TSTP Solution File: GRP472-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP472-1 : 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 : 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 01:18:34 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP472-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n006.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 22:29:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.64 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.64
% 0.20/0.64 % SZS status Unsatisfiable
% 0.20/0.64
% 2.33/0.72 % SZS output start Proof
% 2.33/0.72 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 2.33/0.72 Axiom 2 (single_axiom): divide(divide(inverse(divide(X, Y)), divide(divide(Z, W), X)), divide(W, Z)) = Y.
% 2.33/0.72
% 2.33/0.72 Lemma 3: divide(divide(inverse(divide(X, Y)), divide(multiply(Z, W), X)), divide(inverse(W), Z)) = Y.
% 2.33/0.72 Proof:
% 2.33/0.72 divide(divide(inverse(divide(X, Y)), divide(multiply(Z, W), X)), divide(inverse(W), Z))
% 2.33/0.72 = { by axiom 1 (multiply) }
% 2.33/0.72 divide(divide(inverse(divide(X, Y)), divide(divide(Z, inverse(W)), X)), divide(inverse(W), Z))
% 2.33/0.72 = { by axiom 2 (single_axiom) }
% 2.33/0.72 Y
% 2.33/0.72
% 2.33/0.72 Lemma 4: divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W))) = Z.
% 2.33/0.72 Proof:
% 2.33/0.72 divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W)))
% 2.33/0.72 = { by axiom 1 (multiply) }
% 2.33/0.72 divide(divide(inverse(divide(divide(X, Y), Z)), W), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 2.33/0.72 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.72 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))))
% 2.33/0.72 = { by axiom 2 (single_axiom) }
% 2.33/0.72 Z
% 2.33/0.72
% 2.33/0.72 Lemma 5: divide(divide(inverse(X), Y), multiply(divide(multiply(divide(multiply(Z, W), V), divide(V, X)), U), divide(U, Y))) = divide(inverse(W), Z).
% 2.33/0.72 Proof:
% 2.33/0.72 divide(divide(inverse(X), Y), multiply(divide(multiply(divide(multiply(Z, W), V), divide(V, X)), U), divide(U, Y)))
% 2.33/0.72 = { by axiom 1 (multiply) }
% 2.33/0.72 divide(divide(inverse(X), Y), multiply(divide(divide(divide(multiply(Z, W), V), inverse(divide(V, X))), U), divide(U, Y)))
% 2.33/0.72 = { by lemma 3 R->L }
% 2.33/0.72 divide(divide(inverse(divide(divide(inverse(divide(V, X)), divide(multiply(Z, W), V)), divide(inverse(W), Z))), Y), multiply(divide(divide(divide(multiply(Z, W), V), inverse(divide(V, X))), U), divide(U, Y)))
% 2.33/0.72 = { by lemma 4 }
% 2.33/0.72 divide(inverse(W), Z)
% 2.33/0.72
% 2.33/0.72 Lemma 6: divide(divide(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), divide(U, Y))) = divide(W, Z).
% 2.33/0.72 Proof:
% 2.33/0.72 divide(divide(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), divide(U, Y)))
% 2.33/0.72 = { by axiom 1 (multiply) }
% 2.33/0.72 divide(divide(inverse(X), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), divide(U, Y)))
% 2.33/0.72 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.72 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)))
% 2.33/0.72 = { by lemma 4 }
% 2.33/0.72 divide(W, Z)
% 2.33/0.72
% 2.33/0.72 Lemma 7: divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V)) = X.
% 2.33/0.72 Proof:
% 2.33/0.72 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V))
% 2.33/0.72 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.72 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))
% 2.33/0.72 = { by lemma 6 R->L }
% 2.33/0.72 divide(divide(inverse(X2), Y2), multiply(divide(multiply(divide(divide(divide(inverse(Z), V), 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))), Z2), divide(Z2, X2)), W2), divide(W2, Y2)))
% 2.33/0.72 = { by lemma 6 }
% 2.33/0.73 divide(divide(inverse(X2), Y2), multiply(divide(multiply(divide(divide(divide(S, T), divide(inverse(divide(U, X)), divide(divide(T, S), U))), Z2), divide(Z2, X2)), W2), divide(W2, Y2)))
% 2.33/0.73 = { by lemma 6 }
% 2.33/0.73 divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T))
% 2.33/0.73 = { by axiom 2 (single_axiom) }
% 2.33/0.73 X
% 2.33/0.73
% 2.33/0.73 Lemma 8: multiply(divide(X, W), divide(W, Z)) = multiply(divide(X, Y), divide(Y, Z)).
