%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE083+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 11:39:47 AM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE083+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 : n008.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 13:09:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 Command-line arguments: --no-flatten-goal
% 0.13/0.45
% 0.13/0.45 % SZS status Theorem
% 0.13/0.45
% 0.13/0.45 % SZS output start Proof
% 0.13/0.45 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 0.13/0.45 Axiom 2 (additive_identity): addition(X, zero) = X.
% 0.13/0.45 Axiom 3 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.13/0.45 Axiom 4 (domain1): multiplication(antidomain(X), X) = zero.
% 0.13/0.45 Axiom 5 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 0.13/0.45 Axiom 6 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.13/0.45
% 0.13/0.45 Goal 1 (goals): x0 = multiplication(domain(x0), x0).
% 0.13/0.45 Proof:
% 0.13/0.45 x0
% 0.13/0.45 = { by axiom 3 (multiplicative_left_identity) R->L }
% 0.13/0.45 multiplication(one, x0)
% 0.13/0.45 = { by axiom 5 (domain3) R->L }
% 0.13/0.45 multiplication(addition(antidomain(antidomain(x0)), antidomain(x0)), x0)
% 0.13/0.45 = { by axiom 1 (domain4) R->L }
% 0.13/0.45 multiplication(addition(domain(x0), antidomain(x0)), x0)
% 0.13/0.45 = { by axiom 6 (left_distributivity) }
% 0.13/0.45 addition(multiplication(domain(x0), x0), multiplication(antidomain(x0), x0))
% 0.13/0.45 = { by axiom 4 (domain1) }
% 0.13/0.45 addition(multiplication(domain(x0), x0), zero)
% 0.13/0.45 = { by axiom 2 (additive_identity) }
% 0.13/0.45 multiplication(domain(x0), x0)
% 0.13/0.45 % SZS output end Proof
% 0.13/0.45
% 0.13/0.45 RESULT: Theorem (the conjecture is true).
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