TSTP Solution File: BOO070-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO070-1 : 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 : n013.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 : Wed Aug 30 18:11:36 EDT 2023
% Result : Unsatisfiable 0.21s 0.74s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO070-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 08:21:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.73 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.74
% 0.21/0.74 % SZS status Unsatisfiable
% 0.21/0.74
% 0.21/0.81 % SZS output start Proof
% 0.21/0.81 Axiom 1 (single_axiom): multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, V), U, multiply(Z, W, T))), multiply(W, multiply(T, U, V), Z)) = Y.
% 0.21/0.81
% 0.21/0.81 Lemma 2: multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, Z2, Z)) = Y.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, Z2, Z))
% 0.21/0.81 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, multiply(multiply(Y2, inverse(Y2), Z2), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(V, multiply(U, T, S), X2)), Z))
% 0.21/0.81 = { by axiom 1 (single_axiom) }
% 0.21/0.81 Y
% 0.21/0.81
% 0.21/0.81 Lemma 3: multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z)) = Y.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z))
% 0.21/0.81 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, multiply(multiply(U, inverse(U), inverse(Z)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z))
% 0.21/0.81 = { by lemma 2 R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), multiply(Z, multiply(multiply(U, inverse(U), inverse(Z)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)), multiply(W, inverse(W), V))), inverse(multiply(multiply(multiply(W, inverse(W), V), Z, multiply(S, multiply(Z2, Y2, X2), T)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(multiply(W, inverse(W), V), Z, multiply(U, inverse(U), inverse(Z))))), multiply(Z, inverse(Z), multiply(W, inverse(W), V)))), multiply(inverse(Z), V, Z))
% 0.21/0.81 = { by lemma 2 }
% 0.21/0.81 Y
% 0.21/0.81
% 0.21/0.81 Lemma 4: multiply(inverse(X), Y, X) = Y.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(inverse(X), Y, X)
% 0.21/0.81 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.81 multiply(multiply(multiply(X, inverse(X), multiply(Z, inverse(Z), Y)), inverse(multiply(X, inverse(X), multiply(Z, inverse(Z), Y))), multiply(inverse(X), Y, X)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.81 = { by lemma 3 }
% 0.21/0.81 multiply(multiply(Z, inverse(Z), Y), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.81 = { by axiom 1 (single_axiom) }
% 0.21/0.81 Y
% 0.21/0.81
% 0.21/0.81 Lemma 5: multiply(multiply(X, Y, Z), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W)) = multiply(Y, multiply(Z, inverse(multiply(X, Y, X2)), X2), X).
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(multiply(X, Y, Z), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.81 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.81 multiply(multiply(multiply(multiply(X, Y, X2), inverse(multiply(X, Y, X2)), multiply(X, Y, Z)), inverse(multiply(multiply(X, Y, X2), inverse(multiply(X, Y, X2)), multiply(X, Y, Z))), multiply(Y, multiply(Z, inverse(multiply(X, Y, X2)), X2), X)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.81 = { by axiom 1 (single_axiom) }
% 0.21/0.81 multiply(Y, multiply(Z, inverse(multiply(X, Y, X2)), X2), X)
% 0.21/0.81
% 0.21/0.81 Lemma 6: multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X) = Y.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X)
% 0.21/0.81 = { by lemma 5 R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.81 = { by axiom 1 (single_axiom) }
% 0.21/0.81 Y
% 0.21/0.81
% 0.21/0.81 Lemma 7: multiply(X, inverse(inverse(inverse(Y))), Y) = X.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(X, inverse(inverse(inverse(Y))), Y)
% 0.21/0.81 = { by lemma 4 R->L }
% 0.21/0.81 multiply(inverse(inverse(Y)), multiply(X, inverse(inverse(inverse(Y))), Y), inverse(Y))
% 0.21/0.81 = { by lemma 4 R->L }
% 0.21/0.81 multiply(inverse(inverse(Y)), multiply(X, inverse(multiply(inverse(Y), inverse(inverse(Y)), Y)), Y), inverse(Y))
% 0.21/0.81 = { by lemma 6 }
% 0.21/0.81 X
% 0.21/0.81
% 0.21/0.81 Lemma 8: inverse(multiply(X, inverse(X), Y)) = inverse(Y).
