%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE063+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 11:39:44 AM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE063+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 13:09:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.50 Command-line arguments: --no-flatten-goal
% 0.18/0.50
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 Axiom 1 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.18/0.50 Axiom 2 (domain3): addition(domain(X), one) = one.
% 0.18/0.50 Axiom 3 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.18/0.50 Axiom 4 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.18/0.50 Axiom 5 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 0.18/0.50 Axiom 6 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 0.18/0.50 Axiom 7 (goals): addition(x0, multiplication(domain(x1), x0)) = multiplication(domain(x1), x0).
% 0.18/0.50 Axiom 8 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 0.18/0.50 Axiom 9 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.18/0.50
% 0.18/0.50 Lemma 10: domain(domain(X)) = domain(X).
% 0.18/0.50 Proof:
% 0.18/0.50 domain(domain(X))
% 0.18/0.50 = { by axiom 4 (multiplicative_left_identity) R->L }
% 0.18/0.50 domain(multiplication(one, domain(X)))
% 0.18/0.50 = { by axiom 6 (domain2) R->L }
% 0.18/0.50 domain(multiplication(one, X))
% 0.18/0.50 = { by axiom 4 (multiplicative_left_identity) }
% 0.18/0.50 domain(X)
% 0.18/0.50
% 0.18/0.50 Lemma 11: addition(one, domain(X)) = one.
% 0.18/0.50 Proof:
% 0.18/0.50 addition(one, domain(X))
% 0.18/0.50 = { by axiom 1 (additive_commutativity) R->L }
% 0.18/0.50 addition(domain(X), one)
% 0.18/0.50 = { by axiom 2 (domain3) }
% 0.18/0.50 one
% 0.18/0.50
% 0.18/0.50 Goal 1 (goals_1): addition(domain(x0), domain(x1)) = domain(x1).
% 0.18/0.50 Proof:
% 0.18/0.50 addition(domain(x0), domain(x1))
% 0.18/0.50 = { by axiom 1 (additive_commutativity) R->L }
% 0.18/0.50 addition(domain(x1), domain(x0))
% 0.18/0.50 = { by lemma 10 R->L }
% 0.18/0.50 addition(domain(domain(x1)), domain(x0))
% 0.18/0.50 = { by axiom 4 (multiplicative_left_identity) R->L }
% 0.18/0.50 addition(domain(domain(x1)), domain(multiplication(one, x0)))
% 0.18/0.50 = { by lemma 11 R->L }
% 0.18/0.50 addition(domain(domain(x1)), domain(multiplication(addition(one, domain(x1)), x0)))
% 0.18/0.50 = { by axiom 9 (left_distributivity) }
% 0.18/0.50 addition(domain(domain(x1)), domain(addition(multiplication(one, x0), multiplication(domain(x1), x0))))
% 0.18/0.50 = { by axiom 4 (multiplicative_left_identity) }
% 0.18/0.50 addition(domain(domain(x1)), domain(addition(x0, multiplication(domain(x1), x0))))
% 0.18/0.50 = { by axiom 7 (goals) }
% 0.18/0.50 addition(domain(domain(x1)), domain(multiplication(domain(x1), x0)))
% 0.18/0.50 = { by axiom 6 (domain2) }
% 0.18/0.50 addition(domain(domain(x1)), domain(multiplication(domain(x1), domain(x0))))
% 0.18/0.50 = { by axiom 5 (domain5) R->L }
% 0.18/0.50 domain(addition(domain(x1), multiplication(domain(x1), domain(x0))))
% 0.18/0.50 = { by axiom 3 (multiplicative_right_identity) R->L }
% 0.18/0.50 domain(addition(multiplication(domain(x1), one), multiplication(domain(x1), domain(x0))))
% 0.18/0.50 = { by axiom 8 (right_distributivity) R->L }
% 0.18/0.50 domain(multiplication(domain(x1), addition(one, domain(x0))))
% 0.18/0.50 = { by lemma 11 }
% 0.18/0.50 domain(multiplication(domain(x1), one))
% 0.18/0.50 = { by axiom 3 (multiplicative_right_identity) }
% 0.18/0.50 domain(domain(x1))
% 0.18/0.50 = { by lemma 10 }
% 0.18/0.50 domain(x1)
% 0.18/0.50 % SZS output end Proof
% 0.18/0.50
% 0.18/0.50 RESULT: Theorem (the conjecture is true).
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