%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 11:39:48 AM UTC 2026
% Result : Theorem 1.84s 0.67s
% Output : Proof 1.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 13:13:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.84/0.67 Command-line arguments: --flatten-regeneralise
% 1.84/0.67
% 1.84/0.67 % SZS status Theorem
% 1.84/0.67
% 1.84/0.69 % SZS output start Proof
% 1.84/0.69 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 1.84/0.69 Axiom 2 (additive_idempotence): addition(X, X) = X.
% 1.84/0.69 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 1.84/0.69 Axiom 4 (additive_identity): addition(X, zero) = X.
% 1.84/0.69 Axiom 5 (codomain3): addition(coantidomain(coantidomain(X)), coantidomain(X)) = one.
% 1.84/0.69 Axiom 6 (multiplicative_right_identity): multiplication(X, one) = X.
% 1.84/0.69 Axiom 7 (codomain1): multiplication(X, coantidomain(X)) = zero.
% 1.84/0.69 Axiom 8 (multiplicative_left_identity): multiplication(one, X) = X.
% 1.84/0.69 Axiom 9 (domain1): multiplication(antidomain(X), X) = zero.
% 1.84/0.69 Axiom 10 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 1.84/0.69 Axiom 11 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 1.84/0.69 Axiom 12 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 1.84/0.69 Axiom 13 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 1.84/0.69 Axiom 14 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 1.84/0.69
% 1.84/0.69 Lemma 15: antidomain(one) = zero.
% 1.84/0.69 Proof:
% 1.84/0.69 antidomain(one)
% 1.84/0.69 = { by axiom 6 (multiplicative_right_identity) R->L }
% 1.84/0.69 multiplication(antidomain(one), one)
% 1.84/0.69 = { by axiom 9 (domain1) }
% 1.84/0.69 zero
% 1.84/0.69
% 1.84/0.69 Lemma 16: addition(zero, X) = X.
% 1.84/0.69 Proof:
% 1.84/0.69 addition(zero, X)
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 addition(X, zero)
% 1.84/0.69 = { by axiom 4 (additive_identity) }
% 1.84/0.69 X
% 1.84/0.69
% 1.84/0.69 Lemma 17: addition(domain(X), antidomain(X)) = one.
% 1.84/0.69 Proof:
% 1.84/0.69 addition(domain(X), antidomain(X))
% 1.84/0.69 = { by axiom 1 (domain4) }
% 1.84/0.69 addition(antidomain(antidomain(X)), antidomain(X))
% 1.84/0.69 = { by axiom 11 (domain3) }
% 1.84/0.69 one
% 1.84/0.69
% 1.84/0.69 Lemma 18: multiplication(antidomain(X), addition(X, Y)) = multiplication(antidomain(X), Y).
% 1.84/0.69 Proof:
% 1.84/0.69 multiplication(antidomain(X), addition(X, Y))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 multiplication(antidomain(X), addition(Y, X))
% 1.84/0.69 = { by axiom 12 (right_distributivity) }
% 1.84/0.69 addition(multiplication(antidomain(X), Y), multiplication(antidomain(X), X))
% 1.84/0.69 = { by axiom 9 (domain1) }
% 1.84/0.69 addition(multiplication(antidomain(X), Y), zero)
% 1.84/0.69 = { by axiom 4 (additive_identity) }
% 1.84/0.69 multiplication(antidomain(X), Y)
% 1.84/0.69
% 1.84/0.69 Lemma 19: antidomain(domain(X)) = domain(antidomain(X)).
% 1.84/0.69 Proof:
% 1.84/0.69 antidomain(domain(X))
% 1.84/0.69 = { by axiom 1 (domain4) }
% 1.84/0.69 antidomain(antidomain(antidomain(X)))
% 1.84/0.69 = { by axiom 1 (domain4) R->L }
% 1.84/0.69 domain(antidomain(X))
% 1.84/0.69
% 1.84/0.69 Lemma 20: antidomain(domain(X)) = antidomain(X).