% 2.33/0.73 Proof:
% 2.33/0.73 multiply(divide(X, W), divide(W, Z))
% 2.33/0.73 = { by lemma 7 R->L }
% 2.33/0.73 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))
% 2.33/0.73 = { by lemma 7 }
% 2.33/0.73 divide(multiply(X, divide(divide(inverse(Z), U), T)), divide(inverse(U), T))
% 2.33/0.73 = { by lemma 7 R->L }
% 2.33/0.73 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))
% 2.33/0.73 = { by lemma 7 }
% 2.33/0.73 multiply(divide(X, Y), divide(Y, Z))
% 2.33/0.73
% 2.33/0.73 Lemma 9: divide(divide(inverse(divide(inverse(divide(X, Y)), Z)), multiply(divide(W, V), divide(V, Y))), divide(X, W)) = Z.
% 2.33/0.73 Proof:
% 2.33/0.73 divide(divide(inverse(divide(inverse(divide(X, Y)), Z)), multiply(divide(W, V), divide(V, Y))), divide(X, W))
% 2.33/0.73 = { by lemma 8 }
% 2.33/0.73 divide(divide(inverse(divide(inverse(divide(X, Y)), Z)), multiply(divide(W, X), divide(X, Y))), divide(X, W))
% 2.33/0.73 = { by axiom 1 (multiply) }
% 2.33/0.73 divide(divide(inverse(divide(inverse(divide(X, Y)), Z)), divide(divide(W, X), inverse(divide(X, Y)))), divide(X, W))
% 2.33/0.73 = { by axiom 2 (single_axiom) }
% 2.33/0.73 Z
% 2.33/0.73
% 2.33/0.73 Lemma 10: divide(divide(inverse(divide(inverse(divide(X, Y)), divide(Z, X))), multiply(divide(W, V), divide(V, Y))), divide(U, W)) = divide(Z, U).
% 2.33/0.73 Proof:
% 2.33/0.73 divide(divide(inverse(divide(inverse(divide(X, Y)), divide(Z, X))), multiply(divide(W, V), divide(V, Y))), divide(U, W))
% 2.33/0.73 = { by lemma 5 R->L }
% 2.33/0.73 divide(divide(inverse(divide(divide(inverse(T), S), multiply(divide(multiply(divide(multiply(divide(Z, X), divide(X, Y)), X2), divide(X2, T)), Y2), divide(Y2, S)))), multiply(divide(W, V), divide(V, Y))), divide(U, W))
% 2.33/0.73 = { by lemma 8 }
% 2.33/0.73 divide(divide(inverse(divide(divide(inverse(T), S), multiply(divide(multiply(divide(multiply(divide(Z, U), divide(U, Y)), X2), divide(X2, T)), Y2), divide(Y2, S)))), multiply(divide(W, V), divide(V, Y))), divide(U, W))
% 2.33/0.73 = { by lemma 5 }
% 2.33/0.73 divide(divide(inverse(divide(inverse(divide(U, Y)), divide(Z, U))), multiply(divide(W, V), divide(V, Y))), divide(U, W))
% 2.33/0.73 = { by lemma 9 }
% 2.33/0.73 divide(Z, U)
% 2.33/0.73
% 2.33/0.73 Lemma 11: divide(multiply(X, divide(divide(inverse(Y), Z), W)), divide(inverse(Z), W)) = multiply(divide(X, V), divide(V, Y)).