% 0.21/0.81 Proof:
% 0.21/0.81 inverse(multiply(X, inverse(X), Y))
% 0.21/0.81 = { by lemma 4 R->L }
% 0.21/0.81 multiply(inverse(X), inverse(multiply(X, inverse(X), Y)), X)
% 0.21/0.81 = { by lemma 4 R->L }
% 0.21/0.81 multiply(inverse(X), multiply(inverse(Y), inverse(multiply(X, inverse(X), Y)), Y), X)
% 0.21/0.81 = { by lemma 6 }
% 0.21/0.81 inverse(Y)
% 0.21/0.81
% 0.21/0.81 Lemma 9: multiply(multiply(X, inverse(X), Y), inverse(inverse(inverse(multiply(Z, inverse(Z), W)))), W) = Y.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(inverse(inverse(multiply(Z, inverse(Z), W)))), W)
% 0.21/0.81 = { by lemma 4 R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(inverse(inverse(multiply(Z, inverse(Z), W)))), multiply(inverse(inverse(multiply(Z, inverse(Z), W))), W, inverse(multiply(Z, inverse(Z), W))))
% 0.21/0.81 = { by lemma 6 R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(inverse(Z), multiply(inverse(inverse(multiply(Z, inverse(Z), W))), inverse(multiply(Z, inverse(Z), W)), W), Z)), multiply(inverse(inverse(multiply(Z, inverse(Z), W))), W, inverse(multiply(Z, inverse(Z), W))))
% 0.21/0.81 = { by lemma 3 R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(inverse(multiply(Z, inverse(Z), W)), inverse(inverse(multiply(Z, inverse(Z), W))), multiply(inverse(Z), multiply(inverse(inverse(multiply(Z, inverse(Z), W))), inverse(multiply(Z, inverse(Z), W)), W), Z)), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), inverse(inverse(multiply(Z, inverse(Z), W)))))), multiply(inverse(multiply(Z, inverse(Z), W)), inverse(inverse(multiply(Z, inverse(Z), W))), multiply(Z, inverse(Z), W)))), multiply(inverse(inverse(multiply(Z, inverse(Z), W))), W, inverse(multiply(Z, inverse(Z), W))))
% 0.21/0.81 = { by lemma 2 }
% 0.21/0.81 Y
% 0.21/0.81
% 0.21/0.81 Lemma 10: inverse(inverse(X)) = X.
% 0.21/0.81 Proof:
% 0.21/0.81 inverse(inverse(X))
% 0.21/0.81 = { by lemma 7 R->L }
% 0.21/0.81 multiply(inverse(inverse(X)), inverse(inverse(inverse(Y))), Y)
% 0.21/0.81 = { by lemma 8 R->L }
% 0.21/0.81 multiply(inverse(inverse(X)), inverse(inverse(inverse(multiply(Z, inverse(Z), Y)))), Y)
% 0.21/0.81 = { by lemma 4 R->L }
% 0.21/0.81 multiply(multiply(inverse(X), inverse(inverse(X)), X), inverse(inverse(inverse(multiply(Z, inverse(Z), Y)))), Y)
% 0.21/0.81 = { by lemma 9 }
% 0.21/0.81 X
% 0.21/0.81
% 0.21/0.81 Lemma 11: multiply(X, inverse(X), Y) = Y.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(X, inverse(X), Y)
% 0.21/0.81 = { by lemma 7 R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(inverse(inverse(Z))), Z)
% 0.21/0.81 = { by lemma 8 R->L }
% 0.21/0.81 multiply(multiply(X, inverse(X), Y), inverse(inverse(inverse(multiply(W, inverse(W), Z)))), Z)
% 0.21/0.81 = { by lemma 9 }
% 0.21/0.81 Y
% 0.21/0.81
% 0.21/0.81 Lemma 12: multiply(X, inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y)) = X.
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(X, inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.81 = { by lemma 11 R->L }
% 0.21/0.81 multiply(multiply(T, inverse(T), X), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.81 = { by lemma 5 }
% 0.21/0.81 multiply(inverse(T), multiply(X, inverse(multiply(T, inverse(T), S)), S), T)
% 0.21/0.81 = { by lemma 6 }
% 0.21/0.81 X
% 0.21/0.81
% 0.21/0.81 Lemma 13: multiply(X, Y, Z) = multiply(Z, Y, X).
