%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE091+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 4.18s 1.19s
% Output : Proof 5.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE091+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.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 13:09:48 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/1.19 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
% 4.18/1.19
% 4.18/1.19 % SZS status Theorem
% 4.18/1.19
% 5.83/1.22 % SZS output start Proof
% 5.83/1.22 Axiom 1 (codomain4): codomain(X) = coantidomain(coantidomain(X)).
% 5.83/1.22 Axiom 2 (multiplicative_right_identity): multiplication(X, one) = X.
% 5.83/1.22 Axiom 3 (codomain1): multiplication(X, coantidomain(X)) = zero.
% 5.83/1.22 Axiom 4 (multiplicative_left_identity): multiplication(one, X) = X.
% 5.83/1.22 Axiom 5 (additive_idempotence): addition(X, X) = X.
% 5.83/1.22 Axiom 6 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 5.83/1.22 Axiom 7 (additive_identity): addition(X, zero) = X.
% 5.83/1.22 Axiom 8 (codomain3): addition(coantidomain(coantidomain(X)), coantidomain(X)) = one.
% 5.83/1.22 Axiom 9 (domain4): domain(X) = antidomain(antidomain(X)).
% 5.83/1.22 Axiom 10 (domain1): multiplication(antidomain(X), X) = zero.
% 5.83/1.22 Axiom 11 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 5.83/1.22 Axiom 12 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 5.83/1.22 Axiom 13 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 5.83/1.22 Axiom 14 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 5.83/1.22 Axiom 15 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 5.83/1.22 Axiom 16 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 5.83/1.22 Axiom 17 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 5.83/1.22 Axiom 18 (codomain2): addition(coantidomain(multiplication(X, Y)), coantidomain(multiplication(coantidomain(coantidomain(X)), Y))) = coantidomain(multiplication(coantidomain(coantidomain(X)), Y)).
% 5.83/1.22 Axiom 19 (order_1): ifeq(leq(X, Y), true, addition(X, Y), Y) = Y.
% 5.83/1.22 Axiom 20 (order): ifeq2(addition(X, Y), Y, leq(X, Y), true) = true.
% 5.83/1.22 Axiom 21 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 5.83/1.22
% 5.83/1.22 Lemma 22: antidomain(one) = zero.
% 5.83/1.22 Proof:
% 5.83/1.22 antidomain(one)
% 5.83/1.22 = { by axiom 2 (multiplicative_right_identity) R->L }
% 5.83/1.22 multiplication(antidomain(one), one)
% 5.83/1.22 = { by axiom 10 (domain1) }
% 5.83/1.22 zero
% 5.83/1.22
% 5.83/1.22 Lemma 23: addition(zero, X) = X.
% 5.83/1.22 Proof:
% 5.83/1.22 addition(zero, X)
% 5.83/1.22 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.22 addition(X, zero)
% 5.83/1.22 = { by axiom 7 (additive_identity) }
% 5.83/1.22 X
% 5.83/1.22
% 5.83/1.22 Lemma 24: addition(X, addition(X, Y)) = addition(X, Y).
% 5.83/1.22 Proof:
% 5.83/1.22 addition(X, addition(X, Y))
% 5.83/1.22 = { by axiom 12 (additive_associativity) }
% 5.83/1.22 addition(addition(X, X), Y)
% 5.83/1.22 = { by axiom 5 (additive_idempotence) }
% 5.83/1.22 addition(X, Y)
% 5.83/1.22
% 5.83/1.22 Lemma 25: addition(antidomain(X), domain(X)) = one.
% 5.83/1.22 Proof:
% 5.83/1.22 addition(antidomain(X), domain(X))
% 5.83/1.22 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.22 addition(domain(X), antidomain(X))
% 5.83/1.22 = { by axiom 9 (domain4) }
% 5.83/1.22 addition(antidomain(antidomain(X)), antidomain(X))
% 5.83/1.22 = { by axiom 15 (domain3) }
% 5.83/1.22 one
% 5.83/1.22
% 5.83/1.22 Lemma 26: addition(domain(X), antidomain(X)) = one.
