TSTP Solution File: GRP054-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP054-1 : 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 : n006.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 01:16:48 EDT 2023
% Result : Unsatisfiable 3.43s 0.77s
% Output : Proof 4.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP054-1 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.30 % Computer : n006.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon Aug 28 22:57:51 EDT 2023
% 0.11/0.30 % CPUTime :
% 3.43/0.77 Command-line arguments: --no-flatten-goal
% 3.43/0.77
% 3.43/0.77 % SZS status Unsatisfiable
% 3.43/0.77
% 4.82/0.92 % SZS output start Proof
% 4.82/0.92 Take the following subset of the input axioms:
% 4.82/0.93 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)))).
% 4.82/0.93 fof(single_axiom, axiom, ![Z, X, Y]: inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(Z, Y)))=X).
% 4.82/0.93
% 4.82/0.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.82/0.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.82/0.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.82/0.93 fresh(y, y, x1...xn) = u
% 4.82/0.93 C => fresh(s, t, x1...xn) = v
% 4.82/0.93 where fresh is a fresh function symbol and x1..xn are the free
% 4.82/0.93 variables of u and v.
% 4.82/0.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.82/0.93 input problem has no model of domain size 1).
% 4.82/0.93
% 4.82/0.93 The encoding turns the above axioms into the following unit equations and goals:
% 4.82/0.93
% 4.82/0.93 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))) = Y.
% 4.82/0.93
% 4.82/0.93 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z)) = inverse(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V))).
% 4.82/0.93 Proof:
% 4.82/0.93 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 4.82/0.93 = { by axiom 1 (single_axiom) }
% 4.82/0.93 inverse(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 4.82/0.93
% 4.82/0.93 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y)) = W.
% 4.82/0.93 Proof:
% 4.82/0.93 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))))
% 4.82/0.93 = { by lemma 2 R->L }
% 4.82/0.93 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))))
% 4.82/0.93 = { by axiom 1 (single_axiom) }
% 4.82/0.93 W
% 4.82/0.93
% 4.82/0.93 Lemma 4: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 4.82/0.93 Proof:
% 4.82/0.93 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.93 = { by lemma 3 R->L }
% 4.82/0.93 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(W, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.93 = { by axiom 1 (single_axiom) }
% 4.82/0.93 inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S)))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.93 = { by lemma 3 }
% 4.82/0.93 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.93 = { by axiom 1 (single_axiom) }
% 4.82/0.93 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 4.82/0.93
% 4.82/0.93 Lemma 5: multiply(X, multiply(inverse(multiply(Y, inverse(multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), W)) = multiply(inverse(multiply(V, multiply(Y, Z))), multiply(V, W)).
% 4.82/0.93 Proof:
% 4.82/0.93 multiply(X, multiply(inverse(multiply(Y, inverse(multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), W))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(Y, Z))), multiply(inverse(multiply(Y, inverse(multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), W))
% 4.82/0.93 = { by lemma 4 R->L }
% 4.82/0.93 multiply(inverse(multiply(V, multiply(Y, Z))), multiply(V, W))
% 4.82/0.93
% 4.82/0.93 Lemma 6: multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y) = inverse(multiply(inverse(multiply(V, inverse(multiply(W, inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U))).
% 4.82/0.93 Proof:
% 4.82/0.93 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y)
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y)), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.93 = { by lemma 3 }
% 4.82/0.93 inverse(multiply(inverse(multiply(V, inverse(multiply(W, inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.93
% 4.82/0.93 Lemma 7: inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))) = Y.
% 4.82/0.93 Proof:
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))))
% 4.82/0.93 = { by lemma 2 R->L }
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 4.82/0.93 = { by lemma 3 R->L }
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z)))), multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 4.82/0.93 = { by axiom 1 (single_axiom) }
% 4.82/0.93 inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 4.82/0.93 = { by axiom 1 (single_axiom) }
% 4.82/0.93 Y
% 4.82/0.93
% 4.82/0.93 Lemma 8: inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Y)))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))) = multiply(Z, W).
% 4.82/0.93 Proof:
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Y)))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U))))), multiply(X, Y)))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.93 = { by lemma 2 R->L }
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(Y)), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), multiply(T, S)))), multiply(X, Y)))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.93 = { by lemma 5 R->L }
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(X2, multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(Y)), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(X2), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), Y)))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.93 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.93 inverse(multiply(inverse(inverse(multiply(X2, multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(Y)), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(inverse(X2)), inverse(multiply(Z2, inverse(multiply(inverse(Z2), Z2)))))))), multiply(Y2, Z2))), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), Y)))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.93 = { by lemma 6 }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(W2, inverse(multiply(multiply(inverse(multiply(Y2, inverse(multiply(inverse(inverse(X2)), inverse(multiply(Z2, inverse(multiply(inverse(Z2), Z2)))))))), multiply(Y2, Z2)), inverse(multiply(V2, inverse(multiply(inverse(V2), V2)))))))), multiply(W2, V2)))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.94 = { by lemma 2 }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X2), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))), inverse(multiply(V2, inverse(multiply(inverse(V2), V2)))))))), multiply(W2, V2)))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.94 = { by axiom 1 (single_axiom) }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(X2, multiply(inverse(multiply(Z, inverse(multiply(inverse(X2), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.94 = { by lemma 5 }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(inverse(multiply(U2, multiply(Z, W))), multiply(U2, multiply(Z, W))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W)))))))
% 4.82/0.94 = { by lemma 7 }
% 4.82/0.94 multiply(Z, W)
% 4.82/0.94
% 4.82/0.94 Lemma 9: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(Y), Y)
% 4.82/0.94 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(X2, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Y2, inverse(multiply(inverse(Y2), Y2)))))))), multiply(X2, Y2))), Y)
% 4.82/0.94 = { by lemma 8 R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(X2, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Y2, inverse(multiply(inverse(Y2), Y2)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, U)), multiply(V, U)))), inverse(multiply(multiply(X2, Y2), inverse(multiply(inverse(multiply(X2, Y2)), multiply(X2, Y2))))))))), Y)
% 4.82/0.94 = { by lemma 6 }
% 4.82/0.94 inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, U))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), multiply(T, S)))
% 4.82/0.94 = { by lemma 6 R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(X)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, U)), multiply(V, U)))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))))), X)
% 4.82/0.94 = { by lemma 8 }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(X)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))), X)
% 4.82/0.94 = { by axiom 1 (single_axiom) }
% 4.82/0.94 multiply(inverse(X), X)
% 4.82/0.94
% 4.82/0.94 Lemma 10: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(Y, inverse(multiply(inverse(Z), Z)))))) = Y.
