%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE114+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.14s 0.49s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE114+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 13:13:41 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.49 Command-line arguments: --flatten --complete-subsets
% 0.14/0.49
% 0.14/0.49 % SZS status Theorem
% 0.14/0.49
% 0.14/0.49 % SZS output start Proof
% 0.14/0.49 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 0.14/0.49 Axiom 2 (complement): c(X) = antidomain(domain(X)).
% 0.14/0.49 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.14/0.49 Axiom 4 (additive_identity): addition(X, zero) = X.
% 0.14/0.49 Axiom 5 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 0.14/0.49 Axiom 6 (right_annihilation): multiplication(X, zero) = zero.
% 0.14/0.49 Axiom 7 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.14/0.49 Axiom 8 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.14/0.49 Axiom 9 (domain1): multiplication(antidomain(X), X) = zero.
% 0.14/0.49 Axiom 10 (forward_diamond): forward_diamond(X, Y) = domain(multiplication(X, domain(Y))).
% 0.14/0.49 Axiom 11 (forward_box): forward_box(X, Y) = c(forward_diamond(X, c(Y))).
% 0.14/0.49 Axiom 12 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 0.14/0.49 Axiom 13 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.14/0.49
% 0.14/0.49 Lemma 14: antidomain(one) = zero.
% 0.14/0.49 Proof:
% 0.14/0.49 antidomain(one)
% 0.14/0.49 = { by axiom 7 (multiplicative_right_identity) R->L }
% 0.14/0.49 multiplication(antidomain(one), one)
% 0.14/0.49 = { by axiom 9 (domain1) }
% 0.14/0.49 zero
% 0.14/0.49
% 0.14/0.49 Lemma 15: addition(antidomain(X), antidomain(antidomain(X))) = one.
% 0.14/0.49 Proof:
% 0.14/0.49 addition(antidomain(X), antidomain(antidomain(X)))
% 0.14/0.49 = { by axiom 3 (additive_commutativity) R->L }
% 0.14/0.49 addition(antidomain(antidomain(X)), antidomain(X))
% 0.14/0.49 = { by axiom 5 (domain3) }
% 0.14/0.49 one
% 0.14/0.49
% 0.14/0.49 Lemma 16: antidomain(zero) = one.
% 0.14/0.49 Proof:
% 0.14/0.49 antidomain(zero)
% 0.14/0.49 = { by lemma 14 R->L }
% 0.14/0.49 antidomain(antidomain(one))
% 0.14/0.49 = { by axiom 4 (additive_identity) R->L }
% 0.14/0.49 addition(antidomain(antidomain(one)), zero)
% 0.14/0.49 = { by axiom 3 (additive_commutativity) }
% 0.14/0.49 addition(zero, antidomain(antidomain(one)))
% 0.14/0.49 = { by lemma 14 R->L }
% 0.14/0.49 addition(antidomain(one), antidomain(antidomain(one)))
% 0.14/0.49 = { by lemma 15 }
% 0.14/0.49 one
% 0.14/0.49
% 0.14/0.49 Lemma 17: c(X) = antidomain(antidomain(antidomain(X))).
% 0.14/0.49 Proof:
% 0.14/0.49 c(X)
% 0.14/0.49 = { by axiom 2 (complement) }
% 0.14/0.49 antidomain(domain(X))
% 0.14/0.49 = { by axiom 1 (domain4) }
% 0.14/0.49 antidomain(antidomain(antidomain(X)))
% 0.14/0.49
% 0.14/0.49 Lemma 18: antidomain(antidomain(antidomain(X))) = antidomain(X).
