%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 09:35:38 AM UTC 2026
% Result : Unsatisfiable 109.80s 14.20s
% Output : Proof 111.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.27 % Computer : n026.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 21:07:26 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 109.80/14.20 Command-line arguments: --no-flatten-goal
% 109.80/14.20
% 109.80/14.20 % SZS status Unsatisfiable
% 109.80/14.20
% 110.61/14.37 % SZS output start Proof
% 110.61/14.37 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.
% 110.61/14.37
% 110.61/14.37 Lemma 2: multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V)) = multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z).
% 110.61/14.37 Proof:
% 110.61/14.37 multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 110.61/14.37 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.37 multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 110.61/14.37 = { by axiom 1 (single_axiom) }
% 110.61/14.37 multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)
% 110.61/14.37
% 110.61/14.37 Lemma 3: multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X) = Y.
% 110.61/14.37 Proof:
% 110.61/14.37 multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X)
% 110.61/14.37 = { by lemma 2 R->L }
% 110.61/14.37 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 110.61/14.37 = { by axiom 1 (single_axiom) }
% 110.61/14.37 Y
% 110.61/14.37
% 110.61/14.37 Lemma 4: multiply(X, inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y)) = multiply(X, inverse(multiply(multiply(T, inverse(T), S), inverse(multiply(T, inverse(T), S)), multiply(T, inverse(T), X2))), X2).
% 110.61/14.37 Proof:
% 110.61/14.37 multiply(X, inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 110.61/14.37 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.37 multiply(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2)), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 110.61/14.37 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.37 multiply(multiply(multiply(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2), inverse(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2)), multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2))), inverse(multiply(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2), inverse(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2)), multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2)))), multiply(inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(multiply(W2, multiply(T2, U2, V2), Z2), inverse(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2)), S2), multiply(Y2, inverse(Y2), X))), inverse(multiply(multiply(Y, Z, W), V, multiply(Y, Z, U))), multiply(Z, multiply(U, V, W), Y))
% 110.61/14.37 = { by axiom 1 (single_axiom) }
% 110.61/14.37 multiply(inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(multiply(W2, multiply(T2, U2, V2), Z2), inverse(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2)), S2), multiply(Y2, inverse(Y2), X))
% 110.61/14.37 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.37 multiply(multiply(multiply(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2), inverse(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2)), multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2))), inverse(multiply(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2), inverse(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2)), multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2)))), multiply(inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(multiply(W2, multiply(T2, U2, V2), Z2), inverse(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), S2)), S2), multiply(Y2, inverse(Y2), X))), inverse(multiply(multiply(T, inverse(T), S), inverse(multiply(T, inverse(T), S)), multiply(T, inverse(T), X2))), multiply(inverse(T), multiply(X2, inverse(multiply(T, inverse(T), S)), S), T))
% 110.61/14.37 = { by axiom 1 (single_axiom) }
% 110.61/14.37 multiply(multiply(multiply(Y2, inverse(Y2), X), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2)), inverse(multiply(multiply(T, inverse(T), S), inverse(multiply(T, inverse(T), S)), multiply(T, inverse(T), X2))), multiply(inverse(T), multiply(X2, inverse(multiply(T, inverse(T), S)), S), T))
% 110.61/14.37 = { by axiom 1 (single_axiom) }
% 110.61/14.37 multiply(X, inverse(multiply(multiply(T, inverse(T), S), inverse(multiply(T, inverse(T), S)), multiply(T, inverse(T), X2))), multiply(inverse(T), multiply(X2, inverse(multiply(T, inverse(T), S)), S), T))
% 110.61/14.37 = { by lemma 3 }
% 110.61/14.38 multiply(X, inverse(multiply(multiply(T, inverse(T), S), inverse(multiply(T, inverse(T), S)), multiply(T, inverse(T), X2))), X2)
% 110.61/14.38
% 110.61/14.38 Lemma 5: multiply(multiply(multiply(multiply(X, Y, Z), W, multiply(X, Y, V)), inverse(multiply(multiply(U, inverse(U), T), inverse(multiply(U, inverse(U), T)), multiply(U, inverse(U), S))), S), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2) = multiply(Y, multiply(V, W, Z), X).
