TSTP Solution File: RNG035-7 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG035-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:58:57 EDT 2023
% Result : Unsatisfiable 83.07s 11.00s
% Output : Proof 86.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG035-7 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 03:13:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 83.07/11.00 Command-line arguments: --flatten
% 83.07/11.00
% 83.07/11.00 % SZS status Unsatisfiable
% 83.07/11.00
% 85.14/11.33 % SZS output start Proof
% 85.14/11.33 Axiom 1 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 85.14/11.33 Axiom 2 (right_additive_identity): add(X, additive_identity) = X.
% 85.14/11.33 Axiom 3 (left_additive_identity): add(additive_identity, X) = X.
% 85.14/11.33 Axiom 4 (a_times_b_is_c): multiply(a, b) = c.
% 85.14/11.33 Axiom 5 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 85.14/11.33 Axiom 6 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 85.14/11.33 Axiom 7 (associativity_for_multiplication): multiply(X, multiply(Y, Z)) = multiply(multiply(X, Y), Z).
% 85.14/11.33 Axiom 8 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 85.14/11.33 Axiom 9 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 85.14/11.33 Axiom 10 (x_fourthed_is_x): multiply(X, multiply(X, multiply(X, X))) = X.
% 85.14/11.33
% 85.14/11.33 Lemma 11: add(X, add(Y, additive_inverse(X))) = Y.
% 85.14/11.33 Proof:
% 85.14/11.33 add(X, add(Y, additive_inverse(X)))
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.33 add(X, add(additive_inverse(X), Y))
% 85.14/11.33 = { by axiom 6 (associativity_for_addition) }
% 85.14/11.33 add(add(X, additive_inverse(X)), Y)
% 85.14/11.33 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.33 add(additive_identity, Y)
% 85.14/11.33 = { by axiom 3 (left_additive_identity) }
% 85.14/11.33 Y
% 85.14/11.33
% 85.14/11.33 Lemma 12: add(X, add(additive_inverse(X), Y)) = Y.
% 85.14/11.33 Proof:
% 85.14/11.33 add(X, add(additive_inverse(X), Y))
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.33 add(X, add(Y, additive_inverse(X)))
% 85.14/11.33 = { by lemma 11 }
% 85.14/11.33 Y
% 85.14/11.33
% 85.14/11.33 Lemma 13: add(multiply(X, Y), add(Z, multiply(W, Y))) = add(Z, multiply(add(X, W), Y)).
% 85.14/11.33 Proof:
% 85.14/11.33 add(multiply(X, Y), add(Z, multiply(W, Y)))
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.33 add(multiply(X, Y), add(multiply(W, Y), Z))
% 85.14/11.33 = { by axiom 6 (associativity_for_addition) }
% 85.14/11.33 add(add(multiply(X, Y), multiply(W, Y)), Z)
% 85.14/11.33 = { by axiom 9 (distribute2) R->L }
% 85.14/11.33 add(multiply(add(X, W), Y), Z)
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.33 add(Z, multiply(add(X, W), Y))
% 85.14/11.33
% 85.14/11.33 Lemma 14: add(multiply(X, Z), multiply(X, Y)) = multiply(X, add(Y, Z)).
% 85.14/11.33 Proof:
% 85.14/11.33 add(multiply(X, Z), multiply(X, Y))
% 85.14/11.33 = { by axiom 8 (distribute1) R->L }
% 85.14/11.33 multiply(X, add(Z, Y))
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.33 multiply(X, add(Y, Z))
% 85.14/11.33
% 85.14/11.33 Lemma 15: multiply(X, additive_identity) = additive_identity.
% 85.14/11.33 Proof:
% 85.14/11.33 multiply(X, additive_identity)
% 85.14/11.33 = { by lemma 11 R->L }
% 85.14/11.33 add(multiply(X, Y), add(multiply(X, additive_identity), additive_inverse(multiply(X, Y))))
% 85.14/11.33 = { by axiom 3 (left_additive_identity) R->L }
% 85.14/11.33 add(multiply(X, Y), add(multiply(X, additive_identity), additive_inverse(multiply(X, add(additive_identity, Y)))))
% 85.14/11.33 = { by lemma 14 R->L }
% 85.14/11.33 add(multiply(X, Y), add(multiply(X, additive_identity), additive_inverse(add(multiply(X, Y), multiply(X, additive_identity)))))
% 85.14/11.33 = { by axiom 6 (associativity_for_addition) }
% 85.14/11.33 add(add(multiply(X, Y), multiply(X, additive_identity)), additive_inverse(add(multiply(X, Y), multiply(X, additive_identity))))
% 85.14/11.33 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.33 additive_identity
% 85.14/11.33
% 85.14/11.33 Lemma 16: multiply(additive_identity, X) = additive_identity.
% 85.14/11.33 Proof:
% 85.14/11.33 multiply(additive_identity, X)
% 85.14/11.33 = { by axiom 2 (right_additive_identity) R->L }
% 85.14/11.33 multiply(additive_identity, add(X, additive_identity))
% 85.14/11.33 = { by axiom 5 (right_additive_inverse) R->L }
% 85.14/11.33 multiply(additive_identity, add(X, add(X, additive_inverse(X))))
% 85.14/11.33 = { by axiom 6 (associativity_for_addition) }
% 85.14/11.33 multiply(additive_identity, add(add(X, X), additive_inverse(X)))
% 85.14/11.33 = { by axiom 8 (distribute1) }
% 85.14/11.33 add(multiply(additive_identity, add(X, X)), multiply(additive_identity, additive_inverse(X)))
% 85.14/11.33 = { by axiom 8 (distribute1) }
% 85.14/11.33 add(add(multiply(additive_identity, X), multiply(additive_identity, X)), multiply(additive_identity, additive_inverse(X)))
% 85.14/11.33 = { by axiom 9 (distribute2) R->L }
% 85.14/11.33 add(multiply(add(additive_identity, additive_identity), X), multiply(additive_identity, additive_inverse(X)))
% 85.14/11.33 = { by axiom 2 (right_additive_identity) }
% 85.14/11.33 add(multiply(additive_identity, X), multiply(additive_identity, additive_inverse(X)))
% 85.14/11.33 = { by axiom 8 (distribute1) R->L }
% 85.14/11.33 multiply(additive_identity, add(X, additive_inverse(X)))
% 85.14/11.33 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.33 multiply(additive_identity, additive_identity)
% 85.14/11.33 = { by lemma 15 }
% 85.14/11.33 additive_identity
% 85.14/11.33
% 85.14/11.33 Lemma 17: multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)).
% 85.14/11.33 Proof:
% 85.14/11.33 multiply(additive_inverse(X), Y)
% 85.14/11.33 = { by lemma 12 R->L }
% 85.14/11.33 add(multiply(X, Y), add(additive_inverse(multiply(X, Y)), multiply(additive_inverse(X), Y)))
% 85.14/11.33 = { by lemma 13 }
% 85.14/11.33 add(additive_inverse(multiply(X, Y)), multiply(add(X, additive_inverse(X)), Y))
% 85.14/11.33 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.33 add(additive_inverse(multiply(X, Y)), multiply(additive_identity, Y))
% 85.14/11.33 = { by lemma 16 }
% 85.14/11.33 add(additive_inverse(multiply(X, Y)), additive_identity)
% 85.14/11.33 = { by axiom 2 (right_additive_identity) }
% 85.14/11.33 additive_inverse(multiply(X, Y))
% 85.14/11.33
% 85.14/11.33 Lemma 18: add(multiply(X, Y), add(Z, multiply(X, W))) = add(Z, multiply(X, add(Y, W))).
% 85.14/11.33 Proof:
% 85.14/11.33 add(multiply(X, Y), add(Z, multiply(X, W)))
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.33 add(multiply(X, Y), add(multiply(X, W), Z))
% 85.14/11.33 = { by axiom 6 (associativity_for_addition) }
% 85.14/11.33 add(add(multiply(X, Y), multiply(X, W)), Z)
% 85.14/11.33 = { by axiom 8 (distribute1) R->L }
% 85.14/11.33 add(multiply(X, add(Y, W)), Z)
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.33 add(Z, multiply(X, add(Y, W)))
% 85.14/11.33
% 85.14/11.33 Lemma 19: additive_inverse(multiply(X, additive_inverse(Y))) = multiply(X, Y).
% 85.14/11.33 Proof:
% 85.14/11.33 additive_inverse(multiply(X, additive_inverse(Y)))
% 85.14/11.33 = { by axiom 2 (right_additive_identity) R->L }
% 85.14/11.33 add(additive_inverse(multiply(X, additive_inverse(Y))), additive_identity)
% 85.14/11.33 = { by lemma 15 R->L }
% 85.14/11.33 add(additive_inverse(multiply(X, additive_inverse(Y))), multiply(X, additive_identity))
% 85.14/11.33 = { by axiom 5 (right_additive_inverse) R->L }
% 85.14/11.33 add(additive_inverse(multiply(X, additive_inverse(Y))), multiply(X, add(Y, additive_inverse(Y))))
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.33 add(additive_inverse(multiply(X, additive_inverse(Y))), multiply(X, add(additive_inverse(Y), Y)))
% 85.14/11.33 = { by lemma 18 R->L }
% 85.14/11.33 add(multiply(X, additive_inverse(Y)), add(additive_inverse(multiply(X, additive_inverse(Y))), multiply(X, Y)))
% 85.14/11.33 = { by lemma 12 }
% 85.14/11.33 multiply(X, Y)
% 85.14/11.33
% 85.14/11.33 Lemma 20: additive_inverse(additive_inverse(X)) = X.
% 85.14/11.33 Proof:
% 85.14/11.33 additive_inverse(additive_inverse(X))
% 85.14/11.33 = { by lemma 12 R->L }
% 85.14/11.33 add(X, add(additive_inverse(X), additive_inverse(additive_inverse(X))))
% 85.14/11.33 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.33 add(X, additive_identity)
% 85.14/11.33 = { by axiom 2 (right_additive_identity) }
% 85.14/11.33 X
% 85.14/11.33
% 85.14/11.33 Lemma 21: multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)).
% 85.14/11.33 Proof:
% 85.14/11.33 multiply(X, additive_inverse(Y))
% 85.14/11.33 = { by lemma 20 R->L }
% 85.14/11.33 additive_inverse(additive_inverse(multiply(X, additive_inverse(Y))))
% 85.14/11.33 = { by lemma 19 }
% 85.14/11.33 additive_inverse(multiply(X, Y))
% 85.14/11.33
% 85.14/11.33 Lemma 22: multiply(X, add(Y, multiply(X, multiply(X, X)))) = add(X, multiply(X, Y)).
% 85.14/11.33 Proof:
% 85.14/11.33 multiply(X, add(Y, multiply(X, multiply(X, X))))
% 85.14/11.33 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.33 multiply(X, add(multiply(X, multiply(X, X)), Y))
% 85.14/11.33 = { by axiom 8 (distribute1) }
% 85.14/11.33 add(multiply(X, multiply(X, multiply(X, X))), multiply(X, Y))
% 85.14/11.33 = { by axiom 10 (x_fourthed_is_x) }
% 85.14/11.33 add(X, multiply(X, Y))
% 85.14/11.34
% 85.14/11.34 Lemma 23: multiply(X, multiply(additive_inverse(X), multiply(X, X))) = additive_inverse(X).
