%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP073-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:12 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.57s
% Output : Proof 1.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP073-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:20:08 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.57 Command-line arguments: --no-flatten-goal
% 0.19/0.57
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57
% 1.26/0.66 % SZS output start Proof
% 1.26/0.66 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 1.26/0.66 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, Y), Z), divide(W, Z))), divide(Y, X)) = W.
% 1.26/0.66
% 1.26/0.66 Lemma 3: divide(inverse(divide(divide(divide(X, Y), divide(Z, W)), V)), divide(Y, X)) = inverse(divide(divide(divide(W, Z), U), divide(V, U))).
% 1.26/0.66 Proof:
% 1.26/0.66 divide(inverse(divide(divide(divide(X, Y), divide(Z, W)), V)), divide(Y, X))
% 1.26/0.66 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(X, Y), divide(Z, W)), divide(inverse(divide(divide(divide(W, Z), U), divide(V, U))), divide(Z, W)))), divide(Y, X))
% 1.26/0.66 = { by axiom 2 (single_axiom) }
% 1.26/0.66 inverse(divide(divide(divide(W, Z), U), divide(V, U)))
% 1.26/0.66
% 1.26/0.66 Lemma 4: inverse(divide(divide(divide(X, Y), Z), divide(divide(W, divide(Y, X)), Z))) = W.
% 1.26/0.66 Proof:
% 1.26/0.66 inverse(divide(divide(divide(X, Y), Z), divide(divide(W, divide(Y, X)), Z)))
% 1.26/0.66 = { by lemma 3 R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(V, U), divide(Y, X)), divide(W, divide(Y, X)))), divide(U, V))
% 1.26/0.66 = { by axiom 2 (single_axiom) }
% 1.26/0.66 W
% 1.26/0.66
% 1.26/0.66 Lemma 5: inverse(divide(divide(X, Y), divide(divide(Z, divide(divide(W, V), inverse(divide(divide(divide(V, W), U), divide(X, U))))), Y))) = Z.
% 1.26/0.66 Proof:
% 1.26/0.66 inverse(divide(divide(X, Y), divide(divide(Z, divide(divide(W, V), inverse(divide(divide(divide(V, W), U), divide(X, U))))), Y)))
% 1.26/0.66 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.66 inverse(divide(divide(divide(inverse(divide(divide(divide(V, W), U), divide(X, U))), divide(W, V)), Y), divide(divide(Z, divide(divide(W, V), inverse(divide(divide(divide(V, W), U), divide(X, U))))), Y)))
% 1.26/0.66 = { by lemma 4 }
% 1.26/0.66 Z
% 1.26/0.66
% 1.26/0.66 Lemma 6: divide(X, divide(divide(Y, Z), inverse(divide(divide(divide(Z, Y), W), divide(divide(V, U), W))))) = divide(X, divide(U, V)).
% 1.26/0.66 Proof:
% 1.26/0.66 divide(X, divide(divide(Y, Z), inverse(divide(divide(divide(Z, Y), W), divide(divide(V, U), W)))))
% 1.26/0.66 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(V, U), T), divide(divide(X, divide(divide(Y, Z), inverse(divide(divide(divide(Z, Y), W), divide(divide(V, U), W))))), T))), divide(U, V))
% 1.26/0.66 = { by lemma 5 }
% 1.26/0.66 divide(X, divide(U, V))
% 1.26/0.66
% 1.26/0.66 Lemma 7: divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, divide(V, U)), Z)))) = divide(divide(V, U), W).
% 1.26/0.66 Proof:
% 1.26/0.66 divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, divide(V, U)), Z))))
% 1.26/0.66 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, divide(V, U)), Z)))), X2))), divide(S, T))
% 1.26/0.66 = { by lemma 6 R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(Y2, Z2), inverse(divide(divide(divide(Z2, Y2), W2), divide(divide(X2, divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, divide(V, U)), Z))))), W2)))))), divide(S, T))
% 1.26/0.66 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(Y2, Z2), inverse(divide(divide(divide(Z2, Y2), W2), divide(divide(X2, divide(divide(X, Y), inverse(divide(divide(divide(Y, X), divide(inverse(divide(divide(divide(V2, U2), T2), divide(Z, T2))), divide(U2, V2))), divide(divide(W, divide(V, U)), Z))))), W2)))))), divide(S, T))
% 1.26/0.66 = { by lemma 6 R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(Y2, Z2), inverse(divide(divide(divide(Z2, Y2), W2), divide(divide(X2, divide(divide(S2, X3), inverse(divide(divide(divide(X3, S2), Y3), divide(divide(inverse(divide(divide(divide(Y, X), divide(inverse(divide(divide(divide(V2, U2), T2), divide(Z, T2))), divide(U2, V2))), divide(divide(W, divide(V, U)), Z))), divide(X, Y)), Y3))))), W2)))))), divide(S, T))
% 1.26/0.66 = { by lemma 3 }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(Y2, Z2), inverse(divide(divide(divide(Z2, Y2), W2), divide(divide(X2, divide(divide(S2, X3), inverse(divide(divide(divide(X3, S2), Y3), divide(inverse(divide(divide(divide(divide(U2, V2), inverse(divide(divide(divide(V2, U2), T2), divide(Z, T2)))), Z3), divide(divide(divide(W, divide(V, U)), Z), Z3))), Y3))))), W2)))))), divide(S, T))
% 1.26/0.66 = { by lemma 3 R->L }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(Y2, Z2), inverse(divide(divide(divide(Z2, Y2), W2), divide(divide(X2, divide(divide(S2, X3), inverse(divide(divide(divide(X3, S2), Y3), divide(divide(inverse(divide(divide(divide(U, V), divide(inverse(divide(divide(divide(V2, U2), T2), divide(Z, T2))), divide(U2, V2))), divide(divide(W, divide(V, U)), Z))), divide(V, U)), Y3))))), W2)))))), divide(S, T))
% 1.26/0.66 = { by lemma 6 }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(Y2, Z2), inverse(divide(divide(divide(Z2, Y2), W2), divide(divide(X2, divide(divide(V, U), inverse(divide(divide(divide(U, V), divide(inverse(divide(divide(divide(V2, U2), T2), divide(Z, T2))), divide(U2, V2))), divide(divide(W, divide(V, U)), Z))))), W2)))))), divide(S, T))
% 1.26/0.66 = { by axiom 2 (single_axiom) }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(Y2, Z2), inverse(divide(divide(divide(Z2, Y2), W2), divide(divide(X2, divide(divide(V, U), inverse(divide(divide(divide(U, V), Z), divide(divide(W, divide(V, U)), Z))))), W2)))))), divide(S, T))
% 1.26/0.66 = { by lemma 6 }
% 1.26/0.66 divide(inverse(divide(divide(divide(T, S), X2), divide(divide(divide(V, U), inverse(divide(divide(divide(U, V), Z), divide(divide(W, divide(V, U)), Z)))), X2))), divide(S, T))
% 1.26/0.67 = { by axiom 2 (single_axiom) }
% 1.26/0.67 divide(divide(V, U), inverse(divide(divide(divide(U, V), Z), divide(divide(W, divide(V, U)), Z))))
% 1.26/0.67 = { by lemma 4 }
% 1.26/0.67 divide(divide(V, U), W)
% 1.26/0.67
% 1.26/0.67 Lemma 8: divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, V), Z)))), U) = divide(divide(V, W), U).
