TSTP Solution File: GRP473-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP473-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n027.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 01:18:34 EDT 2023
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP473-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % 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 : n027.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 : Mon Aug 28 22:34:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.55
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55
% 0.20/0.58 % SZS output start Proof
% 0.20/0.58 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.20/0.58 Axiom 2 (single_axiom): divide(divide(inverse(divide(X, Y)), divide(divide(Z, W), X)), divide(W, Z)) = Y.
% 0.20/0.58
% 0.20/0.58 Lemma 3: divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W))) = Z.
% 0.20/0.58 Proof:
% 0.20/0.58 divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W)))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 divide(divide(inverse(divide(divide(X, Y), Z)), W), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 0.20/0.58 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.58 divide(divide(inverse(divide(divide(X, Y), Z)), divide(divide(inverse(divide(V, W)), divide(divide(Y, X), V)), divide(X, Y))), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 0.20/0.58 = { by axiom 2 (single_axiom) }
% 0.20/0.58 Z
% 0.20/0.58
% 0.20/0.58 Lemma 4: divide(divide(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), divide(U, Y))) = divide(W, Z).
% 0.20/0.58 Proof:
% 0.20/0.58 divide(divide(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), divide(U, Y)))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 divide(divide(inverse(X), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), divide(U, Y)))
% 0.20/0.58 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.58 divide(divide(inverse(divide(divide(inverse(divide(V, X)), divide(divide(Z, W), V)), divide(W, Z))), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), divide(U, Y)))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 divide(W, Z)
% 0.20/0.58
% 0.20/0.58 Lemma 5: multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X)))) = divide(V, W).
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X))))
% 0.20/0.58 = { by lemma 3 R->L }
% 0.20/0.58 divide(divide(inverse(divide(divide(inverse(divide(divide(Y, X), U)), divide(divide(W, V), divide(Y, X))), multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X)))))), T), multiply(divide(divide(divide(divide(W, V), divide(Y, X)), inverse(divide(divide(Y, X), U))), S), divide(S, T)))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 divide(divide(inverse(U), T), multiply(divide(divide(divide(divide(W, V), divide(Y, X)), inverse(divide(divide(Y, X), U))), S), divide(S, T)))
% 0.20/0.58 = { by axiom 1 (multiply) R->L }
% 0.20/0.58 divide(divide(inverse(U), T), multiply(divide(multiply(divide(divide(W, V), divide(Y, X)), divide(divide(Y, X), U)), S), divide(S, T)))
% 0.20/0.58 = { by lemma 4 }
% 0.20/0.58 divide(V, W)
% 0.20/0.58
% 0.20/0.58 Lemma 6: divide(multiply(divide(multiply(divide(divide(X, Y), Z), divide(Z, W)), V), divide(V, U)), divide(inverse(W), U)) = divide(X, Y).
% 0.20/0.58 Proof:
% 0.20/0.58 divide(multiply(divide(multiply(divide(divide(X, Y), Z), divide(Z, W)), V), divide(V, U)), divide(inverse(W), U))
% 0.20/0.58 = { by lemma 4 R->L }
% 0.20/0.58 divide(divide(inverse(T), S), multiply(divide(multiply(divide(divide(divide(inverse(W), U), multiply(divide(multiply(divide(divide(X, Y), Z), divide(Z, W)), V), divide(V, U))), X2), divide(X2, T)), Y2), divide(Y2, S)))
% 0.20/0.58 = { by lemma 4 }
% 0.20/0.58 divide(divide(inverse(T), S), multiply(divide(multiply(divide(divide(Y, X), X2), divide(X2, T)), Y2), divide(Y2, S)))
% 0.20/0.58 = { by lemma 4 }
% 0.20/0.59 divide(X, Y)
% 0.20/0.59
% 0.20/0.59 Lemma 7: divide(multiply(divide(divide(X, Y), Z), divide(Z, W)), divide(inverse(divide(divide(Y, X), divide(V, U))), W)) = divide(U, V).
