%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 11:39:47 AM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 13:14:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.46 Command-line arguments: --no-flatten-goal
% 0.09/0.46
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46
% 0.09/0.46 % SZS output start Proof
% 0.09/0.46 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 0.09/0.46 Axiom 2 (additive_idempotence): addition(X, X) = X.
% 0.09/0.46 Axiom 3 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.09/0.46 Axiom 4 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 0.09/0.46
% 0.09/0.46 Lemma 5: addition(domain(X), antidomain(X)) = one.
% 0.09/0.46 Proof:
% 0.09/0.46 addition(domain(X), antidomain(X))
% 0.09/0.46 = { by axiom 1 (domain4) }
% 0.09/0.46 addition(antidomain(antidomain(X)), antidomain(X))
% 0.09/0.46 = { by axiom 4 (domain3) }
% 0.09/0.46 one
% 0.09/0.46
% 0.09/0.46 Goal 1 (goals): addition(domain(x0), one) = one.
% 0.09/0.46 Proof:
% 0.09/0.46 addition(domain(x0), one)
% 0.09/0.46 = { by lemma 5 R->L }
% 0.09/0.46 addition(domain(x0), addition(domain(x0), antidomain(x0)))
% 0.09/0.46 = { by axiom 3 (additive_associativity) }
% 0.09/0.46 addition(addition(domain(x0), domain(x0)), antidomain(x0))
% 0.09/0.46 = { by axiom 2 (additive_idempotence) }
% 0.09/0.46 addition(domain(x0), antidomain(x0))
% 0.09/0.46 = { by lemma 5 }
% 0.09/0.46 one
% 0.09/0.46 % SZS output end Proof
% 0.09/0.46
% 0.09/0.46 RESULT: Theorem (the conjecture is true).
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