% 110.61/14.38 Proof:
% 110.61/14.38 multiply(multiply(multiply(multiply(X, Y, Z), W, multiply(X, Y, V)), inverse(multiply(multiply(U, inverse(U), T), inverse(multiply(U, inverse(U), T)), multiply(U, inverse(U), S))), S), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2)
% 110.61/14.38 = { by lemma 4 R->L }
% 110.61/14.38 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(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2)
% 110.61/14.38 = { by lemma 4 R->L }
% 110.61/14.38 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(W2, V2, U2), T2, multiply(W2, V2, S2))), multiply(V2, multiply(S2, T2, U2), W2))
% 110.61/14.38 = { by axiom 1 (single_axiom) }
% 110.61/14.38 multiply(Y, multiply(V, W, Z), X)
% 110.61/14.38
% 110.61/14.38 Lemma 6: multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), V))), V) = Y.
% 110.61/14.38 Proof:
% 110.61/14.38 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), V))), V)
% 110.61/14.38 = { by lemma 3 R->L }
% 110.61/14.38 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), V))), multiply(inverse(Z), multiply(V, inverse(multiply(Z, inverse(Z), W)), W), Z))
% 110.61/14.38 = { by axiom 1 (single_axiom) }
% 110.61/14.38 Y
% 110.61/14.38
% 110.61/14.38 Lemma 7: multiply(X, inverse(multiply(multiply(Y, inverse(Y), Z), inverse(multiply(Y, inverse(Y), Z)), multiply(Y, inverse(Y), W))), W) = multiply(X, inverse(multiply(V, inverse(V), multiply(U, inverse(U), T))), T).
% 110.61/14.38 Proof:
% 110.61/14.38 multiply(X, inverse(multiply(multiply(Y, inverse(Y), Z), inverse(multiply(Y, inverse(Y), Z)), multiply(Y, inverse(Y), W))), W)
% 110.61/14.38 = { by lemma 4 R->L }
% 110.61/14.38 multiply(X, inverse(multiply(multiply(S, inverse(S), multiply(V, inverse(V), multiply(U, inverse(U), T))), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), multiply(S, inverse(S), Z2)))), multiply(S, inverse(S), Z2))), multiply(inverse(S), multiply(Z2, inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), multiply(S, inverse(S), Z2)))), multiply(V, inverse(V), multiply(U, inverse(U), T))), S))
% 110.61/14.38 = { by lemma 5 R->L }
% 110.61/14.38 multiply(X, inverse(multiply(multiply(S, inverse(S), multiply(V, inverse(V), multiply(U, inverse(U), T))), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), multiply(S, inverse(S), Z2)))), multiply(S, inverse(S), Z2))), multiply(multiply(multiply(multiply(S, inverse(S), multiply(V, inverse(V), multiply(U, inverse(U), T))), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), multiply(S, inverse(S), Z2)))), multiply(S, inverse(S), Z2)), inverse(multiply(multiply(W2, inverse(W2), V2), inverse(multiply(W2, inverse(W2), V2)), multiply(W2, inverse(W2), U2))), U2), inverse(multiply(multiply(T2, inverse(T2), S2), inverse(multiply(T2, inverse(T2), S2)), multiply(T2, inverse(T2), X3))), X3))
% 110.61/14.38 = { by lemma 6 }
% 110.61/14.38 multiply(X, inverse(multiply(multiply(S, inverse(S), multiply(V, inverse(V), multiply(U, inverse(U), T))), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), multiply(S, inverse(S), Z2)))), multiply(S, inverse(S), Z2))), multiply(multiply(multiply(V, inverse(V), multiply(U, inverse(U), T)), inverse(multiply(multiply(W2, inverse(W2), V2), inverse(multiply(W2, inverse(W2), V2)), multiply(W2, inverse(W2), U2))), U2), inverse(multiply(multiply(T2, inverse(T2), S2), inverse(multiply(T2, inverse(T2), S2)), multiply(T2, inverse(T2), X3))), X3))
% 110.61/14.38 = { by lemma 6 }
% 110.61/14.38 multiply(X, inverse(multiply(V, inverse(V), multiply(U, inverse(U), T))), multiply(multiply(multiply(V, inverse(V), multiply(U, inverse(U), T)), inverse(multiply(multiply(W2, inverse(W2), V2), inverse(multiply(W2, inverse(W2), V2)), multiply(W2, inverse(W2), U2))), U2), inverse(multiply(multiply(T2, inverse(T2), S2), inverse(multiply(T2, inverse(T2), S2)), multiply(T2, inverse(T2), X3))), X3))
% 110.61/14.38 = { by lemma 6 }
% 110.61/14.38 multiply(X, inverse(multiply(V, inverse(V), multiply(U, inverse(U), T))), multiply(multiply(U, inverse(U), T), inverse(multiply(multiply(T2, inverse(T2), S2), inverse(multiply(T2, inverse(T2), S2)), multiply(T2, inverse(T2), X3))), X3))
% 110.61/14.38 = { by lemma 6 }
% 110.61/14.38 multiply(X, inverse(multiply(V, inverse(V), multiply(U, inverse(U), T))), T)
% 110.61/14.38
% 110.61/14.38 Lemma 8: multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), V) = Y.