% 0.21/0.81 Proof:
% 0.21/0.81 multiply(X, Y, Z)
% 0.21/0.81 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.81 multiply(multiply(multiply(Z, Y, X), inverse(multiply(Z, Y, X)), multiply(X, Y, Z)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.81 = { by lemma 11 R->L }
% 0.21/0.81 multiply(multiply(multiply(Z, Y, X), inverse(multiply(Z, Y, multiply(X2, inverse(X2), X))), multiply(X, Y, Z)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.81 = { by lemma 11 R->L }
% 0.21/0.82 multiply(multiply(multiply(Z, Y, X), inverse(multiply(multiply(X2, inverse(X2), Z), Y, multiply(X2, inverse(X2), X))), multiply(X, Y, Z)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.82 = { by lemma 4 R->L }
% 0.21/0.82 multiply(multiply(multiply(Z, Y, X), inverse(multiply(multiply(X2, inverse(X2), Z), Y, multiply(X2, inverse(X2), X))), multiply(inverse(X2), multiply(X, Y, Z), X2)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.82 = { by lemma 12 }
% 0.21/0.82 multiply(multiply(Z, Y, X), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.82 = { by lemma 12 }
% 0.21/0.82 multiply(Z, Y, X)
% 0.21/0.82
% 0.21/0.82 Lemma 14: multiply(multiply(X, Y, Z), W, multiply(X, Y, V)) = multiply(Y, multiply(V, W, Z), X).
% 0.21/0.82 Proof:
% 0.21/0.82 multiply(multiply(X, Y, Z), W, multiply(X, Y, V))
% 0.21/0.82 = { by lemma 12 R->L }
% 0.21/0.82 multiply(multiply(multiply(X, Y, Z), W, multiply(X, Y, V)), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(T, multiply(Y2, X2, S), U))
% 0.21/0.82 = { by lemma 12 R->L }
% 0.21/0.82 multiply(multiply(multiply(multiply(X, Y, Z), W, multiply(X, Y, V)), inverse(multiply(multiply(X, Y, Z), W, multiply(X, Y, V))), multiply(Y, multiply(V, W, Z), X)), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(T, multiply(Y2, X2, S), U))
% 0.21/0.82 = { by axiom 1 (single_axiom) }
% 0.21/0.82 multiply(Y, multiply(V, W, Z), X)
% 0.21/0.82
% 0.21/0.82 Lemma 15: multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z) = multiply(Z, X, Y).
% 0.21/0.82 Proof:
% 0.21/0.82 multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)
% 0.21/0.82 = { by lemma 5 R->L }
% 0.21/0.82 multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 0.21/0.82 = { by lemma 12 }
% 0.21/0.82 multiply(Z, X, Y)
% 0.21/0.82
% 0.21/0.82 Lemma 16: multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, W, multiply(multiply(V, inverse(V), Z), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), Z2))), multiply(inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(Z2, W, multiply(T, multiply(Y2, X2, S), U)), multiply(V, inverse(V), Z))) = Y.
% 0.21/0.82 Proof:
% 0.21/0.82 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, W, multiply(multiply(V, inverse(V), Z), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), Z2))), multiply(inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(Z2, W, multiply(T, multiply(Y2, X2, S), U)), multiply(V, inverse(V), Z)))
% 0.21/0.82 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.82 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(multiply(V, inverse(V), Z), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(T, multiply(Y2, X2, S), U)), W, multiply(multiply(V, inverse(V), Z), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), Z2))), multiply(inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(Z2, W, multiply(T, multiply(Y2, X2, S), U)), multiply(V, inverse(V), Z)))
% 0.21/0.82 = { by axiom 1 (single_axiom) }
% 0.21/0.82 Y
% 0.21/0.82
% 0.21/0.82 Lemma 17: multiply(X, multiply(Y, Z, Y), inverse(multiply(inverse(multiply(W, multiply(V, U, T), S)), multiply(multiply(V, U, T), multiply(S, Z, S), W), Y))) = X.