% 2.33/0.73 Proof:
% 2.33/0.73 divide(multiply(X, divide(divide(inverse(Y), Z), W)), divide(inverse(Z), W))
% 2.33/0.73 = { by lemma 7 R->L }
% 2.33/0.73 divide(multiply(divide(multiply(divide(multiply(divide(X, V), divide(V, Y)), U), divide(U, Z)), divide(inverse(Y), Z)), divide(divide(inverse(Y), Z), W)), divide(inverse(Z), W))
% 2.33/0.73 = { by lemma 7 }
% 2.33/0.73 multiply(divide(X, V), divide(V, Y))
% 2.33/0.73
% 2.33/0.73 Lemma 12: multiply(divide(divide(X, divide(inverse(V), Z)), U), divide(U, V)) = multiply(divide(divide(X, divide(inverse(Y), Z)), W), divide(W, Y)).
% 2.33/0.73 Proof:
% 2.33/0.73 multiply(divide(divide(X, divide(inverse(V), Z)), U), divide(U, V))
% 2.33/0.73 = { by lemma 11 R->L }
% 2.33/0.73 divide(multiply(divide(X, divide(inverse(V), Z)), divide(divide(inverse(V), Z), T)), divide(inverse(Z), T))
% 2.33/0.73 = { by lemma 8 R->L }
% 2.33/0.73 divide(multiply(divide(X, divide(inverse(Y), Z)), divide(divide(inverse(Y), Z), T)), divide(inverse(Z), T))
% 2.33/0.73 = { by lemma 11 }
% 2.33/0.73 multiply(divide(divide(X, divide(inverse(Y), Z)), W), divide(W, Y))
% 2.33/0.73
% 2.33/0.73 Lemma 13: divide(divide(inverse(divide(X, Y)), divide(multiply(Z, Y), X)), divide(inverse(W), Z)) = W.
% 2.33/0.73 Proof:
% 2.33/0.73 divide(divide(inverse(divide(X, Y)), divide(multiply(Z, Y), X)), divide(inverse(W), Z))
% 2.33/0.73 = { by lemma 5 R->L }
% 2.33/0.73 divide(divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(multiply(Z, Y), X), divide(X, Y)), T), divide(T, V)), S), divide(S, U))), divide(inverse(W), Z))
% 2.33/0.73 = { by axiom 1 (multiply) }
% 2.33/0.73 divide(divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(divide(Z, inverse(Y)), X), divide(X, Y)), T), divide(T, V)), S), divide(S, U))), divide(inverse(W), Z))
% 2.33/0.73 = { by lemma 10 R->L }
% 2.33/0.73 divide(divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(divide(divide(inverse(divide(inverse(divide(X2, Y2)), divide(Z, X2))), multiply(divide(Z2, W2), divide(W2, Y2))), divide(inverse(Y), Z2)), X), divide(X, Y)), T), divide(T, V)), S), divide(S, U))), divide(inverse(W), Z))
% 2.33/0.73 = { by lemma 12 }
% 2.33/0.73 divide(divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(divide(divide(inverse(divide(inverse(divide(X2, Y2)), divide(Z, X2))), multiply(divide(Z2, W2), divide(W2, Y2))), divide(inverse(W), Z2)), V2), divide(V2, W)), T), divide(T, V)), S), divide(S, U))), divide(inverse(W), Z))
% 2.33/0.73 = { by lemma 10 }
% 2.33/0.73 divide(divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(divide(Z, inverse(W)), V2), divide(V2, W)), T), divide(T, V)), S), divide(S, U))), divide(inverse(W), Z))
% 2.33/0.73 = { by axiom 1 (multiply) R->L }
% 2.33/0.73 divide(divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(multiply(Z, W), V2), divide(V2, W)), T), divide(T, V)), S), divide(S, U))), divide(inverse(W), Z))
% 2.33/0.73 = { by lemma 5 }
% 2.33/0.73 divide(divide(inverse(divide(V2, W)), divide(multiply(Z, W), V2)), divide(inverse(W), Z))
% 2.33/0.73 = { by lemma 3 }
% 2.33/0.73 W
% 2.33/0.73
% 2.33/0.73 Lemma 14: divide(inverse(divide(Z, W)), divide(W, Z)) = divide(inverse(divide(X, Y)), divide(Y, X)).
