TSTP Solution File: LAT078-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT078-1 : 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 : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:27:21 EDT 2023
% Result : Unsatisfiable 165.43s 21.62s
% Output : Proof 171.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT078-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 08:41:20 EDT 2023
% 0.14/0.34 % CPUTime :
% 165.43/21.62 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 165.43/21.62
% 165.43/21.62 % SZS status Unsatisfiable
% 165.43/21.62
% 169.46/22.09 % SZS output start Proof
% 169.46/22.09 Axiom 1 (mol_27B2): f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z))) = Y.
% 169.46/22.09
% 169.46/22.09 Lemma 2: f(X, f(f(X, Y), f(f(f(f(Z, X), f(f(Z, X), f(f(W, W), f(X, Y)))), f(X, Y)), W))) = f(X, Y).
% 169.46/22.09 Proof:
% 169.46/22.09 f(X, f(f(X, Y), f(f(f(f(Z, X), f(f(Z, X), f(f(W, W), f(X, Y)))), f(X, Y)), W)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) R->L }
% 169.46/22.09 f(f(f(f(f(Z, X), f(X, Y)), f(f(X, Y), W)), f(X, f(f(f(Z, f(Z, f(f(Y, Y), X))), X), Y))), f(f(X, Y), f(f(f(f(Z, X), f(f(Z, X), f(f(W, W), f(X, Y)))), f(X, Y)), W)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) }
% 169.46/22.09 f(X, Y)
% 169.46/22.09
% 169.46/22.09 Lemma 3: f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(U, U), Y))), Y), U))) = Y.
% 169.46/22.09 Proof:
% 169.46/22.09 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(U, U), Y))), Y), U)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) R->L }
% 169.46/22.09 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(U, U), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))))), Y), U)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) R->L }
% 169.46/22.09 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(U, U), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))))), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))), U)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) R->L }
% 169.46/22.09 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z))), f(f(f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(U, U), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))))), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))), U)))
% 169.46/22.09 = { by lemma 2 }
% 169.46/22.09 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) }
% 169.46/22.09 Y
% 169.46/22.09
% 169.46/22.09 Lemma 4: f(f(X, Y), f(X, f(f(f(f(Z, f(X, Y)), f(f(Z, f(X, Y)), f(f(W, W), X))), X), W))) = X.
% 169.46/22.09 Proof:
% 169.46/22.09 f(f(X, Y), f(X, f(f(f(f(Z, f(X, Y)), f(f(Z, f(X, Y)), f(f(W, W), X))), X), W)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) R->L }
% 169.46/22.09 f(f(X, Y), f(X, f(f(f(f(Z, f(f(f(f(f(V, X), f(X, U)), X), f(X, f(f(f(V, f(V, f(f(U, U), X))), X), U))), Y)), f(f(Z, f(X, Y)), f(f(W, W), X))), X), W)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) R->L }
% 169.46/22.09 f(f(X, Y), f(X, f(f(f(f(Z, f(f(f(f(f(V, X), f(X, U)), X), f(X, f(f(f(V, f(V, f(f(U, U), X))), X), U))), Y)), f(f(Z, f(f(f(f(f(V, X), f(X, U)), X), f(X, f(f(f(V, f(V, f(f(U, U), X))), X), U))), Y)), f(f(W, W), X))), X), W)))
% 169.46/22.09 = { by axiom 1 (mol_27B2) R->L }
% 169.46/22.09 f(f(f(f(f(f(V, X), f(X, U)), X), f(X, f(f(f(V, f(V, f(f(U, U), X))), X), U))), Y), f(X, f(f(f(f(Z, f(f(f(f(f(V, X), f(X, U)), X), f(X, f(f(f(V, f(V, f(f(U, U), X))), X), U))), Y)), f(f(Z, f(f(f(f(f(V, X), f(X, U)), X), f(X, f(f(f(V, f(V, f(f(U, U), X))), X), U))), Y)), f(f(W, W), X))), X), W)))
% 169.46/22.09 = { by lemma 3 }
% 169.46/22.09 X
% 169.46/22.09
% 169.46/22.09 Lemma 5: f(f(X, Y), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z))) = Y.
