%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE100+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 11:39:49 AM UTC 2026
% Result : Theorem 15.10s 2.49s
% Output : Proof 15.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE100+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.42 % Computer : n014.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Sun Sep 27 13:10:02 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.10/2.49 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 15.10/2.49
% 15.10/2.49 % SZS status Theorem
% 15.10/2.49
% 15.91/2.55 % SZS output start Proof
% 15.91/2.55 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 15.91/2.55 Axiom 2 (multiplicative_right_identity): multiplication(X, one) = X.
% 15.91/2.55 Axiom 3 (multiplicative_left_identity): multiplication(one, X) = X.
% 15.91/2.55 Axiom 4 (domain1): multiplication(antidomain(X), X) = zero.
% 15.91/2.55 Axiom 5 (additive_idempotence): addition(X, X) = X.
% 15.91/2.55 Axiom 6 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 15.91/2.55 Axiom 7 (additive_identity): addition(X, zero) = X.
% 15.91/2.55 Axiom 8 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 15.91/2.55 Axiom 9 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 15.91/2.55 Axiom 10 (forward_diamond): forward_diamond(X, Y) = domain(multiplication(X, domain(Y))).
% 15.91/2.55 Axiom 11 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 15.91/2.55 Axiom 12 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 15.91/2.55 Axiom 13 (goals): multiplication(antidomain(x2), multiplication(x0, domain(x1))) = zero.
% 15.91/2.55 Axiom 14 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 15.91/2.55 Axiom 15 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 15.91/2.55 Axiom 16 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 15.91/2.55 Axiom 17 (order_1): ifeq(leq(X, Y), true, addition(X, Y), Y) = Y.
% 15.91/2.55 Axiom 18 (order): ifeq2(addition(X, Y), Y, leq(X, Y), true) = true.
% 15.91/2.55
% 15.91/2.55 Lemma 19: antidomain(one) = zero.
% 15.91/2.55 Proof:
% 15.91/2.55 antidomain(one)
% 15.91/2.55 = { by axiom 2 (multiplicative_right_identity) R->L }
% 15.91/2.56 multiplication(antidomain(one), one)
% 15.91/2.56 = { by axiom 4 (domain1) }
% 15.91/2.56 zero
% 15.91/2.56
% 15.91/2.56 Lemma 20: addition(antidomain(X), antidomain(antidomain(X))) = one.
% 15.91/2.56 Proof:
% 15.91/2.56 addition(antidomain(X), antidomain(antidomain(X)))
% 15.91/2.56 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.56 addition(antidomain(antidomain(X)), antidomain(X))
% 15.91/2.56 = { by axiom 8 (domain3) }
% 15.91/2.56 one
% 15.91/2.56
% 15.91/2.56 Lemma 21: multiplication(antidomain(X), addition(X, Y)) = multiplication(antidomain(X), Y).
% 15.91/2.56 Proof:
% 15.91/2.56 multiplication(antidomain(X), addition(X, Y))
% 15.91/2.56 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.56 multiplication(antidomain(X), addition(Y, X))
% 15.91/2.56 = { by axiom 14 (right_distributivity) }
% 15.91/2.56 addition(multiplication(antidomain(X), Y), multiplication(antidomain(X), X))
% 15.91/2.56 = { by axiom 4 (domain1) }
% 15.91/2.56 addition(multiplication(antidomain(X), Y), zero)
% 15.91/2.56 = { by axiom 7 (additive_identity) }
% 15.91/2.56 multiplication(antidomain(X), Y)
% 15.91/2.56
% 15.91/2.56 Lemma 22: multiplication(antidomain(X), addition(Y, X)) = multiplication(antidomain(X), Y).
% 15.91/2.56 Proof:
% 15.91/2.56 multiplication(antidomain(X), addition(Y, X))
% 15.91/2.56 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.56 multiplication(antidomain(X), addition(X, Y))
% 15.91/2.56 = { by lemma 21 }
% 15.91/2.56 multiplication(antidomain(X), Y)
% 15.91/2.56
% 15.91/2.56 Lemma 23: multiplication(antidomain(antidomain(X)), X) = X.