% 0.21/0.82 Proof:
% 0.21/0.82 multiply(X, multiply(Y, Z, Y), inverse(multiply(inverse(multiply(W, multiply(V, U, T), S)), multiply(multiply(V, U, T), multiply(S, Z, S), W), Y)))
% 0.21/0.82 = { by lemma 14 R->L }
% 0.21/0.82 multiply(X, multiply(Y, Z, Y), inverse(multiply(inverse(multiply(W, multiply(V, U, T), S)), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)))
% 0.21/0.82 = { by lemma 14 R->L }
% 0.21/0.82 multiply(X, multiply(Y, Z, Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)))
% 0.21/0.82 = { by lemma 10 R->L }
% 0.21/0.82 multiply(X, inverse(inverse(multiply(Y, Z, Y))), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)))
% 0.21/0.82 = { by lemma 11 R->L }
% 0.21/0.82 multiply(X, inverse(multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y)))), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)))
% 0.21/0.82 = { by lemma 11 R->L }
% 0.21/0.82 multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y))))), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)))
% 0.21/0.82 = { by lemma 11 R->L }
% 0.21/0.82 multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y))))), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)))
% 0.21/0.82 = { by lemma 16 R->L }
% 0.21/0.82 multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y))))), multiply(multiply(Z2, inverse(Z2), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y))), inverse(multiply(Y, Z, multiply(multiply(W2, inverse(W2), Y), inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(W, multiply(V, U, T), S)))), multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), multiply(W2, inverse(W2), Y))))
% 0.21/0.82 = { by lemma 5 }
% 0.21/0.82 multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y))))), multiply(multiply(Z2, inverse(Z2), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y))), inverse(multiply(Y, Z, multiply(inverse(W2), multiply(Y, inverse(multiply(W2, inverse(W2), V2)), V2), W2))), multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), multiply(W2, inverse(W2), Y))))
% 0.21/0.82 = { by lemma 11 }
% 0.21/0.82 multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y))))), multiply(inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), inverse(multiply(Y, Z, multiply(inverse(W2), multiply(Y, inverse(multiply(W2, inverse(W2), V2)), V2), W2))), multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), multiply(W2, inverse(W2), Y))))
% 0.21/0.82 = { by lemma 6 }
% 0.21/0.82 multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y))))), multiply(inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), inverse(multiply(Y, Z, Y)), multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), multiply(W2, inverse(W2), Y))))
% 0.21/0.82 = { by lemma 11 }
% 0.21/0.82 multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y), inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), multiply(X2, inverse(X2), inverse(multiply(Y, Z, Y))))), multiply(inverse(multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)), inverse(multiply(Y, Z, Y)), multiply(inverse(multiply(multiply(S, W, T), U, multiply(S, W, V))), multiply(multiply(W, multiply(V, U, T), S), Z, multiply(W, multiply(V, U, T), S)), Y)))
% 0.21/0.82 = { by lemma 3 }
% 0.21/0.82 X
% 0.21/0.82
% 0.21/0.82 Lemma 18: multiply(X, inverse(multiply(Y, multiply(Z, W, V), U)), multiply(multiply(Z, W, V), multiply(T, inverse(multiply(multiply(T, Y, V), W, multiply(T, Y, Z))), U), Y)) = X.
% 0.21/0.82 Proof:
% 0.21/0.82 multiply(X, inverse(multiply(Y, multiply(Z, W, V), U)), multiply(multiply(Z, W, V), multiply(T, inverse(multiply(multiply(T, Y, V), W, multiply(T, Y, Z))), U), Y))
% 0.21/0.82 = { by lemma 15 R->L }
% 0.21/0.82 multiply(X, inverse(multiply(multiply(Z, W, V), multiply(U, inverse(multiply(Y, multiply(Z, W, V), S)), S), Y)), multiply(multiply(Z, W, V), multiply(T, inverse(multiply(multiply(T, Y, V), W, multiply(T, Y, Z))), U), Y))
% 0.21/0.82 = { by lemma 11 R->L }
% 0.21/0.82 multiply(multiply(X2, inverse(X2), X), inverse(multiply(multiply(Z, W, V), multiply(U, inverse(multiply(Y, multiply(Z, W, V), S)), S), Y)), multiply(multiply(Z, W, V), multiply(T, inverse(multiply(multiply(T, Y, V), W, multiply(T, Y, Z))), U), Y))
% 0.21/0.82 = { by lemma 5 R->L }
% 0.21/0.82 multiply(multiply(X2, inverse(X2), X), inverse(multiply(multiply(Y, multiply(Z, W, V), U), inverse(multiply(multiply(T, Y, V), W, multiply(T, Y, Z))), multiply(Y, multiply(Z, W, V), T))), multiply(multiply(Z, W, V), multiply(T, inverse(multiply(multiply(T, Y, V), W, multiply(T, Y, Z))), U), Y))
% 0.21/0.82 = { by axiom 1 (single_axiom) }
% 0.21/0.82 X
% 0.21/0.82
% 0.21/0.82 Goal 1 (prove_tba_axioms_4): multiply(a, a, b) = a.