% 110.61/14.38 Proof:
% 110.61/14.38 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), V)
% 110.61/14.38 = { by lemma 7 R->L }
% 110.61/14.38 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(U, inverse(U), T), inverse(multiply(U, inverse(U), T)), multiply(U, inverse(U), S))), S)
% 110.61/14.38 = { by lemma 6 }
% 110.61/14.38 Y
% 110.61/14.38
% 110.61/14.38 Lemma 9: multiply(inverse(X), Y, X) = Y.
% 110.61/14.38 Proof:
% 110.61/14.39 multiply(inverse(X), Y, X)
% 110.61/14.39 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.39 multiply(inverse(X), multiply(multiply(Z, inverse(Z), Y), inverse(multiply(multiply(W, inverse(W), V), inverse(multiply(W, inverse(W), V)), multiply(W, inverse(W), multiply(X, inverse(X), multiply(Z, inverse(Z), Y))))), multiply(inverse(W), multiply(multiply(X, inverse(X), multiply(Z, inverse(Z), Y)), inverse(multiply(W, inverse(W), V)), V), W)), X)
% 110.61/14.39 = { by lemma 5 R->L }
% 110.61/14.39 multiply(multiply(multiply(multiply(X, inverse(X), multiply(inverse(W), multiply(multiply(X, inverse(X), multiply(Z, inverse(Z), Y)), inverse(multiply(W, inverse(W), V)), V), W)), inverse(multiply(multiply(W, inverse(W), V), inverse(multiply(W, inverse(W), V)), multiply(W, inverse(W), multiply(X, inverse(X), multiply(Z, inverse(Z), Y))))), multiply(X, inverse(X), multiply(Z, inverse(Z), Y))), inverse(multiply(multiply(U, inverse(U), T), inverse(multiply(U, inverse(U), T)), multiply(U, inverse(U), S))), S), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2)
% 110.61/14.39 = { by lemma 6 }
% 110.61/14.39 multiply(multiply(multiply(inverse(W), multiply(multiply(X, inverse(X), multiply(Z, inverse(Z), Y)), inverse(multiply(W, inverse(W), V)), V), W), inverse(multiply(multiply(U, inverse(U), T), inverse(multiply(U, inverse(U), T)), multiply(U, inverse(U), S))), S), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2)
% 110.61/14.39 = { by lemma 3 }
% 110.61/14.39 multiply(multiply(multiply(X, inverse(X), multiply(Z, inverse(Z), Y)), inverse(multiply(multiply(U, inverse(U), T), inverse(multiply(U, inverse(U), T)), multiply(U, inverse(U), S))), S), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2)
% 110.61/14.39 = { by lemma 8 }
% 110.61/14.39 multiply(multiply(Z, inverse(Z), Y), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2)
% 110.61/14.39 = { by lemma 8 }
% 110.61/14.39 Y
% 110.61/14.39
% 110.61/14.39 Lemma 10: inverse(multiply(X, inverse(X), Y)) = inverse(Y).
% 110.61/14.39 Proof:
% 110.61/14.39 inverse(multiply(X, inverse(X), Y))
% 110.61/14.39 = { by lemma 9 R->L }
% 110.61/14.39 multiply(inverse(X), inverse(multiply(X, inverse(X), Y)), X)
% 110.61/14.39 = { by lemma 9 R->L }
% 110.61/14.39 multiply(inverse(X), multiply(inverse(Y), inverse(multiply(X, inverse(X), Y)), Y), X)
% 110.61/14.39 = { by lemma 3 }
% 110.61/14.39 inverse(Y)
% 110.61/14.39
% 110.61/14.39 Lemma 11: multiply(X, inverse(Y), Y) = X.