% 5.83/1.22 Proof:
% 5.83/1.22 addition(domain(X), antidomain(X))
% 5.83/1.22 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.22 addition(antidomain(X), domain(X))
% 5.83/1.22 = { by lemma 25 }
% 5.83/1.22 one
% 5.83/1.22
% 5.83/1.22 Lemma 27: addition(coantidomain(X), coantidomain(coantidomain(X))) = one.
% 5.83/1.22 Proof:
% 5.83/1.22 addition(coantidomain(X), coantidomain(coantidomain(X)))
% 5.83/1.22 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.22 addition(coantidomain(coantidomain(X)), coantidomain(X))
% 5.83/1.22 = { by axiom 8 (codomain3) }
% 5.83/1.22 one
% 5.83/1.22
% 5.83/1.22 Lemma 28: addition(codomain(X), coantidomain(codomain(X))) = one.
% 5.83/1.22 Proof:
% 5.83/1.22 addition(codomain(X), coantidomain(codomain(X)))
% 5.83/1.22 = { by axiom 1 (codomain4) }
% 5.83/1.22 addition(codomain(X), coantidomain(coantidomain(coantidomain(X))))
% 5.83/1.22 = { by axiom 1 (codomain4) }
% 5.83/1.23 addition(coantidomain(coantidomain(X)), coantidomain(coantidomain(coantidomain(X))))
% 5.83/1.23 = { by lemma 27 }
% 5.83/1.23 one
% 5.83/1.23
% 5.83/1.23 Lemma 29: multiplication(X, addition(Y, coantidomain(X))) = multiplication(X, Y).
% 5.83/1.23 Proof:
% 5.83/1.23 multiplication(X, addition(Y, coantidomain(X)))
% 5.83/1.23 = { by axiom 16 (right_distributivity) }
% 5.83/1.23 addition(multiplication(X, Y), multiplication(X, coantidomain(X)))
% 5.83/1.23 = { by axiom 3 (codomain1) }
% 5.83/1.23 addition(multiplication(X, Y), zero)
% 5.83/1.23 = { by axiom 7 (additive_identity) }
% 5.83/1.23 multiplication(X, Y)
% 5.83/1.23
% 5.83/1.23 Goal 1 (goals): domain(codomain(x0)) = codomain(x0).
% 5.83/1.23 Proof:
% 5.83/1.23 domain(codomain(x0))
% 5.83/1.23 = { by axiom 4 (multiplicative_left_identity) R->L }
% 5.83/1.23 multiplication(one, domain(codomain(x0)))
% 5.83/1.23 = { by lemma 27 R->L }
% 5.83/1.23 multiplication(addition(coantidomain(x0), coantidomain(coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 1 (codomain4) R->L }
% 5.83/1.23 multiplication(addition(coantidomain(x0), codomain(x0)), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 6 (additive_commutativity) }
% 5.83/1.23 multiplication(addition(codomain(x0), coantidomain(x0)), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 4 (multiplicative_left_identity) R->L }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(one, coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by lemma 25 R->L }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(addition(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), domain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by lemma 24 R->L }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(addition(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), addition(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), domain(multiplication(coantidomain(x0), domain(codomain(x0)))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by lemma 25 }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(addition(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), one), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 6 (additive_commutativity) }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 13 (ifeq_axiom) R->L }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(true, true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 20 (order) R->L }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(ifeq2(addition(antidomain(multiplication(coantidomain(x0), codomain(x0))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), leq(antidomain(multiplication(coantidomain(x0), codomain(x0))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 9 (domain4) }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(ifeq2(addition(antidomain(multiplication(coantidomain(x0), codomain(x0))), antidomain(multiplication(coantidomain(x0), antidomain(antidomain(codomain(x0)))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), leq(antidomain(multiplication(coantidomain(x0), codomain(x0))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 21 (domain2) }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(ifeq2(antidomain(multiplication(coantidomain(x0), antidomain(antidomain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), leq(antidomain(multiplication(coantidomain(x0), codomain(x0))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 9 (domain4) R->L }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(ifeq2(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), leq(antidomain(multiplication(coantidomain(x0), codomain(x0))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 14 (ifeq_axiom) }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(leq(antidomain(multiplication(coantidomain(x0), codomain(x0))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 1 (codomain4) }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(leq(antidomain(multiplication(coantidomain(x0), coantidomain(coantidomain(x0)))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 3 (codomain1) }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(leq(antidomain(zero), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by lemma 22 R->L }
% 5.83/1.23 multiplication(addition(codomain(x0), multiplication(ifeq(leq(antidomain(antidomain(one)), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.23 = { by axiom 9 (domain4) R->L }
% 5.83/1.24 multiplication(addition(codomain(x0), multiplication(ifeq(leq(domain(one), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.24 = { by lemma 23 R->L }
% 5.83/1.24 multiplication(addition(codomain(x0), multiplication(ifeq(leq(addition(zero, domain(one)), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.24 = { by lemma 22 R->L }
% 5.83/1.24 multiplication(addition(codomain(x0), multiplication(ifeq(leq(addition(antidomain(one), domain(one)), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.24 = { by lemma 25 }
% 5.83/1.24 multiplication(addition(codomain(x0), multiplication(ifeq(leq(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), true, addition(one, antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), antidomain(multiplication(coantidomain(x0), domain(codomain(x0))))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.24 = { by axiom 19 (order_1) }
% 5.83/1.24 multiplication(addition(codomain(x0), multiplication(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), coantidomain(x0))), domain(codomain(x0)))
% 5.83/1.24 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.24 multiplication(addition(multiplication(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), coantidomain(x0)), codomain(x0)), domain(codomain(x0)))
% 5.83/1.24 = { by axiom 17 (left_distributivity) }
% 5.83/1.24 addition(multiplication(multiplication(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), coantidomain(x0)), domain(codomain(x0))), multiplication(codomain(x0), domain(codomain(x0))))
% 5.83/1.24 = { by axiom 11 (multiplicative_associativity) R->L }
% 5.83/1.24 addition(multiplication(antidomain(multiplication(coantidomain(x0), domain(codomain(x0)))), multiplication(coantidomain(x0), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 5.83/1.24 = { by axiom 10 (domain1) }
% 5.83/1.24 addition(zero, multiplication(codomain(x0), domain(codomain(x0))))
% 5.83/1.24 = { by lemma 23 }
% 5.83/1.24 multiplication(codomain(x0), domain(codomain(x0)))
% 5.83/1.24 = { by lemma 29 R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), coantidomain(codomain(x0))))
% 5.83/1.24 = { by axiom 1 (codomain4) }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), coantidomain(coantidomain(coantidomain(x0)))))
% 5.83/1.24 = { by axiom 2 (multiplicative_right_identity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), coantidomain(multiplication(coantidomain(coantidomain(x0)), one))))
% 5.83/1.24 = { by axiom 18 (codomain2) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(coantidomain(multiplication(x0, one)), coantidomain(multiplication(coantidomain(coantidomain(x0)), one)))))
% 5.83/1.24 = { by axiom 2 (multiplicative_right_identity) }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(coantidomain(x0), coantidomain(multiplication(coantidomain(coantidomain(x0)), one)))))
% 5.83/1.24 = { by axiom 2 (multiplicative_right_identity) }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(coantidomain(x0), coantidomain(coantidomain(coantidomain(x0))))))