% 1.26/0.67 Proof:
% 1.26/0.67 divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, V), Z)))), U)
% 1.26/0.67 = { by lemma 7 R->L }
% 1.26/0.67 divide(divide(V, W), inverse(divide(divide(divide(W, V), T), divide(divide(U, divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, V), Z))))), T))))
% 1.26/0.67 = { by lemma 5 }
% 1.26/0.67 divide(divide(V, W), U)
% 1.26/0.67
% 1.26/0.67 Lemma 9: divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, V), Z)))) = divide(V, W).
% 1.26/0.67 Proof:
% 1.26/0.67 divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, V), Z))))
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(inverse(divide(divide(divide(U, T), S), divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(divide(W, V), Z)))), S))), divide(T, U))
% 1.26/0.67 = { by lemma 8 }
% 1.26/0.67 divide(inverse(divide(divide(divide(U, T), S), divide(divide(V, W), S))), divide(T, U))
% 1.26/0.67 = { by axiom 2 (single_axiom) }
% 1.26/0.67 divide(V, W)
% 1.26/0.67
% 1.26/0.67 Lemma 10: divide(inverse(divide(X, divide(Y, Z))), divide(divide(W, V), inverse(divide(divide(divide(V, W), Z), X)))) = Y.
% 1.26/0.67 Proof:
% 1.26/0.67 divide(inverse(divide(X, divide(Y, Z))), divide(divide(W, V), inverse(divide(divide(divide(V, W), Z), X))))
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(inverse(divide(X, divide(Y, Z))), divide(divide(W, V), inverse(divide(divide(divide(V, W), divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))), X))))
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(inverse(divide(X, divide(Y, divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))))), divide(divide(W, V), inverse(divide(divide(divide(V, W), divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))), X))))
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(inverse(divide(divide(inverse(divide(divide(divide(divide(T, U), inverse(divide(divide(divide(U, T), S), divide(Z, S)))), X2), divide(X, X2))), divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))), divide(Y, divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))))), divide(divide(W, V), inverse(divide(divide(divide(V, W), divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))), X))))
% 1.26/0.67 = { by lemma 3 R->L }
% 1.26/0.67 divide(inverse(divide(divide(divide(inverse(divide(divide(divide(V, W), divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))), X)), divide(W, V)), divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))), divide(Y, divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))))), divide(divide(W, V), inverse(divide(divide(divide(V, W), divide(inverse(divide(divide(divide(U, T), S), divide(Z, S))), divide(T, U))), X))))
% 1.26/0.67 = { by axiom 2 (single_axiom) }
% 1.26/0.67 Y
% 1.26/0.67
% 1.26/0.67 Lemma 11: divide(inverse(divide(X, divide(Y, Z))), divide(divide(W, V), inverse(divide(divide(Y, Z), X)))) = divide(V, W).
% 1.26/0.67 Proof:
% 1.26/0.67 divide(inverse(divide(X, divide(Y, Z))), divide(divide(W, V), inverse(divide(divide(Y, Z), X))))
% 1.26/0.67 = { by lemma 8 R->L }
% 1.26/0.67 divide(inverse(divide(X, divide(Y, Z))), divide(divide(W, V), inverse(divide(divide(divide(V, W), inverse(divide(divide(divide(W, V), U), divide(divide(Z, Y), U)))), X))))
% 1.26/0.67 = { by lemma 9 R->L }
% 1.26/0.67 divide(inverse(divide(X, divide(divide(V, W), inverse(divide(divide(divide(W, V), U), divide(divide(Z, Y), U)))))), divide(divide(W, V), inverse(divide(divide(divide(V, W), inverse(divide(divide(divide(W, V), U), divide(divide(Z, Y), U)))), X))))
% 1.26/0.67 = { by lemma 10 }
% 1.26/0.67 divide(V, W)
% 1.26/0.67
% 1.26/0.67 Lemma 12: divide(inverse(divide(X, Y)), divide(divide(Z, W), inverse(divide(Y, X)))) = divide(W, Z).
% 1.26/0.67 Proof:
% 1.26/0.67 divide(inverse(divide(X, Y)), divide(divide(Z, W), inverse(divide(Y, X))))
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(inverse(divide(inverse(divide(divide(divide(V, U), T), divide(divide(X, Y), T))), divide(U, V))), divide(divide(Z, W), inverse(divide(Y, X))))
% 1.26/0.67 = { by lemma 9 R->L }
% 1.26/0.67 divide(inverse(divide(inverse(divide(divide(divide(V, U), T), divide(divide(X, Y), T))), divide(U, V))), divide(divide(Z, W), inverse(divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(divide(X, Y), T)))))))
% 1.26/0.67 = { by lemma 11 }
% 1.26/0.67 divide(W, Z)
% 1.26/0.67
% 1.26/0.67 Lemma 13: divide(divide(divide(X, Y), inverse(divide(Z, W))), inverse(divide(W, Z))) = divide(X, Y).
