%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE090+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 11:39:48 AM UTC 2026
% Result : Theorem 2.19s 0.73s
% Output : Proof 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE090+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n017.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 13:05:05 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.19/0.73 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.19/0.73
% 2.19/0.73 % SZS status Theorem
% 2.19/0.73
% 2.19/0.74 % SZS output start Proof
% 2.19/0.74 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 2.19/0.74 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 2.19/0.74 Axiom 3 (domain1): multiplication(antidomain(X), X) = zero.
% 2.19/0.74 Axiom 4 (additive_idempotence): addition(X, X) = X.
% 2.19/0.74 Axiom 5 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 2.19/0.74 Axiom 6 (additive_identity): addition(X, zero) = X.
% 2.19/0.74 Axiom 7 (goals): addition(x0, x1) = x1.
% 2.19/0.74 Axiom 8 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 2.19/0.74 Axiom 9 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 2.19/0.74 Axiom 10 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 2.19/0.74 Axiom 11 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 2.19/0.74 Axiom 12 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 2.19/0.74
% 2.19/0.74 Lemma 13: antidomain(one) = zero.
% 2.19/0.74 Proof:
% 2.19/0.74 antidomain(one)
% 2.19/0.74 = { by axiom 1 (multiplicative_right_identity) R->L }
% 2.19/0.74 multiplication(antidomain(one), one)
% 2.19/0.74 = { by axiom 3 (domain1) }
% 2.19/0.74 zero
% 2.19/0.74
% 2.19/0.74 Lemma 14: addition(zero, X) = X.
% 2.19/0.74 Proof:
% 2.19/0.74 addition(zero, X)
% 2.19/0.74 = { by axiom 5 (additive_commutativity) R->L }
% 2.19/0.74 addition(X, zero)
% 2.19/0.74 = { by axiom 6 (additive_identity) }
% 2.19/0.74 X
% 2.19/0.74
% 2.19/0.74 Lemma 15: addition(antidomain(X), antidomain(antidomain(X))) = one.
% 2.19/0.74 Proof:
% 2.19/0.74 addition(antidomain(X), antidomain(antidomain(X)))
% 2.19/0.74 = { by axiom 5 (additive_commutativity) R->L }
% 2.19/0.74 addition(antidomain(antidomain(X)), antidomain(X))
% 2.19/0.74 = { by axiom 8 (domain3) }
% 2.19/0.74 one
% 2.19/0.74
% 2.19/0.74 Lemma 16: addition(one, antidomain(X)) = one.
% 2.19/0.74 Proof:
% 2.19/0.74 addition(one, antidomain(X))
% 2.19/0.74 = { by axiom 5 (additive_commutativity) R->L }
% 2.19/0.74 addition(antidomain(X), one)
% 2.19/0.74 = { by lemma 15 R->L }
% 2.19/0.74 addition(antidomain(X), addition(antidomain(X), antidomain(antidomain(X))))
% 2.19/0.74 = { by axiom 9 (additive_associativity) }
% 2.19/0.74 addition(addition(antidomain(X), antidomain(X)), antidomain(antidomain(X)))
% 2.19/0.74 = { by axiom 4 (additive_idempotence) }
% 2.19/0.74 addition(antidomain(X), antidomain(antidomain(X)))
% 2.19/0.74 = { by lemma 15 }
% 2.19/0.74 one
% 2.19/0.74
% 2.19/0.74 Goal 1 (goals_1): addition(antidomain(x1), antidomain(x0)) = antidomain(x0).
% 2.19/0.74 Proof:
% 2.19/0.74 addition(antidomain(x1), antidomain(x0))
% 2.19/0.74 = { by axiom 5 (additive_commutativity) }
% 2.19/0.74 addition(antidomain(x0), antidomain(x1))
% 2.19/0.74 = { by axiom 1 (multiplicative_right_identity) R->L }
% 2.19/0.74 addition(antidomain(x0), multiplication(antidomain(x1), one))
% 2.19/0.74 = { by lemma 15 R->L }
% 2.19/0.74 addition(antidomain(x0), multiplication(antidomain(x1), addition(antidomain(x0), antidomain(antidomain(x0)))))
% 2.19/0.74 = { by axiom 5 (additive_commutativity) R->L }
% 2.19/0.74 addition(antidomain(x0), multiplication(antidomain(x1), addition(antidomain(antidomain(x0)), antidomain(x0))))
% 2.19/0.74 = { by axiom 10 (right_distributivity) }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(antidomain(x1), antidomain(antidomain(x0))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 2 (multiplicative_left_identity) R->L }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(one, multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by lemma 16 R->L }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(one, antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by lemma 15 R->L }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(addition(antidomain(one), antidomain(antidomain(one))), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by lemma 13 }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(addition(zero, antidomain(antidomain(one))), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by lemma 14 }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(antidomain(one)), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by lemma 13 }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(zero), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 3 (domain1) R->L }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(multiplication(antidomain(x1), x1)), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 7 (goals) R->L }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(multiplication(antidomain(x1), addition(x0, x1))), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 5 (additive_commutativity) R->L }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(multiplication(antidomain(x1), addition(x1, x0))), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 10 (right_distributivity) }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(addition(multiplication(antidomain(x1), x1), multiplication(antidomain(x1), x0))), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 3 (domain1) }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(addition(zero, multiplication(antidomain(x1), x0))), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by lemma 14 }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(addition(antidomain(multiplication(antidomain(x1), x0)), antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0))))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 12 (domain2) }
% 2.19/0.74 addition(antidomain(x0), addition(multiplication(antidomain(multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(antidomain(x0)))), multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by axiom 3 (domain1) }
% 2.19/0.74 addition(antidomain(x0), addition(zero, multiplication(antidomain(x1), antidomain(x0))))
% 2.19/0.74 = { by lemma 14 }
% 2.19/0.74 addition(antidomain(x0), multiplication(antidomain(x1), antidomain(x0)))
% 2.19/0.74 = { by axiom 2 (multiplicative_left_identity) R->L }
% 2.19/0.74 addition(multiplication(one, antidomain(x0)), multiplication(antidomain(x1), antidomain(x0)))
% 2.19/0.74 = { by axiom 11 (left_distributivity) R->L }
% 2.19/0.74 multiplication(addition(one, antidomain(x1)), antidomain(x0))
% 2.19/0.74 = { by lemma 16 }
% 2.19/0.74 multiplication(one, antidomain(x0))
% 2.19/0.74 = { by axiom 2 (multiplicative_left_identity) }
% 2.19/0.74 antidomain(x0)
% 2.19/0.74 % SZS output end Proof
% 2.19/0.74
% 2.19/0.74 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------