% 110.61/14.39 Proof:
% 110.61/14.39 multiply(X, inverse(Y), Y)
% 110.61/14.39 = { by lemma 9 R->L }
% 110.61/14.39 multiply(inverse(Z), multiply(X, inverse(Y), Y), Z)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(inverse(Z), multiply(X, inverse(multiply(Z, inverse(Z), Y)), Y), Z)
% 110.61/14.39 = { by lemma 2 R->L }
% 110.61/14.39 multiply(multiply(Z, inverse(Z), X), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 110.61/14.39 = { by lemma 4 }
% 110.61/14.39 multiply(multiply(Z, inverse(Z), X), inverse(multiply(multiply(X2, inverse(X2), Y2), inverse(multiply(X2, inverse(X2), Y2)), multiply(X2, inverse(X2), Z2))), Z2)
% 110.61/14.39 = { by lemma 6 }
% 110.61/14.39 X
% 110.61/14.39
% 110.61/14.39 Lemma 12: multiply(X, inverse(X), Y) = Y.
% 110.61/14.39 Proof:
% 110.61/14.39 multiply(X, inverse(X), Y)
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(X, inverse(X), Y), inverse(Z), Z)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), Z)), Z)
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), Z))), Z)
% 110.61/14.39 = { by lemma 6 }
% 110.61/14.39 Y
% 110.61/14.39
% 110.61/14.39 Lemma 13: inverse(inverse(X)) = X.
% 110.61/14.39 Proof:
% 110.61/14.39 inverse(inverse(X))
% 110.61/14.39 = { by lemma 9 R->L }
% 110.61/14.39 multiply(inverse(X), inverse(inverse(X)), X)
% 110.61/14.39 = { by lemma 12 }
% 110.61/14.39 X
% 110.61/14.39
% 110.61/14.39 Lemma 14: multiply(Z, Y, X) = multiply(X, Y, Z).
% 110.61/14.39 Proof:
% 110.61/14.39 multiply(Z, Y, X)
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(Z, Y, X), inverse(T), T)
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, Y, X), inverse(T), T), inverse(Y2), Y2)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, Y, X), inverse(T), T), inverse(multiply(S, inverse(S), Y2)), Y2)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, Y, X), inverse(multiply(V, inverse(V), T)), T), inverse(multiply(S, inverse(S), Y2)), Y2)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, Y, X), inverse(multiply(V, inverse(V), T)), T), inverse(multiply(multiply(S, inverse(S), X2), inverse(multiply(S, inverse(S), X2)), multiply(S, inverse(S), Y2))), Y2)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, Y, X), inverse(multiply(multiply(V, inverse(V), U), inverse(multiply(V, inverse(V), U)), multiply(V, inverse(V), T))), T), inverse(multiply(multiply(S, inverse(S), X2), inverse(multiply(S, inverse(S), X2)), multiply(S, inverse(S), Y2))), Y2)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, Y, multiply(W, inverse(W), X)), inverse(multiply(multiply(V, inverse(V), U), inverse(multiply(V, inverse(V), U)), multiply(V, inverse(V), T))), T), inverse(multiply(multiply(S, inverse(S), X2), inverse(multiply(S, inverse(S), X2)), multiply(S, inverse(S), Y2))), Y2)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(multiply(multiply(W, inverse(W), Z), Y, multiply(W, inverse(W), X)), inverse(multiply(multiply(V, inverse(V), U), inverse(multiply(V, inverse(V), U)), multiply(V, inverse(V), T))), T), inverse(multiply(multiply(S, inverse(S), X2), inverse(multiply(S, inverse(S), X2)), multiply(S, inverse(S), Y2))), Y2)
% 110.61/14.39 = { by lemma 5 }
% 110.61/14.39 multiply(inverse(W), multiply(X, Y, Z), W)
% 110.61/14.39 = { by lemma 9 }
% 110.61/14.39 multiply(X, Y, Z)
% 110.61/14.39
% 110.61/14.39 Lemma 15: multiply(X, Y, inverse(Y)) = X.
% 110.61/14.39 Proof:
% 110.61/14.39 multiply(X, Y, inverse(Y))
% 110.61/14.39 = { by lemma 14 }
% 110.61/14.39 multiply(inverse(Y), Y, X)
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(inverse(Y), Y, X), inverse(Z), Z)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(multiply(inverse(Y), Y, X), inverse(multiply(W, inverse(W), Z)), Z)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(inverse(Y), Y, X), inverse(multiply(multiply(W, inverse(W), V), inverse(multiply(W, inverse(W), V)), multiply(W, inverse(W), Z))), Z)
% 110.61/14.39 = { by lemma 4 R->L }
% 110.61/14.39 multiply(multiply(inverse(Y), Y, X), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(T, multiply(Y2, X2, S), U))
% 110.61/14.39 = { by lemma 13 R->L }
% 110.61/14.39 multiply(multiply(inverse(Y), inverse(inverse(Y)), X), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(T, multiply(Y2, X2, S), U))
% 110.61/14.39 = { by axiom 1 (single_axiom) }
% 110.61/14.39 X
% 110.61/14.39
% 110.61/14.39 Lemma 16: multiply(X, inverse(Y), X) = X.