% 1.26/0.67 Proof:
% 1.26/0.67 divide(divide(divide(X, Y), inverse(divide(Z, W))), inverse(divide(W, Z)))
% 1.26/0.67 = { by lemma 7 R->L }
% 1.26/0.67 divide(divide(V, U), inverse(divide(divide(divide(U, V), T), divide(divide(inverse(divide(W, Z)), divide(divide(X, Y), inverse(divide(Z, W)))), T))))
% 1.26/0.67 = { by lemma 12 }
% 1.26/0.67 divide(divide(V, U), inverse(divide(divide(divide(U, V), T), divide(divide(Y, X), T))))
% 1.26/0.67 = { by lemma 9 }
% 1.26/0.67 divide(X, Y)
% 1.26/0.67
% 1.26/0.67 Lemma 14: inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(W, Z)))), V), divide(U, V))) = divide(inverse(divide(divide(divide(T, S), W), U)), divide(S, T)).
% 1.26/0.67 Proof:
% 1.26/0.67 inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(W, Z)))), V), divide(U, V)))
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(inverse(divide(divide(divide(T, S), W), divide(inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(W, Z)))), V), divide(U, V))), W))), divide(S, T))
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(inverse(divide(divide(divide(T, S), W), divide(inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(W, Z)))), V), divide(U, V))), divide(inverse(divide(divide(divide(Y, X), Z), divide(W, Z))), divide(X, Y))))), divide(S, T))
% 1.26/0.67 = { by axiom 2 (single_axiom) }
% 1.26/0.67 divide(inverse(divide(divide(divide(T, S), W), U)), divide(S, T))
% 1.26/0.67
% 1.26/0.67 Lemma 15: divide(divide(inverse(divide(divide(divide(X, Y), Z), W)), divide(Y, X)), Z) = W.
% 1.26/0.67 Proof:
% 1.26/0.67 divide(divide(inverse(divide(divide(divide(X, Y), Z), W)), divide(Y, X)), Z)
% 1.26/0.67 = { by axiom 2 (single_axiom) R->L }
% 1.26/0.67 divide(divide(inverse(divide(divide(divide(X, Y), Z), W)), divide(Y, X)), divide(inverse(divide(divide(divide(V, U), T), divide(Z, T))), divide(U, V)))
% 1.26/0.67 = { by lemma 14 R->L }
% 1.26/0.67 divide(inverse(divide(divide(divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(Z, T)))), S), divide(W, S))), divide(inverse(divide(divide(divide(V, U), T), divide(Z, T))), divide(U, V)))
% 1.26/0.67 = { by axiom 2 (single_axiom) }
% 1.26/0.67 W
% 1.26/0.67
% 1.26/0.67 Lemma 16: divide(divide(inverse(divide(X, Y)), divide(Y, X)), inverse(divide(Z, W))) = inverse(divide(W, Z)).
% 1.26/0.67 Proof:
% 1.26/0.67 divide(divide(inverse(divide(X, Y)), divide(Y, X)), inverse(divide(Z, W)))
% 1.26/0.67 = { by lemma 13 R->L }
% 1.26/0.67 divide(divide(inverse(divide(divide(divide(X, Y), inverse(divide(Z, W))), inverse(divide(W, Z)))), divide(Y, X)), inverse(divide(Z, W)))
% 1.26/0.67 = { by lemma 15 }
% 1.26/0.67 inverse(divide(W, Z))
% 1.26/0.67
% 1.26/0.67 Lemma 17: divide(inverse(divide(divide(X, Y), divide(X, Y))), divide(Z, W)) = divide(W, Z).
% 1.26/0.67 Proof:
% 1.26/0.67 divide(inverse(divide(divide(X, Y), divide(X, Y))), divide(Z, W))
% 1.26/0.67 = { by lemma 6 R->L }
% 1.26/0.67 divide(inverse(divide(divide(X, Y), divide(divide(W, Z), inverse(divide(divide(divide(Z, W), V), divide(divide(Y, X), V)))))), divide(Z, W))
% 1.26/0.67 = { by lemma 8 R->L }
% 1.26/0.67 divide(inverse(divide(divide(divide(W, Z), inverse(divide(divide(divide(Z, W), V), divide(divide(Y, X), V)))), divide(divide(W, Z), inverse(divide(divide(divide(Z, W), V), divide(divide(Y, X), V)))))), divide(Z, W))
% 1.26/0.67 = { by axiom 2 (single_axiom) }
% 1.83/0.67 divide(W, Z)
% 1.83/0.67
% 1.83/0.67 Lemma 18: inverse(divide(divide(divide(X, Y), Z), divide(divide(X, Y), Z))) = inverse(divide(divide(W, V), divide(W, V))).
% 1.83/0.67 Proof:
% 1.83/0.67 inverse(divide(divide(divide(X, Y), Z), divide(divide(X, Y), Z)))
% 1.83/0.67 = { by lemma 3 R->L }
% 1.83/0.67 divide(inverse(divide(divide(divide(U, T), divide(Y, X)), divide(X, Y))), divide(T, U))
% 1.83/0.67 = { by lemma 17 R->L }
% 1.83/0.67 divide(inverse(divide(divide(divide(U, T), divide(Y, X)), divide(inverse(divide(divide(W, V), divide(W, V))), divide(Y, X)))), divide(T, U))
% 1.83/0.67 = { by axiom 2 (single_axiom) }
% 1.83/0.67 inverse(divide(divide(W, V), divide(W, V)))
% 1.83/0.67
% 1.83/0.67 Lemma 19: inverse(divide(divide(X, Y), divide(X, Y))) = divide(inverse(divide(Z, W)), divide(W, Z)).
