%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 11:39:50 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.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 13:09:09 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45 Command-line arguments: --flatten --complete-subsets
% 0.12/0.45
% 0.12/0.45 % SZS status Theorem
% 0.12/0.45
% 0.12/0.45 % SZS output start Proof
% 0.12/0.45 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 0.12/0.45 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.12/0.45 Axiom 3 (additive_identity): addition(X, zero) = X.
% 0.12/0.45 Axiom 4 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 0.12/0.45 Axiom 5 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.12/0.45 Axiom 6 (right_annihilation): multiplication(X, zero) = zero.
% 0.12/0.45 Axiom 7 (domain1): multiplication(antidomain(X), X) = zero.
% 0.12/0.45 Axiom 8 (forward_diamond): forward_diamond(X, Y) = domain(multiplication(X, domain(Y))).
% 0.12/0.45
% 0.12/0.45 Lemma 9: antidomain(one) = zero.
% 0.12/0.45 Proof:
% 0.12/0.45 antidomain(one)
% 0.12/0.45 = { by axiom 5 (multiplicative_right_identity) R->L }
% 0.12/0.45 multiplication(antidomain(one), one)
% 0.12/0.45 = { by axiom 7 (domain1) }
% 0.12/0.45 zero
% 0.12/0.45
% 0.12/0.45 Lemma 10: antidomain(zero) = one.
% 0.12/0.45 Proof:
% 0.12/0.45 antidomain(zero)
% 0.12/0.45 = { by lemma 9 R->L }
% 0.12/0.45 antidomain(antidomain(one))
% 0.12/0.45 = { by axiom 3 (additive_identity) R->L }
% 0.12/0.45 addition(antidomain(antidomain(one)), zero)
% 0.12/0.45 = { by axiom 2 (additive_commutativity) }
% 0.12/0.45 addition(zero, antidomain(antidomain(one)))
% 0.12/0.45 = { by lemma 9 R->L }
% 0.12/0.45 addition(antidomain(one), antidomain(antidomain(one)))
% 0.12/0.45 = { by axiom 2 (additive_commutativity) R->L }
% 0.12/0.45 addition(antidomain(antidomain(one)), antidomain(one))
% 0.12/0.45 = { by axiom 4 (domain3) }
% 0.12/0.45 one
% 0.12/0.45
% 0.12/0.45 Goal 1 (goals): forward_diamond(x0, zero) = zero.
% 0.12/0.45 Proof:
% 0.12/0.45 forward_diamond(x0, zero)
% 0.12/0.45 = { by axiom 8 (forward_diamond) }
% 0.12/0.45 domain(multiplication(x0, domain(zero)))
% 0.12/0.45 = { by axiom 1 (domain4) }
% 0.12/0.45 antidomain(antidomain(multiplication(x0, domain(zero))))
% 0.12/0.45 = { by axiom 1 (domain4) }
% 0.12/0.45 antidomain(antidomain(multiplication(x0, antidomain(antidomain(zero)))))
% 0.12/0.45 = { by lemma 10 }
% 0.12/0.45 antidomain(antidomain(multiplication(x0, antidomain(one))))
% 0.12/0.45 = { by lemma 9 }
% 0.12/0.45 antidomain(antidomain(multiplication(x0, zero)))
% 0.12/0.45 = { by axiom 6 (right_annihilation) }
% 0.12/0.45 antidomain(antidomain(zero))
% 0.12/0.45 = { by lemma 10 }
% 0.12/0.45 antidomain(one)
% 0.12/0.45 = { by lemma 9 }
% 0.12/0.45 zero
% 0.12/0.45 % SZS output end Proof
% 0.12/0.45
% 0.12/0.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------