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(Y, inverse(multiply(inverse(Z), Z))))))
% 4.82/0.94 = { by lemma 9 }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(Y, inverse(multiply(inverse(Y), Y))))))
% 4.82/0.94 = { by lemma 9 }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Y)))), inverse(multiply(Y, inverse(multiply(inverse(Y), Y))))))
% 4.82/0.94 = { by lemma 7 }
% 4.82/0.94 Y
% 4.82/0.94
% 4.82/0.94 Lemma 11: inverse(inverse(multiply(inverse(X), X))) = inverse(multiply(inverse(Y), Y)).
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(inverse(multiply(inverse(X), X)))
% 4.82/0.94 = { by lemma 10 R->L }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))
% 4.82/0.94 = { by lemma 9 R->L }
% 4.82/0.94 inverse(multiply(inverse(Y), Y))
% 4.82/0.94
% 4.82/0.94 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(multiply(inverse(X), X))
% 4.82/0.94 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.94 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 4.82/0.94 = { by lemma 11 }
% 4.82/0.94 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 4.82/0.94 = { by axiom 1 (single_axiom) }
% 4.82/0.94 multiply(inverse(Y), Y)
% 4.82/0.94
% 4.82/0.94 Lemma 13: multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z)) = multiply(Z, multiply(inverse(W), W)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 4.82/0.94 = { by lemma 2 }
% 4.82/0.94 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 4.82/0.94 = { by axiom 1 (single_axiom) }
% 4.82/0.94 multiply(Z, inverse(multiply(inverse(Z), Z)))
% 4.82/0.94 = { by lemma 9 R->L }
% 4.82/0.94 multiply(Z, inverse(multiply(inverse(T), T)))
% 4.82/0.94 = { by lemma 12 }
% 4.82/0.94 multiply(Z, multiply(inverse(W), W))
% 4.82/0.94
% 4.82/0.94 Lemma 14: multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), Z)) = multiply(Z, multiply(inverse(W), W)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), Z))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))), multiply(multiply(inverse(Y), Y), Z))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))), multiply(inverse(multiply(inverse(V), V)), Z))
% 4.82/0.94 = { by lemma 13 }
% 4.82/0.94 multiply(Z, multiply(inverse(W), W))
% 4.82/0.94
% 4.82/0.94 Lemma 15: inverse(multiply(multiply(inverse(X), X), inverse(multiply(Y, multiply(inverse(Z), Z))))) = Y.
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(multiply(multiply(inverse(X), X), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(Y, inverse(multiply(inverse(V), V))))))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 inverse(multiply(inverse(inverse(multiply(inverse(U), U))), inverse(multiply(Y, inverse(multiply(inverse(V), V))))))
% 4.82/0.94 = { by lemma 10 }
% 4.82/0.94 Y
% 4.82/0.94
% 4.82/0.94 Lemma 16: inverse(multiply(multiply(inverse(X), X), inverse(multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W)))))) = multiply(multiply(inverse(V), V), Z).
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(multiply(multiply(inverse(X), X), inverse(multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W))))))
% 4.82/0.94 = { by lemma 14 R->L }
% 4.82/0.94 inverse(multiply(multiply(inverse(X), X), inverse(multiply(multiply(inverse(Y), Y), multiply(multiply(inverse(U), U), multiply(multiply(inverse(V), V), Z))))))
% 4.82/0.94 = { by lemma 14 }
% 4.82/0.94 inverse(multiply(multiply(inverse(X), X), inverse(multiply(multiply(multiply(inverse(V), V), Z), multiply(inverse(T), T)))))
% 4.82/0.94 = { by lemma 15 }
% 4.82/0.94 multiply(multiply(inverse(V), V), Z)
% 4.82/0.94
% 4.82/0.94 Lemma 17: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 4.82/0.94 = { by lemma 9 }
% 4.82/0.94 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 4.82/0.94 = { by lemma 4 R->L }
% 4.82/0.94 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 4.82/0.94
% 4.82/0.94 Lemma 18: multiply(multiply(inverse(X), X), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(multiply(inverse(X), X), multiply(inverse(Y), Z))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(Y), Z))
% 4.82/0.94 = { by lemma 17 }
% 4.82/0.94 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 4.82/0.94
% 4.82/0.94 Lemma 19: multiply(inverse(multiply(X, multiply(Y, Z))), multiply(X, multiply(Y, W))) = multiply(multiply(inverse(Z), W), multiply(inverse(V), V)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(multiply(X, multiply(Y, Z))), multiply(X, multiply(Y, W)))
% 4.82/0.94 = { by lemma 18 R->L }
% 4.82/0.94 multiply(multiply(inverse(U), U), multiply(inverse(multiply(Y, Z)), multiply(Y, W)))
% 4.82/0.94 = { by lemma 18 R->L }
% 4.82/0.94 multiply(multiply(inverse(U), U), multiply(multiply(inverse(T), T), multiply(inverse(Z), W)))
% 4.82/0.94 = { by lemma 14 }
% 4.82/0.94 multiply(multiply(inverse(Z), W), multiply(inverse(V), V))
% 4.82/0.94
% 4.82/0.94 Lemma 20: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Z))) = multiply(inverse(Z), Y).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Z)))
% 4.82/0.94 = { by lemma 16 R->L }
% 4.82/0.94 inverse(multiply(multiply(inverse(W), W), inverse(multiply(multiply(inverse(V), V), multiply(inverse(multiply(inverse(Y), Z)), multiply(inverse(Y), Y))))))
% 4.82/0.94 = { by lemma 18 }
% 4.82/0.94 inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(U, multiply(inverse(Y), Z))), multiply(U, multiply(inverse(Y), Y))))))
% 4.82/0.94 = { by lemma 19 }
% 4.82/0.94 inverse(multiply(multiply(inverse(W), W), inverse(multiply(multiply(inverse(Z), Y), multiply(inverse(T), T)))))
% 4.82/0.94 = { by lemma 15 }
% 4.82/0.94 multiply(inverse(Z), Y)
% 4.82/0.94
% 4.82/0.94 Lemma 21: inverse(multiply(multiply(inverse(X), X), Y)) = inverse(Y).