% 15.91/2.56 Proof:
% 15.91/2.56 multiplication(antidomain(antidomain(X)), X)
% 15.91/2.56 = { by axiom 7 (additive_identity) R->L }
% 15.91/2.56 addition(multiplication(antidomain(antidomain(X)), X), zero)
% 15.91/2.56 = { by axiom 4 (domain1) R->L }
% 15.91/2.56 addition(multiplication(antidomain(antidomain(X)), X), multiplication(antidomain(X), X))
% 15.91/2.56 = { by axiom 15 (left_distributivity) R->L }
% 15.91/2.56 multiplication(addition(antidomain(antidomain(X)), antidomain(X)), X)
% 15.91/2.56 = { by axiom 6 (additive_commutativity) }
% 15.91/2.56 multiplication(addition(antidomain(X), antidomain(antidomain(X))), X)
% 15.91/2.56 = { by lemma 20 }
% 15.91/2.56 multiplication(one, X)
% 15.91/2.56 = { by axiom 3 (multiplicative_left_identity) }
% 15.91/2.56 X
% 15.91/2.56
% 15.91/2.56 Lemma 24: antidomain(domain(X)) = antidomain(X).
% 15.91/2.56 Proof:
% 15.91/2.56 antidomain(domain(X))
% 15.91/2.56 = { by axiom 1 (domain4) }
% 15.91/2.56 antidomain(antidomain(antidomain(X)))
% 15.91/2.56 = { by axiom 2 (multiplicative_right_identity) R->L }
% 15.91/2.56 multiplication(antidomain(antidomain(antidomain(X))), one)
% 15.91/2.56 = { by lemma 20 R->L }
% 15.91/2.56 multiplication(antidomain(antidomain(antidomain(X))), addition(antidomain(X), antidomain(antidomain(X))))
% 15.91/2.56 = { by lemma 22 }
% 15.91/2.56 multiplication(antidomain(antidomain(antidomain(X))), antidomain(X))
% 15.91/2.56 = { by lemma 23 }
% 15.91/2.56 antidomain(X)
% 15.91/2.56
% 15.91/2.56 Lemma 25: addition(X, addition(X, Y)) = addition(X, Y).
% 15.91/2.56 Proof:
% 15.91/2.56 addition(X, addition(X, Y))
% 15.91/2.56 = { by axiom 9 (additive_associativity) }
% 15.91/2.56 addition(addition(X, X), Y)
% 15.91/2.56 = { by axiom 5 (additive_idempotence) }
% 15.91/2.56 addition(X, Y)
% 15.91/2.56
% 15.91/2.56 Lemma 26: addition(domain(X), antidomain(X)) = one.
% 15.91/2.56 Proof:
% 15.91/2.56 addition(domain(X), antidomain(X))
% 15.91/2.56 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.56 addition(antidomain(X), domain(X))
% 15.91/2.56 = { by axiom 1 (domain4) }
% 15.91/2.56 addition(antidomain(X), antidomain(antidomain(X)))
% 15.91/2.56 = { by lemma 20 }
% 15.91/2.56 one
% 15.91/2.56
% 15.91/2.56 Lemma 27: antidomain(antidomain(multiplication(X, antidomain(antidomain(Y))))) = forward_diamond(X, Y).
% 15.91/2.56 Proof:
% 15.91/2.56 antidomain(antidomain(multiplication(X, antidomain(antidomain(Y)))))
% 15.91/2.56 = { by axiom 1 (domain4) R->L }
% 15.91/2.56 antidomain(antidomain(multiplication(X, domain(Y))))
% 15.91/2.56 = { by axiom 1 (domain4) R->L }
% 15.91/2.56 domain(multiplication(X, domain(Y)))
% 15.91/2.56 = { by axiom 10 (forward_diamond) R->L }
% 15.91/2.56 forward_diamond(X, Y)
% 15.91/2.56
% 15.91/2.56 Lemma 28: antidomain(antidomain(multiplication(X, domain(Y)))) = forward_diamond(X, Y).
