%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE060+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 1.18s 0.60s
% Output : Proof 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE060+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 13:11:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.18/0.60 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.18/0.60
% 1.18/0.60 % SZS status Theorem
% 1.18/0.60
% 1.18/0.61 % SZS output start Proof
% 1.18/0.61 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 1.18/0.61 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 1.18/0.61 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 1.18/0.61 Axiom 4 (domain3): addition(domain(X), one) = one.
% 1.18/0.61 Axiom 5 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 1.18/0.61 Axiom 6 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 1.18/0.61 Axiom 7 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 1.18/0.61 Axiom 8 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 1.18/0.61 Axiom 9 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 1.18/0.61
% 1.18/0.61 Lemma 10: domain(domain(X)) = domain(X).
% 1.18/0.61 Proof:
% 1.18/0.61 domain(domain(X))
% 1.18/0.61 = { by axiom 2 (multiplicative_left_identity) R->L }
% 1.18/0.61 domain(multiplication(one, domain(X)))
% 1.18/0.61 = { by axiom 5 (domain2) R->L }
% 1.18/0.61 domain(multiplication(one, X))
% 1.18/0.61 = { by axiom 2 (multiplicative_left_identity) }
% 1.18/0.61 domain(X)
% 1.18/0.61
% 1.18/0.61 Lemma 11: addition(one, domain(X)) = one.
% 1.18/0.61 Proof:
% 1.18/0.61 addition(one, domain(X))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) R->L }
% 1.18/0.61 addition(domain(X), one)
% 1.18/0.61 = { by axiom 4 (domain3) }
% 1.18/0.61 one
% 1.18/0.61
% 1.18/0.61 Lemma 12: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 1.18/0.61 Proof:
% 1.18/0.61 addition(X, multiplication(X, Y))
% 1.18/0.61 = { by axiom 1 (multiplicative_right_identity) R->L }
% 1.18/0.61 addition(multiplication(X, one), multiplication(X, Y))
% 1.18/0.61 = { by axiom 8 (right_distributivity) R->L }
% 1.18/0.61 multiplication(X, addition(one, Y))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) }
% 1.18/0.61 multiplication(X, addition(Y, one))
% 1.18/0.61
% 1.18/0.61 Lemma 13: addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(Z, X), Y).
% 1.18/0.61 Proof:
% 1.18/0.61 addition(multiplication(X, Y), multiplication(Z, Y))
% 1.18/0.61 = { by axiom 9 (left_distributivity) R->L }
% 1.18/0.61 multiplication(addition(X, Z), Y)
% 1.18/0.61 = { by axiom 3 (additive_commutativity) }
% 1.18/0.61 multiplication(addition(Z, X), Y)
% 1.18/0.61
% 1.18/0.61 Lemma 14: addition(X, multiplication(domain(Y), X)) = X.
% 1.18/0.61 Proof:
% 1.18/0.61 addition(X, multiplication(domain(Y), X))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) R->L }
% 1.18/0.61 addition(multiplication(domain(Y), X), X)
% 1.18/0.61 = { by axiom 2 (multiplicative_left_identity) R->L }
% 1.18/0.61 addition(multiplication(domain(Y), X), multiplication(one, X))
% 1.18/0.61 = { by lemma 13 }
% 1.18/0.61 multiplication(addition(one, domain(Y)), X)
% 1.18/0.61 = { by lemma 11 }
% 1.18/0.61 multiplication(one, X)
% 1.18/0.61 = { by axiom 2 (multiplicative_left_identity) }
% 1.18/0.61 X
% 1.18/0.61
% 1.18/0.61 Goal 1 (goals): domain(multiplication(domain(x0), x1)) = multiplication(domain(x0), domain(x1)).