% 1.83/0.67 Proof:
% 1.83/0.67 inverse(divide(divide(X, Y), divide(X, Y)))
% 1.83/0.67 = { by lemma 18 R->L }
% 1.83/0.67 inverse(divide(divide(divide(W, Z), V), divide(divide(W, Z), V)))
% 1.83/0.67 = { by lemma 15 R->L }
% 1.83/0.67 divide(divide(inverse(divide(divide(divide(Z, W), inverse(divide(divide(divide(W, Z), U), divide(divide(W, Z), U)))), inverse(divide(divide(divide(W, Z), V), divide(divide(W, Z), V))))), divide(W, Z)), inverse(divide(divide(divide(W, Z), U), divide(divide(W, Z), U))))
% 1.83/0.67 = { by lemma 8 }
% 1.83/0.67 divide(divide(inverse(divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), divide(divide(W, Z), V))))), divide(W, Z)), inverse(divide(divide(divide(W, Z), U), divide(divide(W, Z), U))))
% 1.83/0.67 = { by lemma 18 }
% 1.83/0.67 divide(divide(inverse(divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), divide(divide(W, Z), V))))), divide(W, Z)), inverse(divide(divide(W, Z), divide(W, Z))))
% 1.83/0.67 = { by lemma 9 }
% 1.83/0.67 divide(divide(inverse(divide(Z, W)), divide(W, Z)), inverse(divide(divide(W, Z), divide(W, Z))))
% 1.83/0.67 = { by lemma 7 R->L }
% 1.83/0.67 divide(divide(T, S), inverse(divide(divide(divide(S, T), X2), divide(divide(inverse(divide(divide(W, Z), divide(W, Z))), divide(inverse(divide(Z, W)), divide(W, Z))), X2))))
% 1.83/0.67 = { by lemma 13 R->L }
% 1.83/0.67 divide(divide(T, S), inverse(divide(divide(divide(S, T), X2), divide(divide(inverse(divide(divide(W, Z), divide(divide(divide(W, Z), inverse(divide(Z, W))), inverse(divide(W, Z))))), divide(inverse(divide(Z, W)), divide(W, Z))), X2))))
% 1.83/0.67 = { by lemma 13 R->L }
% 1.83/0.67 divide(divide(T, S), inverse(divide(divide(divide(S, T), X2), divide(divide(inverse(divide(divide(divide(divide(W, Z), inverse(divide(Z, W))), inverse(divide(W, Z))), divide(divide(divide(W, Z), inverse(divide(Z, W))), inverse(divide(W, Z))))), divide(inverse(divide(Z, W)), divide(W, Z))), X2))))
% 1.83/0.67 = { by axiom 2 (single_axiom) }
% 1.83/0.67 divide(divide(T, S), inverse(divide(divide(divide(S, T), X2), divide(divide(divide(W, Z), inverse(divide(Z, W))), X2))))
% 1.83/0.67 = { by lemma 9 }
% 1.83/0.67 divide(inverse(divide(Z, W)), divide(W, Z))
% 1.83/0.67
% 1.83/0.67 Lemma 20: divide(divide(inverse(divide(X, Y)), divide(Z, W)), divide(inverse(divide(V, U)), divide(U, V))) = divide(inverse(divide(X, Y)), divide(Z, W)).
% 1.83/0.67 Proof:
% 1.83/0.67 divide(divide(inverse(divide(X, Y)), divide(Z, W)), divide(inverse(divide(V, U)), divide(U, V)))
% 1.83/0.67 = { by lemma 19 R->L }
% 1.83/0.67 divide(divide(inverse(divide(X, Y)), divide(Z, W)), inverse(divide(divide(Z, W), divide(Z, W))))
% 1.83/0.67 = { by lemma 13 R->L }
% 1.83/0.67 divide(divide(inverse(divide(X, Y)), divide(Z, W)), inverse(divide(divide(divide(divide(Z, W), inverse(divide(X, Y))), inverse(divide(Y, X))), divide(Z, W))))
% 1.83/0.67 = { by lemma 7 R->L }
% 1.83/0.67 divide(divide(T, S), inverse(divide(divide(divide(S, T), X2), divide(divide(inverse(divide(divide(divide(divide(Z, W), inverse(divide(X, Y))), inverse(divide(Y, X))), divide(Z, W))), divide(inverse(divide(X, Y)), divide(Z, W))), X2))))
% 1.83/0.67 = { by lemma 13 R->L }
% 1.83/0.67 divide(divide(T, S), inverse(divide(divide(divide(S, T), X2), divide(divide(inverse(divide(divide(divide(divide(Z, W), inverse(divide(X, Y))), inverse(divide(Y, X))), divide(divide(divide(Z, W), inverse(divide(X, Y))), inverse(divide(Y, X))))), divide(inverse(divide(X, Y)), divide(Z, W))), X2))))
% 1.83/0.67 = { by axiom 2 (single_axiom) }
% 1.83/0.67 divide(divide(T, S), inverse(divide(divide(divide(S, T), X2), divide(divide(divide(Z, W), inverse(divide(X, Y))), X2))))
% 1.83/0.67 = { by lemma 9 }
% 1.83/0.67 divide(inverse(divide(X, Y)), divide(Z, W))
% 1.83/0.67
% 1.83/0.67 Lemma 21: divide(inverse(divide(X, Y)), divide(Y, X)) = divide(divide(Z, W), inverse(divide(W, Z))).
% 1.83/0.67 Proof:
% 1.83/0.67 divide(inverse(divide(X, Y)), divide(Y, X))
% 1.83/0.67 = { by lemma 20 R->L }
% 1.83/0.67 divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(inverse(divide(W, Z)), divide(Z, W)))
% 1.83/0.67 = { by lemma 7 R->L }
% 1.83/0.67 divide(divide(V, U), inverse(divide(divide(divide(U, V), T), divide(divide(divide(inverse(divide(W, Z)), divide(Z, W)), divide(inverse(divide(X, Y)), divide(Y, X))), T))))
% 1.83/0.67 = { by lemma 20 }
% 1.83/0.67 divide(divide(V, U), inverse(divide(divide(divide(U, V), T), divide(divide(inverse(divide(W, Z)), divide(Z, W)), T))))
% 1.83/0.67 = { by lemma 7 }
% 1.83/0.67 divide(divide(Z, W), inverse(divide(W, Z)))
% 1.83/0.67
% 1.83/0.67 Lemma 22: inverse(divide(X, Y)) = divide(Y, X).
% 1.83/0.67 Proof:
% 1.83/0.67 inverse(divide(X, Y))
% 1.83/0.67 = { by lemma 16 R->L }
% 1.83/0.67 divide(divide(inverse(divide(Z, W)), divide(W, Z)), inverse(divide(Y, X)))
% 1.83/0.67 = { by lemma 21 }
% 1.83/0.67 divide(divide(divide(Y, X), inverse(divide(X, Y))), inverse(divide(Y, X)))
% 1.83/0.67 = { by lemma 13 }
% 1.83/0.67 divide(Y, X)
% 1.83/0.67
% 1.83/0.67 Lemma 23: divide(divide(X, Y), inverse(divide(divide(Z, W), divide(Z, W)))) = divide(X, Y).