% 169.46/22.09 Proof:
% 169.46/22.09 f(f(X, Y), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))
% 169.46/22.09 = { by lemma 4 R->L }
% 169.46/22.10 f(f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(f(f(f(W, f(f(X, Y), f(Y, Z))), f(f(W, f(f(X, Y), f(Y, Z))), f(f(V, V), f(X, Y)))), f(X, Y)), V))), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))
% 169.46/22.10 = { by axiom 1 (mol_27B2) }
% 169.46/22.10 Y
% 169.46/22.10
% 169.46/22.10 Lemma 6: f(X, f(f(Y, X), f(f(f(f(Z, X), f(f(Z, X), f(f(W, W), f(Y, X)))), f(Y, X)), W))) = f(Y, X).
% 169.46/22.10 Proof:
% 169.46/22.10 f(X, f(f(Y, X), f(f(f(f(Z, X), f(f(Z, X), f(f(W, W), f(Y, X)))), f(Y, X)), W)))
% 169.46/22.10 = { by lemma 5 R->L }
% 169.46/22.10 f(X, f(f(Y, X), f(f(f(f(Z, f(f(Y, X), f(X, f(f(f(Y, f(Y, f(f(V, V), X))), X), V)))), f(f(Z, X), f(f(W, W), f(Y, X)))), f(Y, X)), W)))
% 169.46/22.10 = { by lemma 5 R->L }
% 169.46/22.10 f(X, f(f(Y, X), f(f(f(f(Z, f(f(Y, X), f(X, f(f(f(Y, f(Y, f(f(V, V), X))), X), V)))), f(f(Z, f(f(Y, X), f(X, f(f(f(Y, f(Y, f(f(V, V), X))), X), V)))), f(f(W, W), f(Y, X)))), f(Y, X)), W)))
% 169.46/22.10 = { by lemma 5 R->L }
% 169.46/22.10 f(f(f(Y, X), f(X, f(f(f(Y, f(Y, f(f(V, V), X))), X), V))), f(f(Y, X), f(f(f(f(Z, f(f(Y, X), f(X, f(f(f(Y, f(Y, f(f(V, V), X))), X), V)))), f(f(Z, f(f(Y, X), f(X, f(f(f(Y, f(Y, f(f(V, V), X))), X), V)))), f(f(W, W), f(Y, X)))), f(Y, X)), W)))
% 169.46/22.10 = { by lemma 4 }
% 169.46/22.10 f(Y, X)
% 169.46/22.10
% 169.46/22.10 Lemma 7: f(f(X, f(f(Y, Z), f(Z, W))), f(Z, f(f(f(Y, f(Y, f(f(W, W), Z))), Z), W))) = Z.
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(X, f(f(Y, Z), f(Z, W))), f(Z, f(f(f(Y, f(Y, f(f(W, W), Z))), Z), W)))
% 169.46/22.10 = { by lemma 6 R->L }
% 169.46/22.10 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, f(f(f(Y, f(Y, f(f(W, W), Z))), Z), W)))
% 169.46/22.10 = { by axiom 1 (mol_27B2) }
% 169.46/22.10 Z
% 169.46/22.10
% 169.46/22.10 Lemma 8: f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), Y)) = f(f(X, Y), f(Y, Z)).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), Y))
% 169.46/22.10 = { by lemma 7 R->L }
% 169.46/22.10 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z))), f(f(X, Y), f(Y, Z))))), f(f(X, Y), f(Y, Z))), f(Y, f(f(f(X, f(X, f(f(Z, Z), Y))), Y), Z)))))
% 169.46/22.10 = { by lemma 4 }
% 169.46/22.10 f(f(X, Y), f(Y, Z))
% 169.46/22.10
% 169.46/22.10 Lemma 9: f(f(f(f(X, Y), f(Y, Z)), f(f(f(X, Y), f(Y, Z)), Y)), f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), W))) = f(f(f(X, Y), f(Y, Z)), Y).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(f(f(X, Y), f(Y, Z)), f(f(f(X, Y), f(Y, Z)), Y)), f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), W)))
% 169.46/22.10 = { by lemma 8 R->L }