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(multiply(multiply(inverse(X), X), Y))
% 4.82/0.94 = { by lemma 12 R->L }
% 4.82/0.94 inverse(multiply(inverse(multiply(inverse(Z), Z)), Y))
% 4.82/0.94 = { by lemma 20 R->L }
% 4.82/0.94 inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(Y), multiply(inverse(Z), Z)))))
% 4.82/0.94 = { by lemma 15 }
% 4.82/0.94 inverse(Y)
% 4.82/0.94
% 4.82/0.94 Lemma 22: inverse(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z)))) = Y.
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))))
% 4.82/0.94 = { by lemma 2 R->L }
% 4.82/0.94 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 4.82/0.94 = { by axiom 1 (single_axiom) }
% 4.82/0.94 Y
% 4.82/0.94
% 4.82/0.94 Lemma 23: multiply(multiply(inverse(X), X), Y) = Y.
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(multiply(inverse(X), X), Y)
% 4.82/0.94 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.94 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(multiply(inverse(X), X), Y)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 4.82/0.94 = { by lemma 21 }
% 4.82/0.94 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(Y), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 4.82/0.94 = { by lemma 2 }
% 4.82/0.94 inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(Y, inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U))))
% 4.82/0.94 = { by lemma 22 }
% 4.82/0.94 Y
% 4.82/0.94
% 4.82/0.94 Lemma 24: multiply(X, multiply(inverse(Y), Y)) = X.
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(X, multiply(inverse(Y), Y))
% 4.82/0.94 = { by lemma 14 R->L }
% 4.82/0.94 multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(W), W), X))
% 4.82/0.94 = { by lemma 23 }
% 4.82/0.94 multiply(multiply(inverse(Z), Z), X)
% 4.82/0.94 = { by lemma 23 }
% 4.82/0.94 X
% 4.82/0.94
% 4.82/0.94 Lemma 25: inverse(inverse(X)) = X.
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(inverse(X))
% 4.82/0.94 = { by lemma 23 R->L }
% 4.82/0.94 inverse(multiply(multiply(inverse(Y), Y), inverse(X)))
% 4.82/0.94 = { by lemma 24 R->L }
% 4.82/0.94 inverse(multiply(multiply(inverse(Y), Y), inverse(multiply(X, multiply(inverse(Z), Z)))))
% 4.82/0.94 = { by lemma 15 }
% 4.82/0.94 X
% 4.82/0.94
% 4.82/0.94 Lemma 26: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(X), X)
% 4.82/0.94 = { by lemma 9 }
% 4.82/0.94 multiply(inverse(inverse(Y)), inverse(Y))
% 4.82/0.94 = { by lemma 25 }
% 4.82/0.94 multiply(Y, inverse(Y))
% 4.82/0.94
% 4.82/0.94 Lemma 27: multiply(inverse(Z), multiply(Z, X)) = multiply(X, multiply(inverse(Y), Y)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(Z), multiply(Z, X))
% 4.82/0.94 = { by lemma 24 R->L }
% 4.82/0.94 multiply(inverse(multiply(Z, multiply(inverse(W), W))), multiply(Z, X))
% 4.82/0.94 = { by lemma 13 }
% 4.82/0.94 multiply(X, multiply(inverse(Y), Y))
% 4.82/0.94
% 4.82/0.94 Lemma 28: multiply(inverse(X), multiply(X, Y)) = multiply(Y, multiply(Z, inverse(Z))).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(X), multiply(X, Y))
% 4.82/0.94 = { by lemma 27 }
% 4.82/0.94 multiply(Y, multiply(inverse(W), W))
% 4.82/0.94 = { by lemma 26 }
% 4.82/0.94 multiply(Y, multiply(Z, inverse(Z)))
% 4.82/0.94
% 4.82/0.94 Lemma 29: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 4.82/0.94 Proof:
% 4.82/0.94 inverse(multiply(inverse(multiply(X, Y)), X))
% 4.82/0.94 = { by lemma 20 R->L }
% 4.82/0.94 inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(X), multiply(X, Y)))))
% 4.82/0.94 = { by lemma 27 }
% 4.82/0.94 inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(Y, multiply(inverse(W), W)))))
% 4.82/0.94 = { by lemma 15 }
% 4.82/0.94 Y
% 4.82/0.94
% 4.82/0.94 Lemma 30: multiply(X, multiply(Y, inverse(Y))) = X.
