%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE054+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 11:39:43 AM UTC 2026
% Result : Theorem 0.45s 0.51s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE054+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 13:11:00 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.51 Command-line arguments: --no-flatten-goal
% 0.45/0.51
% 0.45/0.51 % SZS status Theorem
% 0.45/0.51
% 0.45/0.52 % SZS output start Proof
% 0.45/0.52 Axiom 1 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.45/0.52 Axiom 2 (domain3): addition(domain(X), one) = one.
% 0.45/0.52 Axiom 3 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.45/0.52 Axiom 4 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 0.45/0.52 Axiom 5 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 0.45/0.52 Axiom 6 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 0.45/0.52
% 0.45/0.52 Goal 1 (goals): addition(domain(multiplication(x0, x1)), domain(x0)) = domain(x0).
% 0.45/0.52 Proof:
% 0.45/0.52 addition(domain(multiplication(x0, x1)), domain(x0))
% 0.45/0.52 = { by axiom 1 (additive_commutativity) }
% 0.45/0.52 addition(domain(x0), domain(multiplication(x0, x1)))
% 0.45/0.52 = { by axiom 5 (domain2) }
% 0.45/0.52 addition(domain(x0), domain(multiplication(x0, domain(x1))))
% 0.45/0.52 = { by axiom 4 (domain5) R->L }
% 0.45/0.52 domain(addition(x0, multiplication(x0, domain(x1))))
% 0.45/0.52 = { by axiom 3 (multiplicative_right_identity) R->L }
% 0.45/0.52 domain(addition(multiplication(x0, one), multiplication(x0, domain(x1))))
% 0.45/0.52 = { by axiom 6 (right_distributivity) R->L }
% 0.45/0.52 domain(multiplication(x0, addition(one, domain(x1))))
% 0.45/0.52 = { by axiom 1 (additive_commutativity) R->L }
% 0.45/0.52 domain(multiplication(x0, addition(domain(x1), one)))
% 0.45/0.52 = { by axiom 2 (domain3) }
% 0.45/0.52 domain(multiplication(x0, one))
% 0.45/0.52 = { by axiom 3 (multiplicative_right_identity) }
% 0.45/0.52 domain(x0)
% 0.45/0.52 % SZS output end Proof
% 0.45/0.52
% 0.45/0.52 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------