%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 11:39:48 AM UTC 2026
% Result : Theorem 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:14:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.55 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
% 0.20/0.55
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55
% 0.20/0.55 % SZS output start Proof
% 0.20/0.55 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.20/0.55 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.20/0.55 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.20/0.55 Axiom 4 (domain3): addition(domain(X), one) = one.
% 0.20/0.55 Axiom 5 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 0.20/0.55 Axiom 6 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 0.20/0.55 Axiom 7 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.20/0.55 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.20/0.55 Axiom 9 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.20/0.55 Axiom 10 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 0.20/0.55 Axiom 11 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 0.20/0.55
% 0.20/0.55 Lemma 12: addition(one, domain(X)) = one.
% 0.20/0.55 Proof:
% 0.20/0.55 addition(one, domain(X))
% 0.20/0.55 = { by axiom 3 (additive_commutativity) R->L }
% 0.20/0.55 addition(domain(X), one)
% 0.20/0.55 = { by axiom 4 (domain3) }
% 0.20/0.55 one
% 0.20/0.55
% 0.20/0.55 Goal 1 (goals): domain(star(x0)) = one.
% 0.20/0.55 Proof:
% 0.20/0.55 domain(star(x0))
% 0.20/0.55 = { by axiom 11 (order_1) R->L }
% 0.20/0.56 domain(ifeq2(leq(addition(one, multiplication(x0, star(x0))), star(x0)), true, addition(addition(one, multiplication(x0, star(x0))), star(x0)), star(x0)))
% 0.20/0.56 = { by axiom 10 (star_unfold_right) }
% 0.20/0.56 domain(ifeq2(true, true, addition(addition(one, multiplication(x0, star(x0))), star(x0)), star(x0)))
% 0.20/0.56 = { by axiom 8 (ifeq_axiom) }
% 0.20/0.56 domain(addition(addition(one, multiplication(x0, star(x0))), star(x0)))
% 0.20/0.56 = { by axiom 7 (additive_associativity) R->L }
% 0.20/0.56 domain(addition(one, addition(multiplication(x0, star(x0)), star(x0))))
% 0.20/0.56 = { by axiom 3 (additive_commutativity) }
% 0.20/0.56 domain(addition(one, addition(star(x0), multiplication(x0, star(x0)))))
% 0.20/0.56 = { by axiom 2 (multiplicative_left_identity) R->L }
% 0.20/0.56 domain(addition(one, addition(multiplication(one, star(x0)), multiplication(x0, star(x0)))))
% 0.20/0.56 = { by axiom 9 (left_distributivity) R->L }
% 0.20/0.56 domain(addition(one, multiplication(addition(one, x0), star(x0))))
% 0.20/0.56 = { by axiom 3 (additive_commutativity) }
% 0.20/0.56 domain(addition(one, multiplication(addition(x0, one), star(x0))))
% 0.20/0.56 = { by axiom 5 (domain5) }
% 0.20/0.56 addition(domain(one), domain(multiplication(addition(x0, one), star(x0))))
% 0.20/0.56 = { by axiom 1 (multiplicative_right_identity) R->L }
% 0.20/0.56 addition(multiplication(domain(one), one), domain(multiplication(addition(x0, one), star(x0))))
% 0.20/0.56 = { by axiom 6 (domain1) R->L }
% 0.20/0.56 addition(addition(one, multiplication(domain(one), one)), domain(multiplication(addition(x0, one), star(x0))))
% 0.20/0.56 = { by axiom 1 (multiplicative_right_identity) }
% 0.20/0.56 addition(addition(one, domain(one)), domain(multiplication(addition(x0, one), star(x0))))
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 addition(one, domain(multiplication(addition(x0, one), star(x0))))
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 one
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Theorem (the conjecture is true).
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