% 0.20/0.59 Proof:
% 0.20/0.59 divide(multiply(divide(divide(X, Y), Z), divide(Z, W)), divide(inverse(divide(divide(Y, X), divide(V, U))), W))
% 0.20/0.59 = { by lemma 5 R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(divide(U, V), T), divide(T, divide(divide(Y, X), divide(V, U)))), Z), divide(Z, W)), divide(inverse(divide(divide(Y, X), divide(V, U))), W))
% 0.20/0.59 = { by lemma 6 }
% 0.20/0.59 divide(U, V)
% 0.20/0.59
% 0.20/0.59 Lemma 8: divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V)) = X.
% 0.20/0.59 Proof:
% 0.20/0.59 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V))
% 0.20/0.59 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T)), Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V))
% 0.20/0.59 = { by lemma 6 }
% 0.20/0.59 divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T))
% 0.20/0.59 = { by axiom 2 (single_axiom) }
% 0.20/0.59 X
% 0.20/0.59
% 0.20/0.59 Lemma 9: multiply(divide(X, W), divide(W, Z)) = multiply(divide(X, Y), divide(Y, Z)).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(divide(X, W), divide(W, Z))
% 0.20/0.59 = { by lemma 8 R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(multiply(divide(X, W), divide(W, Z)), S), divide(S, U)), divide(inverse(Z), U)), divide(divide(inverse(Z), U), T)), divide(inverse(U), T))
% 0.20/0.59 = { by lemma 8 }
% 0.20/0.59 divide(multiply(X, divide(divide(inverse(Z), U), T)), divide(inverse(U), T))
% 0.20/0.59 = { by lemma 8 R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), V), divide(V, U)), divide(inverse(Z), U)), divide(divide(inverse(Z), U), T)), divide(inverse(U), T))
% 0.20/0.59 = { by lemma 8 }
% 0.20/0.59 multiply(divide(X, Y), divide(Y, Z))
% 0.20/0.59
% 0.20/0.59 Lemma 10: multiply(divide(X, divide(inverse(divide(Y, Z)), divide(divide(W, V), Y))), Z) = multiply(divide(X, U), divide(U, divide(V, W))).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(divide(X, divide(inverse(divide(Y, Z)), divide(divide(W, V), Y))), Z)
% 0.20/0.59 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.59 multiply(divide(X, divide(inverse(divide(Y, Z)), divide(divide(W, V), Y))), divide(divide(inverse(divide(Y, Z)), divide(divide(W, V), Y)), divide(V, W)))
% 0.20/0.59 = { by lemma 9 R->L }
% 0.20/0.59 multiply(divide(X, U), divide(U, divide(V, W)))
% 0.20/0.59
% 0.20/0.59 Lemma 11: divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(divide(W, V), divide(V, W)), U), divide(U, Z))) = divide(Y, X).
% 0.20/0.59 Proof:
% 0.20/0.59 divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(divide(W, V), divide(V, W)), U), divide(U, Z)))
% 0.20/0.59 = { by lemma 7 R->L }
% 0.20/0.59 divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(divide(multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T)))), divide(inverse(divide(divide(S, T), divide(V, W))), divide(divide(Y, X), divide(S, T)))), divide(V, W)), U), divide(U, Z)))
% 0.20/0.59 = { by lemma 10 }
% 0.20/0.59 divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(divide(multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T)))), Y2), divide(Y2, divide(X, Y))), U), divide(U, Z)))
% 0.20/0.59 = { by lemma 5 }
% 0.20/0.59 divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(divide(divide(X, Y), Y2), divide(Y2, divide(X, Y))), U), divide(U, Z)))
% 0.20/0.59 = { by lemma 4 }
% 0.20/0.59 divide(Y, X)
% 0.20/0.59
% 0.20/0.59 Lemma 12: divide(X, divide(inverse(divide(Y, Z)), divide(Z, Y))) = X.