% 85.14/11.34 Proof:
% 85.14/11.34 multiply(X, multiply(additive_inverse(X), multiply(X, X)))
% 85.14/11.34 = { by lemma 20 R->L }
% 85.14/11.34 multiply(X, multiply(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), X)))
% 85.14/11.34 = { by lemma 20 R->L }
% 85.14/11.34 multiply(X, multiply(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X)))))
% 85.14/11.34 = { by lemma 20 R->L }
% 85.14/11.34 multiply(additive_inverse(additive_inverse(X)), multiply(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X)))))
% 85.14/11.34 = { by lemma 20 R->L }
% 85.14/11.34 multiply(additive_inverse(additive_inverse(X)), multiply(additive_inverse(additive_inverse(additive_inverse(X))), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X)))))
% 85.14/11.34 = { by lemma 12 R->L }
% 85.14/11.34 add(additive_inverse(X), add(additive_inverse(additive_inverse(X)), multiply(additive_inverse(additive_inverse(X)), multiply(additive_inverse(additive_inverse(additive_inverse(X))), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X)))))))
% 85.14/11.34 = { by lemma 22 R->L }
% 85.14/11.34 add(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), add(multiply(additive_inverse(additive_inverse(additive_inverse(X))), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X)))), multiply(additive_inverse(additive_inverse(X)), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X)))))))
% 85.14/11.34 = { by axiom 9 (distribute2) R->L }
% 85.14/11.34 add(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), multiply(add(additive_inverse(additive_inverse(additive_inverse(X))), additive_inverse(additive_inverse(X))), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X))))))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.34 add(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), multiply(add(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(additive_inverse(X)))), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X))))))
% 85.14/11.34 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.34 add(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), multiply(additive_identity, multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X))))))
% 85.14/11.34 = { by lemma 16 }
% 85.14/11.34 add(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), additive_identity))
% 85.14/11.34 = { by lemma 15 }
% 85.14/11.34 add(additive_inverse(X), additive_identity)
% 85.14/11.34 = { by axiom 2 (right_additive_identity) }
% 85.14/11.34 additive_inverse(X)
% 85.14/11.34
% 85.14/11.34 Lemma 24: multiply(X, multiply(X, multiply(X, multiply(X, Y)))) = multiply(X, Y).
% 85.14/11.34 Proof:
% 85.14/11.34 multiply(X, multiply(X, multiply(X, multiply(X, Y))))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(X, multiply(X, multiply(multiply(X, X), Y)))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(X, multiply(multiply(X, multiply(X, X)), Y))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(multiply(X, multiply(X, multiply(X, X))), Y)
% 85.14/11.34 = { by axiom 10 (x_fourthed_is_x) }
% 85.14/11.34 multiply(X, Y)
% 85.14/11.34
% 85.14/11.34 Lemma 25: additive_inverse(X) = X.
% 85.14/11.34 Proof:
% 85.14/11.34 additive_inverse(X)
% 85.14/11.34 = { by axiom 10 (x_fourthed_is_x) R->L }
% 85.14/11.34 multiply(additive_inverse(X), multiply(additive_inverse(X), multiply(additive_inverse(X), additive_inverse(X))))
% 85.14/11.34 = { by lemma 17 }
% 85.14/11.34 multiply(additive_inverse(X), additive_inverse(multiply(X, multiply(additive_inverse(X), additive_inverse(X)))))
% 85.14/11.34 = { by lemma 17 }
% 85.14/11.34 additive_inverse(multiply(X, additive_inverse(multiply(X, multiply(additive_inverse(X), additive_inverse(X))))))
% 85.14/11.34 = { by lemma 19 }
% 85.14/11.34 multiply(X, multiply(X, multiply(additive_inverse(X), additive_inverse(X))))
% 85.14/11.34 = { by lemma 17 }
% 85.14/11.34 multiply(X, multiply(X, additive_inverse(multiply(X, additive_inverse(X)))))
% 85.14/11.34 = { by lemma 21 }
% 85.14/11.34 multiply(X, additive_inverse(multiply(X, multiply(X, additive_inverse(X)))))
% 85.14/11.34 = { by lemma 21 }
% 85.14/11.34 additive_inverse(multiply(X, multiply(X, multiply(X, additive_inverse(X)))))
% 85.14/11.34 = { by lemma 23 R->L }
% 85.14/11.34 additive_inverse(multiply(X, multiply(X, multiply(X, multiply(X, multiply(additive_inverse(X), multiply(X, X)))))))
% 85.14/11.34 = { by lemma 24 }
% 85.14/11.34 additive_inverse(multiply(X, multiply(additive_inverse(X), multiply(X, X))))
% 85.14/11.34 = { by lemma 23 }
% 85.14/11.34 additive_inverse(additive_inverse(X))
% 85.14/11.34 = { by lemma 20 }
% 85.14/11.34 X
% 85.14/11.34
% 85.14/11.34 Lemma 26: add(X, X) = additive_identity.
% 85.14/11.34 Proof:
% 85.14/11.34 add(X, X)
% 85.14/11.34 = { by lemma 25 R->L }
% 85.14/11.34 add(X, additive_inverse(X))
% 85.14/11.34 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.34 additive_identity
% 85.14/11.34
% 85.14/11.34 Lemma 27: add(X, add(X, Y)) = Y.
% 85.14/11.34 Proof:
% 85.14/11.34 add(X, add(X, Y))
% 85.14/11.34 = { by axiom 6 (associativity_for_addition) }
% 85.14/11.34 add(add(X, X), Y)
% 85.14/11.34 = { by lemma 26 }
% 85.14/11.34 add(additive_identity, Y)
% 85.14/11.34 = { by axiom 3 (left_additive_identity) }
% 85.14/11.34 Y
% 85.14/11.34
% 85.14/11.34 Lemma 28: add(Y, add(X, Z)) = add(X, add(Y, Z)).
% 85.14/11.34 Proof:
% 85.14/11.34 add(Y, add(X, Z))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.34 add(add(X, Z), Y)
% 85.14/11.34 = { by axiom 6 (associativity_for_addition) R->L }
% 85.14/11.34 add(X, add(Z, Y))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.34 add(X, add(Y, Z))
% 85.14/11.34
% 85.14/11.34 Lemma 29: multiply(multiply(X, Y), multiply(Z, W)) = multiply(X, multiply(multiply(Y, Z), W)).
% 85.14/11.34 Proof:
% 85.14/11.34 multiply(multiply(X, Y), multiply(Z, W))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.34 multiply(X, multiply(Y, multiply(Z, W)))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(X, multiply(multiply(Y, Z), W))
% 85.14/11.34
% 85.14/11.34 Lemma 30: multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), Z)) = additive_identity.
% 85.14/11.34 Proof:
% 85.14/11.34 multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), Z))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.34 multiply(X, multiply(add(multiply(X, multiply(X, multiply(X, Y))), Y), Z))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(multiply(X, add(multiply(X, multiply(X, multiply(X, Y))), Y)), Z)
% 85.14/11.34 = { by lemma 14 R->L }
% 85.14/11.34 multiply(add(multiply(X, Y), multiply(X, multiply(X, multiply(X, multiply(X, Y))))), Z)
% 85.14/11.34 = { by lemma 24 }
% 85.14/11.34 multiply(add(multiply(X, Y), multiply(X, Y)), Z)
% 85.14/11.34 = { by lemma 26 }
% 85.14/11.34 multiply(additive_identity, Z)
% 85.14/11.34 = { by lemma 16 }
% 85.14/11.34 additive_identity
% 85.14/11.34
% 85.14/11.34 Lemma 31: add(multiply(X, Y), multiply(Z, add(W, Y))) = add(multiply(Z, W), multiply(add(Z, X), Y)).
% 85.14/11.34 Proof:
% 85.14/11.34 add(multiply(X, Y), multiply(Z, add(W, Y)))
% 85.14/11.34 = { by lemma 18 R->L }
% 85.14/11.34 add(multiply(Z, W), add(multiply(X, Y), multiply(Z, Y)))
% 85.14/11.34 = { by axiom 9 (distribute2) R->L }
% 85.14/11.34 add(multiply(Z, W), multiply(add(X, Z), Y))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.34 add(multiply(Z, W), multiply(add(Z, X), Y))
% 85.14/11.34
% 85.14/11.34 Lemma 32: add(multiply(add(X, Y), Z), multiply(X, W)) = add(multiply(Y, Z), multiply(X, add(W, Z))).
% 85.14/11.34 Proof:
% 85.14/11.34 add(multiply(add(X, Y), Z), multiply(X, W))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.34 add(multiply(X, W), multiply(add(X, Y), Z))
% 85.14/11.34 = { by lemma 31 R->L }
% 85.14/11.34 add(multiply(Y, Z), multiply(X, add(W, Z)))
% 85.14/11.34
% 85.14/11.34 Lemma 33: multiply(X, multiply(X, multiply(multiply(X, Y), X))) = multiply(Y, X).
% 85.14/11.34 Proof:
% 85.14/11.34 multiply(X, multiply(X, multiply(multiply(X, Y), X)))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(X, multiply(multiply(X, multiply(X, Y)), X))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(multiply(X, multiply(X, multiply(X, Y))), X)
% 85.14/11.34 = { by lemma 27 R->L }
% 85.14/11.34 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, multiply(X, multiply(X, Y))), X)))
% 85.14/11.34 = { by axiom 9 (distribute2) R->L }
% 85.14/11.34 add(multiply(Y, X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))
% 85.14/11.34 = { by axiom 2 (right_additive_identity) R->L }
% 85.14/11.34 add(multiply(Y, X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), add(X, additive_identity)))
% 85.14/11.34 = { by lemma 30 R->L }
% 85.14/11.34 add(multiply(Y, X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), add(X, multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))))))))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.34 add(multiply(Y, X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), add(multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))))), X)))
% 85.14/11.34 = { by lemma 32 R->L }
% 85.14/11.34 add(multiply(add(add(Y, multiply(X, multiply(X, multiply(X, Y)))), Y), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))))))))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.34 add(multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))))))))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.34 add(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))))))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 add(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 add(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by lemma 25 R->L }
% 85.14/11.34 add(additive_inverse(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(X, multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by lemma 21 R->L }
% 85.14/11.34 add(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), additive_inverse(multiply(X, multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by lemma 17 R->L }
% 85.14/11.34 add(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), multiply(additive_inverse(X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 add(multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), additive_inverse(X)), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by lemma 21 }
% 85.14/11.34 add(multiply(additive_inverse(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))), multiply(add(Y, add(Y, multiply(X, multiply(X, multiply(X, Y))))), X))
% 85.14/11.34 = { by lemma 13 R->L }
% 85.14/11.34 add(multiply(Y, X), add(multiply(additive_inverse(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))
% 85.14/11.34 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.34 add(multiply(Y, X), add(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(additive_inverse(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))))))
% 85.14/11.34 = { by axiom 10 (x_fourthed_is_x) R->L }
% 85.14/11.34 add(multiply(Y, X), add(multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))), multiply(additive_inverse(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))))))
% 85.14/11.34 = { by axiom 9 (distribute2) R->L }
% 85.14/11.34 add(multiply(Y, X), multiply(add(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), additive_inverse(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X))), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))))
% 85.14/11.34 = { by axiom 5 (right_additive_inverse) }
% 85.14/11.34 add(multiply(Y, X), multiply(additive_identity, multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X), multiply(add(Y, multiply(X, multiply(X, multiply(X, Y)))), X)))))
% 85.14/11.34 = { by lemma 16 }
% 85.14/11.34 add(multiply(Y, X), additive_identity)
% 85.14/11.34 = { by axiom 2 (right_additive_identity) }
% 85.14/11.34 multiply(Y, X)
% 85.14/11.34
% 85.14/11.34 Lemma 34: multiply(X, multiply(X, multiply(multiply(X, Y), multiply(X, Z)))) = multiply(multiply(Y, X), Z).
