%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT225-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 11:44:34 AM UTC 2026
% Result : Unsatisfiable 61.54s 8.29s
% Output : Proof 62.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT225-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 14:07:31 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.54/8.29 Command-line arguments: --stitch /export/starexec/sandbox/solver/bin/stitch --hint-skel-cost 0 --hint-skel-factor 0.5 --no-flatten-goal
% 61.54/8.29
% 61.54/8.29 % SZS status Unsatisfiable
% 61.54/8.29
% 62.32/8.30 % SZS output start Proof
% 62.32/8.30 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 62.32/8.30 Axiom 2 (complement_join): join(X, complement(X)) = one.
% 62.32/8.30 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 62.32/8.30 Axiom 4 (complement_meet): meet(X, complement(X)) = zero.
% 62.32/8.30 Axiom 5 (prove_distributivity_hypothesis): meet(b, a) = a.
% 62.32/8.30 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 62.32/8.30 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 62.32/8.30 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 62.32/8.30 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 62.32/8.30 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 62.32/8.30 Axiom 11 (equation_H10): meet(X, join(Y, meet(X, Z))) = meet(X, join(Y, meet(Z, join(X, meet(Y, Z))))).
% 62.32/8.30 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 62.32/8.30
% 62.32/8.30 Lemma 13: meet(X, one) = X.
% 62.32/8.30 Proof:
% 62.32/8.30 meet(X, one)
% 62.32/8.30 = { by axiom 2 (complement_join) R->L }
% 62.32/8.30 meet(X, join(X, complement(X)))
% 62.32/8.30 = { by axiom 9 (absorption1) }
% 62.32/8.30 X
% 62.32/8.30
% 62.32/8.30 Lemma 14: meet(one, X) = X.
% 62.32/8.30 Proof:
% 62.32/8.30 meet(one, X)
% 62.32/8.30 = { by axiom 3 (commutativity_of_meet) R->L }
% 62.32/8.30 meet(X, one)
% 62.32/8.30 = { by lemma 13 }
% 62.32/8.30 X
% 62.32/8.30
% 62.32/8.30 Lemma 15: join(X, one) = one.
% 62.32/8.30 Proof:
% 62.32/8.30 join(X, one)
% 62.32/8.30 = { by axiom 1 (commutativity_of_join) R->L }
% 62.32/8.30 join(one, X)
% 62.32/8.30 = { by lemma 14 R->L }
% 62.32/8.30 join(one, meet(one, X))
% 62.32/8.30 = { by axiom 7 (absorption2) }
% 62.32/8.30 one
% 62.32/8.30
% 62.32/8.30 Lemma 16: join(X, meet(Y, X)) = X.
% 62.32/8.30 Proof:
% 62.32/8.30 join(X, meet(Y, X))
% 62.32/8.30 = { by axiom 3 (commutativity_of_meet) R->L }
% 62.32/8.30 join(X, meet(X, Y))
% 62.32/8.30 = { by axiom 7 (absorption2) }
% 62.32/8.30 X
% 62.32/8.30
% 62.32/8.30 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 62.32/8.30 Proof:
% 62.32/8.30 join(complement(b), complement(a))
% 62.32/8.30 = { by axiom 1 (commutativity_of_join) R->L }
% 62.32/8.30 join(complement(a), complement(b))
% 62.32/8.30 = { by axiom 6 (ifeq_axiom) R->L }
% 62.32/8.30 join(complement(a), ifeq(zero, zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.30 = { by axiom 4 (complement_meet) R->L }
% 62.32/8.30 join(complement(a), ifeq(meet(meet(b, complement(a)), complement(meet(b, complement(a)))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.30 = { by axiom 10 (associativity_of_meet) }
% 62.32/8.30 join(complement(a), ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.30 = { by axiom 6 (ifeq_axiom) R->L }
% 62.32/8.30 join(complement(a), ifeq(one, one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.30 = { by lemma 15 R->L }
% 62.32/8.30 join(complement(a), ifeq(join(b, one), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 2 (complement_join) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(b, complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 8 (associativity_of_join) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(join(b, meet(b, complement(a))), complement(meet(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 7 (absorption2) }
% 62.32/8.31 join(complement(a), ifeq(join(b, complement(meet(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by lemma 14 R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(one, complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by lemma 15 R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(join(b, one), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 2 (complement_join) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(join(b, join(a, complement(a))), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 8 (associativity_of_join) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(join(join(b, a), complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 5 (prove_distributivity_hypothesis) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(join(join(b, meet(b, a)), complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 7 (absorption2) }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(join(b, complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 1 (commutativity_of_join) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(join(complement(a), b), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 3 (commutativity_of_meet) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(complement(meet(b, complement(a))), join(complement(a), b))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 1 (commutativity_of_join) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, meet(complement(meet(b, complement(a))), join(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by lemma 16 R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), meet(complement(meet(b, complement(a))), join(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 3 (commutativity_of_meet) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), meet(join(b, complement(a)), complement(meet(b, complement(a))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 10 (associativity_of_meet) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(meet(complement(a), join(b, complement(a))), complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 3 (commutativity_of_meet) }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), meet(complement(a), join(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 1 (commutativity_of_join) R->L }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), meet(complement(a), join(complement(a), b))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 9 (absorption1) }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 3 (commutativity_of_meet) }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 1 (commutativity_of_join) }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(a), complement(meet(b, complement(a)))), meet(complement(meet(b, complement(a))), join(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.31 = { by axiom 3 (commutativity_of_meet) }
% 62.32/8.31 join(complement(a), ifeq(join(b, join(meet(complement(a), complement(meet(b, complement(a)))), meet(join(b, complement(a)), complement(meet(b, complement(a)))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by axiom 8 (associativity_of_join) R->L }
% 62.32/8.32 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(join(b, complement(a)), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by axiom 3 (commutativity_of_meet) R->L }
% 62.32/8.32 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, complement(a)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by lemma 13 R->L }
% 62.32/8.32 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), one)))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by axiom 2 (complement_join) R->L }
% 62.32/8.32 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(meet(b, complement(a)), complement(meet(b, complement(a)))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by axiom 1 (commutativity_of_join) R->L }
% 62.32/8.32 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by axiom 11 (equation_H10) R->L }
% 62.32/8.32 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(meet(b, complement(a))), complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by axiom 3 (commutativity_of_meet) }
% 62.32/8.32 join(complement(a), ifeq(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), complement(meet(b, complement(a))))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by lemma 16 }
% 62.32/8.32 join(complement(a), ifeq(join(b, meet(complement(a), complement(meet(b, complement(a))))), one, ifeq(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, complement(b), meet(complement(a), complement(meet(b, complement(a))))), meet(complement(a), complement(meet(b, complement(a))))))
% 62.32/8.32 = { by axiom 12 (meet_join_complement) }
% 62.32/8.32 join(complement(a), meet(complement(a), complement(meet(b, complement(a)))))
% 62.32/8.32 = { by axiom 7 (absorption2) }
% 62.32/8.32 complement(a)
% 62.32/8.32 % SZS output end Proof
% 62.32/8.32
% 62.32/8.32 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------