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(X, multiply(Y, inverse(Y)))
% 4.82/0.94 = { by lemma 26 R->L }
% 4.82/0.94 multiply(X, multiply(inverse(Z), Z))
% 4.82/0.94 = { by lemma 24 }
% 4.82/0.94 X
% 4.82/0.94
% 4.82/0.94 Lemma 31: multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), multiply(inverse(multiply(Z, multiply(W, inverse(W)))), V)) = multiply(inverse(multiply(U, multiply(Z, X))), multiply(U, V)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), multiply(inverse(multiply(Z, multiply(W, inverse(W)))), V))
% 4.82/0.94 = { by lemma 26 R->L }
% 4.82/0.94 multiply(inverse(multiply(X, multiply(inverse(T), T))), multiply(inverse(multiply(Z, multiply(W, inverse(W)))), V))
% 4.82/0.94 = { by lemma 26 R->L }
% 4.82/0.94 multiply(inverse(multiply(X, multiply(inverse(T), T))), multiply(inverse(multiply(Z, multiply(inverse(S), S))), V))
% 4.82/0.94 = { by lemma 13 R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(Z, multiply(inverse(S), S))), multiply(Z, X))), multiply(inverse(multiply(Z, multiply(inverse(S), S))), V))
% 4.82/0.94 = { by lemma 4 R->L }
% 4.82/0.94 multiply(inverse(multiply(U, multiply(Z, X))), multiply(U, V))
% 4.82/0.94
% 4.82/0.94 Lemma 32: multiply(inverse(multiply(X, multiply(Y, inverse(multiply(Y, multiply(Z, inverse(Z))))))), X) = multiply(W, inverse(W)).
% 4.82/0.94 Proof:
% 4.82/0.94 multiply(inverse(multiply(X, multiply(Y, inverse(multiply(Y, multiply(Z, inverse(Z))))))), X)
% 4.82/0.94 = { by lemma 30 R->L }
% 4.82/0.94 multiply(inverse(multiply(X, multiply(Y, inverse(multiply(Y, multiply(Z, inverse(Z))))))), multiply(X, multiply(V, inverse(V))))
% 4.82/0.94 = { by lemma 31 R->L }
% 4.82/0.94 multiply(inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(V, inverse(V)))), multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(V, inverse(V))))
% 4.82/0.94 = { by lemma 26 }
% 4.82/0.95 multiply(W, inverse(W))
% 4.82/0.95
% 4.82/0.95 Lemma 33: inverse(multiply(inverse(X), multiply(X, inverse(Y)))) = Y.
% 4.82/0.95 Proof:
% 4.82/0.95 inverse(multiply(inverse(X), multiply(X, inverse(Y))))
% 4.82/0.95 = { by lemma 28 }
% 4.82/0.95 inverse(multiply(inverse(Y), multiply(Z, inverse(Z))))
% 4.82/0.95 = { by lemma 26 R->L }
% 4.82/0.95 inverse(multiply(inverse(Y), multiply(inverse(W), W)))
% 4.82/0.95 = { by lemma 12 R->L }
% 4.82/0.95 inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(V, U)), multiply(V, U)))))
% 4.82/0.95 = { by lemma 24 R->L }
% 4.82/0.95 inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(V, U)), multiply(V, multiply(U, multiply(inverse(T), T)))))))
% 4.82/0.95 = { by lemma 18 R->L }
% 4.82/0.95 inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), multiply(inverse(U), multiply(U, multiply(inverse(T), T)))))))
% 4.82/0.95 = { by lemma 28 }
% 4.82/0.95 inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), multiply(multiply(inverse(T), T), multiply(X2, inverse(X2)))))))
% 4.82/0.95 = { by lemma 14 }
% 4.82/0.95 inverse(multiply(inverse(Y), inverse(multiply(multiply(X2, inverse(X2)), multiply(inverse(Y2), Y2)))))
% 4.82/0.95 = { by lemma 26 }
% 4.82/0.95 inverse(multiply(inverse(Y), inverse(multiply(multiply(X2, inverse(X2)), multiply(Z2, inverse(Z2))))))
% 4.82/0.95 = { by lemma 29 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(Y), inverse(multiply(multiply(X2, inverse(X2)), multiply(Z2, inverse(Z2)))))))), W2))
% 4.82/0.95 = { by lemma 30 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(Y), inverse(multiply(multiply(X2, inverse(X2)), multiply(Z2, inverse(Z2)))))))), multiply(W2, multiply(V2, inverse(V2)))))
% 4.82/0.95 = { by lemma 32 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(Y), inverse(multiply(multiply(X2, inverse(X2)), multiply(Z2, inverse(Z2)))))))), multiply(W2, multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2))))
% 4.82/0.95 = { by lemma 26 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(Y), inverse(multiply(multiply(X2, inverse(X2)), multiply(inverse(X3), X3))))))), multiply(W2, multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2))))
% 4.82/0.95 = { by lemma 12 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(Y), inverse(multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2)), multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2))))))))), multiply(W2, multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2))))
% 4.82/0.95 = { by lemma 32 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2), inverse(multiply(inverse(multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2)), multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2))))))))), multiply(W2, multiply(inverse(multiply(U2, multiply(T2, inverse(multiply(T2, multiply(S2, inverse(S2))))))), U2))))
% 4.82/0.95 = { by axiom 1 (single_axiom) }
% 4.82/0.95 Y
% 4.82/0.95
% 4.82/0.95 Lemma 34: inverse(inverse(multiply(X, multiply(Y, inverse(Y))))) = X.