% 0.20/0.59 Proof:
% 0.20/0.59 divide(X, divide(inverse(divide(Y, Z)), divide(Z, Y)))
% 0.20/0.59 = { by lemma 11 R->L }
% 0.20/0.59 divide(divide(inverse(divide(divide(inverse(divide(Y, Z)), divide(Z, Y)), X)), W), multiply(divide(multiply(divide(Z, Y), divide(Y, Z)), V), divide(V, W)))
% 0.20/0.59 = { by axiom 1 (multiply) }
% 0.20/0.59 divide(divide(inverse(divide(divide(inverse(divide(Y, Z)), divide(Z, Y)), X)), W), multiply(divide(divide(divide(Z, Y), inverse(divide(Y, Z))), V), divide(V, W)))
% 0.20/0.59 = { by lemma 3 }
% 0.20/0.59 X
% 0.20/0.59
% 0.20/0.59 Lemma 13: multiply(X, divide(inverse(divide(Y, Z)), divide(Z, Y))) = multiply(divide(X, W), W).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(X, divide(inverse(divide(Y, Z)), divide(Z, Y)))
% 0.20/0.59 = { by lemma 12 R->L }
% 0.20/0.59 multiply(divide(X, divide(inverse(divide(Y, Z)), divide(Z, Y))), divide(inverse(divide(Y, Z)), divide(Z, Y)))
% 0.20/0.59 = { by lemma 12 R->L }
% 0.20/0.59 multiply(divide(X, divide(inverse(divide(Y, Z)), divide(Z, Y))), divide(divide(inverse(divide(Y, Z)), divide(Z, Y)), divide(inverse(divide(V, U)), divide(U, V))))
% 0.20/0.59 = { by lemma 9 R->L }
% 0.20/0.59 multiply(divide(X, W), divide(W, divide(inverse(divide(V, U)), divide(U, V))))
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 multiply(divide(X, W), W)
% 0.20/0.59
% 0.20/0.59 Lemma 14: multiply(divide(X, Y), Y) = X.
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(divide(X, Y), Y)
% 0.20/0.59 = { by lemma 13 R->L }
% 0.20/0.59 multiply(X, divide(inverse(divide(Z, W)), divide(W, Z)))
% 0.20/0.59 = { by axiom 1 (multiply) }
% 0.20/0.59 divide(X, inverse(divide(inverse(divide(Z, W)), divide(W, Z))))
% 0.20/0.59 = { by lemma 11 R->L }
% 0.20/0.59 divide(divide(inverse(divide(inverse(divide(inverse(divide(Z, W)), divide(W, Z))), X)), divide(inverse(divide(V, U)), divide(U, V))), multiply(divide(multiply(divide(T, S), divide(S, T)), X2), divide(X2, divide(inverse(divide(V, U)), divide(U, V)))))
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 divide(inverse(divide(inverse(divide(inverse(divide(Z, W)), divide(W, Z))), X)), multiply(divide(multiply(divide(T, S), divide(S, T)), X2), divide(X2, divide(inverse(divide(V, U)), divide(U, V)))))
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 divide(inverse(divide(inverse(divide(inverse(divide(Z, W)), divide(W, Z))), X)), multiply(divide(multiply(divide(T, S), divide(S, T)), X2), X2))
% 0.20/0.59 = { by lemma 13 R->L }
% 0.20/0.59 divide(inverse(divide(inverse(divide(inverse(divide(Z, W)), divide(W, Z))), X)), multiply(multiply(divide(T, S), divide(S, T)), divide(inverse(divide(Z, W)), divide(W, Z))))
% 0.20/0.59 = { by axiom 1 (multiply) }
% 0.20/0.59 divide(inverse(divide(inverse(divide(inverse(divide(Z, W)), divide(W, Z))), X)), multiply(divide(divide(T, S), inverse(divide(S, T))), divide(inverse(divide(Z, W)), divide(W, Z))))
% 0.20/0.59 = { by lemma 12 R->L }
% 0.20/0.59 divide(divide(inverse(divide(inverse(divide(inverse(divide(Z, W)), divide(W, Z))), X)), multiply(divide(divide(T, S), inverse(divide(S, T))), divide(inverse(divide(Z, W)), divide(W, Z)))), divide(inverse(divide(S, T)), divide(T, S)))
% 0.20/0.59 = { by axiom 1 (multiply) }
% 0.20/0.59 divide(divide(inverse(divide(inverse(divide(inverse(divide(Z, W)), divide(W, Z))), X)), divide(divide(divide(T, S), inverse(divide(S, T))), inverse(divide(inverse(divide(Z, W)), divide(W, Z))))), divide(inverse(divide(S, T)), divide(T, S)))
% 0.20/0.59 = { by axiom 2 (single_axiom) }
% 0.20/0.59 X
% 0.20/0.59
% 0.20/0.59 Lemma 15: multiply(multiply(X, Y), inverse(Y)) = multiply(divide(X, Z), Z).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(multiply(X, Y), inverse(Y))
% 0.20/0.59 = { by lemma 12 R->L }
% 0.20/0.59 multiply(multiply(X, Y), divide(inverse(Y), divide(inverse(divide(W, V)), divide(V, W))))
% 0.20/0.59 = { by axiom 1 (multiply) }
% 0.20/0.59 multiply(divide(X, inverse(Y)), divide(inverse(Y), divide(inverse(divide(W, V)), divide(V, W))))
% 0.20/0.59 = { by lemma 9 R->L }
% 0.20/0.59 multiply(divide(X, Z), divide(Z, divide(inverse(divide(W, V)), divide(V, W))))
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 multiply(divide(X, Z), Z)
% 0.20/0.59
% 0.20/0.59 Lemma 16: multiply(divide(X, X), Y) = Y.
