%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE065+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 11:39:45 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE065+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 13:08:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44
% 0.13/0.44 % SZS output start Proof
% 0.13/0.44 Axiom 1 (domain4): domain(zero) = zero.
% 0.13/0.44 Axiom 2 (left_annihilation): multiplication(zero, X) = zero.
% 0.13/0.44 Axiom 3 (goals): multiplication(x0, x1) = zero.
% 0.13/0.44 Axiom 4 (additive_identity): addition(X, zero) = X.
% 0.13/0.44 Axiom 5 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 0.13/0.44 Axiom 6 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 0.13/0.44
% 0.13/0.44 Lemma 7: domain(multiplication(x0, domain(x1))) = zero.
% 0.13/0.44 Proof:
% 0.13/0.44 domain(multiplication(x0, domain(x1)))
% 0.13/0.44 = { by axiom 5 (domain2) R->L }
% 0.13/0.44 domain(multiplication(x0, x1))
% 0.13/0.44 = { by axiom 3 (goals) }
% 0.13/0.44 domain(zero)
% 0.13/0.44 = { by axiom 1 (domain4) }
% 0.13/0.44 zero
% 0.13/0.44
% 0.13/0.44 Goal 1 (goals_1): multiplication(x0, domain(x1)) = zero.
% 0.13/0.44 Proof:
% 0.13/0.44 multiplication(x0, domain(x1))
% 0.13/0.44 = { by axiom 4 (additive_identity) R->L }
% 0.13/0.44 addition(multiplication(x0, domain(x1)), zero)
% 0.13/0.44 = { by axiom 2 (left_annihilation) R->L }
% 0.13/0.44 addition(multiplication(x0, domain(x1)), multiplication(zero, multiplication(x0, domain(x1))))
% 0.13/0.44 = { by lemma 7 R->L }
% 0.13/0.44 addition(multiplication(x0, domain(x1)), multiplication(domain(multiplication(x0, domain(x1))), multiplication(x0, domain(x1))))
% 0.13/0.44 = { by axiom 6 (domain1) }
% 0.13/0.44 multiplication(domain(multiplication(x0, domain(x1))), multiplication(x0, domain(x1)))
% 0.13/0.44 = { by lemma 7 }
% 0.13/0.44 multiplication(zero, multiplication(x0, domain(x1)))
% 0.13/0.44 = { by axiom 2 (left_annihilation) }
% 0.13/0.44 zero
% 0.13/0.44 % SZS output end Proof
% 0.13/0.44
% 0.13/0.44 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------