%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE099+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 11:39:49 AM UTC 2026
% Result : Theorem 1.61s 0.67s
% Output : Proof 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n004.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 13:10:07 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.61/0.67 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 1.61/0.67
% 1.61/0.67 % SZS status Theorem
% 1.61/0.67
% 1.61/0.67 % SZS output start Proof
% 1.61/0.67 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 1.61/0.67 Axiom 2 (multiplicative_right_identity): multiplication(X, one) = X.
% 1.61/0.67 Axiom 3 (left_annihilation): multiplication(zero, X) = zero.
% 1.61/0.67 Axiom 4 (multiplicative_left_identity): multiplication(one, X) = X.
% 1.61/0.67 Axiom 5 (domain1): multiplication(antidomain(X), X) = zero.
% 1.61/0.67 Axiom 6 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 1.61/0.67 Axiom 7 (additive_identity): addition(X, zero) = X.
% 1.61/0.67 Axiom 8 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 1.61/0.67 Axiom 9 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 1.61/0.67 Axiom 10 (forward_diamond): forward_diamond(X, Y) = domain(multiplication(X, domain(Y))).
% 1.61/0.67 Axiom 11 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 1.61/0.67 Axiom 12 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 1.61/0.67 Axiom 13 (goals): addition(forward_diamond(x0, domain(x1)), domain(x2)) = domain(x2).
% 1.61/0.67
% 1.61/0.67 Lemma 14: antidomain(one) = zero.
% 1.61/0.67 Proof:
% 1.61/0.67 antidomain(one)
% 1.61/0.67 = { by axiom 2 (multiplicative_right_identity) R->L }
% 1.61/0.67 multiplication(antidomain(one), one)
% 1.61/0.67 = { by axiom 5 (domain1) }
% 1.61/0.67 zero
% 1.61/0.67
% 1.61/0.68 Lemma 15: addition(antidomain(X), antidomain(antidomain(X))) = one.
% 1.61/0.68 Proof:
% 1.61/0.68 addition(antidomain(X), antidomain(antidomain(X)))
% 1.61/0.68 = { by axiom 6 (additive_commutativity) R->L }
% 1.61/0.68 addition(antidomain(antidomain(X)), antidomain(X))
% 1.61/0.68 = { by axiom 8 (domain3) }
% 1.61/0.68 one
% 1.61/0.68
% 1.61/0.68 Lemma 16: multiplication(antidomain(antidomain(X)), X) = X.
% 1.61/0.68 Proof:
% 1.61/0.68 multiplication(antidomain(antidomain(X)), X)
% 1.61/0.68 = { by axiom 7 (additive_identity) R->L }
% 1.61/0.68 addition(multiplication(antidomain(antidomain(X)), X), zero)
% 1.61/0.68 = { by axiom 5 (domain1) R->L }
% 1.61/0.68 addition(multiplication(antidomain(antidomain(X)), X), multiplication(antidomain(X), X))
% 1.61/0.68 = { by axiom 12 (left_distributivity) R->L }
% 1.61/0.68 multiplication(addition(antidomain(antidomain(X)), antidomain(X)), X)
% 1.61/0.68 = { by axiom 6 (additive_commutativity) }
% 1.61/0.68 multiplication(addition(antidomain(X), antidomain(antidomain(X))), X)
% 1.61/0.68 = { by lemma 15 }
% 1.61/0.68 multiplication(one, X)
% 1.61/0.68 = { by axiom 4 (multiplicative_left_identity) }
% 1.61/0.68 X
% 1.61/0.68
% 1.61/0.68 Lemma 17: multiplication(antidomain(X), addition(X, Y)) = multiplication(antidomain(X), Y).
% 1.61/0.68 Proof:
% 1.61/0.68 multiplication(antidomain(X), addition(X, Y))
% 1.61/0.68 = { by axiom 6 (additive_commutativity) R->L }
% 1.61/0.68 multiplication(antidomain(X), addition(Y, X))
% 1.61/0.68 = { by axiom 11 (right_distributivity) }
% 1.61/0.68 addition(multiplication(antidomain(X), Y), multiplication(antidomain(X), X))
% 1.61/0.68 = { by axiom 5 (domain1) }
% 1.61/0.68 addition(multiplication(antidomain(X), Y), zero)
% 1.61/0.68 = { by axiom 7 (additive_identity) }
% 1.61/0.68 multiplication(antidomain(X), Y)
% 1.61/0.68
% 1.61/0.68 Lemma 18: multiplication(antidomain(X), addition(Y, X)) = multiplication(antidomain(X), Y).
