%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE067+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.09s 0.45s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE067+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 : n011.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 13:08:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.45 Command-line arguments: --no-flatten-goal
% 0.09/0.45
% 0.09/0.45 % SZS status Theorem
% 0.09/0.45
% 0.09/0.45 % SZS output start Proof
% 0.09/0.45 Axiom 1 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.09/0.45 Axiom 2 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 0.09/0.45 Axiom 3 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 0.09/0.45
% 0.09/0.45 Lemma 4: domain(domain(X)) = domain(X).
% 0.09/0.45 Proof:
% 0.09/0.45 domain(domain(X))
% 0.09/0.45 = { by axiom 1 (multiplicative_left_identity) R->L }
% 0.09/0.45 domain(multiplication(one, domain(X)))
% 0.09/0.45 = { by axiom 2 (domain2) R->L }
% 0.09/0.45 domain(multiplication(one, X))
% 0.09/0.45 = { by axiom 1 (multiplicative_left_identity) }
% 0.09/0.45 domain(X)
% 0.09/0.45
% 0.09/0.45 Goal 1 (goals): domain(addition(domain(x0), domain(x1))) = addition(domain(x0), domain(x1)).
% 0.09/0.45 Proof:
% 0.09/0.45 domain(addition(domain(x0), domain(x1)))
% 0.09/0.45 = { by axiom 3 (domain5) }
% 0.09/0.45 addition(domain(domain(x0)), domain(domain(x1)))
% 0.09/0.45 = { by lemma 4 }
% 0.09/0.45 addition(domain(x0), domain(domain(x1)))
% 0.09/0.45 = { by lemma 4 }
% 0.09/0.45 addition(domain(x0), domain(x1))
% 0.09/0.45 % SZS output end Proof
% 0.09/0.45
% 0.09/0.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------