% 2.33/0.73 Proof:
% 2.33/0.73 divide(inverse(divide(Z, W)), divide(W, Z))
% 2.33/0.73 = { by lemma 5 R->L }
% 2.33/0.73 divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(W, Z), divide(Z, W)), T), divide(T, V)), S), divide(S, U)))
% 2.33/0.73 = { by lemma 13 R->L }
% 2.33/0.73 divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(divide(divide(inverse(divide(X2, Y2)), divide(multiply(Z2, Y2), X2)), divide(inverse(W), Z2)), Z), divide(Z, W)), T), divide(T, V)), S), divide(S, U)))
% 2.33/0.73 = { by lemma 12 }
% 2.33/0.73 divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(divide(divide(inverse(divide(X2, Y2)), divide(multiply(Z2, Y2), X2)), divide(inverse(Y), Z2)), X), divide(X, Y)), T), divide(T, V)), S), divide(S, U)))
% 2.33/0.73 = { by lemma 13 }
% 2.33/0.73 divide(divide(inverse(V), U), multiply(divide(multiply(divide(multiply(divide(Y, X), divide(X, Y)), T), divide(T, V)), S), divide(S, U)))
% 2.33/0.73 = { by lemma 5 }
% 2.33/0.73 divide(inverse(divide(X, Y)), divide(Y, X))
% 2.33/0.73
% 2.33/0.73 Lemma 15: divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(inverse(Z), W)) = multiply(W, Z).
% 2.33/0.73 Proof:
% 2.33/0.73 divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(inverse(Z), W))
% 2.33/0.73 = { by lemma 14 }
% 2.33/0.73 divide(divide(inverse(divide(V, multiply(W, Z))), divide(multiply(W, Z), V)), divide(inverse(Z), W))
% 2.33/0.73 = { by lemma 3 }
% 2.33/0.73 multiply(W, Z)
% 2.33/0.73
% 2.33/0.73 Lemma 16: multiply(divide(divide(multiply(divide(X, Y), divide(Y, Z)), divide(inverse(W), Z)), V), divide(V, W)) = X.
% 2.33/0.73 Proof:
% 2.33/0.73 multiply(divide(divide(multiply(divide(X, Y), divide(Y, Z)), divide(inverse(W), Z)), V), divide(V, W))
% 2.33/0.73 = { by lemma 11 R->L }
% 2.33/0.73 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), divide(inverse(W), Z)), divide(divide(inverse(W), Z), U)), divide(inverse(Z), U))
% 2.33/0.73 = { by lemma 7 }
% 2.33/0.73 X
% 2.33/0.73
% 2.33/0.73 Lemma 17: divide(divide(inverse(divide(X, Y)), divide(Y, X)), multiply(Z, W)) = divide(inverse(W), Z).
% 2.33/0.73 Proof:
% 2.33/0.73 divide(divide(inverse(divide(X, Y)), divide(Y, X)), multiply(Z, W))
% 2.33/0.73 = { by lemma 14 }
% 2.33/0.73 divide(divide(inverse(divide(V, divide(inverse(W), Z))), divide(divide(inverse(W), Z), V)), multiply(Z, W))
% 2.33/0.73 = { by axiom 1 (multiply) }
% 2.33/0.73 divide(divide(inverse(divide(V, divide(inverse(W), Z))), divide(divide(inverse(W), Z), V)), divide(Z, inverse(W)))
% 2.33/0.73 = { by axiom 2 (single_axiom) }
% 2.33/0.73 divide(inverse(W), Z)
% 2.33/0.73
% 2.33/0.73 Lemma 18: divide(X, divide(inverse(divide(Y, Z)), divide(Z, Y))) = X.