% 110.61/14.39 Proof:
% 110.61/14.39 multiply(X, inverse(Y), X)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(X, inverse(Y), multiply(Y, inverse(Y), X))
% 110.61/14.39 = { by lemma 14 }
% 110.61/14.39 multiply(X, inverse(Y), multiply(X, inverse(Y), Y))
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(X, inverse(Y), multiply(X, inverse(Y), Y)), inverse(Z), Z)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(multiply(X, inverse(Y), multiply(X, inverse(Y), Y)), inverse(multiply(W, inverse(W), Z)), Z)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(X, inverse(Y), multiply(X, inverse(Y), Y)), inverse(multiply(multiply(W, inverse(W), V), inverse(multiply(W, inverse(W), V)), multiply(W, inverse(W), Z))), Z)
% 110.61/14.39 = { by lemma 4 R->L }
% 110.61/14.39 multiply(multiply(X, inverse(Y), multiply(X, inverse(Y), Y)), inverse(multiply(multiply(U, T, S), X2, multiply(U, T, Y2))), multiply(T, multiply(Y2, X2, S), U))
% 110.61/14.39 = { by lemma 2 }
% 110.61/14.39 multiply(inverse(Y), multiply(multiply(X, inverse(Y), Y), inverse(multiply(X, inverse(Y), Y)), Y), X)
% 110.61/14.39 = { by lemma 12 }
% 110.61/14.39 multiply(inverse(Y), Y, X)
% 110.61/14.39 = { by lemma 14 R->L }
% 110.61/14.39 multiply(X, Y, inverse(Y))
% 110.61/14.39 = { by lemma 15 }
% 110.61/14.39 X
% 110.61/14.39
% 110.61/14.39 Lemma 17: multiply(Z, X, Y) = multiply(X, Y, Z).
% 110.61/14.39 Proof:
% 110.61/14.39 multiply(Z, X, Y)
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(Z, X, Y), inverse(T), T)
% 110.61/14.39 = { by lemma 11 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, X, Y), inverse(T), T), inverse(Y2), Y2)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, X, Y), inverse(T), T), inverse(multiply(S, inverse(S), Y2)), Y2)
% 110.61/14.39 = { by lemma 10 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, X, Y), inverse(multiply(V, inverse(V), T)), T), inverse(multiply(S, inverse(S), Y2)), Y2)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, X, Y), inverse(multiply(V, inverse(V), T)), T), inverse(multiply(multiply(S, inverse(S), X2), inverse(multiply(S, inverse(S), X2)), multiply(S, inverse(S), Y2))), Y2)
% 110.61/14.39 = { by lemma 12 R->L }
% 110.61/14.39 multiply(multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, inverse(V), U), inverse(multiply(V, inverse(V), U)), multiply(V, inverse(V), T))), T), inverse(multiply(multiply(S, inverse(S), X2), inverse(multiply(S, inverse(S), X2)), multiply(S, inverse(S), Y2))), Y2)
% 110.61/14.40 = { by lemma 16 R->L }
% 110.61/14.40 multiply(multiply(multiply(multiply(Z, X, Y), inverse(W), multiply(Z, X, Y)), inverse(multiply(multiply(V, inverse(V), U), inverse(multiply(V, inverse(V), U)), multiply(V, inverse(V), T))), T), inverse(multiply(multiply(S, inverse(S), X2), inverse(multiply(S, inverse(S), X2)), multiply(S, inverse(S), Y2))), Y2)
% 110.61/14.40 = { by lemma 5 }
% 110.61/14.40 multiply(X, multiply(Y, inverse(W), Y), Z)
% 110.61/14.40 = { by lemma 16 }
% 110.61/14.40 multiply(X, Y, Z)
% 110.61/14.40
% 110.61/14.40 Lemma 18: multiply(X, Y, Z) = multiply(Y, X, Z).
% 110.61/14.40 Proof:
% 110.61/14.40 multiply(X, Y, Z)
% 110.61/14.40 = { by lemma 14 }
% 110.61/14.40 multiply(Z, Y, X)
% 110.61/14.40 = { by lemma 17 }
% 110.61/14.40 multiply(Y, X, Z)
% 110.61/14.40
% 110.61/14.40 Lemma 19: multiply(X, Y, Z) = multiply(X, Z, Y).
