%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE072+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 11:39:46 AM UTC 2026
% Result : Theorem 0.09s 0.49s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE072+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 : 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 13:08:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.49 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.09/0.49
% 0.09/0.49 % SZS status Theorem
% 0.09/0.49
% 0.09/0.49 % SZS output start Proof
% 0.09/0.49 Axiom 1 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 0.09/0.49 Axiom 2 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.09/0.49
% 0.09/0.49 Goal 1 (goals): domain(multiplication(addition(x0, x1), domain(x2))) = addition(domain(multiplication(x0, domain(x2))), domain(multiplication(x1, domain(x2)))).
% 0.09/0.49 Proof:
% 0.09/0.49 domain(multiplication(addition(x0, x1), domain(x2)))
% 0.09/0.49 = { by axiom 2 (left_distributivity) }
% 0.09/0.49 domain(addition(multiplication(x0, domain(x2)), multiplication(x1, domain(x2))))
% 0.09/0.49 = { by axiom 1 (domain5) }
% 0.09/0.49 addition(domain(multiplication(x0, domain(x2))), domain(multiplication(x1, domain(x2))))
% 0.09/0.49 % SZS output end Proof
% 0.09/0.49
% 0.09/0.49 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------