%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT251-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12.84s 2.13s
% Output : Proof 12.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT251-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n017.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 14:03:50 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.84/2.13 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 12.84/2.13
% 12.84/2.13 % SZS status Unsatisfiable
% 12.84/2.13
% 12.84/2.15 % SZS output start Proof
% 12.84/2.15 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 12.84/2.15 Axiom 2 (complement_meet): meet(X, complement(X)) = zero.
% 12.84/2.15 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 12.84/2.15 Axiom 4 (commutativity_of_join): join(X, Y) = join(Y, X).
% 12.84/2.15 Axiom 5 (complement_join): join(X, complement(X)) = one.
% 12.84/2.15 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 12.84/2.15 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 12.84/2.15 Axiom 8 (absorption2): join(X, meet(X, Y)) = X.
% 12.84/2.15 Axiom 9 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 12.84/2.15 Axiom 10 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 12.84/2.15 Axiom 11 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 12.84/2.15 Axiom 12 (equation_H69): meet(X, join(Y, Z)) = join(meet(X, join(Z, meet(X, Y))), meet(X, join(Y, meet(X, Z)))).
% 12.84/2.15
% 12.84/2.15 Lemma 13: join(X, zero) = X.
% 12.84/2.15 Proof:
% 12.84/2.15 join(X, zero)
% 12.84/2.15 = { by axiom 2 (complement_meet) R->L }
% 12.84/2.15 join(X, meet(X, complement(X)))
% 12.84/2.15 = { by axiom 8 (absorption2) }
% 12.84/2.15 X
% 12.84/2.15
% 12.84/2.15 Lemma 14: meet(X, join(Y, X)) = X.
% 12.84/2.15 Proof:
% 12.84/2.15 meet(X, join(Y, X))
% 12.84/2.15 = { by axiom 4 (commutativity_of_join) R->L }
% 12.84/2.15 meet(X, join(X, Y))
% 12.84/2.15 = { by axiom 6 (absorption1) }
% 12.84/2.15 X
% 12.84/2.15
% 12.84/2.15 Lemma 15: meet(X, zero) = zero.
% 12.84/2.15 Proof:
% 12.84/2.15 meet(X, zero)
% 12.84/2.15 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.84/2.15 meet(zero, X)
% 12.84/2.15 = { by lemma 13 R->L }
% 12.84/2.15 meet(zero, join(X, zero))
% 12.84/2.15 = { by lemma 14 }
% 12.84/2.15 zero
% 12.84/2.15
% 12.84/2.15 Lemma 16: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 12.84/2.15 Proof:
% 12.84/2.15 join(Y, join(X, Z))
% 12.84/2.15 = { by axiom 4 (commutativity_of_join) R->L }
% 12.84/2.15 join(join(X, Z), Y)
% 12.84/2.15 = { by axiom 9 (associativity_of_join) }
% 12.84/2.15 join(X, join(Z, Y))
% 12.84/2.15 = { by axiom 4 (commutativity_of_join) }
% 12.84/2.15 join(X, join(Y, Z))
% 12.84/2.16
% 12.84/2.16 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 12.84/2.16 Proof:
% 12.84/2.16 join(complement(b), complement(a))
% 12.84/2.16 = { by axiom 11 (meet_join_complement) R->L }
% 12.84/2.16 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)))
% 12.84/2.16 = { by lemma 14 R->L }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(a, join(complement(b), complement(a))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 4 (commutativity_of_join) R->L }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(a, join(complement(a), complement(b))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 12 (equation_H69) }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), join(meet(a, join(complement(b), meet(a, complement(a)))), meet(a, join(complement(a), meet(a, complement(b))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 2 (complement_meet) }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), join(meet(a, join(complement(b), zero)), meet(a, join(complement(a), meet(a, complement(b))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by lemma 13 }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), join(meet(a, complement(b)), meet(a, join(complement(a), meet(a, complement(b))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 1 (commutativity_of_meet) }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), join(meet(a, complement(b)), meet(a, join(complement(a), meet(complement(b), a)))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 1 (commutativity_of_meet) }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), join(meet(complement(b), a), meet(a, join(complement(a), meet(complement(b), a)))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 4 (commutativity_of_join) R->L }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), join(meet(complement(b), a), meet(a, join(meet(complement(b), a), complement(a)))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), join(meet(complement(b), a), meet(join(meet(complement(b), a), complement(a)), a)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by lemma 16 }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(meet(complement(b), a), join(complement(a), meet(join(meet(complement(b), a), complement(a)), a)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 9 (associativity_of_join) R->L }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(join(meet(complement(b), a), complement(a)), meet(join(meet(complement(b), a), complement(a)), a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 8 (absorption2) }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(meet(complement(b), a), complement(a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 4 (commutativity_of_join) }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(complement(b), a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.16 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.84/2.16 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(a, complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(meet(b, a), complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 1 (commutativity_of_meet) }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(meet(a, b), complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 7 (associativity_of_meet) }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(a, meet(b, complement(b))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 2 (complement_meet) }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), meet(a, zero))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by lemma 15 }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), join(complement(a), zero)), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by lemma 13 }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, join(complement(b), complement(a))), complement(a)), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 7 (associativity_of_meet) }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, meet(join(complement(b), complement(a)), complement(a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, meet(complement(a), join(complement(b), complement(a)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 7 (associativity_of_meet) R->L }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(meet(a, complement(a)), join(complement(b), complement(a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 2 (complement_meet) }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(zero, join(complement(b), complement(a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(join(complement(b), complement(a)), zero), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by lemma 15 }
% 12.84/2.17 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by lemma 16 }
% 12.84/2.17 ifeq(join(complement(b), join(a, complement(a))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 5 (complement_join) }
% 12.84/2.17 ifeq(join(complement(b), one), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 4 (commutativity_of_join) R->L }
% 12.84/2.17 ifeq(join(one, complement(b)), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 6 (absorption1) R->L }
% 12.84/2.17 ifeq(join(one, meet(complement(b), join(complement(b), complement(complement(b))))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 5 (complement_join) }
% 12.84/2.17 ifeq(join(one, meet(complement(b), one)), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.84/2.17 ifeq(join(one, meet(one, complement(b))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 8 (absorption2) }
% 12.84/2.17 ifeq(one, one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 10 (ifeq_axiom) }
% 12.84/2.17 ifeq(zero, zero, complement(a), join(complement(b), complement(a)))
% 12.84/2.17 = { by axiom 10 (ifeq_axiom) }
% 12.84/2.17 complement(a)
% 12.84/2.17 % SZS output end Proof
% 12.84/2.17
% 12.84/2.17 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------