TSTP Solution File: RNG025-6 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG025-6 : 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 : n004.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 13:58:52 EDT 2023
% Result : Unsatisfiable 21.56s 3.12s
% Output : Proof 21.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG025-6 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 02:48:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 21.56/3.12 Command-line arguments: --flatten
% 21.56/3.12
% 21.56/3.12 % SZS status Unsatisfiable
% 21.56/3.12
% 21.56/3.15 % SZS output start Proof
% 21.56/3.15 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 21.56/3.15 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 21.56/3.15 Axiom 3 (right_additive_identity): add(X, additive_identity) = X.
% 21.56/3.15 Axiom 4 (left_additive_identity): add(additive_identity, X) = X.
% 21.56/3.15 Axiom 5 (right_multiplicative_zero): multiply(X, additive_identity) = additive_identity.
% 21.56/3.15 Axiom 6 (left_multiplicative_zero): multiply(additive_identity, X) = additive_identity.
% 21.56/3.15 Axiom 7 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 21.56/3.15 Axiom 8 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 21.56/3.15 Axiom 9 (left_alternative): multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)).
% 21.56/3.15 Axiom 10 (right_alternative): multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)).
% 21.56/3.15 Axiom 11 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 21.56/3.15 Axiom 12 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 21.56/3.15 Axiom 13 (commutator): commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))).
% 21.56/3.15 Axiom 14 (associator): associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))).
% 21.56/3.15
% 21.56/3.15 Lemma 15: add(X, add(Y, additive_inverse(X))) = Y.
% 21.56/3.15 Proof:
% 21.56/3.15 add(X, add(Y, additive_inverse(X)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(X, add(additive_inverse(X), Y))
% 21.56/3.15 = { by axiom 8 (associativity_for_addition) }
% 21.56/3.15 add(add(X, additive_inverse(X)), Y)
% 21.56/3.15 = { by axiom 7 (right_additive_inverse) }
% 21.56/3.15 add(additive_identity, Y)
% 21.56/3.15 = { by axiom 4 (left_additive_identity) }
% 21.56/3.15 Y
% 21.56/3.15
% 21.56/3.15 Lemma 16: add(X, add(additive_inverse(X), Y)) = Y.
% 21.56/3.15 Proof:
% 21.56/3.15 add(X, add(additive_inverse(X), Y))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(X, add(Y, additive_inverse(X)))
% 21.56/3.15 = { by lemma 15 }
% 21.56/3.15 Y
% 21.56/3.15
% 21.56/3.15 Lemma 17: add(X, add(Y, additive_inverse(add(X, Y)))) = additive_identity.
% 21.56/3.15 Proof:
% 21.56/3.15 add(X, add(Y, additive_inverse(add(X, Y))))
% 21.56/3.15 = { by axiom 8 (associativity_for_addition) }
% 21.56/3.15 add(add(X, Y), additive_inverse(add(X, Y)))
% 21.56/3.15 = { by axiom 7 (right_additive_inverse) }
% 21.56/3.15 additive_identity
% 21.56/3.15
% 21.56/3.15 Lemma 18: add(X, additive_inverse(add(X, Y))) = additive_inverse(Y).
% 21.56/3.15 Proof:
% 21.56/3.15 add(X, additive_inverse(add(X, Y)))
% 21.56/3.15 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 21.56/3.15 add(X, additive_inverse(add(X, additive_inverse(additive_inverse(Y)))))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))
% 21.56/3.15 = { by lemma 16 R->L }
% 21.56/3.15 add(additive_inverse(Y), add(additive_inverse(additive_inverse(Y)), add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))))
% 21.56/3.15 = { by lemma 17 }
% 21.56/3.15 add(additive_inverse(Y), additive_identity)
% 21.56/3.15 = { by axiom 3 (right_additive_identity) }
% 21.56/3.15 additive_inverse(Y)
% 21.56/3.15
% 21.56/3.15 Lemma 19: add(commutator(X, Y), multiply(X, Y)) = multiply(Y, X).
% 21.56/3.15 Proof:
% 21.56/3.15 add(commutator(X, Y), multiply(X, Y))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(multiply(X, Y), commutator(X, Y))
% 21.56/3.15 = { by axiom 13 (commutator) }
% 21.56/3.15 add(multiply(X, Y), add(multiply(Y, X), additive_inverse(multiply(X, Y))))
% 21.56/3.15 = { by lemma 15 }
% 21.56/3.15 multiply(Y, X)
% 21.56/3.15
% 21.56/3.15 Lemma 20: add(multiply(X, Y), add(Z, multiply(X, W))) = add(Z, multiply(X, add(Y, W))).