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(divide(X, X), Y)
% 0.20/0.59 = { by lemma 14 R->L }
% 0.20/0.59 multiply(multiply(divide(divide(X, X), Z), Z), Y)
% 0.20/0.59 = { by lemma 8 R->L }
% 0.20/0.59 multiply(multiply(divide(divide(multiply(divide(multiply(divide(divide(X, X), W), divide(W, divide(inverse(divide(V, U)), divide(U, V)))), divide(inverse(X), divide(inverse(divide(V, U)), divide(U, V)))), divide(divide(inverse(X), divide(inverse(divide(V, U)), divide(U, V))), T)), divide(inverse(divide(inverse(divide(V, U)), divide(U, V))), T)), Z), Z), Y)
% 0.20/0.59 = { by lemma 8 R->L }
% 0.20/0.59 multiply(multiply(divide(divide(multiply(divide(multiply(divide(multiply(divide(divide(multiply(divide(divide(X, X), W), divide(W, divide(inverse(divide(V, U)), divide(U, V)))), divide(inverse(X), divide(inverse(divide(V, U)), divide(U, V)))), X), divide(X, X)), S), divide(S, divide(inverse(divide(V, U)), divide(U, V)))), divide(inverse(X), divide(inverse(divide(V, U)), divide(U, V)))), divide(divide(inverse(X), divide(inverse(divide(V, U)), divide(U, V))), T)), divide(inverse(divide(inverse(divide(V, U)), divide(U, V))), T)), Z), Z), Y)
% 0.20/0.59 = { by lemma 8 }
% 0.20/0.59 multiply(multiply(divide(multiply(divide(divide(multiply(divide(divide(X, X), W), divide(W, divide(inverse(divide(V, U)), divide(U, V)))), divide(inverse(X), divide(inverse(divide(V, U)), divide(U, V)))), X), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 multiply(multiply(divide(multiply(divide(divide(multiply(divide(divide(X, X), W), W), divide(inverse(X), divide(inverse(divide(V, U)), divide(U, V)))), X), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 multiply(multiply(divide(multiply(divide(divide(multiply(divide(divide(X, X), W), W), inverse(X)), X), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by lemma 14 R->L }
% 0.20/0.59 multiply(multiply(divide(multiply(multiply(divide(divide(divide(multiply(divide(divide(X, X), W), W), inverse(X)), X), X2), X2), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by lemma 15 R->L }
% 0.20/0.59 multiply(multiply(divide(multiply(multiply(multiply(divide(divide(multiply(divide(divide(X, X), W), W), inverse(X)), X), X), inverse(X)), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by lemma 14 }
% 0.20/0.59 multiply(multiply(divide(multiply(multiply(divide(multiply(divide(divide(X, X), W), W), inverse(X)), inverse(X)), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by lemma 14 }
% 0.20/0.59 multiply(multiply(divide(multiply(multiply(divide(divide(X, X), W), W), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by lemma 14 }
% 0.20/0.59 multiply(multiply(divide(multiply(divide(X, X), divide(X, X)), Z), Z), Y)
% 0.20/0.59 = { by axiom 1 (multiply) }
% 0.20/0.59 divide(multiply(divide(multiply(divide(X, X), divide(X, X)), Z), Z), inverse(Y))
% 0.20/0.59 = { by lemma 12 R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(X, X), divide(X, X)), Z), Z), divide(inverse(Y), divide(inverse(divide(Y2, Z2)), divide(Z2, Y2))))
