%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE055+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 11:39:43 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
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 13:07:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46 Command-line arguments: --flatten --complete-subsets
% 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_right_identity): multiplication(X, one) = X.
% 0.10/0.46 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.10/0.46 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.10/0.46 Axiom 4 (goals): addition(x0, one) = one.
% 0.10/0.46 Axiom 5 (domain3): addition(domain(X), one) = one.
% 0.10/0.46 Axiom 6 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 0.10/0.46 Axiom 7 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 0.10/0.46 Axiom 8 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.10/0.46
% 0.10/0.46 Goal 1 (goals_1): addition(x0, domain(x0)) = domain(x0).
% 0.10/0.46 Proof:
% 0.10/0.46 addition(x0, domain(x0))
% 0.10/0.46 = { by axiom 3 (additive_commutativity) }
% 0.10/0.46 addition(domain(x0), x0)
% 0.10/0.46 = { by axiom 2 (multiplicative_left_identity) R->L }
% 0.10/0.46 addition(domain(x0), multiplication(one, x0))
% 0.10/0.46 = { by axiom 5 (domain3) R->L }
% 0.10/0.46 addition(domain(x0), multiplication(addition(domain(x0), one), x0))
% 0.10/0.46 = { by axiom 4 (goals) R->L }
% 0.10/0.46 addition(domain(x0), multiplication(addition(domain(x0), addition(x0, one)), x0))
% 0.10/0.46 = { by axiom 3 (additive_commutativity) R->L }
% 0.10/0.46 addition(domain(x0), multiplication(addition(addition(x0, one), domain(x0)), x0))
% 0.10/0.46 = { by axiom 4 (goals) }
% 0.10/0.46 addition(domain(x0), multiplication(addition(one, domain(x0)), x0))
% 0.10/0.46 = { by axiom 8 (left_distributivity) }
% 0.10/0.46 addition(domain(x0), addition(multiplication(one, x0), multiplication(domain(x0), x0)))
% 0.10/0.46 = { by axiom 2 (multiplicative_left_identity) }
% 0.10/0.46 addition(domain(x0), addition(x0, multiplication(domain(x0), x0)))
% 0.10/0.46 = { by axiom 6 (domain1) }
% 0.10/0.46 addition(domain(x0), multiplication(domain(x0), x0))
% 0.10/0.46 = { by axiom 1 (multiplicative_right_identity) R->L }
% 0.10/0.46 addition(multiplication(domain(x0), one), multiplication(domain(x0), x0))
% 0.10/0.46 = { by axiom 7 (right_distributivity) R->L }
% 0.10/0.46 multiplication(domain(x0), addition(one, x0))
% 0.10/0.46 = { by axiom 4 (goals) R->L }
% 0.10/0.46 multiplication(domain(x0), addition(addition(x0, one), x0))
% 0.10/0.46 = { by axiom 3 (additive_commutativity) R->L }
% 0.10/0.46 multiplication(domain(x0), addition(x0, addition(x0, one)))
% 0.10/0.46 = { by axiom 4 (goals) }
% 0.10/0.46 multiplication(domain(x0), addition(x0, one))
% 0.10/0.46 = { by axiom 4 (goals) }
% 0.10/0.46 multiplication(domain(x0), one)
% 0.10/0.46 = { by axiom 1 (multiplicative_right_identity) }
% 0.10/0.46 domain(x0)
% 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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