% 1.84/0.69 Proof:
% 1.84/0.69 antidomain(domain(X))
% 1.84/0.69 = { by axiom 6 (multiplicative_right_identity) R->L }
% 1.84/0.69 multiplication(antidomain(domain(X)), one)
% 1.84/0.69 = { by lemma 17 R->L }
% 1.84/0.69 multiplication(antidomain(domain(X)), addition(domain(X), antidomain(X)))
% 1.84/0.69 = { by lemma 18 }
% 1.84/0.69 multiplication(antidomain(domain(X)), antidomain(X))
% 1.84/0.69 = { by lemma 19 }
% 1.84/0.69 multiplication(domain(antidomain(X)), antidomain(X))
% 1.84/0.69 = { by axiom 4 (additive_identity) R->L }
% 1.84/0.69 addition(multiplication(domain(antidomain(X)), antidomain(X)), zero)
% 1.84/0.69 = { by axiom 9 (domain1) R->L }
% 1.84/0.69 addition(multiplication(domain(antidomain(X)), antidomain(X)), multiplication(antidomain(antidomain(X)), antidomain(X)))
% 1.84/0.69 = { by axiom 13 (left_distributivity) R->L }
% 1.84/0.69 multiplication(addition(domain(antidomain(X)), antidomain(antidomain(X))), antidomain(X))
% 1.84/0.69 = { by lemma 17 }
% 1.84/0.69 multiplication(one, antidomain(X))
% 1.84/0.69 = { by axiom 8 (multiplicative_left_identity) }
% 1.84/0.69 antidomain(X)
% 1.84/0.69
% 1.84/0.69 Lemma 21: addition(coantidomain(X), coantidomain(coantidomain(X))) = one.
% 1.84/0.69 Proof:
% 1.84/0.69 addition(coantidomain(X), coantidomain(coantidomain(X)))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 addition(coantidomain(coantidomain(X)), coantidomain(X))
% 1.84/0.69 = { by axiom 5 (codomain3) }
% 1.84/0.69 one
% 1.84/0.69
% 1.84/0.69 Lemma 22: multiplication(X, addition(Y, coantidomain(X))) = multiplication(X, Y).
% 1.84/0.69 Proof:
% 1.84/0.69 multiplication(X, addition(Y, coantidomain(X)))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 multiplication(X, addition(coantidomain(X), Y))
% 1.84/0.69 = { by axiom 12 (right_distributivity) }
% 1.84/0.69 addition(multiplication(X, coantidomain(X)), multiplication(X, Y))
% 1.84/0.69 = { by axiom 7 (codomain1) }
% 1.84/0.69 addition(zero, multiplication(X, Y))
% 1.84/0.69 = { by lemma 16 }
% 1.84/0.69 multiplication(X, Y)
% 1.84/0.69
% 1.84/0.69 Lemma 23: coantidomain(coantidomain(coantidomain(X))) = coantidomain(X).
% 1.84/0.69 Proof:
% 1.84/0.69 coantidomain(coantidomain(coantidomain(X)))
% 1.84/0.69 = { by axiom 8 (multiplicative_left_identity) R->L }
% 1.84/0.69 multiplication(one, coantidomain(coantidomain(coantidomain(X))))
% 1.84/0.69 = { by lemma 21 R->L }
% 1.84/0.69 multiplication(addition(coantidomain(X), coantidomain(coantidomain(X))), coantidomain(coantidomain(coantidomain(X))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 multiplication(addition(coantidomain(coantidomain(X)), coantidomain(X)), coantidomain(coantidomain(coantidomain(X))))
% 1.84/0.69 = { by axiom 13 (left_distributivity) }
% 1.84/0.69 addition(multiplication(coantidomain(coantidomain(X)), coantidomain(coantidomain(coantidomain(X)))), multiplication(coantidomain(X), coantidomain(coantidomain(coantidomain(X)))))
% 1.84/0.69 = { by axiom 7 (codomain1) }
% 1.84/0.69 addition(zero, multiplication(coantidomain(X), coantidomain(coantidomain(coantidomain(X)))))
% 1.84/0.69 = { by lemma 16 }
% 1.84/0.69 multiplication(coantidomain(X), coantidomain(coantidomain(coantidomain(X))))
% 1.84/0.69 = { by lemma 22 R->L }
% 1.84/0.69 multiplication(coantidomain(X), addition(coantidomain(coantidomain(coantidomain(X))), coantidomain(coantidomain(X))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) }
% 1.84/0.69 multiplication(coantidomain(X), addition(coantidomain(coantidomain(X)), coantidomain(coantidomain(coantidomain(X)))))
% 1.84/0.69 = { by lemma 21 }
% 1.84/0.69 multiplication(coantidomain(X), one)
% 1.84/0.69 = { by axiom 6 (multiplicative_right_identity) }
% 1.84/0.69 coantidomain(X)
% 1.84/0.69
% 1.84/0.69 Lemma 24: addition(X, addition(X, Y)) = addition(X, Y).