% 21.56/3.15 Proof:
% 21.56/3.15 add(multiply(X, Y), add(Z, multiply(X, W)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(multiply(X, Y), add(multiply(X, W), Z))
% 21.56/3.15 = { by axiom 8 (associativity_for_addition) }
% 21.56/3.15 add(add(multiply(X, Y), multiply(X, W)), Z)
% 21.56/3.15 = { by axiom 11 (distribute1) R->L }
% 21.56/3.15 add(multiply(X, add(Y, W)), Z)
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) }
% 21.56/3.15 add(Z, multiply(X, add(Y, W)))
% 21.56/3.15
% 21.56/3.15 Lemma 21: add(multiply(X, Y), multiply(Y, additive_inverse(X))) = commutator(Y, X).
% 21.56/3.15 Proof:
% 21.56/3.15 add(multiply(X, Y), multiply(Y, additive_inverse(X)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(multiply(Y, additive_inverse(X)), multiply(X, Y))
% 21.56/3.15 = { by lemma 19 R->L }
% 21.56/3.15 add(multiply(Y, additive_inverse(X)), add(commutator(Y, X), multiply(Y, X)))
% 21.56/3.15 = { by lemma 20 }
% 21.56/3.15 add(commutator(Y, X), multiply(Y, add(additive_inverse(X), X)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) }
% 21.56/3.15 add(commutator(Y, X), multiply(Y, add(X, additive_inverse(X))))
% 21.56/3.15 = { by axiom 7 (right_additive_inverse) }
% 21.56/3.15 add(commutator(Y, X), multiply(Y, additive_identity))
% 21.56/3.15 = { by axiom 5 (right_multiplicative_zero) }
% 21.56/3.15 add(commutator(Y, X), additive_identity)
% 21.56/3.15 = { by axiom 3 (right_additive_identity) }
% 21.56/3.15 commutator(Y, X)
% 21.56/3.15
% 21.56/3.15 Lemma 22: additive_inverse(commutator(X, Y)) = commutator(Y, X).
% 21.56/3.15 Proof:
% 21.56/3.15 additive_inverse(commutator(X, Y))
% 21.56/3.15 = { by lemma 18 R->L }
% 21.56/3.15 add(commutator(Y, X), additive_inverse(add(commutator(Y, X), commutator(X, Y))))
% 21.56/3.15 = { by axiom 13 (commutator) }
% 21.56/3.15 add(commutator(Y, X), additive_inverse(add(commutator(Y, X), add(multiply(Y, X), additive_inverse(multiply(X, Y))))))
% 21.56/3.15 = { by lemma 19 R->L }
% 21.56/3.15 add(commutator(Y, X), additive_inverse(add(commutator(Y, X), add(multiply(Y, X), additive_inverse(add(commutator(Y, X), multiply(Y, X)))))))
% 21.56/3.15 = { by lemma 17 }
% 21.56/3.15 add(commutator(Y, X), additive_inverse(additive_identity))
% 21.56/3.15 = { by axiom 4 (left_additive_identity) R->L }
% 21.56/3.15 add(commutator(Y, X), add(additive_identity, additive_inverse(additive_identity)))
% 21.56/3.15 = { by axiom 7 (right_additive_inverse) }
% 21.56/3.15 add(commutator(Y, X), additive_identity)
% 21.56/3.15 = { by axiom 3 (right_additive_identity) }
% 21.56/3.15 commutator(Y, X)
% 21.56/3.15
% 21.56/3.15 Lemma 23: multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)).
% 21.56/3.15 Proof:
% 21.56/3.15 multiply(X, additive_inverse(Y))
% 21.56/3.15 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 21.56/3.15 additive_inverse(additive_inverse(multiply(X, additive_inverse(Y))))
% 21.56/3.15 = { by lemma 18 R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(multiply(Y, X), multiply(X, additive_inverse(Y))))))
% 21.56/3.15 = { by lemma 21 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(commutator(X, Y))))
% 21.56/3.15 = { by lemma 22 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), commutator(Y, X)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) }
% 21.56/3.15 additive_inverse(add(commutator(Y, X), multiply(Y, X)))
% 21.56/3.15 = { by lemma 19 }
% 21.56/3.15 additive_inverse(multiply(X, Y))
% 21.56/3.15
% 21.56/3.15 Lemma 24: add(X, additive_inverse(add(Y, X))) = additive_inverse(Y).
% 21.56/3.15 Proof:
% 21.56/3.15 add(X, additive_inverse(add(Y, X)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(X, additive_inverse(add(X, Y)))
% 21.56/3.15 = { by lemma 18 }
% 21.56/3.15 additive_inverse(Y)
% 21.56/3.15
% 21.56/3.15 Lemma 25: multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)).