% 15.91/2.56 Proof:
% 15.91/2.56 antidomain(antidomain(multiplication(X, domain(Y))))
% 15.91/2.56 = { by axiom 1 (domain4) }
% 15.91/2.56 antidomain(antidomain(multiplication(X, antidomain(antidomain(Y)))))
% 15.91/2.56 = { by lemma 27 }
% 15.91/2.56 forward_diamond(X, Y)
% 15.91/2.56
% 15.91/2.56 Lemma 29: addition(forward_diamond(X, Y), antidomain(forward_diamond(X, Y))) = one.
% 15.91/2.56 Proof:
% 15.91/2.56 addition(forward_diamond(X, Y), antidomain(forward_diamond(X, Y)))
% 15.91/2.56 = { by lemma 27 R->L }
% 15.91/2.56 addition(forward_diamond(X, Y), antidomain(antidomain(antidomain(multiplication(X, antidomain(antidomain(Y)))))))
% 15.91/2.56 = { by lemma 27 R->L }
% 15.91/2.56 addition(antidomain(antidomain(multiplication(X, antidomain(antidomain(Y))))), antidomain(antidomain(antidomain(multiplication(X, antidomain(antidomain(Y)))))))
% 15.91/2.56 = { by lemma 20 }
% 15.91/2.56 one
% 15.91/2.56
% 15.91/2.56 Goal 1 (goals_1): addition(forward_diamond(x0, domain(x1)), domain(x2)) = domain(x2).
% 15.91/2.56 Proof:
% 15.91/2.56 addition(forward_diamond(x0, domain(x1)), domain(x2))
% 15.91/2.56 = { by axiom 3 (multiplicative_left_identity) R->L }
% 15.91/2.56 multiplication(one, addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 15.91/2.56 = { by lemma 26 R->L }
% 15.91/2.56 multiplication(addition(domain(x2), antidomain(x2)), addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 15.91/2.56 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.57 multiplication(addition(antidomain(x2), domain(x2)), addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 15.91/2.57 = { by axiom 15 (left_distributivity) }
% 15.91/2.57 addition(multiplication(antidomain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 24 R->L }
% 15.91/2.57 addition(multiplication(antidomain(domain(x2)), addition(forward_diamond(x0, domain(x1)), domain(x2))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 6 (additive_commutativity) }
% 15.91/2.57 addition(multiplication(antidomain(domain(x2)), addition(domain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 21 }
% 15.91/2.57 addition(multiplication(antidomain(domain(x2)), forward_diamond(x0, domain(x1))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 24 }
% 15.91/2.57 addition(multiplication(antidomain(x2), forward_diamond(x0, domain(x1))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 3 (multiplicative_left_identity) R->L }
% 15.91/2.57 addition(multiplication(one, multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 20 R->L }
% 15.91/2.57 addition(multiplication(addition(antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1))), antidomain(antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 25 R->L }
% 15.91/2.57 addition(multiplication(addition(antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1))), addition(antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1))), antidomain(antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 20 }
% 15.91/2.57 addition(multiplication(addition(antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1))), one), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 6 (additive_commutativity) }
% 15.91/2.57 addition(multiplication(addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 11 (ifeq_axiom) R->L }
% 15.91/2.57 addition(multiplication(ifeq(true, true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 18 (order) R->L }
% 15.91/2.57 addition(multiplication(ifeq(ifeq2(addition(antidomain(multiplication(antidomain(x2), multiplication(x0, domain(x1)))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1)))))), leq(antidomain(multiplication(antidomain(x2), multiplication(x0, domain(x1)))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 16 (domain2) }
% 15.91/2.57 addition(multiplication(ifeq(ifeq2(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1)))))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1)))))), leq(antidomain(multiplication(antidomain(x2), multiplication(x0, domain(x1)))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 12 (ifeq_axiom) }
% 15.91/2.57 addition(multiplication(ifeq(leq(antidomain(multiplication(antidomain(x2), multiplication(x0, domain(x1)))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 13 (goals) }
% 15.91/2.57 addition(multiplication(ifeq(leq(antidomain(zero), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 19 R->L }
% 15.91/2.57 addition(multiplication(ifeq(leq(antidomain(antidomain(one)), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 7 (additive_identity) R->L }
