%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE080+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 2.26s 0.74s
% Output : Proof 2.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE080+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 : n005.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 13:09:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.26/0.74 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.26/0.74
% 2.26/0.74 % SZS status Theorem
% 2.26/0.74
% 2.26/0.76 % SZS output start Proof
% 2.26/0.76 Axiom 1 (domain4): domain(zero) = zero.
% 2.26/0.76 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 2.26/0.76 Axiom 3 (additive_identity): addition(X, zero) = X.
% 2.26/0.76 Axiom 4 (domain3): addition(domain(X), one) = one.
% 2.26/0.76 Axiom 5 (multiplicative_right_identity): multiplication(X, one) = X.
% 2.26/0.76 Axiom 6 (left_annihilation): multiplication(zero, X) = zero.
% 2.26/0.76 Axiom 7 (multiplicative_left_identity): multiplication(one, X) = X.
% 2.26/0.76 Axiom 8 (domain5): domain(addition(X, Y)) = addition(domain(X), domain(Y)).
% 2.26/0.76 Axiom 9 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 2.26/0.76 Axiom 10 (goals): addition(domain(X), antidomain(X)) = one.
% 2.26/0.76 Axiom 11 (goals_1): multiplication(domain(X), antidomain(X)) = zero.
% 2.26/0.76 Axiom 12 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 2.26/0.76 Axiom 13 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 2.26/0.76 Axiom 14 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 2.26/0.76
% 2.26/0.76 Lemma 15: addition(one, domain(X)) = one.
% 2.26/0.76 Proof:
% 2.26/0.76 addition(one, domain(X))
% 2.26/0.76 = { by axiom 2 (additive_commutativity) R->L }
% 2.26/0.76 addition(domain(X), one)
% 2.26/0.76 = { by axiom 4 (domain3) }
% 2.26/0.76 one
% 2.26/0.76
% 2.26/0.76 Lemma 16: addition(antidomain(antidomain(X)), multiplication(domain(X), domain(antidomain(X)))) = domain(X).
% 2.26/0.76 Proof:
% 2.26/0.76 addition(antidomain(antidomain(X)), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 7 (multiplicative_left_identity) R->L }
% 2.26/0.76 addition(multiplication(one, antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by lemma 15 R->L }
% 2.26/0.76 addition(multiplication(addition(one, domain(one)), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 5 (multiplicative_right_identity) R->L }
% 2.26/0.76 addition(multiplication(addition(one, multiplication(domain(one), one)), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 12 (domain1) }
% 2.26/0.76 addition(multiplication(multiplication(domain(one), one), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 5 (multiplicative_right_identity) }
% 2.26/0.76 addition(multiplication(domain(one), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 10 (goals) R->L }
% 2.26/0.76 addition(multiplication(domain(addition(domain(X), antidomain(X))), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 8 (domain5) }
% 2.26/0.76 addition(multiplication(addition(domain(domain(X)), domain(antidomain(X))), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 7 (multiplicative_left_identity) R->L }
% 2.26/0.76 addition(multiplication(addition(domain(multiplication(one, domain(X))), domain(antidomain(X))), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 9 (domain2) R->L }
% 2.26/0.76 addition(multiplication(addition(domain(multiplication(one, X)), domain(antidomain(X))), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.76 = { by axiom 7 (multiplicative_left_identity) }
% 2.26/0.76 addition(multiplication(addition(domain(X), domain(antidomain(X))), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.77 = { by axiom 2 (additive_commutativity) R->L }
% 2.26/0.77 addition(multiplication(addition(domain(antidomain(X)), domain(X)), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.77 = { by axiom 14 (left_distributivity) }
% 2.26/0.77 addition(addition(multiplication(domain(antidomain(X)), antidomain(antidomain(X))), multiplication(domain(X), antidomain(antidomain(X)))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.77 = { by axiom 11 (goals_1) }
% 2.26/0.77 addition(addition(zero, multiplication(domain(X), antidomain(antidomain(X)))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.77 = { by axiom 2 (additive_commutativity) R->L }
% 2.26/0.77 addition(addition(multiplication(domain(X), antidomain(antidomain(X))), zero), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.77 = { by axiom 3 (additive_identity) }
% 2.26/0.77 addition(multiplication(domain(X), antidomain(antidomain(X))), multiplication(domain(X), domain(antidomain(X))))
% 2.26/0.77 = { by axiom 13 (right_distributivity) R->L }
% 2.26/0.77 multiplication(domain(X), addition(antidomain(antidomain(X)), domain(antidomain(X))))
% 2.26/0.77 = { by axiom 2 (additive_commutativity) R->L }
% 2.26/0.77 multiplication(domain(X), addition(domain(antidomain(X)), antidomain(antidomain(X))))
% 2.26/0.77 = { by axiom 10 (goals) }
% 2.26/0.77 multiplication(domain(X), one)
% 2.26/0.77 = { by axiom 5 (multiplicative_right_identity) }
% 2.26/0.77 domain(X)
% 2.26/0.77
% 2.26/0.77 Goal 1 (goals_2): antidomain(antidomain(x0)) = domain(x0).