% 21.56/3.15 Proof:
% 21.56/3.15 multiply(additive_inverse(X), Y)
% 21.56/3.15 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 21.56/3.15 additive_inverse(additive_inverse(multiply(additive_inverse(X), Y)))
% 21.56/3.15 = { by lemma 18 R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(multiply(Y, X), multiply(additive_inverse(X), Y)))))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(multiply(additive_inverse(X), Y), multiply(Y, X)))))
% 21.56/3.15 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(multiply(additive_inverse(X), Y), multiply(Y, additive_inverse(additive_inverse(X)))))))
% 21.56/3.15 = { by lemma 21 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(commutator(Y, additive_inverse(X)))))
% 21.56/3.15 = { by lemma 22 R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(additive_inverse(commutator(additive_inverse(X), Y)))))
% 21.56/3.15 = { by axiom 4 (left_additive_identity) R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(additive_inverse(add(additive_identity, commutator(additive_inverse(X), Y))))))
% 21.56/3.15 = { by lemma 22 R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(additive_inverse(add(additive_identity, additive_inverse(commutator(Y, additive_inverse(X))))))))
% 21.56/3.15 = { by lemma 18 R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(commutator(Y, additive_inverse(X)), add(additive_identity, additive_inverse(commutator(Y, additive_inverse(X))))))))))
% 21.56/3.15 = { by lemma 15 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(additive_identity)))))
% 21.56/3.15 = { by axiom 6 (left_multiplicative_zero) R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(multiply(additive_identity, Y))))))
% 21.56/3.15 = { by axiom 7 (right_additive_inverse) R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(multiply(add(X, additive_inverse(X)), Y))))))
% 21.56/3.15 = { by axiom 12 (distribute2) }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(multiply(X, Y), multiply(additive_inverse(X), Y)))))))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(multiply(additive_inverse(X), Y), multiply(X, Y)))))))
% 21.56/3.15 = { by lemma 19 R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(add(commutator(Y, additive_inverse(X)), multiply(Y, additive_inverse(X))), multiply(X, Y)))))))
% 21.56/3.15 = { by axiom 8 (associativity_for_addition) R->L }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(commutator(Y, additive_inverse(X)), add(multiply(Y, additive_inverse(X)), multiply(X, Y))))))))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(commutator(Y, additive_inverse(X)), add(multiply(X, Y), multiply(Y, additive_inverse(X)))))))))
% 21.56/3.15 = { by lemma 21 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(commutator(Y, additive_inverse(X)), commutator(Y, X)))))))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(add(commutator(Y, additive_inverse(X)), additive_inverse(add(commutator(Y, X), commutator(Y, additive_inverse(X))))))))
% 21.56/3.15 = { by lemma 24 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(additive_inverse(commutator(Y, X)))))
% 21.56/3.15 = { by lemma 22 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), additive_inverse(commutator(X, Y))))
% 21.56/3.15 = { by lemma 22 }
% 21.56/3.15 additive_inverse(add(multiply(Y, X), commutator(Y, X)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) }
% 21.56/3.15 additive_inverse(add(commutator(Y, X), multiply(Y, X)))
% 21.56/3.15 = { by lemma 19 }
% 21.56/3.15 additive_inverse(multiply(X, Y))
% 21.56/3.15
% 21.56/3.15 Lemma 26: add(multiply(X, Y), additive_inverse(multiply(X, Z))) = multiply(X, add(Y, additive_inverse(Z))).
% 21.56/3.15 Proof:
% 21.56/3.15 add(multiply(X, Y), additive_inverse(multiply(X, Z)))
% 21.56/3.15 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.15 add(additive_inverse(multiply(X, Z)), multiply(X, Y))
% 21.56/3.15 = { by lemma 15 R->L }
% 21.56/3.15 add(additive_inverse(multiply(X, Z)), multiply(X, add(Z, add(Y, additive_inverse(Z)))))
% 21.56/3.15 = { by lemma 20 R->L }
% 21.56/3.15 add(multiply(X, Z), add(additive_inverse(multiply(X, Z)), multiply(X, add(Y, additive_inverse(Z)))))
% 21.56/3.15 = { by lemma 16 }
% 21.56/3.16 multiply(X, add(Y, additive_inverse(Z)))
% 21.56/3.16
% 21.56/3.16 Goal 1 (prove_flexible_law): associator(x, y, x) = additive_identity.