% 0.21/0.82 Proof:
% 0.21/0.82 multiply(a, a, b)
% 0.21/0.82 = { by lemma 15 R->L }
% 0.21/0.82 multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)
% 0.21/0.83 = { by lemma 12 R->L }
% 0.21/0.83 multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by lemma 16 R->L }
% 0.21/0.83 multiply(multiply(multiply(T, inverse(T), multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(multiply(T2, inverse(T2), a), inverse(multiply(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), X), inverse(multiply(a, a, X)), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), b))), multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))))), multiply(inverse(multiply(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), X), inverse(multiply(a, a, X)), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), b))), multiply(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))), multiply(T2, inverse(T2), a))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by axiom 1 (single_axiom) }
% 0.21/0.83 multiply(multiply(multiply(T, inverse(T), multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(inverse(multiply(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), X), inverse(multiply(a, a, X)), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), b))), multiply(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))), multiply(T2, inverse(T2), a))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by lemma 11 }
% 0.21/0.83 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(inverse(multiply(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), X), inverse(multiply(a, a, X)), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), b))), multiply(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))), multiply(T2, inverse(T2), a))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by lemma 14 }
% 0.21/0.83 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))), multiply(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))), multiply(T2, inverse(T2), a))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by lemma 14 }
% 0.21/0.83 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))), multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), multiply(b, inverse(multiply(a, a, X)), X)), multiply(T2, inverse(T2), a))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by lemma 11 }
% 0.21/0.83 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))), multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), multiply(b, inverse(multiply(a, a, X)), X)), a)), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by lemma 13 }
% 0.21/0.83 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.83 = { by lemma 13 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 2 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), S, multiply(U2, inverse(U2), inverse(S))))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 14 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(S, multiply(multiply(U2, inverse(U2), inverse(S)), inverse(multiply(multiply(V2, X2, W2), Z2, multiply(V2, X2, Y2))), multiply(X2, multiply(Y2, Z2, W2), V2)), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by axiom 1 (single_axiom) }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X))), multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 11 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(multiply(S, inverse(S), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 11 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(inverse(multiply(b, inverse(multiply(a, a, X)), X))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 4 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, inverse(inverse(multiply(b, inverse(multiply(a, a, X)), X))), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 10 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 11 }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(b, inverse(multiply(a, a, X)), X)))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 17 R->L }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, multiply(b, inverse(multiply(a, a, X)), X), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2)))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 17 R->L }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2)))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 12 R->L }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), inverse(multiply(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), inverse(multiply(multiply(T3, S3, X4), Y4, multiply(T3, S3, Z4))), multiply(S3, multiply(Z4, Y4, X4), T3))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 18 R->L }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), inverse(multiply(multiply(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2)))), multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))), inverse(multiply(multiply(T3, S3, X4), Y4, multiply(T3, S3, Z4))), multiply(S3, multiply(Z4, Y4, X4), T3))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by axiom 1 (single_axiom) }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.84 = { by lemma 10 R->L }
% 0.21/0.84 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, inverse(inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))))), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.85 = { by lemma 11 R->L }
% 0.21/0.85 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, inverse(multiply(V4, inverse(V4), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2)))))), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.85 = { by lemma 11 R->L }
% 0.21/0.85 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(a, inverse(multiply(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))), multiply(V4, inverse(V4), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))))))), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.85 = { by lemma 11 R->L }
% 0.21/0.85 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(multiply(U4, inverse(U4), a), inverse(multiply(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))), multiply(V4, inverse(V4), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))))))), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.85 = { by lemma 18 R->L }
% 0.21/0.85 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), multiply(multiply(U4, inverse(U4), a), inverse(multiply(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X)), inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))), multiply(V4, inverse(V4), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))))))), multiply(inverse(multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))), inverse(multiply(multiply(b, inverse(multiply(a, a, X)), X), multiply(S2, X3, S2), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2)))), multiply(multiply(S2, X3, S2), multiply(W4, inverse(multiply(multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2), X3, multiply(W4, multiply(b, inverse(multiply(a, a, X)), X), S2))), inverse(multiply(inverse(multiply(Y3, multiply(Z3, W3, V3), U3)), multiply(multiply(Z3, W3, V3), multiply(U3, X3, U3), Y3), S2))), multiply(b, inverse(multiply(a, a, X)), X))))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.85 = { by lemma 3 }
% 0.21/0.85 multiply(multiply(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a), inverse(multiply(a, multiply(b, inverse(multiply(a, a, X)), X), a)), a), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 0.21/0.85 = { by axiom 1 (single_axiom) }
% 0.21/0.85 a
% 0.21/0.85 % SZS output end Proof
% 0.21/0.85
% 0.21/0.85 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------