% 1.61/0.68 Proof:
% 1.61/0.68 multiplication(antidomain(X), addition(Y, X))
% 1.61/0.68 = { by axiom 6 (additive_commutativity) R->L }
% 1.61/0.68 multiplication(antidomain(X), addition(X, Y))
% 1.61/0.68 = { by lemma 17 }
% 1.61/0.68 multiplication(antidomain(X), Y)
% 1.61/0.68
% 1.61/0.68 Goal 1 (goals_1): multiplication(antidomain(x2), multiplication(x0, domain(x1))) = zero.
% 1.61/0.68 Proof:
% 1.61/0.68 multiplication(antidomain(x2), multiplication(x0, domain(x1)))
% 1.61/0.68 = { by lemma 16 R->L }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, domain(x1)))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by lemma 16 R->L }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), domain(x1))))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by lemma 18 R->L }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), addition(domain(x1), antidomain(domain(x1))))))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 1 (domain4) }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), addition(domain(x1), antidomain(antidomain(antidomain(x1)))))))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 1 (domain4) }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), addition(antidomain(antidomain(x1)), antidomain(antidomain(antidomain(x1)))))))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by lemma 15 }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), one)))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 2 (multiplicative_right_identity) }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, antidomain(antidomain(domain(x1)))))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 1 (domain4) R->L }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(antidomain(antidomain(multiplication(x0, domain(domain(x1))))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 1 (domain4) R->L }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(domain(multiplication(x0, domain(domain(x1)))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 10 (forward_diamond) R->L }
% 1.61/0.68 multiplication(antidomain(x2), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by lemma 16 R->L }
% 1.61/0.68 multiplication(multiplication(antidomain(antidomain(antidomain(x2))), antidomain(x2)), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by lemma 18 R->L }
% 1.61/0.68 multiplication(multiplication(antidomain(antidomain(antidomain(x2))), addition(antidomain(x2), antidomain(antidomain(x2)))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by lemma 15 }
% 1.61/0.68 multiplication(multiplication(antidomain(antidomain(antidomain(x2))), one), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 2 (multiplicative_right_identity) }
% 1.61/0.68 multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 4 (multiplicative_left_identity) R->L }
% 1.61/0.68 multiplication(one, multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by lemma 15 R->L }
% 1.61/0.68 multiplication(addition(antidomain(one), antidomain(antidomain(one))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by lemma 14 }
% 1.61/0.68 multiplication(addition(zero, antidomain(antidomain(one))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 6 (additive_commutativity) R->L }
% 1.61/0.68 multiplication(addition(antidomain(antidomain(one)), zero), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 7 (additive_identity) }
% 1.61/0.68 multiplication(antidomain(antidomain(one)), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by lemma 14 }
% 1.61/0.68 multiplication(antidomain(zero), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 5 (domain1) R->L }
% 1.61/0.68 multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), antidomain(antidomain(x2)))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 1 (domain4) R->L }
% 1.61/0.68 multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), domain(x2))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 13 (goals) R->L }
% 1.61/0.68 multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), addition(forward_diamond(x0, domain(x1)), domain(x2)))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 1 (domain4) }
% 1.61/0.68 multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), addition(forward_diamond(x0, domain(x1)), antidomain(antidomain(x2))))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 6 (additive_commutativity) }
% 1.61/0.68 multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), addition(antidomain(antidomain(x2)), forward_diamond(x0, domain(x1))))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by lemma 17 }
% 1.61/0.68 multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), forward_diamond(x0, domain(x1)))), multiplication(antidomain(antidomain(antidomain(x2))), multiplication(forward_diamond(x0, domain(x1)), multiplication(x0, domain(x1)))))
% 1.61/0.68 = { by axiom 9 (multiplicative_associativity) }
% 1.61/0.68 multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), forward_diamond(x0, domain(x1)))), multiplication(multiplication(antidomain(antidomain(antidomain(x2))), forward_diamond(x0, domain(x1))), multiplication(x0, domain(x1))))
% 1.61/0.68 = { by axiom 9 (multiplicative_associativity) }
% 1.61/0.68 multiplication(multiplication(antidomain(multiplication(antidomain(antidomain(antidomain(x2))), forward_diamond(x0, domain(x1)))), multiplication(antidomain(antidomain(antidomain(x2))), forward_diamond(x0, domain(x1)))), multiplication(x0, domain(x1)))
% 1.61/0.68 = { by axiom 5 (domain1) }
% 1.61/0.68 multiplication(zero, multiplication(x0, domain(x1)))
% 1.61/0.68 = { by axiom 3 (left_annihilation) }
% 1.61/0.68 zero
% 1.61/0.68 % SZS output end Proof
% 1.61/0.68
% 1.61/0.68 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------