%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 11:39:51 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE119+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 : n015.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 13:14:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --flatten --complete-subsets
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44
% 0.13/0.44 % SZS output start Proof
% 0.13/0.44 Axiom 1 (codomain4): codomain(X) = coantidomain(coantidomain(X)).
% 0.13/0.44 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.13/0.44 Axiom 3 (additive_identity): addition(X, zero) = X.
% 0.13/0.44 Axiom 4 (right_annihilation): multiplication(X, zero) = zero.
% 0.13/0.44 Axiom 5 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.13/0.44 Axiom 6 (codomain1): multiplication(X, coantidomain(X)) = zero.
% 0.13/0.44 Axiom 7 (backward_diamond): backward_diamond(X, Y) = codomain(multiplication(codomain(Y), X)).
% 0.13/0.44 Axiom 8 (codomain3): addition(coantidomain(coantidomain(X)), coantidomain(X)) = one.
% 0.13/0.44
% 0.13/0.44 Lemma 9: coantidomain(one) = zero.
% 0.13/0.44 Proof:
% 0.13/0.44 coantidomain(one)
% 0.13/0.44 = { by axiom 5 (multiplicative_left_identity) R->L }
% 0.13/0.44 multiplication(one, coantidomain(one))
% 0.13/0.44 = { by axiom 6 (codomain1) }
% 0.13/0.44 zero
% 0.13/0.44
% 0.13/0.44 Goal 1 (goals): addition(backward_diamond(zero, domain(x0)), domain(x1)) = domain(x1).
% 0.13/0.44 Proof:
% 0.13/0.44 addition(backward_diamond(zero, domain(x0)), domain(x1))
% 0.13/0.44 = { by axiom 2 (additive_commutativity) }
% 0.13/0.44 addition(domain(x1), backward_diamond(zero, domain(x0)))
% 0.13/0.44 = { by axiom 7 (backward_diamond) }
% 0.13/0.44 addition(domain(x1), codomain(multiplication(codomain(domain(x0)), zero)))
% 0.13/0.44 = { by axiom 4 (right_annihilation) }
% 0.13/0.44 addition(domain(x1), codomain(zero))
% 0.13/0.44 = { by axiom 1 (codomain4) }
% 0.13/0.44 addition(domain(x1), coantidomain(coantidomain(zero)))
% 0.13/0.44 = { by lemma 9 R->L }
% 0.13/0.44 addition(domain(x1), coantidomain(coantidomain(coantidomain(one))))
% 0.13/0.44 = { by axiom 1 (codomain4) R->L }
% 0.13/0.44 addition(domain(x1), coantidomain(codomain(one)))
% 0.13/0.44 = { by axiom 3 (additive_identity) R->L }
% 0.13/0.44 addition(domain(x1), coantidomain(addition(codomain(one), zero)))
% 0.13/0.44 = { by lemma 9 R->L }
% 0.13/0.44 addition(domain(x1), coantidomain(addition(codomain(one), coantidomain(one))))
% 0.13/0.44 = { by axiom 1 (codomain4) }
% 0.13/0.44 addition(domain(x1), coantidomain(addition(coantidomain(coantidomain(one)), coantidomain(one))))
% 0.13/0.44 = { by axiom 8 (codomain3) }
% 0.13/0.44 addition(domain(x1), coantidomain(one))
% 0.13/0.44 = { by lemma 9 }
% 0.13/0.44 addition(domain(x1), zero)
% 0.13/0.44 = { by axiom 3 (additive_identity) }
% 0.13/0.44 domain(x1)
% 0.13/0.44 % SZS output end Proof
% 0.13/0.44
% 0.13/0.44 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------