% 110.61/14.40 Proof:
% 110.61/14.40 multiply(X, Y, Z)
% 110.61/14.40 = { by lemma 14 }
% 110.61/14.40 multiply(Z, Y, X)
% 110.61/14.40 = { by lemma 17 R->L }
% 110.61/14.40 multiply(X, Z, Y)
% 110.61/14.40
% 110.61/14.40 Lemma 20: multiply(X, inverse(Y), multiply(Y, Z, inverse(X))) = multiply(X, Z, inverse(Y)).
% 110.61/14.40 Proof:
% 110.61/14.40 multiply(X, inverse(Y), multiply(Y, Z, inverse(X)))
% 110.61/14.40 = { by lemma 18 R->L }
% 110.61/14.40 multiply(X, inverse(Y), multiply(Z, Y, inverse(X)))
% 110.61/14.40 = { by lemma 19 R->L }
% 110.61/14.40 multiply(X, inverse(Y), multiply(Z, inverse(X), Y))
% 110.61/14.40 = { by lemma 19 R->L }
% 110.61/14.40 multiply(X, multiply(Z, inverse(X), Y), inverse(Y))
% 110.61/14.40 = { by lemma 11 R->L }
% 110.61/14.40 multiply(multiply(X, inverse(W), W), multiply(Z, inverse(X), Y), inverse(Y))
% 110.61/14.40 = { by lemma 10 R->L }
% 110.61/14.40 multiply(multiply(X, inverse(multiply(Y, inverse(Y), W)), W), multiply(Z, inverse(X), Y), inverse(Y))
% 110.61/14.40 = { by lemma 3 R->L }
% 110.61/14.40 multiply(multiply(X, inverse(multiply(Y, inverse(Y), W)), W), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y)), Y), inverse(Y))
% 110.61/14.40 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.40 multiply(multiply(multiply(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y), inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y)), multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Z)), inverse(multiply(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y), inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y)), multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Z))), multiply(multiply(X, inverse(multiply(Y, inverse(Y), W)), W), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y)), Y), inverse(Y))), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 110.61/14.40 = { by axiom 1 (single_axiom) }
% 110.61/14.40 multiply(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Z), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 110.61/14.40 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.40 multiply(multiply(multiply(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y2), inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y2)), multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Z)), inverse(multiply(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y2), inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y2)), multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Z))), multiply(multiply(X, inverse(multiply(Y, inverse(Y), W)), W), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y2)), Y2), inverse(Y))), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 110.61/14.40 = { by axiom 1 (single_axiom) }
% 110.61/14.40 multiply(multiply(X, inverse(multiply(Y, inverse(Y), W)), W), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y2)), Y2), inverse(Y))
% 110.61/14.40 = { by lemma 10 }
% 110.61/14.40 multiply(multiply(X, inverse(W), W), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), W)), W), Y2)), Y2), inverse(Y))
% 110.61/14.40 = { by lemma 10 }
% 110.61/14.40 multiply(multiply(X, inverse(W), W), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(W), W), Y2)), Y2), inverse(Y))
% 110.61/14.40 = { by lemma 11 }
% 110.61/14.40 multiply(X, multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(W), W), Y2)), Y2), inverse(Y))
% 110.61/14.40 = { by lemma 11 }
% 110.61/14.40 multiply(X, multiply(Z, inverse(multiply(inverse(Y), X, Y2)), Y2), inverse(Y))
% 110.61/14.40 = { by axiom 1 (single_axiom) R->L }
% 110.61/14.40 multiply(multiply(multiply(multiply(inverse(Y), X, Y2), inverse(multiply(inverse(Y), X, Y2)), multiply(inverse(Y), X, Z)), inverse(multiply(multiply(inverse(Y), X, Y2), inverse(multiply(inverse(Y), X, Y2)), multiply(inverse(Y), X, Z))), multiply(X, multiply(Z, inverse(multiply(inverse(Y), X, Y2)), Y2), inverse(Y))), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2))
% 110.61/14.40 = { by axiom 1 (single_axiom) }
% 110.61/14.40 multiply(multiply(inverse(Y), X, Z), inverse(multiply(multiply(Z2, W2, V2), U2, multiply(Z2, W2, T2))), multiply(W2, multiply(T2, U2, V2), Z2))
% 111.37/14.40 = { by lemma 4 }
% 111.37/14.40 multiply(multiply(inverse(Y), X, Z), inverse(multiply(multiply(S2, inverse(S2), X3), inverse(multiply(S2, inverse(S2), X3)), multiply(S2, inverse(S2), Y3))), Y3)
% 111.37/14.40 = { by lemma 7 }
% 111.37/14.40 multiply(multiply(inverse(Y), X, Z), inverse(multiply(Z3, inverse(Z3), multiply(Z3, inverse(Z3), Z3))), Z3)
% 111.37/14.40 = { by lemma 11 }
% 111.37/14.40 multiply(multiply(inverse(Y), X, Z), inverse(multiply(Z3, inverse(Z3), Z3)), Z3)
% 111.37/14.40 = { by lemma 19 }
% 111.37/14.40 multiply(multiply(inverse(Y), X, Z), inverse(multiply(Z3, Z3, inverse(Z3))), Z3)
% 111.37/14.40 = { by lemma 15 }
% 111.37/14.40 multiply(multiply(inverse(Y), X, Z), inverse(Z3), Z3)
% 111.37/14.40 = { by lemma 11 }
% 111.37/14.40 multiply(inverse(Y), X, Z)
% 111.37/14.40 = { by lemma 18 }
% 111.37/14.40 multiply(X, inverse(Y), Z)
% 111.37/14.40 = { by lemma 19 }
% 111.37/14.40 multiply(X, Z, inverse(Y))
% 111.37/14.40
% 111.37/14.40 Lemma 21: multiply(X, Y, X) = X.