% 1.84/0.69 Proof:
% 1.84/0.69 addition(X, addition(X, Y))
% 1.84/0.69 = { by axiom 10 (additive_associativity) }
% 1.84/0.69 addition(addition(X, X), Y)
% 1.84/0.69 = { by axiom 2 (additive_idempotence) }
% 1.84/0.69 addition(X, Y)
% 1.84/0.69
% 1.84/0.69 Goal 1 (goals): domain(coantidomain(x0)) = coantidomain(x0).
% 1.84/0.69 Proof:
% 1.84/0.69 domain(coantidomain(x0))
% 1.84/0.69 = { by lemma 23 R->L }
% 1.84/0.69 domain(coantidomain(coantidomain(coantidomain(x0))))
% 1.84/0.69 = { by axiom 8 (multiplicative_left_identity) R->L }
% 1.84/0.69 multiplication(one, domain(coantidomain(coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by lemma 21 R->L }
% 1.84/0.69 multiplication(addition(coantidomain(x0), coantidomain(coantidomain(x0))), domain(coantidomain(coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 multiplication(addition(coantidomain(coantidomain(x0)), coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by axiom 13 (left_distributivity) }
% 1.84/0.69 addition(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 8 (multiplicative_left_identity) R->L }
% 1.84/0.69 addition(multiplication(one, multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 17 R->L }
% 1.84/0.69 addition(multiplication(addition(domain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 addition(multiplication(addition(antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), domain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 24 R->L }
% 1.84/0.69 addition(multiplication(addition(antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), addition(antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), domain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) }
% 1.84/0.69 addition(multiplication(addition(antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), addition(domain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 17 }
% 1.84/0.69 addition(multiplication(addition(antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), one), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) }
% 1.84/0.69 addition(multiplication(addition(one, antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 17 R->L }
% 1.84/0.69 addition(multiplication(addition(addition(domain(one), antidomain(one)), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 15 }
% 1.84/0.69 addition(multiplication(addition(addition(domain(one), zero), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 4 (additive_identity) }
% 1.84/0.69 addition(multiplication(addition(domain(one), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 1 (domain4) }
% 1.84/0.69 addition(multiplication(addition(antidomain(antidomain(one)), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 15 }
% 1.84/0.69 addition(multiplication(addition(antidomain(zero), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 7 (codomain1) R->L }
% 1.84/0.69 addition(multiplication(addition(antidomain(multiplication(coantidomain(coantidomain(x0)), coantidomain(coantidomain(coantidomain(x0))))), antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 1 (domain4) }
% 1.84/0.69 addition(multiplication(addition(antidomain(multiplication(coantidomain(coantidomain(x0)), coantidomain(coantidomain(coantidomain(x0))))), antidomain(multiplication(coantidomain(coantidomain(x0)), antidomain(antidomain(coantidomain(coantidomain(coantidomain(x0)))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 14 (domain2) }
% 1.84/0.69 addition(multiplication(antidomain(multiplication(coantidomain(coantidomain(x0)), antidomain(antidomain(coantidomain(coantidomain(coantidomain(x0))))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 1 (domain4) R->L }
% 1.84/0.69 addition(multiplication(antidomain(multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(coantidomain(x0)), domain(coantidomain(coantidomain(coantidomain(x0)))))), multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 9 (domain1) }
% 1.84/0.69 addition(zero, multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 16 }
% 1.84/0.69 multiplication(coantidomain(x0), domain(coantidomain(coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by lemma 23 }