% 4.82/0.95 Proof:
% 4.82/0.95 inverse(inverse(multiply(X, multiply(Y, inverse(Y)))))
% 4.82/0.95 = { by lemma 28 R->L }
% 4.82/0.95 inverse(inverse(multiply(inverse(Z), multiply(Z, X))))
% 4.82/0.95 = { by lemma 33 R->L }
% 4.82/0.95 inverse(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(inverse(W), multiply(W, inverse(X))))))))
% 4.82/0.95 = { by lemma 33 }
% 4.82/0.95 inverse(multiply(inverse(W), multiply(W, inverse(X))))
% 4.82/0.95 = { by lemma 33 }
% 4.82/0.95 X
% 4.82/0.95
% 4.82/0.95 Lemma 35: inverse(multiply(X, inverse(multiply(Y, X)))) = Y.
% 4.82/0.95 Proof:
% 4.82/0.95 inverse(multiply(X, inverse(multiply(Y, X))))
% 4.82/0.95 = { by lemma 33 R->L }
% 4.82/0.95 inverse(multiply(X, inverse(multiply(Y, inverse(multiply(inverse(X), multiply(X, inverse(X))))))))
% 4.82/0.95 = { by lemma 26 R->L }
% 4.82/0.95 inverse(multiply(X, inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), Z)))))))
% 4.82/0.95 = { by lemma 12 R->L }
% 4.82/0.95 inverse(multiply(X, inverse(multiply(Y, inverse(multiply(inverse(X), inverse(multiply(inverse(inverse(X)), inverse(X)))))))))
% 4.82/0.95 = { by lemma 34 R->L }
% 4.82/0.95 inverse(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, inverse(multiply(inverse(X), inverse(multiply(inverse(inverse(X)), inverse(X))))))))), multiply(X, inverse(X)))))
% 4.82/0.95 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.95 inverse(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V))), inverse(multiply(inverse(X), inverse(multiply(inverse(inverse(X)), inverse(X))))))))), multiply(X, inverse(X)))))
% 4.82/0.95 = { by axiom 1 (single_axiom) }
% 4.82/0.95 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 4.82/0.95 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.95 inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 4.82/0.95 = { by axiom 1 (single_axiom) }
% 4.82/0.95 inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(Y, inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 4.82/0.95 = { by lemma 22 }
% 4.82/0.95 Y
% 4.82/0.95
% 4.82/0.95 Lemma 36: multiply(multiply(X, inverse(X)), Y) = Y.
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(multiply(X, inverse(X)), Y)
% 4.82/0.95 = { by lemma 26 R->L }
% 4.82/0.95 multiply(multiply(inverse(Z), Z), Y)
% 4.82/0.95 = { by lemma 23 }
% 4.82/0.95 Y
% 4.82/0.95
% 4.82/0.95 Lemma 37: multiply(V, multiply(inverse(inverse(multiply(inverse(multiply(U, V)), multiply(U, Z)))), W)) = multiply(X, multiply(inverse(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z)))), W)).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(V, multiply(inverse(inverse(multiply(inverse(multiply(U, V)), multiply(U, Z)))), W))
% 4.82/0.95 = { by lemma 7 R->L }
% 4.82/0.95 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, V)), multiply(U, Z)))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), multiply(inverse(inverse(multiply(inverse(multiply(U, V)), multiply(U, Z)))), W))
% 4.82/0.95 = { by lemma 4 R->L }
% 4.82/0.95 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z)))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), multiply(inverse(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z)))), W))
% 4.82/0.95 = { by lemma 7 }
% 4.82/0.95 multiply(X, multiply(inverse(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z)))), W))
% 4.82/0.95
% 4.82/0.95 Lemma 38: multiply(Z, multiply(inverse(Z), Y)) = multiply(X, multiply(inverse(X), Y)).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(Z, multiply(inverse(Z), Y))
% 4.82/0.95 = { by lemma 29 R->L }
% 4.82/0.95 multiply(Z, multiply(inverse(inverse(multiply(inverse(multiply(multiply(W, inverse(W)), Z)), multiply(W, inverse(W))))), Y))
% 4.82/0.95 = { by lemma 36 R->L }
% 4.82/0.95 multiply(Z, multiply(inverse(inverse(multiply(inverse(multiply(multiply(W, inverse(W)), Z)), multiply(multiply(W, inverse(W)), multiply(W, inverse(W)))))), Y))
% 4.82/0.95 = { by lemma 37 }
% 4.82/0.95 multiply(X, multiply(inverse(inverse(multiply(inverse(multiply(multiply(W, inverse(W)), X)), multiply(multiply(W, inverse(W)), multiply(W, inverse(W)))))), Y))
% 4.82/0.95 = { by lemma 36 }
% 4.82/0.95 multiply(X, multiply(inverse(inverse(multiply(inverse(multiply(multiply(W, inverse(W)), X)), multiply(W, inverse(W))))), Y))
% 4.82/0.95 = { by lemma 29 }
% 4.82/0.95 multiply(X, multiply(inverse(X), Y))
% 4.82/0.95
% 4.82/0.95 Lemma 39: multiply(X, multiply(inverse(X), Y)) = multiply(Y, multiply(Z, inverse(Z))).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(X, multiply(inverse(X), Y))
% 4.82/0.95 = { by lemma 38 }
% 4.82/0.95 multiply(Y, multiply(inverse(Y), Y))
% 4.82/0.95 = { by lemma 9 R->L }
% 4.82/0.95 multiply(Y, multiply(inverse(W), W))
% 4.82/0.95 = { by lemma 26 }
% 4.82/0.95 multiply(Y, multiply(Z, inverse(Z)))
% 4.82/0.95
% 4.82/0.95 Lemma 40: inverse(multiply(X, multiply(inverse(X), inverse(Y)))) = Y.