% 2.33/0.73 Proof:
% 2.33/0.73 divide(X, divide(inverse(divide(Y, Z)), divide(Z, Y)))
% 2.33/0.73 = { by lemma 16 R->L }
% 2.33/0.73 divide(multiply(divide(divide(multiply(divide(X, W), divide(W, V)), divide(inverse(U), V)), T), divide(T, U)), divide(inverse(divide(Y, Z)), divide(Z, Y)))
% 2.33/0.73 = { by lemma 6 R->L }
% 2.33/0.73 divide(divide(inverse(S), X2), multiply(divide(multiply(divide(divide(divide(inverse(divide(Y, Z)), divide(Z, Y)), multiply(divide(divide(multiply(divide(X, W), divide(W, V)), divide(inverse(U), V)), T), divide(T, U))), Y2), divide(Y2, S)), Z2), divide(Z2, X2)))
% 2.33/0.73 = { by lemma 17 }
% 2.33/0.73 divide(divide(inverse(S), X2), multiply(divide(multiply(divide(divide(inverse(divide(T, U)), divide(divide(multiply(divide(X, W), divide(W, V)), divide(inverse(U), V)), T)), Y2), divide(Y2, S)), Z2), divide(Z2, X2)))
% 2.33/0.73 = { by lemma 6 }
% 2.33/0.73 divide(divide(divide(multiply(divide(X, W), divide(W, V)), divide(inverse(U), V)), T), inverse(divide(T, U)))
% 2.33/0.73 = { by axiom 1 (multiply) R->L }
% 2.33/0.73 multiply(divide(divide(multiply(divide(X, W), divide(W, V)), divide(inverse(U), V)), T), divide(T, U))
% 2.33/0.73 = { by lemma 16 }
% 2.33/0.73 X
% 2.33/0.73
% 2.33/0.73 Lemma 19: divide(divide(inverse(divide(divide(divide(inverse(X), Y), multiply(divide(Z, W), divide(W, Y))), V)), X), Z) = V.
% 2.33/0.73 Proof:
% 2.33/0.73 divide(divide(inverse(divide(divide(divide(inverse(X), Y), multiply(divide(Z, W), divide(W, Y))), V)), X), Z)
% 2.33/0.73 = { by lemma 16 R->L }
% 2.33/0.73 divide(divide(inverse(divide(divide(divide(inverse(X), Y), multiply(divide(Z, W), divide(W, Y))), V)), X), multiply(divide(divide(multiply(divide(Z, W), divide(W, Y)), divide(inverse(X), Y)), U), divide(U, X)))
% 2.33/0.73 = { by lemma 4 }
% 2.33/0.73 V
% 2.33/0.73
% 2.33/0.73 Lemma 20: divide(inverse(divide(X, Y)), divide(Y, X)) = multiply(divide(Z, W), divide(W, Z)).
% 2.33/0.73 Proof:
% 2.33/0.73 divide(inverse(divide(X, Y)), divide(Y, X))
% 2.33/0.73 = { by lemma 18 R->L }
% 2.33/0.73 divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(inverse(divide(W, Z)), divide(Z, W)))
% 2.33/0.73 = { by lemma 15 }
% 2.33/0.73 multiply(divide(Z, W), divide(W, Z))
% 2.33/0.73
% 2.33/0.73 Lemma 21: divide(X, multiply(divide(Y, Z), divide(Z, Y))) = X.
% 2.33/0.73 Proof:
% 2.33/0.73 divide(X, multiply(divide(Y, Z), divide(Z, Y)))
% 2.33/0.73 = { by lemma 20 R->L }
% 2.33/0.73 divide(X, divide(inverse(divide(W, V)), divide(V, W)))
% 2.33/0.73 = { by lemma 18 }
% 2.33/0.73 X
% 2.33/0.73
% 2.33/0.74 Lemma 22: multiply(divide(X, Y), Y) = X.