% 1.18/0.61 Proof:
% 1.18/0.61 domain(multiplication(domain(x0), x1))
% 1.18/0.61 = { by axiom 1 (multiplicative_right_identity) R->L }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), one)
% 1.18/0.61 = { by lemma 11 R->L }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), addition(one, domain(x1)))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) R->L }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), addition(domain(x1), one))
% 1.18/0.61 = { by lemma 12 R->L }
% 1.18/0.61 addition(domain(multiplication(domain(x0), x1)), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 1 (multiplicative_right_identity) R->L }
% 1.18/0.61 addition(multiplication(domain(multiplication(domain(x0), x1)), one), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by lemma 11 R->L }
% 1.18/0.61 addition(multiplication(domain(multiplication(domain(x0), x1)), addition(one, domain(multiplication(domain(x0), x1)))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) R->L }
% 1.18/0.61 addition(multiplication(domain(multiplication(domain(x0), x1)), addition(domain(multiplication(domain(x0), x1)), one)), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by lemma 12 R->L }
% 1.18/0.61 addition(addition(domain(multiplication(domain(x0), x1)), multiplication(domain(multiplication(domain(x0), x1)), domain(multiplication(domain(x0), x1)))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by lemma 10 R->L }
% 1.18/0.61 addition(addition(domain(multiplication(domain(x0), x1)), multiplication(domain(domain(multiplication(domain(x0), x1))), domain(multiplication(domain(x0), x1)))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 7 (domain1) }
% 1.18/0.61 addition(multiplication(domain(domain(multiplication(domain(x0), x1))), domain(multiplication(domain(x0), x1))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by lemma 10 }
% 1.18/0.61 addition(multiplication(domain(multiplication(domain(x0), x1)), domain(multiplication(domain(x0), x1))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 8 (right_distributivity) R->L }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), addition(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), addition(domain(x1), domain(multiplication(domain(x0), x1))))
% 1.18/0.61 = { by axiom 6 (domain5) R->L }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), domain(addition(x1, multiplication(domain(x0), x1))))
% 1.18/0.61 = { by lemma 14 }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), domain(x1))
% 1.18/0.61 = { by lemma 14 R->L }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), addition(domain(x1), multiplication(domain(x0), domain(x1))))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) R->L }
% 1.18/0.61 multiplication(domain(multiplication(domain(x0), x1)), addition(multiplication(domain(x0), domain(x1)), domain(x1)))
% 1.18/0.61 = { by axiom 8 (right_distributivity) }
% 1.18/0.61 addition(multiplication(domain(multiplication(domain(x0), x1)), multiplication(domain(x0), domain(x1))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 5 (domain2) }
% 1.18/0.61 addition(multiplication(domain(multiplication(domain(x0), domain(x1))), multiplication(domain(x0), domain(x1))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 7 (domain1) R->L }
% 1.18/0.61 addition(addition(multiplication(domain(x0), domain(x1)), multiplication(domain(multiplication(domain(x0), domain(x1))), multiplication(domain(x0), domain(x1)))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 5 (domain2) R->L }
% 1.18/0.61 addition(addition(multiplication(domain(x0), domain(x1)), multiplication(domain(multiplication(domain(x0), x1)), multiplication(domain(x0), domain(x1)))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 2 (multiplicative_left_identity) R->L }
% 1.18/0.61 addition(addition(multiplication(one, multiplication(domain(x0), domain(x1))), multiplication(domain(multiplication(domain(x0), x1)), multiplication(domain(x0), domain(x1)))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 9 (left_distributivity) R->L }
% 1.18/0.61 addition(multiplication(addition(one, domain(multiplication(domain(x0), x1))), multiplication(domain(x0), domain(x1))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by lemma 11 }
% 1.18/0.61 addition(multiplication(one, multiplication(domain(x0), domain(x1))), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by axiom 2 (multiplicative_left_identity) }
% 1.18/0.61 addition(multiplication(domain(x0), domain(x1)), multiplication(domain(multiplication(domain(x0), x1)), domain(x1)))
% 1.18/0.61 = { by lemma 13 }
% 1.18/0.61 multiplication(addition(domain(multiplication(domain(x0), x1)), domain(x0)), domain(x1))
% 1.18/0.61 = { by axiom 3 (additive_commutativity) }
% 1.18/0.61 multiplication(addition(domain(x0), domain(multiplication(domain(x0), x1))), domain(x1))
% 1.18/0.61 = { by axiom 5 (domain2) }
% 1.18/0.61 multiplication(addition(domain(x0), domain(multiplication(domain(x0), domain(x1)))), domain(x1))
% 1.18/0.61 = { by lemma 10 R->L }
% 1.18/0.61 multiplication(addition(domain(domain(x0)), domain(multiplication(domain(x0), domain(x1)))), domain(x1))
% 1.18/0.61 = { by axiom 6 (domain5) R->L }
% 1.18/0.61 multiplication(domain(addition(domain(x0), multiplication(domain(x0), domain(x1)))), domain(x1))
% 1.18/0.62 = { by axiom 3 (additive_commutativity) R->L }
% 1.18/0.62 multiplication(domain(addition(multiplication(domain(x0), domain(x1)), domain(x0))), domain(x1))
% 1.18/0.62 = { by axiom 1 (multiplicative_right_identity) R->L }
% 1.18/0.62 multiplication(domain(addition(multiplication(domain(x0), domain(x1)), multiplication(domain(x0), one))), domain(x1))
% 1.18/0.62 = { by axiom 8 (right_distributivity) R->L }
% 1.18/0.62 multiplication(domain(multiplication(domain(x0), addition(domain(x1), one))), domain(x1))
% 1.18/0.62 = { by axiom 3 (additive_commutativity) }
% 1.18/0.62 multiplication(domain(multiplication(domain(x0), addition(one, domain(x1)))), domain(x1))
% 1.18/0.62 = { by lemma 11 }
% 1.18/0.62 multiplication(domain(multiplication(domain(x0), one)), domain(x1))
% 1.18/0.62 = { by axiom 1 (multiplicative_right_identity) }
% 1.18/0.62 multiplication(domain(domain(x0)), domain(x1))
% 1.18/0.62 = { by lemma 10 }
% 1.18/0.62 multiplication(domain(x0), domain(x1))
% 1.18/0.62 % SZS output end Proof
% 1.18/0.62
% 1.18/0.62 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------