% 2.26/0.77 Proof:
% 2.26/0.77 antidomain(antidomain(x0))
% 2.26/0.77 = { by axiom 3 (additive_identity) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), zero)
% 2.26/0.77 = { by axiom 6 (left_annihilation) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), multiplication(zero, domain(x0)))
% 2.26/0.77 = { by axiom 1 (domain4) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), multiplication(domain(zero), domain(x0)))
% 2.26/0.77 = { by axiom 11 (goals_1) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), multiplication(domain(multiplication(domain(x0), antidomain(x0))), domain(x0)))
% 2.26/0.77 = { by axiom 9 (domain2) }
% 2.26/0.77 addition(antidomain(antidomain(x0)), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), domain(x0)))
% 2.26/0.77 = { by lemma 16 R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), addition(antidomain(antidomain(x0)), multiplication(domain(x0), domain(antidomain(x0))))))
% 2.26/0.77 = { by axiom 2 (additive_commutativity) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), addition(multiplication(domain(x0), domain(antidomain(x0))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 13 (right_distributivity) }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), multiplication(domain(x0), domain(antidomain(x0)))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 12 (domain1) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(addition(multiplication(domain(x0), domain(antidomain(x0))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), multiplication(domain(x0), domain(antidomain(x0))))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 7 (multiplicative_left_identity) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(addition(multiplication(one, multiplication(domain(x0), domain(antidomain(x0)))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), multiplication(domain(x0), domain(antidomain(x0))))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 14 (left_distributivity) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(addition(one, domain(multiplication(domain(x0), domain(antidomain(x0))))), multiplication(domain(x0), domain(antidomain(x0)))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by lemma 15 }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(one, multiplication(domain(x0), domain(antidomain(x0)))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 7 (multiplicative_left_identity) }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(domain(x0), domain(antidomain(x0))), multiplication(domain(multiplication(domain(x0), domain(antidomain(x0)))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 9 (domain2) R->L }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(domain(x0), domain(antidomain(x0))), multiplication(domain(multiplication(domain(x0), antidomain(x0))), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 11 (goals_1) }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(domain(x0), domain(antidomain(x0))), multiplication(domain(zero), antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 1 (domain4) }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(domain(x0), domain(antidomain(x0))), multiplication(zero, antidomain(antidomain(x0)))))
% 2.26/0.77 = { by axiom 6 (left_annihilation) }
% 2.26/0.77 addition(antidomain(antidomain(x0)), addition(multiplication(domain(x0), domain(antidomain(x0))), zero))
% 2.26/0.77 = { by axiom 3 (additive_identity) }
% 2.26/0.77 addition(antidomain(antidomain(x0)), multiplication(domain(x0), domain(antidomain(x0))))
% 2.26/0.77 = { by lemma 16 }
% 2.26/0.77 domain(x0)
% 2.26/0.77 % SZS output end Proof
% 2.26/0.77
% 2.26/0.77 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------