% 4.82/0.95 Proof:
% 4.82/0.95 inverse(multiply(X, multiply(inverse(X), inverse(Y))))
% 4.82/0.95 = { by lemma 35 R->L }
% 4.82/0.95 inverse(multiply(X, multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Y), Z)))))))
% 4.82/0.95 = { by lemma 33 R->L }
% 4.82/0.95 inverse(multiply(X, multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), multiply(Z, inverse(Z)))))))))))
% 4.82/0.95 = { by lemma 26 R->L }
% 4.82/0.95 inverse(multiply(X, multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), multiply(inverse(W), W))))))))))
% 4.82/0.95 = { by lemma 12 R->L }
% 4.82/0.95 inverse(multiply(X, multiply(inverse(X), inverse(multiply(Z, inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), inverse(multiply(inverse(inverse(Z)), inverse(Z))))))))))))
% 4.82/0.95 = { by lemma 39 }
% 4.82/0.95 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), inverse(multiply(inverse(inverse(Z)), inverse(Z))))))))), multiply(Z, inverse(Z))))
% 4.82/0.95 = { by axiom 1 (single_axiom) }
% 4.82/0.95 Y
% 4.82/0.95
% 4.82/0.95 Lemma 41: multiply(inverse(X), multiply(X, Y)) = multiply(Z, multiply(inverse(Z), Y)).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(inverse(X), multiply(X, Y))
% 4.82/0.95 = { by lemma 35 R->L }
% 4.82/0.95 multiply(inverse(multiply(X, inverse(multiply(inverse(X), X)))), multiply(X, Y))
% 4.82/0.95 = { by lemma 17 R->L }
% 4.82/0.95 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(X), X))), Y))
% 4.82/0.95 = { by lemma 38 R->L }
% 4.82/0.95 multiply(Z, multiply(inverse(Z), Y))
% 4.82/0.95
% 4.82/0.95 Lemma 42: inverse(multiply(X, multiply(inverse(X), Y))) = multiply(Z, inverse(multiply(Y, Z))).
% 4.82/0.95 Proof:
% 4.82/0.95 inverse(multiply(X, multiply(inverse(X), Y)))
% 4.82/0.95 = { by lemma 41 R->L }
% 4.82/0.95 inverse(multiply(inverse(W), multiply(W, Y)))
% 4.82/0.95 = { by lemma 35 R->L }
% 4.82/0.95 inverse(multiply(inverse(W), multiply(W, inverse(multiply(Z, inverse(multiply(Y, Z)))))))
% 4.82/0.95 = { by lemma 33 }
% 4.82/0.95 multiply(Z, inverse(multiply(Y, Z)))
% 4.82/0.95
% 4.82/0.95 Lemma 43: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 4.82/0.95 Proof:
% 4.82/0.95 inverse(multiply(inverse(X), Y))
% 4.82/0.95 = { by lemma 40 R->L }
% 4.82/0.95 inverse(multiply(inverse(X), inverse(multiply(Z, multiply(inverse(Z), inverse(Y))))))
% 4.82/0.95 = { by lemma 42 }
% 4.82/0.95 inverse(multiply(inverse(X), multiply(X, inverse(multiply(inverse(Y), X)))))
% 4.82/0.95 = { by lemma 33 }
% 4.82/0.95 multiply(inverse(Y), X)
% 4.82/0.95
% 4.82/0.95 Lemma 44: multiply(multiply(Z, inverse(Z)), X) = multiply(X, multiply(Y, inverse(Y))).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(multiply(Z, inverse(Z)), X)
% 4.82/0.95 = { by lemma 29 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(V2, multiply(multiply(Z, inverse(Z)), X))), V2))
% 4.82/0.95 = { by lemma 26 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(V2, multiply(multiply(inverse(U2), U2), X))), V2))
% 4.82/0.95 = { by lemma 12 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(Y2), Y2)), X))), V2))
% 4.82/0.95 = { by lemma 24 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(Y2), Y2)), X))), multiply(V2, multiply(inverse(multiply(inverse(Y2), Y2)), multiply(inverse(Y2), Y2)))))
% 4.82/0.95 = { by lemma 19 }
% 4.82/0.95 inverse(multiply(multiply(inverse(X), multiply(inverse(Y2), Y2)), multiply(inverse(W2), W2)))
% 4.82/0.95 = { by lemma 26 }
% 4.82/0.95 inverse(multiply(multiply(inverse(X), multiply(inverse(Y2), Y2)), multiply(Z2, inverse(Z2))))
% 4.82/0.95 = { by lemma 28 R->L }
% 4.82/0.95 inverse(multiply(inverse(X2), multiply(X2, multiply(inverse(X), multiply(inverse(Y2), Y2)))))
% 4.82/0.95 = { by lemma 26 }
% 4.82/0.95 inverse(multiply(inverse(X2), multiply(X2, multiply(inverse(X), multiply(V, inverse(V))))))
% 4.82/0.95 = { by lemma 28 }
% 4.82/0.95 inverse(multiply(multiply(inverse(X), multiply(V, inverse(V))), multiply(S, inverse(S))))
% 4.82/0.95 = { by lemma 26 R->L }
% 4.82/0.95 inverse(multiply(multiply(inverse(X), multiply(V, inverse(V))), multiply(inverse(T), T)))
% 4.82/0.95 = { by lemma 19 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(U, multiply(W, X))), multiply(U, multiply(W, multiply(V, inverse(V))))))
% 4.82/0.95 = { by lemma 31 R->L }
% 4.82/0.95 inverse(multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), multiply(inverse(multiply(W, multiply(V, inverse(V)))), multiply(W, multiply(V, inverse(V))))))
% 4.82/0.95 = { by lemma 26 }
% 4.82/0.95 inverse(multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y)))))))
% 4.82/0.95 = { by lemma 33 }
% 4.82/0.95 multiply(X, multiply(Y, inverse(Y)))
% 4.82/0.95
% 4.82/0.95 Lemma 45: multiply(multiply(X, inverse(X)), Y) = multiply(Z, multiply(inverse(Z), Y)).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(multiply(X, inverse(X)), Y)
% 4.82/0.95 = { by lemma 44 }
% 4.82/0.95 multiply(Y, multiply(W, inverse(W)))
% 4.82/0.95 = { by lemma 39 R->L }
% 4.82/0.95 multiply(Z, multiply(inverse(Z), Y))
% 4.82/0.95
% 4.82/0.95 Lemma 46: multiply(inverse(multiply(X, inverse(Y))), X) = multiply(Z, multiply(inverse(Z), Y)).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(inverse(multiply(X, inverse(Y))), X)
% 4.82/0.95 = { by lemma 20 R->L }