% 21.56/3.16 Proof:
% 21.56/3.16 associator(x, y, x)
% 21.56/3.16 = { by axiom 14 (associator) }
% 21.56/3.16 add(multiply(multiply(x, y), x), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 15 R->L }
% 21.56/3.16 add(multiply(multiply(x, y), add(y, add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 15 R->L }
% 21.56/3.16 add(multiply(multiply(add(y, add(x, additive_inverse(y))), y), add(y, add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 11 (distribute1) }
% 21.56/3.16 add(add(multiply(multiply(add(y, add(x, additive_inverse(y))), y), y), multiply(multiply(add(y, add(x, additive_inverse(y))), y), add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 10 (right_alternative) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), multiply(multiply(add(y, add(x, additive_inverse(y))), y), add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), additive_inverse(additive_inverse(multiply(multiply(add(y, add(x, additive_inverse(y))), y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 25 R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), additive_inverse(multiply(additive_inverse(multiply(add(y, add(x, additive_inverse(y))), y)), add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 23 R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), additive_inverse(multiply(multiply(add(y, add(x, additive_inverse(y))), additive_inverse(y)), add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 25 R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), multiply(additive_inverse(multiply(add(y, add(x, additive_inverse(y))), additive_inverse(y))), add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 25 R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), multiply(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), additive_inverse(y)), add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 15 R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))), add(multiply(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), additive_inverse(y)), add(x, additive_inverse(y))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 14 (associator) R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))), associator(additive_inverse(add(y, add(x, additive_inverse(y)))), additive_inverse(y), add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 2 (commutativity_for_addition) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(associator(additive_inverse(add(y, add(x, additive_inverse(y)))), additive_inverse(y), add(x, additive_inverse(y))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 24 R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(associator(additive_inverse(add(y, add(x, additive_inverse(y)))), add(add(x, additive_inverse(y)), additive_inverse(add(y, add(x, additive_inverse(y))))), add(x, additive_inverse(y))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 2 (commutativity_for_addition) R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(associator(additive_inverse(add(y, add(x, additive_inverse(y)))), add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 14 (associator) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(add(multiply(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y)))), add(x, additive_inverse(y))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 11 (distribute1) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(add(multiply(add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), additive_inverse(add(y, add(x, additive_inverse(y))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y)))), add(x, additive_inverse(y))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 12 (distribute2) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(add(add(multiply(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), additive_inverse(add(y, add(x, additive_inverse(y))))), add(x, additive_inverse(y))), multiply(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 9 (left_alternative) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(add(add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y)))), multiply(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 10 (right_alternative) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(add(add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y)))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(x, additive_inverse(y)), add(x, additive_inverse(y))))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 11 (distribute1) R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), multiply(add(x, additive_inverse(y)), add(x, additive_inverse(y))))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 12 (distribute2) R->L }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))), additive_inverse(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 26 }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), add(multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y))), additive_inverse(multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 26 }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), add(add(x, additive_inverse(y)), additive_inverse(add(x, additive_inverse(y)))))), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 7 (right_additive_inverse) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(add(additive_inverse(add(y, add(x, additive_inverse(y)))), add(x, additive_inverse(y))), additive_identity)), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 5 (right_multiplicative_zero) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), additive_identity), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 5 (right_multiplicative_zero) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), add(additive_identity, multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 4 (left_additive_identity) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), multiply(additive_inverse(add(y, add(x, additive_inverse(y)))), multiply(additive_inverse(y), add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 25 }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), additive_inverse(multiply(add(y, add(x, additive_inverse(y))), multiply(additive_inverse(y), add(x, additive_inverse(y)))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 25 }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), additive_inverse(multiply(add(y, add(x, additive_inverse(y))), additive_inverse(multiply(y, add(x, additive_inverse(y))))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 23 }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), additive_inverse(additive_inverse(multiply(add(y, add(x, additive_inverse(y))), multiply(y, add(x, additive_inverse(y))))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 1 (additive_inverse_additive_inverse) }
% 21.56/3.16 add(add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, y)), multiply(add(y, add(x, additive_inverse(y))), multiply(y, add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 11 (distribute1) R->L }
% 21.56/3.16 add(multiply(add(y, add(x, additive_inverse(y))), add(multiply(y, y), multiply(y, add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by axiom 11 (distribute1) R->L }
% 21.56/3.16 add(multiply(add(y, add(x, additive_inverse(y))), multiply(y, add(y, add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 15 }
% 21.56/3.16 add(multiply(x, multiply(y, add(y, add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 15 }
% 21.56/3.16 add(multiply(x, multiply(y, x)), additive_inverse(multiply(x, multiply(y, x))))
% 21.56/3.16 = { by lemma 26 }
% 21.56/3.16 multiply(x, add(multiply(y, x), additive_inverse(multiply(y, x))))
% 21.56/3.16 = { by lemma 26 }
% 21.56/3.16 multiply(x, multiply(y, add(x, additive_inverse(x))))
% 21.56/3.16 = { by axiom 7 (right_additive_inverse) }
% 21.56/3.16 multiply(x, multiply(y, additive_identity))
% 21.56/3.16 = { by axiom 5 (right_multiplicative_zero) }
% 21.56/3.16 multiply(x, additive_identity)
% 21.56/3.16 = { by axiom 5 (right_multiplicative_zero) }
% 21.56/3.16 additive_identity
% 21.56/3.16 % SZS output end Proof
% 21.56/3.16
% 21.56/3.16 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------