% 1.84/0.69 multiplication(coantidomain(x0), domain(coantidomain(x0)))
% 1.84/0.69 = { by lemma 22 R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), coantidomain(coantidomain(x0))))
% 1.84/0.69 = { by axiom 8 (multiplicative_left_identity) R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), multiplication(one, coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by lemma 17 R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), multiplication(addition(domain(antidomain(coantidomain(x0))), antidomain(antidomain(coantidomain(x0)))), coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by lemma 24 R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), multiplication(addition(domain(antidomain(coantidomain(x0))), addition(domain(antidomain(coantidomain(x0))), antidomain(antidomain(coantidomain(x0))))), coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by lemma 17 }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), multiplication(addition(domain(antidomain(coantidomain(x0))), one), coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), multiplication(addition(one, domain(antidomain(coantidomain(x0)))), coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by lemma 19 R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), multiplication(addition(one, antidomain(domain(coantidomain(x0)))), coantidomain(coantidomain(x0)))))
% 1.84/0.69 = { by axiom 13 (left_distributivity) }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(multiplication(one, coantidomain(coantidomain(x0))), multiplication(antidomain(domain(coantidomain(x0))), coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 8 (multiplicative_left_identity) }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), multiplication(antidomain(domain(coantidomain(x0))), coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 20 }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), multiplication(antidomain(coantidomain(x0)), coantidomain(coantidomain(x0))))))
% 1.84/0.69 = { by lemma 18 R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), multiplication(antidomain(coantidomain(x0)), addition(coantidomain(x0), coantidomain(coantidomain(x0)))))))
% 1.84/0.69 = { by lemma 21 }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), multiplication(antidomain(coantidomain(x0)), one))))
% 1.84/0.69 = { by axiom 6 (multiplicative_right_identity) }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), antidomain(coantidomain(x0)))))
% 1.84/0.69 = { by lemma 20 R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), antidomain(domain(coantidomain(x0))))))
% 1.84/0.69 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.69 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(antidomain(domain(coantidomain(x0))), coantidomain(coantidomain(x0)))))
% 1.84/0.70 = { by lemma 20 }
% 1.84/0.70 multiplication(coantidomain(x0), addition(domain(coantidomain(x0)), addition(antidomain(coantidomain(x0)), coantidomain(coantidomain(x0)))))
% 1.84/0.70 = { by axiom 10 (additive_associativity) }
% 1.84/0.70 multiplication(coantidomain(x0), addition(addition(domain(coantidomain(x0)), antidomain(coantidomain(x0))), coantidomain(coantidomain(x0))))
% 1.84/0.70 = { by lemma 17 }
% 1.84/0.70 multiplication(coantidomain(x0), addition(one, coantidomain(coantidomain(x0))))
% 1.84/0.70 = { by axiom 3 (additive_commutativity) R->L }
% 1.84/0.70 multiplication(coantidomain(x0), addition(coantidomain(coantidomain(x0)), one))
% 1.84/0.70 = { by lemma 21 R->L }
% 1.84/0.70 multiplication(coantidomain(x0), addition(coantidomain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), coantidomain(coantidomain(coantidomain(x0))))))
% 1.84/0.70 = { by lemma 24 }
% 1.84/0.70 multiplication(coantidomain(x0), addition(coantidomain(coantidomain(x0)), coantidomain(coantidomain(coantidomain(x0)))))
% 1.84/0.70 = { by lemma 21 }
% 1.84/0.70 multiplication(coantidomain(x0), one)
% 1.84/0.70 = { by axiom 6 (multiplicative_right_identity) }
% 1.84/0.70 coantidomain(x0)
% 1.84/0.70 % SZS output end Proof
% 1.84/0.70
% 1.84/0.70 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------