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(divide(X, Y), Y)
% 2.33/0.74 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.74 divide(divide(inverse(divide(inverse(Z), multiply(divide(X, Y), Y))), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by lemma 18 R->L }
% 2.33/0.74 divide(divide(inverse(divide(inverse(Z), multiply(divide(X, Y), divide(Y, divide(inverse(divide(U, T)), divide(T, U)))))), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by lemma 18 R->L }
% 2.33/0.74 divide(divide(inverse(divide(divide(inverse(Z), divide(inverse(divide(U, T)), divide(T, U))), multiply(divide(X, Y), divide(Y, divide(inverse(divide(U, T)), divide(T, U)))))), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by lemma 19 R->L }
% 2.33/0.74 divide(divide(inverse(divide(divide(inverse(Z), divide(inverse(divide(U, T)), divide(T, U))), multiply(divide(divide(inverse(divide(divide(divide(inverse(S), X2), multiply(divide(Y, Y2), divide(Y2, X2))), divide(X, Y))), S), Y), divide(Y, divide(inverse(divide(U, T)), divide(T, U)))))), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by lemma 6 R->L }
% 2.33/0.74 divide(divide(inverse(divide(divide(inverse(Z), X), multiply(divide(multiply(divide(divide(multiply(divide(divide(inverse(divide(divide(divide(inverse(S), X2), multiply(divide(Y, Y2), divide(Y2, X2))), divide(X, Y))), S), Y), divide(Y, divide(inverse(divide(U, T)), divide(T, U)))), divide(inverse(Z), divide(inverse(divide(U, T)), divide(T, U)))), Z2), divide(Z2, Z)), Y), divide(Y, X)))), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by lemma 16 }
% 2.33/0.74 divide(divide(inverse(divide(divide(inverse(Z), X), multiply(divide(divide(inverse(divide(divide(divide(inverse(S), X2), multiply(divide(Y, Y2), divide(Y2, X2))), divide(X, Y))), S), Y), divide(Y, X)))), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by lemma 19 }
% 2.33/0.74 divide(divide(inverse(divide(divide(inverse(Z), X), multiply(divide(X, Y), divide(Y, X)))), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by lemma 21 }
% 2.33/0.74 divide(divide(inverse(divide(inverse(Z), X)), divide(divide(W, V), inverse(Z))), divide(V, W))
% 2.33/0.74 = { by axiom 2 (single_axiom) }
% 2.33/0.74 X
% 2.33/0.74
% 2.33/0.74 Lemma 23: multiply(divide(X, X), Y) = Y.
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(divide(X, X), Y)
% 2.33/0.74 = { by lemma 15 R->L }
% 2.33/0.74 divide(divide(inverse(divide(Z, X)), divide(X, Z)), divide(inverse(Y), divide(X, X)))
% 2.33/0.74 = { by lemma 22 R->L }
% 2.33/0.74 divide(divide(inverse(divide(Z, X)), divide(multiply(divide(X, X), X), Z)), divide(inverse(Y), divide(X, X)))
% 2.33/0.74 = { by lemma 13 }
% 2.33/0.74 Y
% 2.33/0.74
% 2.33/0.74 Lemma 24: divide(inverse(divide(inverse(X), Y)), X) = Y.
% 2.33/0.74 Proof:
% 2.33/0.74 divide(inverse(divide(inverse(X), Y)), X)
% 2.33/0.74 = { by lemma 21 R->L }
% 2.33/0.74 divide(divide(inverse(divide(inverse(X), Y)), multiply(divide(divide(Z, W), V), divide(V, divide(Z, W)))), X)
% 2.33/0.74 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.74 divide(divide(inverse(divide(inverse(X), Y)), multiply(divide(divide(Z, W), V), divide(V, divide(Z, W)))), divide(divide(inverse(divide(U, X)), divide(divide(W, Z), U)), divide(Z, W)))
% 2.33/0.74 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.74 divide(divide(inverse(divide(inverse(divide(divide(inverse(divide(U, X)), divide(divide(W, Z), U)), divide(Z, W))), Y)), multiply(divide(divide(Z, W), V), divide(V, divide(Z, W)))), divide(divide(inverse(divide(U, X)), divide(divide(W, Z), U)), divide(Z, W)))
% 2.33/0.74 = { by lemma 9 }
% 2.33/0.74 Y
% 2.33/0.74
% 2.33/0.74 Lemma 25: multiply(divide(inverse(divide(inverse(X), Y)), Z), Z) = multiply(Y, X).