% 85.14/11.34 Proof:
% 85.14/11.34 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(X, Z))))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(X, multiply(X, multiply(multiply(multiply(X, Y), X), Z)))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(X, multiply(multiply(X, multiply(multiply(X, Y), X)), Z))
% 85.14/11.34 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.34 multiply(multiply(X, multiply(X, multiply(multiply(X, Y), X))), Z)
% 85.14/11.34 = { by lemma 33 }
% 85.14/11.34 multiply(multiply(Y, X), Z)
% 85.14/11.34
% 85.14/11.34 Lemma 35: multiply(X, multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Z), W)))) = multiply(multiply(Y, X), multiply(Z, W)).
% 85.14/11.34 Proof:
% 85.14/11.35 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Z), W))))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(X, multiply(Z, W)))))
% 85.14/11.35 = { by lemma 34 }
% 85.14/11.35 multiply(multiply(Y, X), multiply(Z, W))
% 85.14/11.35
% 85.14/11.35 Lemma 36: multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), X))) = multiply(Y, multiply(Y, multiply(Y, X))).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), X)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(Y, X))))
% 85.14/11.35 = { by lemma 29 }
% 85.14/11.35 multiply(multiply(X, Y), multiply(X, multiply(multiply(Y, X), multiply(Y, X))))
% 85.14/11.35 = { by lemma 35 R->L }
% 85.14/11.35 multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))))))
% 85.14/11.35 = { by axiom 10 (x_fourthed_is_x) }
% 85.14/11.35 multiply(Y, multiply(Y, multiply(Y, X)))
% 85.14/11.35
% 85.14/11.35 Lemma 37: multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))) = multiply(X, multiply(multiply(X, Y), multiply(Y, multiply(Y, X)))).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X)))
% 85.14/11.35 = { by lemma 29 }
% 85.14/11.35 multiply(multiply(Y, X), multiply(Y, multiply(multiply(X, Y), X)))
% 85.14/11.35 = { by lemma 35 R->L }
% 85.14/11.35 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), X)))))
% 85.14/11.35 = { by lemma 36 }
% 85.14/11.35 multiply(X, multiply(X, multiply(Y, multiply(Y, multiply(Y, X)))))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(X, multiply(multiply(X, Y), multiply(Y, multiply(Y, X))))
% 85.14/11.35
% 85.14/11.35 Lemma 38: multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, Z), Y))) = multiply(X, multiply(Z, Y)).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, Z), Y)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(X, multiply(Y, multiply(Y, multiply(multiply(Y, Z), Y))))
% 85.14/11.35 = { by lemma 33 }
% 85.14/11.35 multiply(X, multiply(Z, Y))
% 85.14/11.35
% 85.14/11.35 Lemma 39: multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, Z), multiply(Y, W)))) = multiply(X, multiply(multiply(Z, Y), W)).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, Z), multiply(Y, W))))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(multiply(X, Y), multiply(Y, multiply(multiply(multiply(Y, Z), Y), W)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(multiply(X, Y), multiply(multiply(Y, multiply(multiply(Y, Z), Y)), W))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, Z), Y))), W)
% 85.14/11.35 = { by lemma 38 }
% 85.14/11.35 multiply(multiply(X, multiply(Z, Y)), W)
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(X, multiply(multiply(Z, Y), W))
% 85.14/11.35
% 85.14/11.35 Lemma 40: add(multiply(X, multiply(Y, Z)), multiply(W, Z)) = multiply(add(W, multiply(X, Y)), Z).
% 85.14/11.35 Proof:
% 85.14/11.35 add(multiply(X, multiply(Y, Z)), multiply(W, Z))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 add(multiply(multiply(X, Y), Z), multiply(W, Z))
% 85.14/11.35 = { by axiom 9 (distribute2) R->L }
% 85.14/11.35 multiply(add(multiply(X, Y), W), Z)
% 85.14/11.35 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.35 multiply(add(W, multiply(X, Y)), Z)
% 85.14/11.35
% 85.14/11.35 Lemma 41: multiply(add(X, multiply(X, Y)), Z) = multiply(X, add(Z, multiply(Y, Z))).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(add(X, multiply(X, Y)), Z)
% 85.14/11.35 = { by lemma 40 R->L }
% 85.14/11.35 add(multiply(X, multiply(Y, Z)), multiply(X, Z))
% 85.14/11.35 = { by axiom 8 (distribute1) R->L }
% 85.14/11.35 multiply(X, add(multiply(Y, Z), Z))
% 85.14/11.35 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.35 multiply(X, add(Z, multiply(Y, Z)))
% 85.14/11.35
% 85.14/11.35 Lemma 42: add(multiply(X, multiply(Y, multiply(Z, W))), multiply(V, W)) = multiply(add(V, multiply(X, multiply(Y, Z))), W).
% 85.14/11.35 Proof:
% 85.14/11.35 add(multiply(X, multiply(Y, multiply(Z, W))), multiply(V, W))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 add(multiply(multiply(X, Y), multiply(Z, W)), multiply(V, W))
% 85.14/11.35 = { by lemma 40 }
% 85.14/11.35 multiply(add(V, multiply(multiply(X, Y), Z)), W)
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(add(V, multiply(X, multiply(Y, Z))), W)
% 85.14/11.35
% 85.14/11.35 Lemma 43: multiply(add(X, multiply(Y, multiply(Y, Y))), Y) = add(Y, multiply(X, Y)).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(add(X, multiply(Y, multiply(Y, Y))), Y)
% 85.14/11.35 = { by lemma 42 R->L }
% 85.14/11.35 add(multiply(Y, multiply(Y, multiply(Y, Y))), multiply(X, Y))
% 85.14/11.35 = { by axiom 10 (x_fourthed_is_x) }
% 85.14/11.35 add(Y, multiply(X, Y))
% 85.14/11.35
% 85.14/11.35 Lemma 44: multiply(X, add(Y, multiply(X, multiply(X, multiply(X, Z))))) = multiply(X, add(Z, Y)).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(X, add(Y, multiply(X, multiply(X, multiply(X, Z)))))
% 85.14/11.35 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.35 multiply(X, add(multiply(X, multiply(X, multiply(X, Z))), Y))
% 85.14/11.35 = { by axiom 8 (distribute1) }
% 85.14/11.35 add(multiply(X, multiply(X, multiply(X, multiply(X, Z)))), multiply(X, Y))
% 85.14/11.35 = { by lemma 24 }
% 85.14/11.35 add(multiply(X, Z), multiply(X, Y))
% 85.14/11.35 = { by axiom 8 (distribute1) R->L }
% 85.14/11.35 multiply(X, add(Z, Y))
% 85.14/11.35
% 85.14/11.35 Lemma 45: multiply(add(X, multiply(X, multiply(Y, multiply(Y, Y)))), Y) = additive_identity.
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(add(X, multiply(X, multiply(Y, multiply(Y, Y)))), Y)
% 85.14/11.35 = { by lemma 22 R->L }
% 85.14/11.35 multiply(multiply(X, add(multiply(Y, multiply(Y, Y)), multiply(X, multiply(X, X)))), Y)
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(X, multiply(add(multiply(Y, multiply(Y, Y)), multiply(X, multiply(X, X))), Y))
% 85.14/11.35 = { by axiom 1 (commutativity_for_addition) R->L }
% 85.14/11.35 multiply(X, multiply(add(multiply(X, multiply(X, X)), multiply(Y, multiply(Y, Y))), Y))
% 85.14/11.35 = { by lemma 43 }
% 85.14/11.35 multiply(X, add(Y, multiply(multiply(X, multiply(X, X)), Y)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(X, add(Y, multiply(X, multiply(multiply(X, X), Y))))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(X, add(Y, multiply(X, multiply(X, multiply(X, Y)))))
% 85.14/11.35 = { by lemma 44 }
% 85.14/11.35 multiply(X, add(Y, Y))
% 85.14/11.35 = { by lemma 26 }
% 85.14/11.35 multiply(X, additive_identity)
% 85.14/11.35 = { by lemma 15 }
% 85.14/11.35 additive_identity
% 85.14/11.35
% 85.14/11.35 Lemma 46: add(multiply(X, Y), multiply(Z, multiply(W, Y))) = multiply(add(X, multiply(Z, W)), Y).
% 85.14/11.35 Proof:
% 85.14/11.35 add(multiply(X, Y), multiply(Z, multiply(W, Y)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 add(multiply(X, Y), multiply(multiply(Z, W), Y))
% 85.14/11.35 = { by axiom 9 (distribute2) R->L }
% 85.14/11.35 multiply(add(X, multiply(Z, W)), Y)
% 85.14/11.35
% 85.14/11.35 Lemma 47: multiply(add(X, multiply(Y, Y)), multiply(Y, Y)) = add(Y, multiply(X, multiply(Y, Y))).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(add(X, multiply(Y, Y)), multiply(Y, Y))
% 85.14/11.35 = { by lemma 40 R->L }
% 85.14/11.35 add(multiply(Y, multiply(Y, multiply(Y, Y))), multiply(X, multiply(Y, Y)))
% 85.14/11.35 = { by axiom 10 (x_fourthed_is_x) }
% 85.14/11.35 add(Y, multiply(X, multiply(Y, Y)))
% 85.14/11.35
% 85.14/11.35 Lemma 48: multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y) = additive_identity.