% 0.20/0.59 = { by lemma 12 R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(X, X), divide(X, X)), Z), divide(Z, divide(inverse(divide(Y2, Z2)), divide(Z2, Y2)))), divide(inverse(Y), divide(inverse(divide(Y2, Z2)), divide(Z2, Y2))))
% 0.20/0.59 = { by lemma 7 R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(multiply(divide(divide(W2, V2), U2), divide(U2, divide(divide(T2, S2), divide(V2, W2)))), divide(inverse(divide(divide(V2, W2), divide(X, X))), divide(divide(T2, S2), divide(V2, W2)))), divide(X, X)), Z), divide(Z, divide(inverse(divide(Y2, Z2)), divide(Z2, Y2)))), divide(inverse(Y), divide(inverse(divide(Y2, Z2)), divide(Z2, Y2))))
% 0.20/0.59 = { by lemma 10 }
% 0.20/0.59 divide(multiply(divide(multiply(divide(multiply(divide(divide(W2, V2), U2), divide(U2, divide(divide(T2, S2), divide(V2, W2)))), X3), divide(X3, divide(S2, T2))), Z), divide(Z, divide(inverse(divide(Y2, Z2)), divide(Z2, Y2)))), divide(inverse(Y), divide(inverse(divide(Y2, Z2)), divide(Z2, Y2))))
% 0.20/0.59 = { by lemma 10 R->L }
% 0.20/0.59 divide(multiply(divide(multiply(divide(multiply(divide(divide(W2, V2), U2), divide(U2, divide(divide(T2, S2), divide(V2, W2)))), divide(inverse(divide(divide(V2, W2), divide(Y3, Y))), divide(divide(T2, S2), divide(V2, W2)))), divide(Y3, Y)), Z), divide(Z, divide(inverse(divide(Y2, Z2)), divide(Z2, Y2)))), divide(inverse(Y), divide(inverse(divide(Y2, Z2)), divide(Z2, Y2))))
% 0.20/0.59 = { by lemma 7 }
% 0.20/0.59 divide(multiply(divide(multiply(divide(Y, Y3), divide(Y3, Y)), Z), divide(Z, divide(inverse(divide(Y2, Z2)), divide(Z2, Y2)))), divide(inverse(Y), divide(inverse(divide(Y2, Z2)), divide(Z2, Y2))))
% 0.20/0.59 = { by lemma 8 }
% 0.20/0.59 Y
% 0.20/0.59
% 0.20/0.59 Lemma 17: multiply(X, inverse(X)) = divide(Y, Y).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(X, inverse(X))
% 0.20/0.59 = { by lemma 16 R->L }
% 0.20/0.59 multiply(multiply(divide(Y, Y), X), inverse(X))
% 0.20/0.59 = { by lemma 15 }
% 0.20/0.59 multiply(divide(divide(Y, Y), Z), Z)
% 0.20/0.59 = { by lemma 14 }
% 0.20/0.60 divide(Y, Y)
% 0.20/0.60
% 0.20/0.60 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.20/0.60 Proof:
% 0.20/0.60 multiply(multiply(inverse(b2), b2), a2)
% 0.20/0.60 = { by lemma 14 R->L }
% 0.20/0.60 multiply(multiply(inverse(b2), multiply(divide(b2, X), X)), a2)
% 0.20/0.60 = { by lemma 15 R->L }
% 0.20/0.60 multiply(multiply(inverse(b2), multiply(multiply(b2, inverse(b2)), inverse(inverse(b2)))), a2)
% 0.20/0.60 = { by lemma 17 }
% 0.20/0.60 multiply(multiply(inverse(b2), multiply(divide(Y, Y), inverse(inverse(b2)))), a2)
% 0.20/0.60 = { by lemma 16 }
% 0.20/0.60 multiply(multiply(inverse(b2), inverse(inverse(b2))), a2)
% 0.20/0.60 = { by lemma 17 }
% 0.20/0.60 multiply(divide(Z, Z), a2)
% 0.20/0.60 = { by lemma 16 }
% 0.20/0.60 a2
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60
% 0.20/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------