% 1.83/0.67 Proof:
% 1.83/0.67 divide(divide(X, Y), inverse(divide(divide(Z, W), divide(Z, W))))
% 1.83/0.67 = { by lemma 7 R->L }
% 1.83/0.67 divide(divide(V, U), inverse(divide(divide(divide(U, V), T), divide(divide(inverse(divide(divide(Z, W), divide(Z, W))), divide(X, Y)), T))))
% 1.83/0.67 = { by lemma 17 }
% 1.83/0.68 divide(divide(V, U), inverse(divide(divide(divide(U, V), T), divide(divide(Y, X), T))))
% 1.83/0.68 = { by lemma 9 }
% 1.83/0.68 divide(X, Y)
% 1.83/0.68
% 1.83/0.68 Lemma 24: divide(X, divide(inverse(divide(divide(divide(Y, Z), X), divide(W, V))), divide(Z, Y))) = divide(V, W).
% 1.83/0.68 Proof:
% 1.83/0.68 divide(X, divide(inverse(divide(divide(divide(Y, Z), X), divide(W, V))), divide(Z, Y)))
% 1.83/0.68 = { by lemma 15 R->L }
% 1.83/0.68 divide(divide(inverse(divide(divide(divide(U, T), S), divide(X, divide(inverse(divide(divide(divide(Y, Z), X), divide(W, V))), divide(Z, Y))))), divide(T, U)), S)
% 1.83/0.68 = { by axiom 2 (single_axiom) R->L }
% 1.83/0.68 divide(divide(inverse(divide(divide(divide(U, T), S), divide(divide(inverse(divide(divide(divide(X2, Y2), Z2), divide(X, Z2))), divide(Y2, X2)), divide(inverse(divide(divide(divide(Y, Z), X), divide(W, V))), divide(Z, Y))))), divide(T, U)), S)
% 1.83/0.68 = { by lemma 14 R->L }
% 1.83/0.68 divide(divide(inverse(divide(divide(divide(U, T), S), divide(divide(inverse(divide(divide(divide(X2, Y2), Z2), divide(X, Z2))), divide(Y2, X2)), inverse(divide(divide(divide(divide(Y2, X2), inverse(divide(divide(divide(X2, Y2), Z2), divide(X, Z2)))), W2), divide(divide(W, V), W2)))))), divide(T, U)), S)
% 1.83/0.68 = { by lemma 6 }
% 1.83/0.68 divide(divide(inverse(divide(divide(divide(U, T), S), divide(V, W))), divide(T, U)), S)
% 1.83/0.68 = { by lemma 15 }
% 1.83/0.68 divide(V, W)
% 1.83/0.68
% 1.83/0.68 Lemma 25: inverse(divide(divide(X, Y), divide(Z, W))) = divide(inverse(divide(W, Z)), divide(X, Y)).
% 1.83/0.68 Proof:
% 1.83/0.68 inverse(divide(divide(X, Y), divide(Z, W)))
% 1.83/0.68 = { by lemma 13 R->L }
% 1.83/0.68 inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(V, U), divide(V, U)))), inverse(divide(divide(V, U), divide(V, U)))), divide(Z, W)))
% 1.83/0.68 = { by lemma 19 }
% 1.83/0.68 inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(V, U), divide(V, U)))), divide(inverse(divide(X, Y)), divide(Y, X))), divide(Z, W)))
% 1.83/0.68 = { by lemma 23 }
% 1.83/0.68 inverse(divide(divide(divide(X, Y), divide(inverse(divide(X, Y)), divide(Y, X))), divide(Z, W)))
% 1.83/0.68 = { by lemma 16 R->L }
% 1.83/0.68 inverse(divide(divide(divide(X, Y), divide(divide(divide(inverse(divide(X, Y)), divide(Y, X)), inverse(divide(Y, X))), divide(Y, X))), divide(Z, W)))
% 1.83/0.68 = { by axiom 2 (single_axiom) R->L }
% 1.83/0.68 divide(inverse(divide(divide(divide(divide(inverse(divide(X, Y)), divide(Y, X)), inverse(divide(Y, X))), divide(Y, X)), divide(inverse(divide(divide(divide(X, Y), divide(divide(divide(inverse(divide(X, Y)), divide(Y, X)), inverse(divide(Y, X))), divide(Y, X))), divide(Z, W))), divide(Y, X)))), divide(inverse(divide(Y, X)), divide(inverse(divide(X, Y)), divide(Y, X))))
% 1.83/0.68 = { by lemma 24 }
% 1.83/0.68 divide(inverse(divide(W, Z)), divide(inverse(divide(Y, X)), divide(inverse(divide(X, Y)), divide(Y, X))))
% 1.83/0.68 = { by lemma 22 }
% 1.83/0.68 divide(inverse(divide(W, Z)), divide(divide(X, Y), divide(inverse(divide(X, Y)), divide(Y, X))))
% 1.83/0.68 = { by lemma 22 }
% 1.83/0.68 divide(inverse(divide(W, Z)), divide(divide(X, Y), divide(divide(Y, X), divide(Y, X))))
% 1.83/0.68 = { by lemma 22 R->L }
% 1.83/0.68 divide(inverse(divide(W, Z)), divide(divide(X, Y), divide(divide(Y, X), inverse(divide(X, Y)))))
% 1.83/0.68 = { by lemma 22 R->L }
% 1.83/0.68 divide(inverse(divide(W, Z)), divide(inverse(divide(Y, X)), divide(divide(Y, X), inverse(divide(X, Y)))))
% 1.83/0.68 = { by lemma 12 }
% 1.83/0.68 divide(inverse(divide(W, Z)), divide(X, Y))
% 1.83/0.68
% 1.83/0.68 Lemma 26: inverse(divide(X, divide(Y, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U)))))) = inverse(divide(divide(inverse(divide(U, divide(X, V))), T), divide(Y, T))).