% 4.82/0.95 multiply(multiply(inverse(W), W), inverse(multiply(inverse(X), multiply(X, inverse(Y)))))
% 4.82/0.95 = { by lemma 33 }
% 4.82/0.95 multiply(multiply(inverse(W), W), Y)
% 4.82/0.95 = { by lemma 26 }
% 4.82/0.95 multiply(multiply(V, inverse(V)), Y)
% 4.82/0.95 = { by lemma 45 }
% 4.82/0.95 multiply(Z, multiply(inverse(Z), Y))
% 4.82/0.95
% 4.82/0.95 Lemma 47: multiply(X, multiply(inverse(X), Y)) = Y.
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(X, multiply(inverse(X), Y))
% 4.82/0.95 = { by lemma 46 R->L }
% 4.82/0.95 multiply(inverse(multiply(Z, inverse(Y))), Z)
% 4.82/0.95 = { by lemma 43 R->L }
% 4.82/0.95 inverse(multiply(inverse(Z), multiply(Z, inverse(Y))))
% 4.82/0.95 = { by lemma 33 }
% 4.82/0.95 Y
% 4.82/0.95
% 4.82/0.95 Lemma 48: multiply(X, multiply(inverse(multiply(Y, X)), Z)) = multiply(inverse(Y), Z).
% 4.82/0.95 Proof:
% 4.82/0.95 multiply(X, multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.95 = { by lemma 35 R->L }
% 4.82/0.95 multiply(inverse(multiply(W, inverse(multiply(X, W)))), multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.95 = { by lemma 42 R->L }
% 4.82/0.95 multiply(inverse(inverse(multiply(V, multiply(inverse(V), X)))), multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.96 = { by lemma 45 R->L }
% 4.82/0.96 multiply(inverse(inverse(multiply(multiply(U, inverse(U)), X))), multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.96 = { by lemma 33 R->L }
% 4.82/0.96 multiply(inverse(inverse(multiply(inverse(Y), multiply(Y, inverse(inverse(multiply(multiply(U, inverse(U)), X))))))), multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.96 = { by lemma 44 }
% 4.82/0.96 multiply(inverse(inverse(multiply(inverse(Y), multiply(Y, inverse(inverse(multiply(X, multiply(T, inverse(T))))))))), multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.96 = { by lemma 34 }
% 4.82/0.96 multiply(inverse(inverse(multiply(inverse(Y), multiply(Y, X)))), multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.96 = { by lemma 43 }
% 4.82/0.96 multiply(inverse(multiply(inverse(multiply(Y, X)), Y)), multiply(inverse(multiply(Y, X)), Z))
% 4.82/0.96 = { by lemma 7 R->L }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(multiply(inverse(multiply(Y, X)), Y)), multiply(inverse(multiply(Y, X)), Z)))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 4 }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(X2), X2), Y)), multiply(multiply(inverse(X2), X2), Z)))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 21 }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(Y), multiply(multiply(inverse(X2), X2), Z)))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 45 R->L }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y2, inverse(Y2)), multiply(multiply(inverse(X2), X2), Z))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 12 R->L }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y2, inverse(Y2)), multiply(inverse(multiply(inverse(Z2), Z2)), Z))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 11 R->L }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y2, inverse(Y2)), multiply(inverse(inverse(multiply(inverse(multiply(W2, multiply(Y2, inverse(Y2)))), multiply(W2, multiply(Y2, inverse(Y2)))))), Z))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 37 R->L }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y2, inverse(Y2)), Y)), multiply(multiply(Y2, inverse(Y2)), multiply(Y2, inverse(Y2)))))), Z))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 36 }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y2, inverse(Y2)), Y)), multiply(Y2, inverse(Y2))))), Z))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 29 }
% 4.82/0.96 inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(Y), Z))), multiply(Y, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S))))))
% 4.82/0.96 = { by lemma 7 }
% 4.82/0.96 multiply(inverse(Y), Z)
% 4.82/0.96
% 4.82/0.96 Lemma 49: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 4.82/0.96 Proof:
% 4.82/0.96 multiply(X, inverse(multiply(Y, X)))
% 4.82/0.96 = { by lemma 47 R->L }
% 4.82/0.96 multiply(X, multiply(Z, multiply(inverse(Z), inverse(multiply(Y, X)))))
% 4.82/0.96 = { by lemma 45 R->L }
% 4.82/0.96 multiply(X, multiply(multiply(W, inverse(W)), inverse(multiply(Y, X))))
% 4.82/0.96 = { by lemma 44 }
% 4.82/0.96 multiply(X, multiply(inverse(multiply(Y, X)), multiply(V, inverse(V))))
% 4.82/0.96 = { by lemma 48 }
% 4.82/0.96 multiply(inverse(Y), multiply(V, inverse(V)))
% 4.82/0.96 = { by lemma 26 R->L }
% 4.82/0.96 multiply(inverse(Y), multiply(inverse(U), U))
% 4.82/0.96 = { by lemma 14 R->L }
% 4.82/0.96 multiply(multiply(inverse(T), T), multiply(multiply(inverse(S), S), inverse(Y)))
% 4.82/0.96 = { by lemma 23 }
% 4.82/0.96 multiply(multiply(inverse(T), T), inverse(Y))
% 4.82/0.96 = { by lemma 23 }
% 4.82/0.96 inverse(Y)
% 4.82/0.96
% 4.82/0.96 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 4.82/0.96 Proof:
% 4.82/0.96 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 4.82/0.96 = { by lemma 26 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 4.82/0.96 = { by lemma 26 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3))
