%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE079+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 11:39:46 AM UTC 2026
% Result : Theorem 0.46s 0.49s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE079+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.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 13:07:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.49 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.46/0.49
% 0.46/0.49 % SZS status Theorem
% 0.46/0.49
% 0.46/0.50 % SZS output start Proof
% 0.46/0.50 Axiom 1 (left_annihilation): multiplication(zero, X) = zero.
% 0.46/0.50 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.46/0.50 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 0.46/0.50 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.46/0.50 Axiom 5 (additive_identity): addition(X, zero) = X.
% 0.46/0.50 Axiom 6 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 0.46/0.50 Axiom 7 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 0.46/0.50 Axiom 8 (goals_1): multiplication(domain(X), antidomain(X)) = zero.
% 0.46/0.50 Axiom 9 (goals): addition(domain(X), antidomain(X)) = one.
% 0.46/0.50 Axiom 10 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 0.46/0.50 Axiom 11 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 0.46/0.50 Axiom 12 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.46/0.50 Axiom 13 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.46/0.50
% 0.46/0.50 Lemma 14: domain(domain(X)) = domain(X).
% 0.46/0.50 Proof:
% 0.46/0.50 domain(domain(X))
% 0.46/0.50 = { by axiom 2 (multiplicative_left_identity) R->L }
% 0.46/0.50 domain(multiplication(one, domain(X)))
% 0.46/0.50 = { by axiom 6 (domain2) R->L }
% 0.46/0.50 domain(multiplication(one, X))
% 0.46/0.50 = { by axiom 2 (multiplicative_left_identity) }
% 0.46/0.50 domain(X)
% 0.46/0.50
% 0.46/0.50 Lemma 15: multiplication(domain(X), multiplication(antidomain(X), Y)) = zero.
% 0.46/0.50 Proof:
% 0.46/0.50 multiplication(domain(X), multiplication(antidomain(X), Y))
% 0.46/0.50 = { by axiom 10 (multiplicative_associativity) }
% 0.46/0.50 multiplication(multiplication(domain(X), antidomain(X)), Y)
% 0.46/0.50 = { by axiom 8 (goals_1) }
% 0.46/0.50 multiplication(zero, Y)
% 0.46/0.50 = { by axiom 1 (left_annihilation) }
% 0.46/0.50 zero
% 0.46/0.50
% 0.46/0.50 Lemma 16: multiplication(domain(multiplication(antidomain(X), domain(Y))), multiplication(antidomain(Y), Z)) = zero.
% 0.46/0.50 Proof:
% 0.46/0.50 multiplication(domain(multiplication(antidomain(X), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 5 (additive_identity) R->L }
% 0.46/0.50 addition(multiplication(domain(multiplication(antidomain(X), domain(Y))), multiplication(antidomain(Y), Z)), zero)
% 0.46/0.50 = { by axiom 4 (additive_commutativity) }
% 0.46/0.50 addition(zero, multiplication(domain(multiplication(antidomain(X), domain(Y))), multiplication(antidomain(Y), Z)))
% 0.46/0.50 = { by lemma 15 R->L }
% 0.46/0.50 addition(multiplication(domain(Y), multiplication(antidomain(Y), Z)), multiplication(domain(multiplication(antidomain(X), domain(Y))), multiplication(antidomain(Y), Z)))
% 0.46/0.50 = { by axiom 13 (left_distributivity) R->L }
% 0.46/0.50 multiplication(addition(domain(Y), domain(multiplication(antidomain(X), domain(Y)))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by lemma 14 R->L }
% 0.46/0.50 multiplication(addition(domain(domain(Y)), domain(multiplication(antidomain(X), domain(Y)))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 7 (domain5) R->L }
% 0.46/0.50 multiplication(domain(addition(domain(Y), multiplication(antidomain(X), domain(Y)))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 4 (additive_commutativity) R->L }
% 0.46/0.50 multiplication(domain(addition(multiplication(antidomain(X), domain(Y)), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 2 (multiplicative_left_identity) R->L }
% 0.46/0.50 multiplication(domain(addition(multiplication(antidomain(X), domain(Y)), multiplication(one, domain(Y)))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 13 (left_distributivity) R->L }
% 0.46/0.50 multiplication(domain(multiplication(addition(antidomain(X), one), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 9 (goals) R->L }
% 0.46/0.50 multiplication(domain(multiplication(addition(antidomain(X), addition(domain(X), antidomain(X))), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 4 (additive_commutativity) R->L }
% 0.46/0.50 multiplication(domain(multiplication(addition(antidomain(X), addition(antidomain(X), domain(X))), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 12 (additive_associativity) }
% 0.46/0.50 multiplication(domain(multiplication(addition(addition(antidomain(X), antidomain(X)), domain(X)), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 3 (additive_idempotence) }
% 0.46/0.50 multiplication(domain(multiplication(addition(antidomain(X), domain(X)), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 4 (additive_commutativity) }
% 0.46/0.50 multiplication(domain(multiplication(addition(domain(X), antidomain(X)), domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 9 (goals) }
% 0.46/0.50 multiplication(domain(multiplication(one, domain(Y))), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by axiom 2 (multiplicative_left_identity) }
% 0.46/0.50 multiplication(domain(domain(Y)), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by lemma 14 }
% 0.46/0.50 multiplication(domain(Y), multiplication(antidomain(Y), Z))
% 0.46/0.50 = { by lemma 15 }
% 0.46/0.50 zero
% 0.46/0.50
% 0.46/0.50 Goal 1 (goals_2): multiplication(antidomain(x0), domain(x0)) = zero.
% 0.46/0.50 Proof:
% 0.46/0.50 multiplication(antidomain(x0), domain(x0))
% 0.46/0.50 = { by axiom 5 (additive_identity) R->L }
% 0.46/0.50 addition(multiplication(antidomain(x0), domain(x0)), zero)
% 0.46/0.50 = { by lemma 16 R->L }
% 0.46/0.50 addition(multiplication(antidomain(x0), domain(x0)), multiplication(domain(multiplication(antidomain(x0), domain(x0))), multiplication(antidomain(x0), domain(x0))))
% 0.46/0.50 = { by axiom 11 (domain1) }
% 0.46/0.50 multiplication(domain(multiplication(antidomain(x0), domain(x0))), multiplication(antidomain(x0), domain(x0)))
% 0.46/0.50 = { by lemma 16 }
% 0.46/0.50 zero
% 0.46/0.50 % SZS output end Proof
% 0.46/0.50
% 0.46/0.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------