% 111.37/14.40 Proof:
% 111.37/14.40 multiply(X, Y, X)
% 111.37/14.40 = { by lemma 13 R->L }
% 111.37/14.40 multiply(X, Y, inverse(inverse(X)))
% 111.37/14.40 = { by lemma 20 R->L }
% 111.37/14.40 multiply(X, inverse(inverse(X)), multiply(inverse(X), Y, inverse(X)))
% 111.37/14.40 = { by lemma 17 }
% 111.37/14.40 multiply(X, inverse(inverse(X)), multiply(Y, inverse(X), inverse(X)))
% 111.37/14.40 = { by lemma 20 R->L }
% 111.37/14.40 multiply(X, inverse(inverse(X)), multiply(Y, inverse(X), multiply(X, inverse(X), inverse(Y))))
% 111.37/14.40 = { by lemma 12 }
% 111.37/14.40 multiply(X, inverse(inverse(X)), multiply(Y, inverse(X), inverse(Y)))
% 111.37/14.40 = { by lemma 11 R->L }
% 111.37/14.40 multiply(X, inverse(inverse(X)), multiply(Y, multiply(inverse(X), inverse(Z), Z), inverse(Y)))
% 111.37/14.40 = { by lemma 10 R->L }
% 111.37/14.40 multiply(X, inverse(inverse(X)), multiply(Y, multiply(inverse(X), inverse(multiply(inverse(Y), inverse(inverse(Y)), Z)), Z), inverse(Y)))
% 111.37/14.40 = { by lemma 13 R->L }
% 111.37/14.40 multiply(X, inverse(inverse(X)), multiply(inverse(inverse(Y)), multiply(inverse(X), inverse(multiply(inverse(Y), inverse(inverse(Y)), Z)), Z), inverse(Y)))
% 111.37/14.40 = { by lemma 3 }
% 111.37/14.40 multiply(X, inverse(inverse(X)), inverse(X))
% 111.37/14.40 = { by lemma 13 }
% 111.37/14.40 multiply(X, X, inverse(X))
% 111.37/14.40 = { by lemma 15 }
% 111.37/14.40 X
% 111.37/14.40
% 111.37/14.40 Goal 1 (prove_tba_axioms): tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), multiply(inverse(b), b, a), multiply(a, a, b), multiply(a, b, inverse(b)), multiply(b, a, a)) = tuple(multiply(d, e, multiply(a, b, c)), a, a, a, a).