% 4.82/0.96 = { by lemma 44 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), multiply(a2, multiply(Z, inverse(Z))), multiply(multiply(a3, b3), c3))
% 4.82/0.96 = { by lemma 39 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), multiply(W, multiply(inverse(W), a2)), multiply(multiply(a3, b3), c3))
% 4.82/0.96 = { by lemma 47 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 4.82/0.96 = { by axiom 1 (single_axiom) R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))), multiply(a3, b3)))))
% 4.82/0.96 = { by lemma 49 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, inverse(inverse(multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3))))))))))
% 4.82/0.96 = { by lemma 25 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3))))))))
% 4.82/0.96 = { by lemma 49 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(c3), multiply(V, inverse(multiply(multiply(b3, inverse(multiply(inverse(b3), b3))), V)))))))
% 4.82/0.96 = { by lemma 42 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(U, multiply(inverse(U), multiply(b3, inverse(multiply(inverse(b3), b3))))))))))
% 4.82/0.96 = { by lemma 46 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), inverse(c3)))))))
% 4.82/0.96 = { by lemma 47 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(T, multiply(inverse(T), inverse(multiply(inverse(c3), inverse(multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), inverse(c3)))))))))
% 4.82/0.96 = { by lemma 45 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(S, inverse(S)), inverse(multiply(inverse(c3), inverse(multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), inverse(c3))))))))
% 4.82/0.96 = { by lemma 26 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(c3), inverse(multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), inverse(c3))))))))
% 4.82/0.96 = { by lemma 16 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(multiply(inverse(Y2), Y2), inverse(multiply(multiply(inverse(Z2), Z2), multiply(inverse(multiply(inverse(c3), inverse(multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), inverse(c3))))), multiply(inverse(c3), c3))))))))
% 4.82/0.96 = { by lemma 26 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(multiply(inverse(Y2), Y2), inverse(multiply(multiply(W2, inverse(W2)), multiply(inverse(multiply(inverse(c3), inverse(multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), inverse(c3))))), multiply(inverse(c3), c3))))))))
% 4.82/0.96 = { by lemma 26 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(multiply(V2, inverse(V2)), inverse(multiply(multiply(W2, inverse(W2)), multiply(inverse(multiply(inverse(c3), inverse(multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), inverse(c3))))), multiply(inverse(c3), c3))))))))
% 4.82/0.96 = { by lemma 49 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(multiply(V2, inverse(V2)), inverse(multiply(multiply(W2, inverse(W2)), multiply(inverse(inverse(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))), multiply(inverse(c3), c3))))))))
% 4.82/0.96 = { by lemma 45 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(U2, multiply(inverse(U2), inverse(multiply(multiply(W2, inverse(W2)), multiply(inverse(inverse(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))), multiply(inverse(c3), c3)))))))))
% 4.82/0.96 = { by lemma 40 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(W2, inverse(W2)), multiply(inverse(inverse(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))), multiply(inverse(c3), c3)))))
% 4.82/0.96 = { by lemma 45 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(T2, multiply(inverse(T2), multiply(inverse(inverse(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))), multiply(inverse(c3), c3))))))
% 4.82/0.96 = { by lemma 47 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(inverse(inverse(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))), multiply(inverse(c3), c3))))
% 4.82/0.96 = { by lemma 25 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), multiply(inverse(c3), c3))))
% 4.82/0.96 = { by lemma 47 R->L }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(b3, inverse(multiply(inverse(b3), b3))), multiply(inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))), multiply(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))), multiply(inverse(c3), c3))))))
% 4.82/0.96 = { by lemma 48 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(b3, inverse(multiply(inverse(b3), b3))), multiply(inverse(inverse(c3)), multiply(inverse(c3), c3)))))
% 4.82/0.96 = { by lemma 41 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(b3, inverse(multiply(inverse(b3), b3))), multiply(S2, multiply(inverse(S2), c3)))))
% 4.82/0.96 = { by lemma 47 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(b3, inverse(multiply(inverse(b3), b3))), c3)))
% 4.82/0.96 = { by lemma 49 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(inverse(inverse(b3)), c3)))
% 4.82/0.96 = { by lemma 25 }
% 4.82/0.96 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 4.82/0.96 = { by lemma 26 R->L }
% 4.82/0.96 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 4.82/0.96 % SZS output end Proof
% 4.82/0.96
% 4.82/0.96 RESULT: Unsatisfiable (the axioms are contradictory).
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