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)
% 85.14/11.35 = { by axiom 2 (right_additive_identity) R->L }
% 85.14/11.35 multiply(add(X, add(multiply(Y, multiply(Y, multiply(Y, X))), additive_identity)), Y)
% 85.14/11.35 = { by lemma 15 R->L }
% 85.14/11.35 multiply(add(X, add(multiply(Y, multiply(Y, multiply(Y, X))), multiply(Z, additive_identity))), Y)
% 85.14/11.35 = { by lemma 15 R->L }
% 85.14/11.35 multiply(add(X, add(multiply(Y, multiply(Y, multiply(Y, X))), multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), additive_identity)))), Y)
% 85.14/11.35 = { by lemma 15 R->L }
% 85.14/11.35 multiply(add(X, add(multiply(Y, multiply(Y, multiply(Y, X))), multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, additive_identity))))), Y)
% 85.14/11.35 = { by lemma 26 R->L }
% 85.14/11.35 multiply(add(X, add(multiply(Y, multiply(Y, multiply(Y, X))), multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, add(X, X)))))), Y)
% 85.14/11.35 = { by lemma 44 R->L }
% 85.14/11.35 multiply(add(X, add(multiply(Y, multiply(Y, multiply(Y, X))), multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, add(X, multiply(Y, multiply(Y, multiply(Y, X))))))))), Y)
% 85.14/11.35 = { by axiom 6 (associativity_for_addition) }
% 85.14/11.35 multiply(add(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, add(X, multiply(Y, multiply(Y, multiply(Y, X)))))))), Y)
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(add(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Z, multiply(multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y), add(X, multiply(Y, multiply(Y, multiply(Y, X))))))), Y)
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(add(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)), add(X, multiply(Y, multiply(Y, multiply(Y, X)))))), Y)
% 85.14/11.35 = { by lemma 46 R->L }
% 85.14/11.35 add(multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y), multiply(multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 add(multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y), multiply(Z, multiply(multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y))))
% 85.14/11.35 = { by lemma 47 R->L }
% 85.14/11.35 multiply(add(Z, multiply(multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y))), multiply(multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(add(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)))), multiply(multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(add(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y)))), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y))))
% 85.14/11.35 = { by lemma 30 }
% 85.14/11.35 multiply(add(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), additive_identity)), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y))))
% 85.14/11.35 = { by lemma 15 }
% 85.14/11.35 multiply(add(Z, additive_identity), multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y))))
% 85.14/11.35 = { by axiom 2 (right_additive_identity) }
% 85.14/11.35 multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), Y))))
% 85.14/11.35 = { by lemma 30 }
% 85.14/11.35 multiply(Z, multiply(add(X, multiply(Y, multiply(Y, multiply(Y, X)))), additive_identity))
% 85.14/11.35 = { by lemma 15 }
% 85.14/11.35 multiply(Z, additive_identity)
% 85.14/11.35 = { by lemma 15 }
% 85.14/11.35 additive_identity
% 85.14/11.35
% 85.14/11.35 Lemma 49: add(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(X, X)))) = additive_identity.
% 85.14/11.35 Proof:
% 85.14/11.35 add(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(X, X))))
% 85.14/11.35 = { by lemma 29 }
% 85.14/11.35 add(multiply(X, Y), multiply(X, multiply(multiply(Y, X), multiply(X, X))))
% 85.14/11.35 = { by axiom 8 (distribute1) R->L }
% 85.14/11.35 multiply(X, add(Y, multiply(multiply(Y, X), multiply(X, X))))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.35 multiply(X, add(Y, multiply(Y, multiply(X, multiply(X, X)))))
% 85.14/11.35 = { by axiom 2 (right_additive_identity) R->L }
% 85.14/11.35 multiply(add(X, additive_identity), add(Y, multiply(Y, multiply(X, multiply(X, X)))))
% 85.14/11.35 = { by lemma 15 R->L }
% 85.14/11.35 multiply(add(X, multiply(add(Y, multiply(Y, multiply(X, multiply(X, X)))), additive_identity)), add(Y, multiply(Y, multiply(X, multiply(X, X)))))
% 85.14/11.35 = { by lemma 15 R->L }
% 85.14/11.35 multiply(add(X, multiply(add(Y, multiply(Y, multiply(X, multiply(X, X)))), multiply(add(Y, multiply(Y, multiply(X, multiply(X, X)))), additive_identity))), add(Y, multiply(Y, multiply(X, multiply(X, X)))))
% 85.14/11.35 = { by lemma 45 R->L }
% 85.14/11.35 multiply(add(X, multiply(add(Y, multiply(Y, multiply(X, multiply(X, X)))), multiply(add(Y, multiply(Y, multiply(X, multiply(X, X)))), multiply(add(Y, multiply(Y, multiply(X, multiply(X, X)))), X)))), add(Y, multiply(Y, multiply(X, multiply(X, X)))))
% 85.14/11.35 = { by lemma 48 }
% 85.14/11.35 additive_identity
% 85.14/11.35
% 85.14/11.35 Lemma 50: multiply(multiply(X, Y), multiply(X, multiply(X, multiply(X, Z)))) = multiply(multiply(X, Y), Z).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(multiply(X, Y), multiply(X, multiply(X, multiply(X, Z))))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(multiply(X, Y), multiply(X, multiply(multiply(X, X), Z)))
% 85.14/11.35 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.35 multiply(multiply(X, Y), multiply(multiply(X, multiply(X, X)), Z))
% 85.14/11.35 = { by lemma 27 R->L }
% 85.14/11.35 multiply(multiply(X, Y), add(Z, add(Z, multiply(multiply(X, multiply(X, X)), Z))))
% 85.14/11.35 = { by axiom 8 (distribute1) }
% 85.14/11.35 add(multiply(multiply(X, Y), Z), multiply(multiply(X, Y), add(Z, multiply(multiply(X, multiply(X, X)), Z))))
% 85.14/11.35 = { by lemma 41 R->L }
% 85.14/11.35 add(multiply(multiply(X, Y), Z), multiply(add(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(X, X)))), Z))
% 85.14/11.35 = { by axiom 9 (distribute2) R->L }
% 85.14/11.35 multiply(add(multiply(X, Y), add(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(X, X))))), Z)
% 85.14/11.35 = { by lemma 49 }
% 85.14/11.35 multiply(add(multiply(X, Y), additive_identity), Z)
% 85.14/11.35 = { by axiom 2 (right_additive_identity) }
% 85.14/11.35 multiply(multiply(X, Y), Z)
% 85.14/11.35
% 85.14/11.35 Lemma 51: multiply(multiply(Y, X), multiply(X, multiply(X, Z))) = multiply(X, multiply(X, multiply(multiply(X, Y), Z))).
% 85.14/11.35 Proof:
% 85.14/11.35 multiply(multiply(Y, X), multiply(X, multiply(X, Z)))
% 85.14/11.35 = { by lemma 34 R->L }
% 85.14/11.35 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(X, multiply(X, multiply(X, Z))))))
% 85.14/11.35 = { by lemma 50 }
% 85.14/11.36 multiply(X, multiply(X, multiply(multiply(X, Y), Z)))
% 85.14/11.36
% 85.14/11.36 Lemma 52: multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(Y, multiply(Y, Z)))) = multiply(multiply(X, Y), multiply(X, Z)).
% 85.14/11.36 Proof:
% 85.14/11.36 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(Y, multiply(Y, Z))))
% 85.14/11.36 = { by lemma 51 }
% 85.14/11.36 multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(multiply(Y, X), Z))))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.36 multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, multiply(Y, X)), Z)))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.36 multiply(multiply(X, Y), multiply(multiply(Y, multiply(Y, multiply(Y, X))), Z))
% 85.14/11.36 = { by lemma 27 R->L }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), add(multiply(Y, X), multiply(Y, multiply(Y, multiply(Y, X))))), Z))
% 85.14/11.36 = { by lemma 36 R->L }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), X))))), Z))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(Y, X)))))), Z))
% 85.14/11.36 = { by lemma 29 }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(Y, X), multiply(Y, X)))))), Z))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(multiply(X, Y), X), multiply(multiply(Y, X), multiply(Y, X))))), Z))
% 85.14/11.36 = { by lemma 47 R->L }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), multiply(add(multiply(multiply(X, Y), X), multiply(multiply(Y, X), multiply(Y, X))), multiply(multiply(Y, X), multiply(Y, X)))), Z))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), multiply(add(multiply(X, multiply(Y, X)), multiply(multiply(Y, X), multiply(Y, X))), multiply(multiply(Y, X), multiply(Y, X)))), Z))
% 85.14/11.36 = { by axiom 9 (distribute2) R->L }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), multiply(multiply(add(X, multiply(Y, X)), multiply(Y, X)), multiply(multiply(Y, X), multiply(Y, X)))), Z))
% 85.14/11.36 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), multiply(multiply(add(multiply(Y, X), X), multiply(Y, X)), multiply(multiply(Y, X), multiply(Y, X)))), Z))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.36 multiply(multiply(X, Y), multiply(add(multiply(Y, X), multiply(add(multiply(Y, X), X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))))), Z))
% 85.14/11.36 = { by lemma 46 R->L }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), Z), multiply(add(multiply(Y, X), X), multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))), Z))))
% 85.14/11.36 = { by lemma 31 R->L }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(X, multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))), Z)), multiply(multiply(Y, X), add(Z, multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))), Z)))))
% 85.14/11.36 = { by axiom 1 (commutativity_for_addition) }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), add(Z, multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))), Z))), multiply(X, multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))), Z))))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), add(Z, multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))), Z))), multiply(X, multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, X)), Z)))))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), add(Z, multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, X)), Z)))), multiply(X, multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, X)), Z)))))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), add(Z, multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, X)), Z)))), multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Z))))))
% 85.14/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), add(Z, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Z))))), multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Z))))))
% 85.14/11.36 = { by lemma 44 }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), add(Z, Z)), multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Z))))))
% 85.14/11.36 = { by lemma 26 }
% 85.14/11.36 multiply(multiply(X, Y), add(multiply(multiply(Y, X), additive_identity), multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Z))))))
% 85.14/11.36 = { by lemma 15 }
% 85.14/11.36 multiply(multiply(X, Y), add(additive_identity, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Z))))))
% 85.14/11.36 = { by axiom 3 (left_additive_identity) }
% 86.06/11.36 multiply(multiply(X, Y), multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Z)))))
% 86.06/11.36 = { by lemma 29 R->L }
% 86.06/11.36 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), Z)))))
% 86.06/11.36 = { by lemma 29 R->L }
% 86.06/11.36 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(multiply(Y, X), Z)))))
% 86.06/11.36 = { by lemma 29 R->L }
% 86.06/11.36 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, Z)))))
% 86.06/11.36 = { by lemma 24 }
% 86.06/11.36 multiply(multiply(X, Y), multiply(X, Z))
% 86.06/11.36
% 86.06/11.36 Lemma 53: multiply(multiply(X, Y), multiply(multiply(Z, X), multiply(X, multiply(X, W)))) = multiply(multiply(X, Y), multiply(Z, W)).
% 86.06/11.36 Proof:
% 86.06/11.36 multiply(multiply(X, Y), multiply(multiply(Z, X), multiply(X, multiply(X, W))))
% 86.06/11.36 = { by lemma 51 }
% 86.06/11.36 multiply(multiply(X, Y), multiply(X, multiply(X, multiply(multiply(X, Z), W))))
% 86.06/11.36 = { by lemma 35 R->L }
% 86.06/11.36 multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(X, multiply(multiply(X, Z), W))))))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.36 multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(X, multiply(X, multiply(Z, W)))))))
% 86.06/11.36 = { by lemma 52 }
% 86.06/11.36 multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(Y, multiply(Z, W)))))
% 86.06/11.36 = { by lemma 34 }
% 86.06/11.36 multiply(multiply(X, Y), multiply(Z, W))
% 86.06/11.36
% 86.06/11.36 Lemma 54: multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))) = multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, X), X))).
