.00 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 66.74/9.00 Axiom 2 (complement_meet): meet(X, complement(X)) = zero.
% 66.74/9.00 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 66.74/9.00 Axiom 4 (idempotence_of_join): join(X, X) = X.
% 66.74/9.00 Axiom 5 (commutativity_of_join): join(X, Y) = join(Y, X).
% 66.74/9.00 Axiom 6 (complement_join): join(X, complement(X)) = one.
% 66.74/9.00 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 66.74/9.00 Axiom 8 (absorption1): meet(X, join(X, Y)) = X.
% 66.74/9.00 Axiom 9 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 66.74/9.00 Axiom 10 (absorption2): join(X, meet(X, Y)) = X.
% 66.74/9.00 Axiom 11 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 66.74/9.00 Axiom 12 (equation_H55): join(X, meet(Y, join(X, Z))) = join(X, meet(Y, join(Z, meet(X, join(Z, Y))))).
% 66.74/9.00 Axiom 13 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 66.74/9.00
% 66.74/9.00 Lemma 14: join(X, zero) = X.
% 66.74/9.00 Proof:
% 66.74/9.00 join(X, zero)
% 66.74/9.00 = { by axiom 2 (complement_meet) R->L }
% 66.74/9.00 join(X, meet(X, complement(X)))
% 66.74/9.00 = { by axiom 10 (absorption2) }
% 66.74/9.00 X
% 66.74/9.00
% 66.74/9.00 Lemma 15: join(zero, X) = X.
% 66.74/9.00 Proof:
% 66.74/9.00 join(zero, X)
% 66.74/9.00 = { by axiom 5 (commutativity_of_join) R->L }
% 66.74/9.00 join(X, zero)
% 66.74/9.00 = { by lemma 14 }
% 66.74/9.00 X
% 66.74/9.00
% 66.74/9.00 Lemma 16: meet(X, zero) = zero.
% 66.74/9.00 Proof:
% 66.74/9.00 meet(X, zero)
% 66.74/9.00 = { by axiom 1 (commutativity_of_meet) R->L }
% 66.74/9.00 meet(zero, X)
% 66.74/9.00 = { by lemma 15 R->L }
% 66.74/9.00 meet(zero, join(zero, X))
% 66.74/9.00 = { by axiom 8 (absorption1) }
% 66.74/9.00 zero
% 66.74/9.01
% 66.74/9.01 Lemma 17: meet(X, join(Y, X)) = X.
% 66.74/9.01 Proof:
% 66.74/9.01 meet(X, join(Y, X))
% 66.74/9.01 = { by axiom 5 (commutativity_of_join) R->L }
% 66.74/9.01 meet(X, join(X, Y))
% 66.74/9.01 = { by axiom 8 (absorption1) }
% 66.74/9.01 X
% 66.74/9.01
% 66.74/9.01 Lemma 18: join(complement(b), complement(join(a, complement(b)))) = complement(a).
% 66.74/9.01 Proof:
% 66.74/9.01 join(complement(b), complement(join(a, complement(b))))
% 66.74/9.01 = { by axiom 13 (meet_join_complement) R->L }
% 66.74/9.01 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)))))
% 66.74/9.01 = { by lemma 17 R->L }
% 66.74/9.01 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(a, complement(b))), 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)))))
% 66.74/9.01 = { by axiom 5 (commutativity_of_join) R->L }
% 66.74/9.01 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(complement(b), a)), 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)))))
% 66.74/9.01 = { by axiom 5 (commutativity_of_join) R->L }
% 66.74/9.01 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(complement(b), a)), meet(a, join(complement(b), complement(join(complement(b), a)))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.01 = { by axiom 5 (commutativity_of_join) R->L }
% 66.74/9.01 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(complement(b), a)), meet(a, join(complement(join(complement(b), a)), complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.01 = { by axiom 12 (equation_H55) }
% 66.74/9.01 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(complement(b), a)), meet(a, join(complement(b), meet(complement(join(complement(b), a)), join(complement(b), a)))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.01 = { by axiom 1 (commutativity_of_meet) }
% 66.74/9.01 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(complement(b), a)), meet(a, join(complement(b), meet(join(complement(b), a), complement(join(complement(b), a))))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.01 = { by axiom 2 (complement_meet) }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(complement(b), a)), 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)))))
% 66.74/9.02 = { by lemma 14 }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(complement(join(complement(b), a)), meet(a, complement(b)))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by axiom 5 (commutativity_of_join) }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(meet(a, complement(b)), complement(join(complement(b), a)))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by axiom 5 (commutativity_of_join) }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, join(complement(b), complement(join(a, complement(b))))), join(meet(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)))))
% 66.74/9.02 = { by axiom 9 (associativity_of_meet) }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(join(complement(b), complement(join(a, complement(b)))), join(meet(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)))))
% 66.74/9.02 = { by axiom 5 (commutativity_of_join) R->L }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(join(complement(b), complement(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)))))