% 111.37/14.40 Proof:
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), multiply(inverse(b), b, a), multiply(a, a, b), multiply(a, b, inverse(b)), multiply(b, a, a))
% 111.37/14.40 = { by lemma 13 R->L }
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), multiply(inverse(b), inverse(inverse(b)), a), multiply(a, a, b), multiply(a, b, inverse(b)), multiply(b, a, a))
% 111.37/14.40 = { by lemma 12 }
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), a, multiply(a, a, b), multiply(a, b, inverse(b)), multiply(b, a, a))
% 111.37/14.40 = { by lemma 15 }
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), a, multiply(a, a, b), a, multiply(b, a, a))
% 111.37/14.40 = { by lemma 19 R->L }
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), a, multiply(a, b, a), a, multiply(b, a, a))
% 111.37/14.40 = { by lemma 21 }
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), a, a, a, multiply(b, a, a))
% 111.37/14.40 = { by lemma 18 R->L }
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), a, a, a, multiply(a, b, a))
% 111.37/14.40 = { by lemma 21 }
% 111.37/14.40 tuple(multiply(multiply(d, e, a), b, multiply(d, e, c)), a, a, a, a)
% 111.37/14.41 = { by lemma 18 }
% 111.37/14.41 tuple(multiply(b, multiply(d, e, a), multiply(d, e, c)), a, a, a, a)
% 111.37/14.41 = { by lemma 19 R->L }
% 111.37/14.41 tuple(multiply(b, multiply(d, e, c), multiply(d, e, a)), a, a, a, a)
% 111.37/14.41 = { by lemma 18 R->L }
% 111.37/14.41 tuple(multiply(multiply(d, e, c), b, multiply(d, e, a)), a, a, a, a)
% 111.37/14.41 = { by lemma 11 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(d, e, c), b, multiply(d, e, a)), inverse(X), X), a, a, a, a)
% 111.37/14.41 = { by lemma 11 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, c), b, multiply(d, e, a)), inverse(X), X), inverse(Y), Y), a, a, a, a)
% 111.37/14.41 = { by lemma 10 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, c), b, multiply(d, e, a)), inverse(multiply(Z, inverse(Z), X)), X), inverse(Y), Y), a, a, a, a)
% 111.37/14.41 = { by lemma 10 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, c), b, multiply(d, e, a)), inverse(multiply(Z, inverse(Z), X)), X), inverse(multiply(W, inverse(W), Y)), Y), a, a, a, a)
% 111.37/14.41 = { by lemma 12 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, c), b, multiply(d, e, a)), inverse(multiply(multiply(Z, inverse(Z), V), inverse(multiply(Z, inverse(Z), V)), multiply(Z, inverse(Z), X))), X), inverse(multiply(W, inverse(W), Y)), Y), a, a, a, a)
% 111.37/14.41 = { by lemma 12 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, c), b, multiply(d, e, a)), inverse(multiply(multiply(Z, inverse(Z), V), inverse(multiply(Z, inverse(Z), V)), multiply(Z, inverse(Z), X))), X), inverse(multiply(multiply(W, inverse(W), U), inverse(multiply(W, inverse(W), U)), multiply(W, inverse(W), Y))), Y), a, a, a, a)
% 111.37/14.41 = { by lemma 14 }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, a), b, multiply(d, e, c)), inverse(multiply(multiply(Z, inverse(Z), V), inverse(multiply(Z, inverse(Z), V)), multiply(Z, inverse(Z), X))), X), inverse(multiply(multiply(W, inverse(W), U), inverse(multiply(W, inverse(W), U)), multiply(W, inverse(W), Y))), Y), a, a, a, a)
% 111.37/14.41 = { by lemma 4 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, a), b, multiply(d, e, c)), inverse(multiply(multiply(d, e, a), b, multiply(d, e, c))), multiply(e, multiply(c, b, a), d)), inverse(multiply(multiply(W, inverse(W), U), inverse(multiply(W, inverse(W), U)), multiply(W, inverse(W), Y))), Y), a, a, a, a)
% 111.37/14.41 = { by lemma 4 R->L }
% 111.37/14.41 tuple(multiply(multiply(multiply(multiply(d, e, a), b, multiply(d, e, c)), inverse(multiply(multiply(d, e, a), b, multiply(d, e, c))), multiply(e, multiply(c, b, a), d)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)), a, a, a, a)
% 111.37/14.41 = { by axiom 1 (single_axiom) }
% 111.37/14.41 tuple(multiply(e, multiply(c, b, a), d), a, a, a, a)
% 111.37/14.41 = { by lemma 19 }
% 111.37/14.41 tuple(multiply(e, d, multiply(c, b, a)), a, a, a, a)
% 111.37/14.41 = { by lemma 18 }
% 111.37/14.41 tuple(multiply(d, e, multiply(c, b, a)), a, a, a, a)
% 111.37/14.41 = { by lemma 18 }
% 111.37/14.41 tuple(multiply(d, e, multiply(b, c, a)), a, a, a, a)
% 111.37/14.41 = { by lemma 19 }
% 111.37/14.41 tuple(multiply(d, e, multiply(b, a, c)), a, a, a, a)
% 111.37/14.41 = { by lemma 18 }
% 111.37/14.41 tuple(multiply(d, e, multiply(a, b, c)), a, a, a, a)
% 111.37/14.41 % SZS output end Proof
% 111.37/14.41
% 111.37/14.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------