% 86.06/11.36 Proof:
% 86.06/11.36 multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X)))
% 86.06/11.36 = { by lemma 37 }
% 86.06/11.36 multiply(X, multiply(multiply(X, Y), multiply(Y, multiply(Y, X))))
% 86.06/11.36 = { by lemma 39 R->L }
% 86.06/11.36 multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, X), multiply(Y, multiply(Y, multiply(Y, X))))))
% 86.06/11.36 = { by lemma 29 }
% 86.06/11.36 multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(multiply(X, Y), multiply(Y, multiply(Y, X))))))
% 86.06/11.36 = { by lemma 51 }
% 86.06/11.36 multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(multiply(X, Y), multiply(Y, multiply(Y, X))))))
% 86.06/11.36 = { by lemma 53 }
% 86.06/11.36 multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(X, X))))
% 86.06/11.36 = { by lemma 51 R->L }
% 86.06/11.36 multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(X, X))))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.36 multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, X), X)))
% 86.06/11.36
% 86.06/11.36 Lemma 55: multiply(multiply(X, Y), multiply(X, multiply(X, X))) = multiply(X, Y).
% 86.06/11.36 Proof:
% 86.06/11.36 multiply(multiply(X, Y), multiply(X, multiply(X, X)))
% 86.06/11.36 = { by lemma 27 R->L }
% 86.06/11.36 add(multiply(X, Y), add(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(X, X)))))
% 86.06/11.36 = { by lemma 49 }
% 86.06/11.36 add(multiply(X, Y), additive_identity)
% 86.06/11.36 = { by axiom 2 (right_additive_identity) }
% 86.06/11.36 multiply(X, Y)
% 86.06/11.36
% 86.06/11.36 Lemma 56: multiply(multiply(Y, X), multiply(multiply(Y, X), Y)) = multiply(multiply(X, Y), multiply(Y, multiply(Y, X))).
% 86.06/11.36 Proof:
% 86.06/11.36 multiply(multiply(Y, X), multiply(multiply(Y, X), Y))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.36 multiply(multiply(Y, X), multiply(Y, multiply(X, Y)))
% 86.06/11.36 = { by lemma 35 R->L }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, Y)))))
% 86.06/11.36 = { by lemma 54 }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(X, multiply(multiply(X, Y), Y)))))
% 86.06/11.36 = { by lemma 24 R->L }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(X, multiply(multiply(X, Y), Y))))))))
% 86.06/11.36 = { by lemma 54 R->L }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, Y))))))))
% 86.06/11.36 = { by lemma 37 }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, multiply(multiply(Y, X), multiply(X, multiply(X, Y)))))))))
% 86.06/11.36 = { by lemma 29 }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, multiply(X, Y)))))))))
% 86.06/11.36 = { by lemma 53 }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, multiply(multiply(X, Y), multiply(Y, Y)))))))
% 86.06/11.36 = { by lemma 29 R->L }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, multiply(Y, Y)))))))
% 86.06/11.36 = { by lemma 55 }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X)))))
% 86.06/11.36 = { by lemma 29 R->L }
% 86.06/11.36 multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(Y, X), multiply(Y, X)))))
% 86.06/11.36 = { by lemma 29 R->L }
% 86.06/11.36 multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(Y, X)))))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.36 multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), X))))
% 86.06/11.36 = { by lemma 36 }
% 86.06/11.36 multiply(X, multiply(Y, multiply(Y, multiply(Y, X))))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.36 multiply(multiply(X, Y), multiply(Y, multiply(Y, X)))
% 86.06/11.36
% 86.06/11.36 Lemma 57: multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, X))) = multiply(Y, multiply(Y, X)).
% 86.06/11.36 Proof:
% 86.06/11.36 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, X)))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.36 multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), X), X))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.36 multiply(multiply(multiply(X, Y), multiply(multiply(X, Y), X)), X)
% 86.06/11.36 = { by axiom 3 (left_additive_identity) R->L }
% 86.06/11.36 multiply(add(additive_identity, multiply(multiply(X, Y), multiply(multiply(X, Y), X))), X)
% 86.06/11.36 = { by lemma 56 }
% 86.06/11.36 multiply(add(additive_identity, multiply(multiply(Y, X), multiply(X, multiply(X, Y)))), X)
% 86.06/11.36 = { by lemma 42 R->L }
% 86.06/11.36 add(multiply(multiply(Y, X), multiply(X, multiply(multiply(X, Y), X))), multiply(additive_identity, X))
% 86.06/11.36 = { by lemma 38 }
% 86.06/11.36 add(multiply(Y, multiply(Y, X)), multiply(additive_identity, X))
% 86.06/11.36 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.36 add(multiply(additive_identity, X), multiply(Y, multiply(Y, X)))
% 86.06/11.36 = { by lemma 16 }
% 86.06/11.36 add(additive_identity, multiply(Y, multiply(Y, X)))
% 86.06/11.36 = { by axiom 3 (left_additive_identity) }
% 86.06/11.36 multiply(Y, multiply(Y, X))
% 86.06/11.36
% 86.06/11.36 Lemma 58: multiply(multiply(Y, X), multiply(multiply(Y, X), X)) = multiply(X, multiply(multiply(X, Y), multiply(Y, X))).
% 86.06/11.36 Proof:
% 86.06/11.36 multiply(multiply(Y, X), multiply(multiply(Y, X), X))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.36 multiply(multiply(Y, X), multiply(Y, multiply(X, X)))
% 86.06/11.36 = { by lemma 35 R->L }
% 86.06/11.36 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, X)))))
% 86.06/11.36 = { by lemma 57 }
% 86.06/11.36 multiply(X, multiply(X, multiply(Y, multiply(Y, X))))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.36 multiply(X, multiply(multiply(X, Y), multiply(Y, X)))
% 86.06/11.36
% 86.06/11.36 Lemma 59: multiply(multiply(X, Z), multiply(multiply(Z, Y), multiply(Y, Z))) = multiply(X, multiply(multiply(Y, Z), multiply(multiply(Y, Z), Z))).
% 86.06/11.36 Proof:
% 86.06/11.36 multiply(multiply(X, Z), multiply(multiply(Z, Y), multiply(Y, Z)))
% 86.06/11.36 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.36 multiply(X, multiply(Z, multiply(multiply(Z, Y), multiply(Y, Z))))
% 86.06/11.36 = { by lemma 58 R->L }
% 86.06/11.37 multiply(X, multiply(multiply(Y, Z), multiply(multiply(Y, Z), Z)))
% 86.06/11.37
% 86.06/11.37 Lemma 60: multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y)))) = multiply(Y, X).
% 86.06/11.37 Proof:
% 86.06/11.37 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))
% 86.06/11.37 = { by lemma 27 R->L }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))))
% 86.06/11.37 = { by lemma 59 }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), Y))))))
% 86.06/11.37 = { by lemma 50 R->L }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(X, multiply(X, multiply(X, Y)))))))))
% 86.06/11.37 = { by lemma 29 }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(Y, X), multiply(X, multiply(X, Y)))))))))
% 86.06/11.37 = { by lemma 56 R->L }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), X))))))))
% 86.06/11.37 = { by lemma 50 R->L }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(X, multiply(X, multiply(multiply(X, Y), X)))))))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(X, X), multiply(multiply(X, Y), X))))))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(multiply(X, Y), X), multiply(multiply(X, X), multiply(multiply(X, Y), X)))))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(X, Y), multiply(X, multiply(multiply(multiply(multiply(X, Y), X), multiply(X, X)), multiply(multiply(X, Y), X))))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(multiply(X, Y), X), multiply(X, X)), multiply(multiply(X, Y), X)))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(X, Y), multiply(X, multiply(multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(X, X))), multiply(multiply(X, Y), X))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(X, X))), multiply(multiply(X, Y), X)))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(X, X)))), multiply(multiply(X, Y), X))))
% 86.06/11.37 = { by lemma 33 R->L }
% 86.06/11.37 add(multiply(Y, X), add(multiply(X, multiply(X, multiply(multiply(X, Y), X))), multiply(multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(X, X)))), multiply(multiply(X, Y), X))))
% 86.06/11.37 = { by lemma 40 }
% 86.06/11.37 add(multiply(Y, X), multiply(add(multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(X, X)))), multiply(X, X)), multiply(multiply(X, Y), X)))
% 86.06/11.37 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.37 add(multiply(Y, X), multiply(add(multiply(X, X), multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(multiply(multiply(X, Y), X), multiply(X, X))))), multiply(multiply(X, Y), X)))
% 86.06/11.37 = { by lemma 48 }
% 86.06/11.37 add(multiply(Y, X), additive_identity)
% 86.06/11.37 = { by axiom 2 (right_additive_identity) }
% 86.06/11.37 multiply(Y, X)
% 86.06/11.37
% 86.06/11.37 Lemma 61: multiply(multiply(Y, X), multiply(X, Y)) = multiply(multiply(X, Y), multiply(Y, X)).
% 86.06/11.37 Proof:
% 86.06/11.37 multiply(multiply(Y, X), multiply(X, Y))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.37 multiply(Y, multiply(X, multiply(X, Y)))
% 86.06/11.37 = { by lemma 57 R->L }
% 86.06/11.37 multiply(Y, multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, Y))))
% 86.06/11.37 = { by lemma 35 R->L }
% 86.06/11.37 multiply(Y, multiply(multiply(Y, X), multiply(X, multiply(X, multiply(multiply(X, Y), multiply(multiply(X, Y), Y))))))
% 86.06/11.37 = { by lemma 59 R->L }
% 86.06/11.37 multiply(Y, multiply(multiply(Y, X), multiply(X, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))))
% 86.06/11.37 = { by lemma 53 R->L }
% 86.06/11.37 multiply(Y, multiply(multiply(Y, X), multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 multiply(Y, multiply(multiply(multiply(Y, X), multiply(X, Y)), multiply(Y, multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y)))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 multiply(multiply(Y, multiply(multiply(Y, X), multiply(X, Y))), multiply(Y, multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))))
% 86.06/11.37 = { by lemma 58 R->L }
% 86.06/11.37 multiply(multiply(multiply(X, Y), multiply(multiply(X, Y), Y)), multiply(Y, multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.37 multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), multiply(Y, multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y)))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.37 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))))))
% 86.06/11.37 = { by lemma 52 }
% 86.06/11.37 multiply(multiply(X, Y), multiply(X, multiply(Y, multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y))))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(X, Y)))))
% 86.06/11.37 = { by lemma 60 }
% 86.06/11.37 multiply(multiply(X, Y), multiply(Y, X))
% 86.06/11.37
% 86.06/11.37 Lemma 62: add(multiply(multiply(X, Y), Z), multiply(X, W)) = multiply(X, add(W, multiply(Y, Z))).
