%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE037+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 11:39:40 AM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE037+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.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 13:05:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.10/0.46
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46
% 0.10/0.46 % SZS output start Proof
% 0.10/0.46 Axiom 1 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.10/0.46 Axiom 2 (additive_idempotence): addition(X, X) = X.
% 0.10/0.46 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.10/0.46 Axiom 4 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.10/0.46 Axiom 5 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.10/0.46 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.10/0.46 Axiom 7 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.10/0.46 Axiom 8 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 0.10/0.46 Axiom 9 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 0.10/0.46 Axiom 10 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 0.10/0.46
% 0.10/0.46 Lemma 11: addition(one, multiplication(addition(X, one), star(X))) = star(X).
% 0.10/0.46 Proof:
% 0.10/0.46 addition(one, multiplication(addition(X, one), star(X)))
% 0.10/0.46 = { by axiom 3 (additive_commutativity) R->L }
% 0.10/0.46 addition(one, multiplication(addition(one, X), star(X)))
% 0.10/0.46 = { by axiom 7 (left_distributivity) }
% 0.10/0.46 addition(one, addition(multiplication(one, star(X)), multiplication(X, star(X))))
% 0.10/0.46 = { by axiom 1 (multiplicative_left_identity) }
% 0.10/0.46 addition(one, addition(star(X), multiplication(X, star(X))))
% 0.10/0.46 = { by axiom 3 (additive_commutativity) R->L }
% 0.10/0.46 addition(one, addition(multiplication(X, star(X)), star(X)))
% 0.10/0.46 = { by axiom 4 (additive_associativity) }
% 0.10/0.46 addition(addition(one, multiplication(X, star(X))), star(X))
% 0.10/0.46 = { by axiom 6 (ifeq_axiom) R->L }
% 0.10/0.46 ifeq2(true, true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 0.10/0.46 = { by axiom 8 (star_unfold_right) R->L }
% 0.10/0.46 ifeq2(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 0.10/0.46 = { by axiom 10 (order_1) }
% 0.10/0.46 star(X)
% 0.10/0.46
% 0.10/0.46 Goal 1 (goals): leq(one, star(x0)) = true.
% 0.10/0.46 Proof:
% 0.10/0.46 leq(one, star(x0))
% 0.10/0.46 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.46 ifeq3(star(x0), star(x0), leq(one, star(x0)), true)
% 0.10/0.46 = { by lemma 11 R->L }
% 0.10/0.46 ifeq3(addition(one, multiplication(addition(x0, one), star(x0))), star(x0), leq(one, star(x0)), true)
% 0.10/0.46 = { by axiom 2 (additive_idempotence) R->L }
% 0.10/0.46 ifeq3(addition(addition(one, one), multiplication(addition(x0, one), star(x0))), star(x0), leq(one, star(x0)), true)
% 0.10/0.46 = { by axiom 4 (additive_associativity) R->L }
% 0.10/0.46 ifeq3(addition(one, addition(one, multiplication(addition(x0, one), star(x0)))), star(x0), leq(one, star(x0)), true)
% 0.10/0.46 = { by lemma 11 }
% 0.10/0.46 ifeq3(addition(one, star(x0)), star(x0), leq(one, star(x0)), true)
% 0.10/0.46 = { by axiom 9 (order) }
% 0.10/0.46 true
% 0.10/0.46 % SZS output end Proof
% 0.10/0.46
% 0.10/0.46 RESULT: Theorem (the conjecture is true).
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