% 66.74/9.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(join(complement(b), complement(join(a, complement(b)))), join(complement(join(a, complement(b))), meet(complement(b), a)))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(join(complement(join(a, complement(b))), meet(complement(b), 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)))))
% 66.74/9.02 = { by axiom 10 (absorption2) R->L }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(join(complement(join(a, complement(b))), meet(complement(b), a)), join(join(complement(b), meet(complement(b), a)), complement(join(a, complement(b)))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by axiom 11 (associativity_of_join) }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(join(complement(join(a, complement(b))), meet(complement(b), a)), join(complement(b), join(meet(complement(b), a), complement(join(a, complement(b))))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by axiom 5 (commutativity_of_join) }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, meet(join(complement(join(a, complement(b))), meet(complement(b), a)), join(complement(b), join(complement(join(a, complement(b))), meet(complement(b), a))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by lemma 17 }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(complement(join(a, complement(b))), meet(complement(b), a))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by axiom 5 (commutativity_of_join) }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(complement(b), a), complement(join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 66.74/9.02 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(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)))))
% 66.74/9.02 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(meet(b, 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)))))
% 66.74/9.03 = { by axiom 9 (associativity_of_meet) }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(b, meet(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)))))
% 66.74/9.03 = { by axiom 1 (commutativity_of_meet) R->L }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(b, meet(complement(b), a)), complement(join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by axiom 9 (associativity_of_meet) R->L }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(meet(b, complement(b)), a), complement(join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by axiom 2 (complement_meet) }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(zero, a), complement(join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by axiom 1 (commutativity_of_meet) R->L }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(meet(a, zero), complement(join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by lemma 16 }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, join(zero, complement(join(a, complement(b))))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by lemma 15 }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, complement(join(a, complement(b)))), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by axiom 8 (absorption1) R->L }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(meet(a, 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)))))
% 66.74/9.03 = { by axiom 9 (associativity_of_meet) }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, 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)))))
% 66.74/9.03 = { by axiom 2 (complement_meet) }
% 66.74/9.03 ifeq(join(a, join(complement(b), complement(join(a, complement(b))))), one, ifeq(meet(a, zero), zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by lemma 16 }
% 66.74/9.03 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)))))
% 66.74/9.03 = { by axiom 11 (associativity_of_join) R->L }
% 66.74/9.03 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)))))
% 66.74/9.03 = { by axiom 6 (complement_join) }
% 66.74/9.03 ifeq(one, one, ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b))))), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by axiom 7 (ifeq_axiom) }
% 66.74/9.03 ifeq(zero, zero, complement(a), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by axiom 7 (ifeq_axiom) }
% 66.74/9.03 complement(a)
% 66.74/9.03
% 66.74/9.03 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 66.74/9.03 Proof:
% 66.74/9.03 join(complement(b), complement(a))
% 66.74/9.03 = { by lemma 18 R->L }
% 66.74/9.03 join(complement(b), join(complement(b), complement(join(a, complement(b)))))
% 66.74/9.03 = { by axiom 11 (associativity_of_join) R->L }
% 66.74/9.03 join(join(complement(b), complement(b)), complement(join(a, complement(b))))
% 66.74/9.03 = { by axiom 4 (idempotence_of_join) }
% 66.74/9.03 join(complement(b), complement(join(a, complement(b))))
% 66.74/9.03 = { by lemma 18 }
% 66.74/9.03 complement(a)
% 66.74/9.03 % SZS output end Proof
% 66.74/9.03
% 66.74/9.03 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------