% 86.06/11.37 Proof:
% 86.06/11.37 add(multiply(multiply(X, Y), Z), multiply(X, W))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.37 add(multiply(X, multiply(Y, Z)), multiply(X, W))
% 86.06/11.37 = { by axiom 8 (distribute1) R->L }
% 86.06/11.37 multiply(X, add(multiply(Y, Z), W))
% 86.06/11.37 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.37 multiply(X, add(W, multiply(Y, Z)))
% 86.06/11.37
% 86.06/11.37 Lemma 63: multiply(multiply(X, Y), add(Z, multiply(Y, multiply(multiply(Y, W), Y)))) = add(multiply(multiply(X, Y), Z), multiply(X, multiply(W, Y))).
% 86.06/11.37 Proof:
% 86.06/11.37 multiply(multiply(X, Y), add(Z, multiply(Y, multiply(multiply(Y, W), Y))))
% 86.06/11.37 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.37 multiply(multiply(X, Y), add(multiply(Y, multiply(multiply(Y, W), Y)), Z))
% 86.06/11.37 = { by axiom 8 (distribute1) }
% 86.06/11.37 add(multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, W), Y))), multiply(multiply(X, Y), Z))
% 86.06/11.37 = { by lemma 38 }
% 86.06/11.37 add(multiply(X, multiply(W, Y)), multiply(multiply(X, Y), Z))
% 86.06/11.37 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.37 add(multiply(multiply(X, Y), Z), multiply(X, multiply(W, Y)))
% 86.06/11.37
% 86.06/11.37 Lemma 64: multiply(X, multiply(X, multiply(X, add(Y, multiply(X, Z))))) = add(multiply(X, Z), multiply(X, multiply(X, multiply(X, Y)))).
% 86.06/11.37 Proof:
% 86.06/11.37 multiply(X, multiply(X, multiply(X, add(Y, multiply(X, Z)))))
% 86.06/11.37 = { by lemma 44 R->L }
% 86.06/11.37 multiply(X, multiply(X, multiply(X, add(multiply(X, Z), multiply(X, multiply(X, multiply(X, Y)))))))
% 86.06/11.37 = { by lemma 14 }
% 86.06/11.37 multiply(X, multiply(X, multiply(X, multiply(X, add(multiply(X, multiply(X, Y)), Z)))))
% 86.06/11.37 = { by lemma 24 }
% 86.06/11.37 multiply(X, add(multiply(X, multiply(X, Y)), Z))
% 86.06/11.37 = { by lemma 14 R->L }
% 86.06/11.37 add(multiply(X, Z), multiply(X, multiply(X, multiply(X, Y))))
% 86.06/11.37
% 86.06/11.37 Lemma 65: multiply(add(X, multiply(Y, multiply(Y, Y))), multiply(Y, Z)) = multiply(add(Y, multiply(X, Y)), Z).
% 86.06/11.37 Proof:
% 86.06/11.37 multiply(add(X, multiply(Y, multiply(Y, Y))), multiply(Y, Z))
% 86.06/11.37 = { by lemma 42 R->L }
% 86.06/11.37 add(multiply(Y, multiply(Y, multiply(Y, multiply(Y, Z)))), multiply(X, multiply(Y, Z)))
% 86.06/11.37 = { by lemma 24 }
% 86.06/11.37 add(multiply(Y, Z), multiply(X, multiply(Y, Z)))
% 86.06/11.37 = { by lemma 46 }
% 86.06/11.37 multiply(add(Y, multiply(X, Y)), Z)
% 86.06/11.37
% 86.06/11.37 Lemma 66: multiply(add(X, multiply(X, X)), add(X, multiply(X, X))) = add(X, multiply(X, X)).
% 86.06/11.37 Proof:
% 86.06/11.37 multiply(add(X, multiply(X, X)), add(X, multiply(X, X)))
% 86.06/11.37 = { by lemma 43 R->L }
% 86.06/11.37 multiply(add(X, multiply(X, X)), multiply(add(X, multiply(X, multiply(X, X))), X))
% 86.06/11.37 = { by lemma 65 R->L }
% 86.06/11.37 multiply(add(X, multiply(X, multiply(X, X))), multiply(X, multiply(add(X, multiply(X, multiply(X, X))), X)))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 multiply(add(X, multiply(multiply(X, X), X)), multiply(X, multiply(add(X, multiply(X, multiply(X, X))), X)))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 multiply(add(X, multiply(multiply(X, X), X)), multiply(X, multiply(add(X, multiply(multiply(X, X), X)), X)))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 multiply(multiply(add(X, multiply(multiply(X, X), X)), X), multiply(add(X, multiply(multiply(X, X), X)), X))
% 86.06/11.37 = { by lemma 46 R->L }
% 86.06/11.37 multiply(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(add(X, multiply(multiply(X, X), X)), X))
% 86.06/11.37 = { by lemma 46 R->L }
% 86.06/11.37 multiply(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))))
% 86.06/11.37 = { by lemma 41 R->L }
% 86.06/11.37 multiply(add(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(X, X))), multiply(X, X))
% 86.06/11.37 = { by lemma 40 R->L }
% 86.06/11.37 add(multiply(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(multiply(X, X), multiply(X, X))), multiply(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(X, X)))
% 86.06/11.37 = { by lemma 47 }
% 86.06/11.37 add(add(multiply(X, X), multiply(multiply(X, X), multiply(multiply(X, X), multiply(X, X)))), multiply(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(X, X)))
% 86.06/11.37 = { by axiom 6 (associativity_for_addition) R->L }
% 86.06/11.37 add(multiply(X, X), add(multiply(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(X, X))))
% 86.06/11.37 = { by lemma 40 }
% 86.06/11.37 add(multiply(X, X), multiply(add(add(multiply(X, X), multiply(multiply(X, X), multiply(X, X))), multiply(multiply(X, X), multiply(X, X))), multiply(X, X)))
% 86.06/11.37 = { by axiom 6 (associativity_for_addition) R->L }
% 86.06/11.37 add(multiply(X, X), multiply(add(multiply(X, X), add(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(X, X), multiply(X, X)))), multiply(X, X)))
% 86.06/11.37 = { by axiom 9 (distribute2) R->L }
% 86.06/11.37 add(multiply(X, X), multiply(add(multiply(X, X), multiply(add(multiply(X, X), multiply(X, X)), multiply(X, X))), multiply(X, X)))
% 86.06/11.37 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.37 add(multiply(X, X), multiply(add(multiply(add(multiply(X, X), multiply(X, X)), multiply(X, X)), multiply(X, X)), multiply(X, X)))
% 86.06/11.37 = { by lemma 47 }
% 86.06/11.37 add(multiply(X, X), add(X, multiply(multiply(add(multiply(X, X), multiply(X, X)), multiply(X, X)), multiply(X, X))))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 add(multiply(X, X), add(X, multiply(multiply(multiply(add(multiply(X, X), multiply(X, X)), multiply(X, X)), X), X)))
% 86.06/11.37 = { by lemma 13 }
% 86.06/11.37 add(X, multiply(add(X, multiply(multiply(add(multiply(X, X), multiply(X, X)), multiply(X, X)), X)), X))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.37 add(X, multiply(add(X, multiply(add(multiply(X, X), multiply(X, X)), multiply(multiply(X, X), X))), X))
% 86.06/11.37 = { by axiom 8 (distribute1) R->L }
% 86.06/11.37 add(X, multiply(add(X, multiply(multiply(X, add(X, X)), multiply(multiply(X, X), X))), X))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.37 add(X, multiply(add(X, multiply(X, multiply(add(X, X), multiply(multiply(X, X), X)))), X))
% 86.06/11.37 = { by lemma 26 }
% 86.06/11.37 add(X, multiply(add(X, multiply(X, multiply(additive_identity, multiply(multiply(X, X), X)))), X))
% 86.06/11.37 = { by lemma 16 }
% 86.06/11.37 add(X, multiply(add(X, multiply(X, additive_identity)), X))
% 86.06/11.37 = { by lemma 15 }
% 86.06/11.37 add(X, multiply(add(X, additive_identity), X))
% 86.06/11.37 = { by axiom 2 (right_additive_identity) }
% 86.06/11.37 add(X, multiply(X, X))
% 86.06/11.37
% 86.06/11.37 Lemma 67: multiply(add(X, multiply(X, X)), multiply(add(X, multiply(X, X)), Y)) = multiply(add(X, multiply(X, X)), Y).
% 86.06/11.37 Proof:
% 86.06/11.37 multiply(add(X, multiply(X, X)), multiply(add(X, multiply(X, X)), Y))
% 86.06/11.37 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.37 multiply(multiply(add(X, multiply(X, X)), add(X, multiply(X, X))), Y)
% 86.06/11.37 = { by lemma 66 }
% 86.06/11.37 multiply(add(X, multiply(X, X)), Y)
% 86.06/11.37
% 86.06/11.37 Lemma 68: add(multiply(X, Y), add(multiply(Y, X), multiply(X, multiply(X, Y)))) = multiply(multiply(Y, X), X).
% 86.06/11.37 Proof:
% 86.06/11.37 add(multiply(X, Y), add(multiply(Y, X), multiply(X, multiply(X, Y))))
% 86.06/11.38 = { by lemma 28 }
% 86.06/11.38 add(multiply(Y, X), add(multiply(X, Y), multiply(X, multiply(X, Y))))
% 86.06/11.38 = { by axiom 8 (distribute1) R->L }
% 86.06/11.38 add(multiply(Y, X), multiply(X, add(Y, multiply(X, Y))))
% 86.06/11.38 = { by lemma 41 R->L }
% 86.06/11.38 add(multiply(Y, X), multiply(add(X, multiply(X, X)), Y))
% 86.06/11.38 = { by axiom 2 (right_additive_identity) R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(add(X, multiply(X, X)), Y), additive_identity))
% 86.06/11.38 = { by lemma 48 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(add(X, multiply(X, X)), Y), multiply(add(Y, multiply(add(X, multiply(X, X)), multiply(add(X, multiply(X, X)), multiply(add(X, multiply(X, X)), Y)))), add(X, multiply(X, X)))))
% 86.06/11.38 = { by lemma 67 }
% 86.06/11.38 add(multiply(Y, X), add(multiply(add(X, multiply(X, X)), Y), multiply(add(Y, multiply(add(X, multiply(X, X)), multiply(add(X, multiply(X, X)), Y))), add(X, multiply(X, X)))))
% 86.06/11.38 = { by lemma 67 }
% 86.06/11.38 add(multiply(Y, X), add(multiply(add(X, multiply(X, X)), Y), multiply(add(Y, multiply(add(X, multiply(X, X)), Y)), add(X, multiply(X, X)))))
% 86.06/11.38 = { by lemma 65 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(add(X, multiply(X, X)), Y), multiply(add(add(X, multiply(X, X)), multiply(Y, multiply(Y, Y))), multiply(Y, add(X, multiply(X, X))))))
% 86.06/11.38 = { by lemma 40 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(add(X, multiply(X, X)), Y), add(multiply(Y, multiply(multiply(Y, Y), multiply(Y, add(X, multiply(X, X))))), multiply(add(X, multiply(X, X)), multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 18 }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, multiply(multiply(Y, Y), multiply(Y, add(X, multiply(X, X))))), multiply(add(X, multiply(X, X)), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, multiply(Y, multiply(Y, multiply(Y, add(X, multiply(X, X)))))), multiply(add(X, multiply(X, X)), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 24 }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(X, multiply(X, X)), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by axiom 2 (right_additive_identity) R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(X, add(multiply(X, X), additive_identity)), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 15 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(X, add(multiply(X, X), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), additive_identity))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 15 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(X, add(multiply(X, X), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), additive_identity)))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by axiom 6 (associativity_for_addition) }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), additive_identity))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 15 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(Y, additive_identity)))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 15 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(Y, multiply(X, additive_identity))))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 26 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(Y, multiply(X, add(X, X)))))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 27 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(Y, add(X, add(X, multiply(X, add(X, X)))))))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 18 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(Y, add(X, add(multiply(X, X), add(X, multiply(X, X)))))))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by axiom 6 (associativity_for_addition) }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(Y, add(add(X, multiply(X, X)), add(X, multiply(X, X))))))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 66 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(Y, add(add(X, multiply(X, X)), multiply(add(X, multiply(X, X)), add(X, multiply(X, X)))))))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 41 R->L }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), multiply(add(add(X, multiply(X, X)), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), multiply(add(Y, multiply(Y, add(X, multiply(X, X)))), add(X, multiply(X, X)))))), add(Y, multiply(Y, add(X, multiply(X, X)))))))
% 86.06/11.38 = { by lemma 48 }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, add(X, multiply(X, X))), additive_identity))
% 86.06/11.38 = { by axiom 2 (right_additive_identity) }
% 86.06/11.38 add(multiply(Y, X), multiply(Y, add(X, multiply(X, X))))
% 86.06/11.38 = { by axiom 8 (distribute1) }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, X), multiply(Y, multiply(X, X))))
% 86.06/11.38 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.38 add(multiply(Y, X), add(multiply(Y, X), multiply(multiply(Y, X), X)))
% 86.06/11.38 = { by lemma 27 }
% 86.06/11.38 multiply(multiply(Y, X), X)
% 86.06/11.38
% 86.06/11.38 Lemma 69: multiply(X, add(multiply(X, Y), multiply(Y, X))) = add(multiply(X, Y), multiply(Y, X)).