% 5.83/1.24 = { by axiom 1 (codomain4) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(coantidomain(x0), coantidomain(codomain(x0)))))
% 5.83/1.24 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(addition(coantidomain(x0), coantidomain(codomain(x0))), domain(codomain(x0))))
% 5.83/1.24 = { by axiom 12 (additive_associativity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(coantidomain(codomain(x0)), domain(codomain(x0)))))
% 5.83/1.24 = { by axiom 6 (additive_commutativity) }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), coantidomain(codomain(x0)))))
% 5.83/1.24 = { by axiom 12 (additive_associativity) }
% 5.83/1.24 multiplication(codomain(x0), addition(addition(coantidomain(x0), domain(codomain(x0))), coantidomain(codomain(x0))))
% 5.83/1.24 = { by lemma 29 }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), domain(codomain(x0))))
% 5.83/1.24 = { by axiom 2 (multiplicative_right_identity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), multiplication(domain(codomain(x0)), one)))
% 5.83/1.24 = { by lemma 28 R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), multiplication(domain(codomain(x0)), addition(codomain(x0), coantidomain(codomain(x0))))))
% 5.83/1.24 = { by lemma 24 R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), multiplication(domain(codomain(x0)), addition(codomain(x0), addition(codomain(x0), coantidomain(codomain(x0)))))))
% 5.83/1.24 = { by lemma 28 }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), multiplication(domain(codomain(x0)), addition(codomain(x0), one))))
% 5.83/1.24 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), multiplication(domain(codomain(x0)), addition(one, codomain(x0)))))
% 5.83/1.24 = { by axiom 16 (right_distributivity) }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(multiplication(domain(codomain(x0)), one), multiplication(domain(codomain(x0)), codomain(x0)))))
% 5.83/1.24 = { by axiom 2 (multiplicative_right_identity) }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), multiplication(domain(codomain(x0)), codomain(x0)))))
% 5.83/1.24 = { by axiom 7 (additive_identity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), addition(multiplication(domain(codomain(x0)), codomain(x0)), zero))))
% 5.83/1.24 = { by axiom 10 (domain1) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), addition(multiplication(domain(codomain(x0)), codomain(x0)), multiplication(antidomain(codomain(x0)), codomain(x0))))))
% 5.83/1.24 = { by axiom 17 (left_distributivity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), multiplication(addition(domain(codomain(x0)), antidomain(codomain(x0))), codomain(x0)))))
% 5.83/1.24 = { by lemma 26 }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), multiplication(one, codomain(x0)))))
% 5.83/1.24 = { by axiom 4 (multiplicative_left_identity) }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), codomain(x0))))
% 5.83/1.24 = { by axiom 1 (codomain4) }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(domain(codomain(x0)), coantidomain(coantidomain(x0)))))
% 5.83/1.24 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(coantidomain(x0), addition(coantidomain(coantidomain(x0)), domain(codomain(x0)))))
% 5.83/1.24 = { by axiom 12 (additive_associativity) }
% 5.83/1.24 multiplication(codomain(x0), addition(addition(coantidomain(x0), coantidomain(coantidomain(x0))), domain(codomain(x0))))
% 5.83/1.24 = { by lemma 27 }
% 5.83/1.24 multiplication(codomain(x0), addition(one, domain(codomain(x0))))
% 5.83/1.24 = { by axiom 6 (additive_commutativity) R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), one))
% 5.83/1.24 = { by lemma 26 R->L }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(domain(codomain(x0)), antidomain(codomain(x0)))))
% 5.83/1.24 = { by lemma 24 }
% 5.83/1.24 multiplication(codomain(x0), addition(domain(codomain(x0)), antidomain(codomain(x0))))
% 5.83/1.24 = { by lemma 26 }
% 5.83/1.24 multiplication(codomain(x0), one)
% 5.83/1.24 = { by axiom 2 (multiplicative_right_identity) }
% 5.83/1.24 codomain(x0)
% 5.83/1.24 % SZS output end Proof
% 5.83/1.24
% 5.83/1.24 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------