%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE081+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 11:39:47 AM UTC 2026
% Result : Theorem 0.79s 0.52s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE081+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n019.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sun Sep 27 13:09:34 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.79/0.52 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.79/0.52
% 0.79/0.52 % SZS status Theorem
% 0.79/0.52
% 0.79/0.54 % SZS output start Proof
% 0.79/0.54 Axiom 1 (left_annihilation): multiplication(zero, X) = zero.
% 0.79/0.54 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.79/0.54 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 0.79/0.54 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.79/0.54 Axiom 5 (additive_identity): addition(X, zero) = X.
% 0.79/0.54 Axiom 6 (domain3): addition(domain(X), one) = one.
% 0.79/0.54 Axiom 7 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 0.79/0.54 Axiom 8 (goals_1): multiplication(domain(X), antidomain(X)) = zero.
% 0.79/0.54 Axiom 9 (goals): addition(domain(X), antidomain(X)) = one.
% 0.79/0.54 Axiom 10 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 0.79/0.54 Axiom 11 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 0.79/0.54 Axiom 12 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.79/0.54 Axiom 13 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.79/0.54
% 0.79/0.54 Lemma 14: addition(antidomain(X), domain(X)) = one.
% 0.79/0.54 Proof:
% 0.79/0.54 addition(antidomain(X), domain(X))
% 0.79/0.54 = { by axiom 4 (additive_commutativity) R->L }
% 0.79/0.54 addition(domain(X), antidomain(X))
% 0.79/0.54 = { by axiom 9 (goals) }
% 0.79/0.54 one
% 0.79/0.54
% 0.79/0.54 Goal 1 (goals_2): multiplication(antidomain(x0), x0) = zero.
% 0.79/0.54 Proof:
% 0.79/0.54 multiplication(antidomain(x0), x0)
% 0.79/0.54 = { by axiom 2 (multiplicative_left_identity) R->L }
% 0.79/0.54 multiplication(one, multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by lemma 14 R->L }
% 0.79/0.54 multiplication(addition(antidomain(x0), domain(x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 13 (left_distributivity) }
% 0.79/0.54 addition(multiplication(antidomain(x0), multiplication(antidomain(x0), x0)), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 10 (multiplicative_associativity) }
% 0.79/0.54 addition(multiplication(multiplication(antidomain(x0), antidomain(x0)), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 5 (additive_identity) R->L }
% 0.79/0.54 addition(multiplication(addition(multiplication(antidomain(x0), antidomain(x0)), zero), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 4 (additive_commutativity) }
% 0.79/0.54 addition(multiplication(addition(zero, multiplication(antidomain(x0), antidomain(x0))), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 8 (goals_1) R->L }
% 0.79/0.54 addition(multiplication(addition(multiplication(domain(x0), antidomain(x0)), multiplication(antidomain(x0), antidomain(x0))), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 13 (left_distributivity) R->L }
% 0.79/0.54 addition(multiplication(multiplication(addition(domain(x0), antidomain(x0)), antidomain(x0)), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 4 (additive_commutativity) }
% 0.79/0.54 addition(multiplication(multiplication(addition(antidomain(x0), domain(x0)), antidomain(x0)), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by lemma 14 }
% 0.79/0.54 addition(multiplication(multiplication(one, antidomain(x0)), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 2 (multiplicative_left_identity) }
% 0.79/0.54 addition(multiplication(antidomain(x0), x0), multiplication(domain(x0), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 4 (additive_commutativity) R->L }
% 0.79/0.54 addition(multiplication(domain(x0), multiplication(antidomain(x0), x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 2 (multiplicative_left_identity) R->L }
% 0.79/0.54 addition(multiplication(domain(x0), multiplication(antidomain(x0), x0)), multiplication(one, multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 6 (domain3) R->L }
% 0.79/0.54 addition(multiplication(domain(x0), multiplication(antidomain(x0), x0)), multiplication(addition(domain(multiplication(antidomain(x0), x0)), one), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 4 (additive_commutativity) R->L }
% 0.79/0.54 addition(multiplication(domain(x0), multiplication(antidomain(x0), x0)), multiplication(addition(one, domain(multiplication(antidomain(x0), x0))), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 13 (left_distributivity) }
% 0.79/0.54 addition(multiplication(domain(x0), multiplication(antidomain(x0), x0)), addition(multiplication(one, multiplication(antidomain(x0), x0)), multiplication(domain(multiplication(antidomain(x0), x0)), multiplication(antidomain(x0), x0))))
% 0.79/0.54 = { by axiom 2 (multiplicative_left_identity) }
% 0.79/0.54 addition(multiplication(domain(x0), multiplication(antidomain(x0), x0)), addition(multiplication(antidomain(x0), x0), multiplication(domain(multiplication(antidomain(x0), x0)), multiplication(antidomain(x0), x0))))
% 0.79/0.54 = { by axiom 11 (domain1) }
% 0.79/0.54 addition(multiplication(domain(x0), multiplication(antidomain(x0), x0)), multiplication(domain(multiplication(antidomain(x0), x0)), multiplication(antidomain(x0), x0)))
% 0.79/0.54 = { by axiom 13 (left_distributivity) R->L }
% 0.79/0.54 multiplication(addition(domain(x0), domain(multiplication(antidomain(x0), x0))), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 7 (domain5) R->L }
% 0.79/0.54 multiplication(domain(addition(x0, multiplication(antidomain(x0), x0))), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 4 (additive_commutativity) R->L }
% 0.79/0.54 multiplication(domain(addition(multiplication(antidomain(x0), x0), x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 2 (multiplicative_left_identity) R->L }
% 0.79/0.54 multiplication(domain(addition(multiplication(antidomain(x0), x0), multiplication(one, x0))), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 13 (left_distributivity) R->L }
% 0.79/0.54 multiplication(domain(multiplication(addition(antidomain(x0), one), x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by lemma 14 R->L }
% 0.79/0.54 multiplication(domain(multiplication(addition(antidomain(x0), addition(antidomain(x0), domain(x0))), x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 12 (additive_associativity) }
% 0.79/0.54 multiplication(domain(multiplication(addition(addition(antidomain(x0), antidomain(x0)), domain(x0)), x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 3 (additive_idempotence) }
% 0.79/0.54 multiplication(domain(multiplication(addition(antidomain(x0), domain(x0)), x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by lemma 14 }
% 0.79/0.54 multiplication(domain(multiplication(one, x0)), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 2 (multiplicative_left_identity) }
% 0.79/0.54 multiplication(domain(x0), multiplication(antidomain(x0), x0))
% 0.79/0.54 = { by axiom 10 (multiplicative_associativity) }
% 0.79/0.54 multiplication(multiplication(domain(x0), antidomain(x0)), x0)
% 0.79/0.54 = { by axiom 8 (goals_1) }
% 0.79/0.54 multiplication(zero, x0)
% 0.79/0.54 = { by axiom 1 (left_annihilation) }
% 0.79/0.54 zero
% 0.79/0.54 % SZS output end Proof
% 0.79/0.54
% 0.79/0.54 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------