% 1.83/0.68 Proof:
% 1.83/0.68 inverse(divide(X, divide(Y, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U))))))
% 1.83/0.68 = { by lemma 10 R->L }
% 1.83/0.68 inverse(divide(divide(inverse(divide(U, divide(X, V))), divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U)))), divide(Y, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U))))))
% 1.83/0.68 = { by axiom 2 (single_axiom) R->L }
% 1.83/0.68 inverse(divide(divide(divide(inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))), divide(X2, S)), divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U)))), divide(Y, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U))))))
% 1.83/0.68 = { by axiom 2 (single_axiom) R->L }
% 1.83/0.68 divide(inverse(divide(divide(divide(Z2, W2), divide(divide(X2, S), inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))))), divide(inverse(divide(divide(divide(inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))), divide(X2, S)), divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U)))), divide(Y, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), U)))))), divide(divide(X2, S), inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))))))), divide(W2, Z2))
% 1.83/0.68 = { by axiom 2 (single_axiom) }
% 1.83/0.68 divide(inverse(divide(divide(divide(Z2, W2), divide(divide(X2, S), inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))))), Y)), divide(W2, Z2))
% 1.83/0.68 = { by axiom 2 (single_axiom) R->L }
% 1.83/0.68 divide(inverse(divide(divide(divide(Z2, W2), divide(divide(X2, S), inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))))), divide(inverse(divide(divide(divide(inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))), divide(X2, S)), T), divide(Y, T))), divide(divide(X2, S), inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))))))), divide(W2, Z2))
% 1.83/0.68 = { by axiom 2 (single_axiom) }
% 1.83/0.68 inverse(divide(divide(divide(inverse(divide(divide(divide(S, X2), Y2), divide(inverse(divide(U, divide(X, V))), Y2))), divide(X2, S)), T), divide(Y, T)))
% 1.83/0.68 = { by axiom 2 (single_axiom) }
% 1.83/0.68 inverse(divide(divide(inverse(divide(U, divide(X, V))), T), divide(Y, T)))
% 1.83/0.68
% 1.83/0.68 Lemma 27: divide(divide(X, Y), divide(X, Y)) = divide(Z, Z).
% 1.83/0.68 Proof:
% 1.83/0.68 divide(divide(X, Y), divide(X, Y))
% 1.83/0.68 = { by lemma 22 R->L }
% 1.83/0.68 divide(divide(X, Y), inverse(divide(Y, X)))
% 1.83/0.68 = { by lemma 21 R->L }
% 1.83/0.68 divide(inverse(divide(W, V)), divide(V, W))
% 1.83/0.68 = { by lemma 19 R->L }
% 1.83/0.68 inverse(divide(divide(divide(U, T), S), divide(divide(U, T), S)))
% 1.83/0.68 = { by lemma 5 R->L }
% 1.83/0.68 inverse(divide(divide(Z, Z), divide(divide(inverse(divide(divide(divide(U, T), S), divide(divide(U, T), S))), divide(divide(X2, Y2), inverse(divide(divide(divide(Y2, X2), Z2), divide(Z, Z2))))), Z)))
% 1.83/0.68 = { by lemma 25 }
% 1.83/0.68 divide(inverse(divide(Z, divide(inverse(divide(divide(divide(U, T), S), divide(divide(U, T), S))), divide(divide(X2, Y2), inverse(divide(divide(divide(Y2, X2), Z2), divide(Z, Z2))))))), divide(Z, Z))
% 1.83/0.68 = { by lemma 26 }
% 1.83/0.68 divide(inverse(divide(divide(inverse(divide(divide(Z, Z2), divide(Z, Z2))), divide(T, U)), divide(inverse(divide(divide(divide(U, T), S), divide(divide(U, T), S))), divide(T, U)))), divide(Z, Z))
% 1.83/0.68 = { by lemma 17 }
% 1.83/0.68 divide(inverse(divide(divide(U, T), divide(inverse(divide(divide(divide(U, T), S), divide(divide(U, T), S))), divide(T, U)))), divide(Z, Z))
% 1.83/0.68 = { by lemma 25 }
% 1.83/0.68 divide(divide(inverse(divide(divide(T, U), inverse(divide(divide(divide(U, T), S), divide(divide(U, T), S))))), divide(U, T)), divide(Z, Z))
% 1.83/0.68 = { by lemma 9 }
% 1.83/0.68 divide(divide(inverse(divide(T, U)), divide(U, T)), divide(Z, Z))
% 1.83/0.68 = { by lemma 23 R->L }
% 1.83/0.68 divide(divide(inverse(divide(T, U)), divide(U, T)), divide(divide(Z, Z), inverse(divide(divide(W2, V2), divide(W2, V2)))))
% 1.83/0.68 = { by lemma 19 R->L }
% 1.83/0.68 divide(inverse(divide(divide(W2, V2), divide(W2, V2))), divide(divide(Z, Z), inverse(divide(divide(W2, V2), divide(W2, V2)))))
% 1.83/0.68 = { by lemma 11 }
% 1.83/0.68 divide(Z, Z)
% 1.83/0.68
% 1.83/0.68 Lemma 28: divide(divide(X, X), inverse(divide(Y, Z))) = inverse(divide(Z, Y)).
% 1.83/0.68 Proof:
% 1.83/0.68 divide(divide(X, X), inverse(divide(Y, Z)))
% 1.83/0.68 = { by lemma 27 R->L }
% 1.83/0.68 divide(divide(divide(W, V), divide(W, V)), inverse(divide(Y, Z)))
% 1.83/0.68 = { by lemma 22 R->L }
% 1.83/0.68 divide(divide(divide(W, V), inverse(divide(V, W))), inverse(divide(Y, Z)))
% 1.83/0.68 = { by lemma 21 R->L }
% 1.83/0.68 divide(divide(inverse(divide(U, T)), divide(T, U)), inverse(divide(Y, Z)))
% 1.83/0.68 = { by lemma 13 R->L }
% 1.83/0.68 divide(divide(inverse(divide(divide(divide(U, T), inverse(divide(Y, Z))), inverse(divide(Z, Y)))), divide(T, U)), inverse(divide(Y, Z)))
% 1.83/0.68 = { by lemma 15 }
% 1.83/0.68 inverse(divide(Z, Y))
% 1.83/0.68
% 1.83/0.68 Lemma 29: divide(Y, Y) = divide(X, X).
% 1.83/0.68 Proof:
% 1.83/0.68 divide(Y, Y)
% 1.83/0.68 = { by lemma 4 R->L }
% 1.83/0.68 divide(Y, inverse(divide(divide(divide(U, T), S), divide(divide(Y, divide(T, U)), S))))
% 1.83/0.68 = { by lemma 4 R->L }
% 1.83/0.68 divide(inverse(divide(divide(divide(U, T), S), divide(divide(Y, divide(T, U)), S))), inverse(divide(divide(divide(U, T), S), divide(divide(Y, divide(T, U)), S))))
% 1.83/0.68 = { by lemma 28 R->L }
% 1.83/0.68 divide(inverse(divide(divide(divide(U, T), S), divide(divide(Y, divide(T, U)), S))), divide(divide(inverse(divide(divide(divide(Z, W), V), divide(divide(X, divide(W, Z)), V))), inverse(divide(divide(divide(Z, W), V), divide(divide(X, divide(W, Z)), V)))), inverse(divide(divide(divide(Y, divide(T, U)), S), divide(divide(U, T), S)))))
% 1.83/0.68 = { by lemma 12 }
% 1.83/0.68 divide(inverse(divide(divide(divide(Z, W), V), divide(divide(X, divide(W, Z)), V))), inverse(divide(divide(divide(Z, W), V), divide(divide(X, divide(W, Z)), V))))
% 1.83/0.68 = { by lemma 4 }
% 1.83/0.68 divide(X, inverse(divide(divide(divide(Z, W), V), divide(divide(X, divide(W, Z)), V))))
% 1.83/0.68 = { by lemma 4 }
% 1.83/0.68 divide(X, X)
% 1.83/0.68
% 1.83/0.68 Lemma 30: divide(divide(X, X), divide(Y, Z)) = divide(Z, Y).