% 15.91/2.57 addition(multiplication(ifeq(leq(addition(antidomain(antidomain(one)), zero), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by axiom 6 (additive_commutativity) }
% 15.91/2.57 addition(multiplication(ifeq(leq(addition(zero, antidomain(antidomain(one))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.57 = { by lemma 19 R->L }
% 15.91/2.58 addition(multiplication(ifeq(leq(addition(antidomain(one), antidomain(antidomain(one))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by lemma 20 }
% 15.91/2.58 addition(multiplication(ifeq(leq(one, antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by lemma 28 }
% 15.91/2.58 addition(multiplication(ifeq(leq(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), true, addition(one, antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 17 (order_1) }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), forward_diamond(x0, x1))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by lemma 28 R->L }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1)))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by lemma 23 R->L }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), domain(x1))))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by lemma 22 R->L }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), addition(domain(x1), antidomain(domain(x1))))))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 1 (domain4) }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), addition(domain(x1), antidomain(antidomain(antidomain(x1)))))))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 1 (domain4) }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), addition(antidomain(antidomain(x1)), antidomain(antidomain(antidomain(x1)))))))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by lemma 20 }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, multiplication(antidomain(antidomain(domain(x1))), one)))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 2 (multiplicative_right_identity) }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, antidomain(antidomain(domain(x1)))))))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by lemma 27 }
% 15.91/2.58 addition(multiplication(antidomain(multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(antidomain(x2), forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 4 (domain1) }
% 15.91/2.58 addition(zero, multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 4 (domain1) R->L }
% 15.91/2.58 addition(multiplication(antidomain(antidomain(x2)), antidomain(x2)), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 1 (domain4) R->L }
% 15.91/2.58 addition(multiplication(domain(x2), antidomain(x2)), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 14 (right_distributivity) R->L }
% 15.91/2.58 multiplication(domain(x2), addition(antidomain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 15.91/2.58 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.58 multiplication(domain(x2), addition(addition(forward_diamond(x0, domain(x1)), domain(x2)), antidomain(x2)))
% 15.91/2.58 = { by axiom 6 (additive_commutativity) }
% 15.91/2.58 multiplication(domain(x2), addition(addition(domain(x2), forward_diamond(x0, domain(x1))), antidomain(x2)))
% 15.91/2.58 = { by axiom 9 (additive_associativity) R->L }
% 15.91/2.58 multiplication(domain(x2), addition(domain(x2), addition(forward_diamond(x0, domain(x1)), antidomain(x2))))
% 15.91/2.58 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.58 multiplication(domain(x2), addition(domain(x2), addition(antidomain(x2), forward_diamond(x0, domain(x1)))))
% 15.91/2.58 = { by axiom 9 (additive_associativity) }
% 15.91/2.58 multiplication(domain(x2), addition(addition(domain(x2), antidomain(x2)), forward_diamond(x0, domain(x1))))
% 15.91/2.58 = { by lemma 26 }
% 15.91/2.58 multiplication(domain(x2), addition(one, forward_diamond(x0, domain(x1))))
% 15.91/2.58 = { by axiom 6 (additive_commutativity) R->L }
% 15.91/2.58 multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), one))
% 15.91/2.58 = { by lemma 29 R->L }
% 15.91/2.58 multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), addition(forward_diamond(x0, domain(x1)), antidomain(forward_diamond(x0, domain(x1))))))
% 15.91/2.58 = { by lemma 25 }
% 15.91/2.58 multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), antidomain(forward_diamond(x0, domain(x1)))))
% 15.91/2.58 = { by lemma 29 }
% 15.91/2.58 multiplication(domain(x2), one)
% 15.91/2.58 = { by axiom 2 (multiplicative_right_identity) }
% 15.91/2.58 domain(x2)
% 15.91/2.58 % SZS output end Proof
% 15.91/2.58
% 15.91/2.58 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------