% 0.14/0.49 Proof:
% 0.14/0.49 antidomain(antidomain(antidomain(X)))
% 0.14/0.49 = { by axiom 7 (multiplicative_right_identity) R->L }
% 0.14/0.49 multiplication(antidomain(antidomain(antidomain(X))), one)
% 0.14/0.49 = { by lemma 15 R->L }
% 0.14/0.49 multiplication(antidomain(antidomain(antidomain(X))), addition(antidomain(X), antidomain(antidomain(X))))
% 0.14/0.49 = { by axiom 12 (right_distributivity) }
% 0.14/0.49 addition(multiplication(antidomain(antidomain(antidomain(X))), antidomain(X)), multiplication(antidomain(antidomain(antidomain(X))), antidomain(antidomain(X))))
% 0.14/0.49 = { by axiom 9 (domain1) }
% 0.14/0.49 addition(multiplication(antidomain(antidomain(antidomain(X))), antidomain(X)), zero)
% 0.14/0.49 = { by axiom 9 (domain1) R->L }
% 0.14/0.49 addition(multiplication(antidomain(antidomain(antidomain(X))), antidomain(X)), multiplication(antidomain(antidomain(X)), antidomain(X)))
% 0.14/0.49 = { by axiom 13 (left_distributivity) R->L }
% 0.14/0.49 multiplication(addition(antidomain(antidomain(antidomain(X))), antidomain(antidomain(X))), antidomain(X))
% 0.14/0.49 = { by axiom 3 (additive_commutativity) }
% 0.14/0.49 multiplication(addition(antidomain(antidomain(X)), antidomain(antidomain(antidomain(X)))), antidomain(X))
% 0.14/0.49 = { by lemma 15 }
% 0.14/0.49 multiplication(one, antidomain(X))
% 0.14/0.49 = { by axiom 8 (multiplicative_left_identity) }
% 0.14/0.49 antidomain(X)
% 0.14/0.49
% 0.14/0.49 Lemma 19: antidomain(antidomain(multiplication(X, antidomain(antidomain(Y))))) = forward_diamond(X, Y).
% 0.14/0.49 Proof:
% 0.14/0.49 antidomain(antidomain(multiplication(X, antidomain(antidomain(Y)))))
% 0.14/0.49 = { by axiom 1 (domain4) R->L }
% 0.14/0.49 antidomain(antidomain(multiplication(X, domain(Y))))
% 0.14/0.49 = { by axiom 1 (domain4) R->L }
% 0.14/0.49 domain(multiplication(X, domain(Y)))
% 0.14/0.49 = { by axiom 10 (forward_diamond) R->L }
% 0.14/0.49 forward_diamond(X, Y)
% 0.14/0.49
% 0.14/0.49 Goal 1 (goals): forward_box(x0, one) = one.
% 0.14/0.49 Proof:
% 0.14/0.49 forward_box(x0, one)
% 0.14/0.49 = { by axiom 11 (forward_box) }
% 0.14/0.49 c(forward_diamond(x0, c(one)))
% 0.14/0.49 = { by lemma 17 }
% 0.14/0.49 antidomain(antidomain(antidomain(forward_diamond(x0, c(one)))))
% 0.14/0.49 = { by lemma 17 }
% 0.14/0.49 antidomain(antidomain(antidomain(forward_diamond(x0, antidomain(antidomain(antidomain(one)))))))
% 0.14/0.49 = { by lemma 18 }
% 0.14/0.49 antidomain(forward_diamond(x0, antidomain(antidomain(antidomain(one)))))
% 0.14/0.49 = { by lemma 19 R->L }
% 0.14/0.49 antidomain(antidomain(antidomain(multiplication(x0, antidomain(antidomain(antidomain(antidomain(antidomain(one)))))))))
% 0.14/0.49 = { by lemma 18 }
% 0.14/0.49 antidomain(antidomain(antidomain(multiplication(x0, antidomain(antidomain(antidomain(one)))))))
% 0.14/0.49 = { by lemma 19 }
% 0.14/0.49 antidomain(forward_diamond(x0, antidomain(one)))
% 0.14/0.49 = { by lemma 14 }
% 0.14/0.49 antidomain(forward_diamond(x0, zero))
% 0.14/0.49 = { by lemma 19 R->L }
% 0.14/0.49 antidomain(antidomain(antidomain(multiplication(x0, antidomain(antidomain(zero))))))
% 0.14/0.49 = { by lemma 16 }
% 0.14/0.49 antidomain(antidomain(antidomain(multiplication(x0, antidomain(one)))))
% 0.14/0.49 = { by lemma 14 }
% 0.14/0.49 antidomain(antidomain(antidomain(multiplication(x0, zero))))
% 0.14/0.49 = { by axiom 6 (right_annihilation) }
% 0.14/0.49 antidomain(antidomain(antidomain(zero)))
% 0.14/0.49 = { by lemma 16 }
% 0.14/0.49 antidomain(antidomain(one))
% 0.14/0.49 = { by lemma 14 }
% 0.14/0.49 antidomain(zero)
% 0.14/0.49 = { by lemma 16 }
% 0.14/0.49 one
% 0.14/0.49 % SZS output end Proof
% 0.14/0.49
% 0.14/0.49 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------