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(divide(inverse(divide(inverse(X), Y)), Z), Z)
% 2.33/0.74 = { by lemma 18 R->L }
% 2.33/0.74 multiply(divide(inverse(divide(inverse(X), Y)), Z), divide(Z, divide(inverse(divide(W, V)), divide(V, W))))
% 2.33/0.74 = { by lemma 8 }
% 2.33/0.74 multiply(divide(inverse(divide(inverse(X), Y)), X), divide(X, divide(inverse(divide(W, V)), divide(V, W))))
% 2.33/0.74 = { by lemma 18 }
% 2.33/0.74 multiply(divide(inverse(divide(inverse(X), Y)), X), X)
% 2.33/0.74 = { by lemma 24 }
% 2.33/0.74 multiply(Y, X)
% 2.33/0.74
% 2.33/0.74 Lemma 26: multiply(Z, divide(inverse(Z), Y)) = multiply(X, divide(inverse(X), Y)).
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(Z, divide(inverse(Z), Y))
% 2.33/0.74 = { by lemma 25 R->L }
% 2.33/0.74 multiply(divide(inverse(divide(inverse(divide(inverse(Z), Y)), Z)), W), W)
% 2.33/0.74 = { by lemma 24 }
% 2.33/0.74 multiply(divide(inverse(Y), W), W)
% 2.33/0.74 = { by lemma 24 R->L }
% 2.33/0.74 multiply(divide(inverse(divide(inverse(divide(inverse(X), Y)), X)), W), W)
% 2.33/0.74 = { by lemma 25 }
% 2.33/0.74 multiply(X, divide(inverse(X), Y))
% 2.33/0.74
% 2.33/0.74 Lemma 27: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(Y, inverse(Y))
% 2.33/0.74 = { by lemma 18 R->L }
% 2.33/0.74 multiply(Y, divide(inverse(Y), divide(inverse(divide(Z, W)), divide(W, Z))))
% 2.33/0.74 = { by lemma 26 }
% 2.33/0.74 multiply(X, divide(inverse(X), divide(inverse(divide(Z, W)), divide(W, Z))))
% 2.33/0.74 = { by lemma 18 }
% 2.33/0.74 multiply(X, inverse(X))
% 2.33/0.74
% 2.33/0.74 Lemma 28: inverse(divide(X, X)) = multiply(Y, inverse(Y)).
% 2.33/0.74 Proof:
% 2.33/0.74 inverse(divide(X, X))
% 2.33/0.74 = { by lemma 23 R->L }
% 2.33/0.74 multiply(divide(X, X), inverse(divide(X, X)))
% 2.33/0.74 = { by lemma 27 R->L }
% 2.33/0.74 multiply(Y, inverse(Y))
% 2.33/0.74
% 2.33/0.74 Lemma 29: multiply(multiply(X, inverse(X)), Y) = multiply(Z, multiply(inverse(Z), Y)).
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(multiply(X, inverse(X)), Y)
% 2.33/0.74 = { by lemma 23 R->L }
% 2.33/0.74 multiply(divide(W, W), multiply(multiply(X, inverse(X)), Y))
% 2.33/0.74 = { by lemma 28 R->L }
% 2.33/0.74 multiply(divide(W, W), multiply(inverse(divide(W, W)), Y))
% 2.33/0.74 = { by axiom 1 (multiply) }
% 2.33/0.74 multiply(divide(W, W), divide(inverse(divide(W, W)), inverse(Y)))
% 2.33/0.74 = { by lemma 26 R->L }
% 2.33/0.74 multiply(Z, divide(inverse(Z), inverse(Y)))
% 2.33/0.74 = { by axiom 1 (multiply) R->L }
% 2.33/0.74 multiply(Z, multiply(inverse(Z), Y))
% 2.33/0.74
% 2.33/0.74 Lemma 30: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(inverse(X), X)
% 2.33/0.74 = { by lemma 22 R->L }
% 2.33/0.74 multiply(inverse(X), multiply(divide(X, inverse(inverse(X))), inverse(inverse(X))))
% 2.33/0.74 = { by lemma 18 R->L }
% 2.33/0.74 multiply(inverse(X), multiply(divide(X, inverse(inverse(X))), divide(inverse(inverse(X)), divide(inverse(divide(Z, W)), divide(W, Z)))))
% 2.33/0.74 = { by axiom 1 (multiply) R->L }