% 1.83/0.68 Proof:
% 1.83/0.68 divide(divide(X, X), divide(Y, Z))
% 1.83/0.68 = { by lemma 22 R->L }
% 1.83/0.68 divide(inverse(divide(X, X)), divide(Y, Z))
% 1.83/0.68 = { by lemma 29 }
% 1.83/0.68 divide(inverse(divide(divide(divide(Z, Y), W), divide(divide(Z, Y), W))), divide(Y, Z))
% 1.83/0.68 = { by axiom 2 (single_axiom) }
% 1.83/0.69 divide(Z, Y)
% 1.83/0.69
% 1.83/0.69 Lemma 31: inverse(divide(divide(X, divide(Y, Z)), divide(Z, Y))) = divide(divide(W, W), X).
% 1.83/0.69 Proof:
% 1.83/0.69 inverse(divide(divide(X, divide(Y, Z)), divide(Z, Y)))
% 1.83/0.69 = { by lemma 28 R->L }
% 1.83/0.69 divide(divide(V, V), inverse(divide(divide(Z, Y), divide(X, divide(Y, Z)))))
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 divide(inverse(divide(V, V)), inverse(divide(divide(Z, Y), divide(X, divide(Y, Z)))))
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 divide(inverse(divide(V, V)), inverse(divide(inverse(divide(Y, Z)), divide(X, divide(Y, Z)))))
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 divide(inverse(divide(V, V)), inverse(divide(inverse(divide(Y, Z)), divide(X, inverse(divide(Z, Y))))))
% 1.83/0.69 = { by lemma 28 R->L }
% 1.83/0.69 divide(divide(divide(V, V), inverse(divide(V, V))), inverse(divide(inverse(divide(Y, Z)), divide(X, inverse(divide(Z, Y))))))
% 1.83/0.69 = { by lemma 30 R->L }
% 1.83/0.69 divide(divide(W, W), divide(inverse(divide(inverse(divide(Y, Z)), divide(X, inverse(divide(Z, Y))))), divide(divide(V, V), inverse(divide(V, V)))))
% 1.83/0.69 = { by lemma 13 R->L }
% 1.83/0.69 divide(divide(W, W), divide(inverse(divide(inverse(divide(Y, Z)), divide(X, inverse(divide(Z, Y))))), divide(divide(V, V), inverse(divide(divide(divide(V, V), inverse(divide(Z, Y))), inverse(divide(Y, Z)))))))
% 1.83/0.69 = { by lemma 10 }
% 1.83/0.69 divide(divide(W, W), X)
% 1.83/0.69
% 1.83/0.69 Lemma 32: inverse(divide(X, divide(Y, Y))) = inverse(X).
% 1.83/0.69 Proof:
% 1.83/0.69 inverse(divide(X, divide(Y, Y)))
% 1.83/0.69 = { by lemma 27 R->L }
% 1.83/0.69 inverse(divide(X, divide(divide(Z, W), divide(Z, W))))
% 1.83/0.69 = { by lemma 28 R->L }
% 1.83/0.69 divide(divide(V, V), inverse(divide(divide(divide(Z, W), divide(Z, W)), X)))
% 1.83/0.69 = { by lemma 31 R->L }
% 1.83/0.69 inverse(divide(divide(inverse(divide(divide(divide(Z, W), divide(Z, W)), X)), divide(W, Z)), divide(Z, W)))
% 1.83/0.69 = { by lemma 15 }
% 1.83/0.69 inverse(X)
% 1.83/0.69
% 1.83/0.69 Lemma 33: divide(divide(X, X), Y) = inverse(Y).
% 1.83/0.69 Proof:
% 1.83/0.69 divide(divide(X, X), Y)
% 1.83/0.69 = { by lemma 31 R->L }
% 1.83/0.69 inverse(divide(divide(Y, divide(Z, Z)), divide(Z, Z)))
% 1.83/0.69 = { by lemma 32 }
% 1.83/0.69 inverse(divide(Y, divide(Z, Z)))
% 1.83/0.69 = { by lemma 32 }
% 1.83/0.69 inverse(Y)
% 1.83/0.69
% 1.83/0.69 Lemma 34: inverse(inverse(X)) = X.
% 1.83/0.69 Proof:
% 1.83/0.69 inverse(inverse(X))
% 1.83/0.69 = { by lemma 33 R->L }
% 1.83/0.69 inverse(divide(divide(Y, Y), X))
% 1.83/0.69 = { by lemma 31 R->L }
% 1.83/0.69 inverse(inverse(divide(divide(X, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), divide(U, V))))), divide(inverse(divide(divide(divide(W, Z), V), divide(U, V))), divide(Z, W)))))
% 1.83/0.69 = { by lemma 17 R->L }
% 1.83/0.69 inverse(inverse(divide(divide(X, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), divide(U, V))))), divide(inverse(divide(divide(U, V), divide(U, V))), divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), divide(U, V))))))))
% 1.83/0.69 = { by lemma 10 }
% 1.83/0.69 inverse(inverse(divide(divide(X, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), divide(U, V))))), U)))
% 1.83/0.69 = { by lemma 33 R->L }
% 1.83/0.69 inverse(divide(divide(U, U), divide(divide(X, divide(divide(Z, W), inverse(divide(divide(divide(W, Z), V), divide(U, V))))), U)))
% 1.83/0.69 = { by lemma 5 }
% 1.83/0.69 X
% 1.83/0.69
% 1.83/0.69 Lemma 35: divide(X, divide(Y, Y)) = X.