% 86.06/11.38 Proof:
% 86.06/11.38 multiply(X, add(multiply(X, Y), multiply(Y, X)))
% 86.06/11.38 = { by lemma 62 R->L }
% 86.06/11.38 add(multiply(multiply(X, Y), X), multiply(X, multiply(X, Y)))
% 86.06/11.38 = { by lemma 63 R->L }
% 86.06/11.38 multiply(multiply(X, Y), add(X, multiply(Y, multiply(multiply(Y, X), Y))))
% 86.06/11.38 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.38 multiply(multiply(X, Y), add(X, multiply(Y, multiply(Y, multiply(X, Y)))))
% 86.06/11.38 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.38 multiply(multiply(X, Y), add(multiply(Y, multiply(Y, multiply(X, Y))), X))
% 86.06/11.38 = { by axiom 8 (distribute1) }
% 86.06/11.38 add(multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(X, Y)))), multiply(multiply(X, Y), X))
% 86.06/11.38 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.38 add(multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(X, Y)))), multiply(X, multiply(Y, X)))
% 86.06/11.38 = { by lemma 62 }
% 86.06/11.38 multiply(X, add(multiply(Y, X), multiply(Y, multiply(Y, multiply(Y, multiply(X, Y))))))
% 86.06/11.38 = { by lemma 64 R->L }
% 86.06/11.38 multiply(X, multiply(Y, multiply(Y, multiply(Y, add(multiply(X, Y), multiply(Y, X))))))
% 86.06/11.38 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.38 multiply(multiply(X, Y), multiply(Y, multiply(Y, add(multiply(X, Y), multiply(Y, X)))))
% 86.06/11.38 = { by lemma 51 }
% 86.06/11.38 multiply(Y, multiply(Y, multiply(multiply(Y, X), add(multiply(X, Y), multiply(Y, X)))))
% 86.06/11.39 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, multiply(multiply(Y, X), add(multiply(Y, X), multiply(X, Y)))))
% 86.06/11.39 = { by axiom 8 (distribute1) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), multiply(Y, X)), multiply(multiply(Y, X), multiply(X, Y)))))
% 86.06/11.39 = { by axiom 2 (right_additive_identity) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), multiply(Y, X)), multiply(add(multiply(Y, X), additive_identity), multiply(X, Y)))))
% 86.06/11.39 = { by lemma 26 R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), multiply(Y, X)), multiply(add(multiply(Y, X), add(Y, Y)), multiply(X, Y)))))
% 86.06/11.39 = { by axiom 6 (associativity_for_addition) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), multiply(Y, X)), multiply(add(add(multiply(Y, X), Y), Y), multiply(X, Y)))))
% 86.06/11.39 = { by axiom 9 (distribute2) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), multiply(Y, X)), add(multiply(add(multiply(Y, X), Y), multiply(X, Y)), multiply(Y, multiply(X, Y))))))
% 86.06/11.39 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), multiply(Y, X)), add(multiply(add(multiply(Y, X), Y), multiply(X, Y)), multiply(multiply(Y, X), Y)))))
% 86.06/11.39 = { by lemma 18 }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(add(multiply(Y, X), Y), multiply(X, Y)), multiply(multiply(Y, X), add(multiply(Y, X), Y)))))
% 86.06/11.39 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), add(multiply(Y, X), Y)), multiply(add(multiply(Y, X), Y), multiply(X, Y)))))
% 86.06/11.39 = { by lemma 31 R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(Y, multiply(X, Y)), multiply(multiply(Y, X), add(add(multiply(Y, X), Y), multiply(X, Y))))))
% 86.06/11.39 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), multiply(multiply(Y, X), add(add(multiply(Y, X), Y), multiply(X, Y))))))
% 86.06/11.39 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), multiply(multiply(Y, X), add(multiply(X, Y), add(multiply(Y, X), Y))))))
% 86.06/11.39 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), multiply(multiply(Y, X), add(multiply(X, Y), add(Y, multiply(Y, X)))))))
% 86.06/11.39 = { by lemma 28 }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), multiply(multiply(Y, X), add(Y, add(multiply(X, Y), multiply(Y, X)))))))
% 86.06/11.39 = { by axiom 8 (distribute1) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(multiply(Y, X), Y), multiply(multiply(Y, X), add(multiply(X, Y), multiply(Y, X)))))))
% 86.06/11.39 = { by axiom 2 (right_additive_identity) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(multiply(Y, X), Y), multiply(add(multiply(Y, X), additive_identity), add(multiply(X, Y), multiply(Y, X)))))))
% 86.06/11.39 = { by lemma 26 R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(multiply(Y, X), Y), multiply(add(multiply(Y, X), add(Y, Y)), add(multiply(X, Y), multiply(Y, X)))))))
% 86.06/11.39 = { by axiom 6 (associativity_for_addition) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(multiply(Y, X), Y), multiply(add(add(multiply(Y, X), Y), Y), add(multiply(X, Y), multiply(Y, X)))))))
% 86.06/11.39 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(multiply(Y, X), Y), multiply(add(Y, add(multiply(Y, X), Y)), add(multiply(X, Y), multiply(Y, X)))))))
% 86.06/11.39 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(Y, add(multiply(Y, X), Y)), add(multiply(X, Y), multiply(Y, X))), multiply(multiply(Y, X), Y)))))
% 86.06/11.39 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(Y, add(multiply(Y, X), Y)), add(multiply(X, Y), multiply(Y, X))), multiply(Y, multiply(X, Y))))))
% 86.06/11.39 = { by lemma 32 }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(multiply(Y, X), Y), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by axiom 2 (right_additive_identity) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(multiply(Y, X), add(Y, additive_identity)), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by lemma 15 R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(multiply(Y, X), add(Y, multiply(add(multiply(X, Y), multiply(Y, X)), additive_identity))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by lemma 15 R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(multiply(Y, X), add(Y, multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), additive_identity)))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by axiom 6 (associativity_for_addition) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), additive_identity))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by lemma 45 R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(Y, X), multiply(add(multiply(Y, X), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, X), Y)), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(Y, multiply(Y, X))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by lemma 44 R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), Y))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.39 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.39 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, X), multiply(Y, multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by axiom 3 (left_additive_identity) R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, X), multiply(Y, add(additive_identity, multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, X), multiply(Y, add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), additive_identity)))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by lemma 24 R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, multiply(Y, multiply(Y, multiply(Y, X)))), multiply(Y, add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), additive_identity)))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by axiom 8 (distribute1) R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(multiply(Y, multiply(Y, multiply(Y, X))), add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), additive_identity)))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), additive_identity), multiply(Y, multiply(Y, multiply(Y, X)))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by axiom 6 (associativity_for_addition) R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), add(additive_identity, multiply(Y, multiply(Y, multiply(Y, X))))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by lemma 55 R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), add(additive_identity, multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(Y, multiply(Y, Y))))))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by lemma 34 }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), add(additive_identity, multiply(multiply(X, Y), multiply(Y, Y)))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by lemma 28 R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(additive_identity, add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), multiply(multiply(X, Y), multiply(Y, Y)))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by axiom 3 (left_additive_identity) }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), multiply(multiply(X, Y), multiply(Y, Y))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, add(multiply(multiply(X, Y), multiply(Y, Y)), multiply(X, multiply(multiply(multiply(Y, X), multiply(Y, X)), Y))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by lemma 62 R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), multiply(Y, multiply(multiply(X, Y), multiply(Y, Y))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.40 = { by lemma 29 R->L }
% 86.06/11.40 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(Y, X)), Y)), multiply(multiply(Y, X), multiply(Y, multiply(Y, Y))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 8 (distribute1) R->L }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), add(multiply(multiply(multiply(Y, X), multiply(Y, X)), Y), multiply(Y, multiply(Y, Y))))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by lemma 46 }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(add(multiply(multiply(Y, X), multiply(Y, X)), multiply(Y, Y)), Y))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(add(multiply(Y, Y), multiply(multiply(Y, X), multiply(Y, X))), Y))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), add(multiply(Y, Y), multiply(multiply(Y, X), multiply(Y, X)))), Y)), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(multiply(Y, X), multiply(multiply(Y, X), add(multiply(Y, Y), multiply(multiply(Y, X), multiply(Y, X))))), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 8 (distribute1) }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(multiply(Y, X), add(multiply(multiply(Y, X), multiply(Y, Y)), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, X))))), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by lemma 22 }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(add(multiply(Y, X), multiply(multiply(Y, X), multiply(multiply(Y, X), multiply(Y, Y)))), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by lemma 57 }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(add(multiply(Y, X), multiply(X, multiply(X, Y))), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by lemma 27 R->L }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(add(multiply(X, Y), add(multiply(X, Y), add(multiply(Y, X), multiply(X, multiply(X, Y))))), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by lemma 68 }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(add(multiply(X, Y), multiply(multiply(Y, X), X)), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by lemma 46 R->L }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(add(multiply(multiply(X, Y), Y), multiply(multiply(Y, X), multiply(X, Y))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by lemma 61 R->L }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(add(multiply(multiply(X, Y), Y), multiply(multiply(X, Y), multiply(Y, X))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 8 (distribute1) R->L }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(X, Y), add(Y, multiply(Y, X))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(X, Y), add(multiply(Y, X), Y)), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.41 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.41 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(X, Y), multiply(add(multiply(Y, X), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(X, Y), multiply(multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)), add(multiply(Y, X), Y)))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), multiply(multiply(multiply(X, Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))), add(multiply(Y, X), Y))), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by lemma 46 R->L }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), add(multiply(multiply(Y, X), add(multiply(Y, X), Y)), multiply(multiply(multiply(X, Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 10 (x_fourthed_is_x) R->L }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), add(multiply(multiply(Y, X), multiply(add(multiply(Y, X), Y), multiply(add(multiply(Y, X), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))))), multiply(multiply(multiply(X, Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by lemma 42 }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(multiply(X, Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))), multiply(multiply(Y, X), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 9 (distribute2) R->L }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y))))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(Y, X), Y), multiply(add(multiply(Y, X), Y), multiply(add(multiply(Y, X), Y), add(multiply(Y, X), Y)))))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 10 (x_fourthed_is_x) }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(multiply(add(add(multiply(Y, X), Y), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), multiply(add(multiply(X, Y), multiply(Y, X)), add(multiply(Y, X), Y))))), add(multiply(X, Y), multiply(Y, X))), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by lemma 48 }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), add(additive_identity, multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X))))))))
% 86.06/11.42 = { by axiom 3 (left_additive_identity) }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), multiply(Y, add(multiply(X, Y), add(multiply(X, Y), multiply(Y, X)))))))
% 86.06/11.42 = { by lemma 27 }
% 86.06/11.42 multiply(Y, multiply(Y, add(multiply(multiply(Y, X), Y), multiply(Y, multiply(Y, X)))))
% 86.06/11.42 = { by lemma 62 }
% 86.06/11.42 multiply(Y, multiply(Y, multiply(Y, add(multiply(Y, X), multiply(X, Y)))))
% 86.06/11.42 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.42 multiply(Y, multiply(Y, multiply(Y, add(multiply(X, Y), multiply(Y, X)))))
% 86.06/11.42 = { by lemma 64 }
% 86.06/11.42 add(multiply(Y, X), multiply(Y, multiply(Y, multiply(Y, multiply(X, Y)))))
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.42 add(multiply(Y, X), multiply(Y, multiply(Y, multiply(multiply(Y, X), Y))))
% 86.06/11.42 = { by lemma 33 }
% 86.06/11.42 add(multiply(Y, X), multiply(X, Y))
% 86.06/11.42 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.42 add(multiply(X, Y), multiply(Y, X))
% 86.06/11.42
% 86.06/11.42 Lemma 70: multiply(multiply(Y, X), multiply(multiply(X, Y), Z)) = multiply(multiply(X, Y), multiply(multiply(Y, X), Z)).