% 2.33/0.74 multiply(inverse(X), multiply(multiply(X, inverse(X)), divide(inverse(inverse(X)), divide(inverse(divide(Z, W)), divide(W, Z)))))
% 2.33/0.74 = { by lemma 18 }
% 2.33/0.74 multiply(inverse(X), multiply(multiply(X, inverse(X)), inverse(inverse(X))))
% 2.33/0.74 = { by lemma 29 }
% 2.33/0.74 multiply(inverse(X), multiply(V, multiply(inverse(V), inverse(inverse(X)))))
% 2.33/0.74 = { by lemma 29 R->L }
% 2.33/0.74 multiply(inverse(X), multiply(multiply(U, inverse(U)), inverse(inverse(X))))
% 2.33/0.74 = { by lemma 28 R->L }
% 2.33/0.74 multiply(inverse(X), multiply(inverse(divide(T, T)), inverse(inverse(X))))
% 2.33/0.74 = { by axiom 1 (multiply) }
% 2.33/0.74 multiply(inverse(X), divide(inverse(divide(T, T)), inverse(inverse(inverse(X)))))
% 2.33/0.74 = { by lemma 17 R->L }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), multiply(inverse(inverse(inverse(X))), divide(T, T))))
% 2.33/0.74 = { by axiom 1 (multiply) }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), divide(inverse(inverse(inverse(X))), inverse(divide(T, T)))))
% 2.33/0.74 = { by lemma 28 }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), divide(inverse(inverse(inverse(X))), multiply(Y2, inverse(Y2)))))
% 2.33/0.74 = { by lemma 5 R->L }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), divide(divide(inverse(Z2), W2), multiply(divide(multiply(divide(multiply(multiply(Y2, inverse(Y2)), inverse(inverse(X))), V2), divide(V2, Z2)), U2), divide(U2, W2)))))
% 2.33/0.74 = { by lemma 29 }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), divide(divide(inverse(Z2), W2), multiply(divide(multiply(divide(multiply(T2, multiply(inverse(T2), inverse(inverse(X)))), V2), divide(V2, Z2)), U2), divide(U2, W2)))))
% 2.33/0.74 = { by lemma 5 }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), divide(inverse(multiply(inverse(T2), inverse(inverse(X)))), T2)))
% 2.33/0.74 = { by axiom 1 (multiply) }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), divide(inverse(divide(inverse(T2), inverse(inverse(inverse(X))))), T2)))
% 2.33/0.74 = { by lemma 24 }
% 2.33/0.74 multiply(inverse(X), divide(divide(inverse(divide(S, X2)), divide(X2, S)), inverse(inverse(inverse(X)))))
% 2.33/0.74 = { by axiom 1 (multiply) R->L }
% 2.33/0.74 multiply(inverse(X), multiply(divide(inverse(divide(S, X2)), divide(X2, S)), inverse(inverse(X))))
% 2.33/0.74 = { by lemma 20 }
% 2.33/0.74 multiply(inverse(X), multiply(multiply(divide(S2, S2), divide(S2, S2)), inverse(inverse(X))))
% 2.33/0.74 = { by lemma 23 }
% 2.33/0.74 multiply(inverse(X), multiply(divide(S2, S2), inverse(inverse(X))))
% 2.33/0.74 = { by lemma 23 }
% 2.33/0.74 multiply(inverse(X), inverse(inverse(X)))
% 2.33/0.74 = { by lemma 27 R->L }
% 2.33/0.74 multiply(Y, inverse(Y))
% 2.33/0.74
% 2.33/0.74 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 2.33/0.74 Proof:
% 2.33/0.74 multiply(inverse(a1), a1)
% 2.33/0.74 = { by lemma 30 }
% 2.33/0.74 multiply(X, inverse(X))
% 2.33/0.74 = { by lemma 30 R->L }
% 2.33/0.74 multiply(inverse(b1), b1)
% 2.33/0.74 % SZS output end Proof
% 2.33/0.74
% 2.33/0.74 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------