% 1.83/0.69 Proof:
% 1.83/0.69 divide(X, divide(Y, Y))
% 1.83/0.69 = { by lemma 30 R->L }
% 1.83/0.69 divide(divide(Z, Z), divide(divide(Y, Y), X))
% 1.83/0.69 = { by lemma 33 }
% 1.83/0.69 divide(divide(Z, Z), inverse(X))
% 1.83/0.69 = { by lemma 33 }
% 1.83/0.69 inverse(inverse(X))
% 1.83/0.69 = { by lemma 34 }
% 1.83/0.69 X
% 1.83/0.69
% 1.83/0.69 Lemma 36: divide(divide(X, divide(Y, divide(Z, inverse(Y)))), Z) = X.
% 1.83/0.69 Proof:
% 1.83/0.69 divide(divide(X, divide(Y, divide(Z, inverse(Y)))), Z)
% 1.83/0.69 = { by lemma 33 R->L }
% 1.83/0.69 divide(divide(X, divide(Y, divide(Z, divide(divide(W, W), Y)))), Z)
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 divide(divide(X, divide(Y, inverse(divide(divide(divide(W, W), Y), Z)))), Z)
% 1.83/0.69 = { by lemma 35 R->L }
% 1.83/0.69 divide(divide(X, divide(Y, divide(inverse(divide(divide(divide(W, W), Y), Z)), divide(W, W)))), Z)
% 1.83/0.69 = { by axiom 2 (single_axiom) R->L }
% 1.83/0.69 divide(divide(X, divide(Y, divide(inverse(divide(divide(divide(W, W), Y), divide(inverse(divide(divide(divide(V, U), T), divide(Z, T))), divide(U, V)))), divide(W, W)))), Z)
% 1.83/0.69 = { by lemma 24 }
% 1.83/0.69 divide(divide(X, divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(Z, T))))), Z)
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 inverse(divide(Z, divide(X, divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(Z, T)))))))
% 1.83/0.69 = { by lemma 30 R->L }
% 1.83/0.69 inverse(divide(divide(Z, Z), divide(divide(X, divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(Z, T))))), Z)))
% 1.83/0.69 = { by lemma 5 }
% 1.83/0.69 X
% 1.83/0.69
% 1.83/0.69 Lemma 37: divide(divide(X, Y), divide(Z, Y)) = divide(X, Z).
% 1.83/0.69 Proof:
% 1.83/0.69 divide(divide(X, Y), divide(Z, Y))
% 1.83/0.69 = { by lemma 36 R->L }
% 1.83/0.69 divide(divide(X, Y), divide(divide(divide(Z, divide(W, divide(V, inverse(W)))), V), Y))
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 divide(divide(X, Y), divide(inverse(divide(V, divide(Z, divide(W, divide(V, inverse(W)))))), Y))
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 inverse(divide(divide(inverse(divide(V, divide(Z, divide(W, divide(V, inverse(W)))))), Y), divide(X, Y)))
% 1.83/0.69 = { by lemma 26 R->L }
% 1.83/0.69 inverse(divide(Z, divide(X, divide(divide(U, U), inverse(divide(divide(divide(U, U), divide(W, divide(V, inverse(W)))), V))))))
% 1.83/0.69 = { by lemma 36 }
% 1.83/0.69 inverse(divide(Z, divide(X, divide(divide(U, U), inverse(divide(U, U))))))
% 1.83/0.69 = { by lemma 22 }
% 1.83/0.69 divide(divide(X, divide(divide(U, U), inverse(divide(U, U)))), Z)
% 1.83/0.69 = { by lemma 28 }
% 1.83/0.69 divide(divide(X, inverse(divide(U, U))), Z)
% 1.83/0.69 = { by lemma 22 }
% 1.83/0.69 divide(divide(X, divide(U, U)), Z)
% 1.83/0.69 = { by lemma 35 }
% 1.83/0.69 divide(X, Z)
% 1.83/0.69
% 1.83/0.69 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))).
% 1.83/0.69 Proof:
% 1.83/0.69 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 1.83/0.69 = { by axiom 1 (multiply) }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 1.83/0.69 = { by axiom 1 (multiply) }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3))
% 1.83/0.69 = { by axiom 1 (multiply) }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3))
% 1.83/0.69 = { by axiom 1 (multiply) }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(divide(a3, inverse(b3)), c3))
% 1.83/0.69 = { by axiom 1 (multiply) }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 1.83/0.69 = { by lemma 33 }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 1.83/0.69 = { by lemma 34 }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), inverse(c3)))
% 1.83/0.69 = { by lemma 32 R->L }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(divide(b3, divide(X, X)))), inverse(c3)))
% 1.83/0.69 = { by lemma 28 R->L }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, divide(divide(X, X), inverse(divide(divide(X, X), b3)))), inverse(c3)))
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, inverse(divide(inverse(c3), divide(a3, divide(divide(X, X), inverse(divide(divide(X, X), b3)))))))
% 1.83/0.69 = { by lemma 37 R->L }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, inverse(divide(inverse(c3), divide(a3, divide(divide(X, X), inverse(divide(divide(divide(X, X), Y), divide(b3, Y))))))))
% 1.83/0.69 = { by lemma 26 }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, inverse(divide(divide(inverse(divide(divide(b3, Y), divide(inverse(c3), Y))), Z), divide(a3, Z))))
% 1.83/0.69 = { by lemma 22 }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, Z), divide(inverse(divide(divide(b3, Y), divide(inverse(c3), Y))), Z)))
% 1.83/0.69 = { by lemma 37 }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(divide(b3, Y), divide(inverse(c3), Y)))))
% 1.83/0.69 = { by lemma 22 }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(divide(inverse(c3), Y), divide(b3, Y))))
% 1.83/0.69 = { by lemma 37 }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), b3)))
% 1.83/0.69 = { by lemma 22 R->L }
% 1.83/0.69 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.83/0.69 = { by lemma 29 }
% 1.83/0.69 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.83/0.69 = { by axiom 1 (multiply) R->L }
% 1.83/0.69 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, divide(b3, inverse(c3))))
% 1.83/0.69 = { by axiom 1 (multiply) R->L }
% 1.83/0.69 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, multiply(b3, c3)))
% 1.83/0.69 = { by axiom 1 (multiply) R->L }
% 1.83/0.69 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 1.83/0.69 % SZS output end Proof
% 1.83/0.69
% 1.83/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------