% 86.06/11.42 Proof:
% 86.06/11.42 multiply(multiply(Y, X), multiply(multiply(X, Y), Z))
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.42 multiply(multiply(multiply(Y, X), multiply(X, Y)), Z)
% 86.06/11.42 = { by lemma 61 }
% 86.06/11.42 multiply(multiply(multiply(X, Y), multiply(Y, X)), Z)
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.42 multiply(multiply(X, Y), multiply(multiply(Y, X), Z))
% 86.06/11.42
% 86.06/11.42 Lemma 71: multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, X), multiply(multiply(X, Y), X)))) = multiply(Y, X).
% 86.06/11.42 Proof:
% 86.06/11.42 multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, X), multiply(multiply(X, Y), X))))
% 86.06/11.42 = { by lemma 34 R->L }
% 86.06/11.42 multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, X), multiply(Y, multiply(Y, multiply(multiply(Y, X), multiply(Y, X)))))))
% 86.06/11.42 = { by lemma 39 }
% 86.06/11.42 multiply(X, multiply(multiply(X, Y), multiply(Y, multiply(multiply(Y, X), multiply(Y, X)))))
% 86.06/11.42 = { by lemma 39 }
% 86.06/11.42 multiply(X, multiply(X, multiply(multiply(X, Y), X)))
% 86.06/11.42 = { by lemma 33 }
% 86.06/11.42 multiply(Y, X)
% 86.06/11.42
% 86.06/11.42 Goal 1 (prove_commutativity): multiply(b, a) = c.
% 86.06/11.42 Proof:
% 86.06/11.42 multiply(b, a)
% 86.06/11.42 = { by lemma 27 R->L }
% 86.06/11.42 add(multiply(a, b), add(multiply(a, b), multiply(b, a)))
% 86.06/11.42 = { by lemma 69 R->L }
% 86.06/11.42 add(multiply(a, b), multiply(a, add(multiply(a, b), multiply(b, a))))
% 86.06/11.42 = { by lemma 62 R->L }
% 86.06/11.42 add(multiply(a, b), add(multiply(multiply(a, b), a), multiply(a, multiply(a, b))))
% 86.06/11.42 = { by lemma 63 R->L }
% 86.06/11.42 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(b, multiply(multiply(b, a), b)))))
% 86.06/11.42 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.42 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(b, multiply(b, multiply(a, b))))))
% 86.06/11.43 = { by lemma 71 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(b, multiply(b, multiply(multiply(b, a), multiply(a, multiply(multiply(a, b), multiply(multiply(b, a), b)))))))))
% 86.06/11.43 = { by lemma 24 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(b, multiply(b, multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(multiply(a, b), multiply(multiply(b, a), b))))))))))))
% 86.06/11.43 = { by lemma 71 }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(b, multiply(b, multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, b)))))))))
% 86.06/11.43 = { by lemma 35 }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(a, multiply(multiply(b, a), multiply(a, b)))))))
% 86.06/11.43 = { by lemma 29 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b)))))))
% 86.06/11.43 = { by lemma 35 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(b, multiply(b, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, b)))))))))
% 86.06/11.43 = { by lemma 60 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(b, multiply(b, multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(a, b), multiply(b, a))))))))))))
% 86.06/11.43 = { by lemma 24 }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(b, multiply(b, multiply(multiply(b, a), multiply(multiply(a, b), multiply(b, a)))))))))
% 86.06/11.43 = { by lemma 51 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(b, multiply(b, multiply(multiply(a, b), multiply(b, a)))))))))
% 86.06/11.43 = { by lemma 29 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(b, multiply(multiply(b, a), multiply(b, multiply(b, a)))))))))
% 86.06/11.43 = { by lemma 39 }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(b, a)))))))
% 86.06/11.43 = { by lemma 58 R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(a, b), multiply(multiply(b, a), multiply(multiply(b, a), a))))))
% 86.06/11.43 = { by lemma 70 }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(b, a), multiply(multiply(a, b), multiply(multiply(b, a), a))))))
% 86.06/11.43 = { by lemma 70 }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(a, b), a))))))
% 86.06/11.43 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))))))
% 86.06/11.43 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a))))))
% 86.06/11.43 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(a, multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(b, a)))))
% 86.06/11.43 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.43 add(multiply(a, b), multiply(multiply(a, b), add(multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(b, a)), a)))
% 86.06/11.43 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.43 add(multiply(a, b), multiply(a, multiply(b, add(multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(b, a)), a))))
% 86.06/11.44 = { by lemma 14 R->L }
% 86.06/11.44 add(multiply(a, b), multiply(a, add(multiply(b, a), multiply(b, multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(b, a))))))
% 86.06/11.44 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.44 add(multiply(a, b), multiply(a, add(multiply(b, a), multiply(multiply(b, multiply(multiply(b, a), multiply(multiply(b, a), a))), multiply(b, a)))))
% 86.06/11.44 = { by lemma 41 R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(a, multiply(b, multiply(multiply(b, a), multiply(multiply(b, a), a))))), multiply(b, a)))
% 86.06/11.44 = { by axiom 7 (associativity_for_multiplication) }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(a, b), multiply(multiply(b, a), multiply(multiply(b, a), a)))), multiply(b, a)))
% 86.06/11.44 = { by lemma 70 }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(a, b), multiply(multiply(b, a), a)))), multiply(b, a)))
% 86.06/11.44 = { by lemma 70 }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(a, b), a)))), multiply(b, a)))
% 86.06/11.44 = { by axiom 2 (right_additive_identity) R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(multiply(a, b), a), additive_identity)))), multiply(b, a)))
% 86.06/11.44 = { by lemma 16 R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(multiply(a, b), a), multiply(additive_identity, add(multiply(a, b), multiply(b, a))))))), multiply(b, a)))
% 86.06/11.44 = { by lemma 26 R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(multiply(a, b), a), multiply(add(a, a), add(multiply(a, b), multiply(b, a))))))), multiply(b, a)))
% 86.06/11.44 = { by axiom 1 (commutativity_for_addition) R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(add(a, a), add(multiply(a, b), multiply(b, a))), multiply(multiply(a, b), a))))), multiply(b, a)))
% 86.06/11.44 = { by axiom 7 (associativity_for_multiplication) R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(add(a, a), add(multiply(a, b), multiply(b, a))), multiply(a, multiply(b, a)))))), multiply(b, a)))
% 86.06/11.44 = { by lemma 32 }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(a, add(multiply(a, b), multiply(b, a))), multiply(a, add(multiply(b, a), add(multiply(a, b), multiply(b, a)))))))), multiply(b, a)))
% 86.06/11.44 = { by axiom 1 (commutativity_for_addition) }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(a, add(multiply(a, b), multiply(b, a))), multiply(a, add(add(multiply(a, b), multiply(b, a)), multiply(b, a))))))), multiply(b, a)))
% 86.06/11.44 = { by lemma 69 }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(add(multiply(a, b), multiply(b, a)), multiply(a, add(add(multiply(a, b), multiply(b, a)), multiply(b, a))))))), multiply(b, a)))
% 86.06/11.44 = { by axiom 6 (associativity_for_addition) R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(a, b), add(multiply(b, a), multiply(a, add(add(multiply(a, b), multiply(b, a)), multiply(b, a)))))))), multiply(b, a)))
% 86.06/11.44 = { by axiom 6 (associativity_for_addition) R->L }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(a, b), add(multiply(b, a), multiply(a, add(multiply(a, b), add(multiply(b, a), multiply(b, a))))))))), multiply(b, a)))
% 86.06/11.44 = { by lemma 26 }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(a, b), add(multiply(b, a), multiply(a, add(multiply(a, b), additive_identity))))))), multiply(b, a)))
% 86.06/11.44 = { by axiom 2 (right_additive_identity) }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), add(multiply(a, b), add(multiply(b, a), multiply(a, multiply(a, b))))))), multiply(b, a)))
% 86.06/11.44 = { by lemma 68 }
% 86.06/11.44 add(multiply(a, b), multiply(add(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), a)))), multiply(b, a)))
% 86.06/11.44 = { by lemma 48 }
% 86.06/11.44 add(multiply(a, b), additive_identity)
% 86.06/11.44 = { by axiom 2 (right_additive_identity) }
% 86.06/11.44 multiply(a, b)
% 86.06/11.44 = { by axiom 4 (a_times_b_is_c) }
% 86.06/11.44 c
% 86.06/11.44 % SZS output end Proof
% 86.06/11.44
% 86.06/11.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------