% 169.46/22.10 f(f(f(f(X, Y), f(Y, Z)), f(f(f(X, Y), f(Y, Z)), Y)), f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(f(f(X, Y), f(Y, Z)), f(f(f(X, Y), f(Y, Z)), f(f(W, W), f(f(f(X, Y), f(Y, Z)), Y)))), f(f(f(X, Y), f(Y, Z)), Y)), W)))
% 169.46/22.10 = { by lemma 5 }
% 169.46/22.10 f(f(f(X, Y), f(Y, Z)), Y)
% 169.46/22.10
% 169.46/22.10 Lemma 10: f(f(X, f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(Y, Z), f(Z, W)), f(Y, Z)))) = f(f(f(Y, Z), f(Z, W)), Z).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(X, f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(Y, Z), f(Z, W)), f(Y, Z))))
% 169.46/22.10 = { by lemma 6 R->L }
% 169.46/22.10 f(f(f(f(f(Y, Z), f(Z, W)), Z), f(f(X, f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(U, U), f(X, f(f(f(Y, Z), f(Z, W)), Z))))), f(X, f(f(f(Y, Z), f(Z, W)), Z))), U))), f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(Y, Z), f(Z, W)), f(Y, Z))))
% 169.46/22.10 = { by lemma 8 R->L }
% 169.46/22.10 f(f(f(f(f(Y, Z), f(Z, W)), Z), f(f(X, f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(U, U), f(X, f(f(f(Y, Z), f(Z, W)), Z))))), f(X, f(f(f(Y, Z), f(Z, W)), Z))), U))), f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Y, Z)), f(f(f(Y, Z), f(Z, W)), Z)))), f(f(f(Y, Z), f(Z, W)), Z)), f(Y, Z))))
% 169.46/22.10 = { by lemma 9 R->L }
% 169.46/22.10 f(f(f(f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(f(f(f(T, f(f(Y, Z), f(Z, W))), f(f(T, f(f(Y, Z), f(Z, W))), f(f(S, S), f(Y, Z)))), f(Y, Z)), S))))), f(f(X, f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(U, U), f(X, f(f(f(Y, Z), f(Z, W)), Z))))), f(X, f(f(f(Y, Z), f(Z, W)), Z))), U))), f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Y, Z)), f(f(f(Y, Z), f(Z, W)), Z)))), f(f(f(Y, Z), f(Z, W)), Z)), f(Y, Z))))
% 169.46/22.10 = { by lemma 4 }
% 169.46/22.10 f(f(f(f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(Y, Z), f(Z, W)), Z), f(Y, Z))), f(f(X, f(f(f(Y, Z), f(Z, W)), Z)), f(f(f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(V, f(f(f(Y, Z), f(Z, W)), Z)), f(f(U, U), f(X, f(f(f(Y, Z), f(Z, W)), Z))))), f(X, f(f(f(Y, Z), f(Z, W)), Z))), U))), f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Y, Z)), f(f(f(Y, Z), f(Z, W)), Z)))), f(f(f(Y, Z), f(Z, W)), Z)), f(Y, Z))))
% 169.46/22.10 = { by axiom 1 (mol_27B2) }
% 169.46/22.10 f(f(f(Y, Z), f(Z, W)), Z)
% 169.46/22.10
% 169.46/22.10 Lemma 11: f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), Z)) = f(f(Y, Z), f(Z, W)).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), Z))
% 169.46/22.10 = { by lemma 7 R->L }
% 169.46/22.10 f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(f(X, f(X, f(f(f(Z, f(f(f(Y, f(Y, f(f(W, W), Z))), Z), W)), f(Z, f(f(f(Y, f(Y, f(f(W, W), Z))), Z), W))), f(f(Y, Z), f(Z, W))))), f(f(Y, Z), f(Z, W))), f(Z, f(f(f(Y, f(Y, f(f(W, W), Z))), Z), W)))))
% 169.46/22.10 = { by lemma 5 }
% 169.46/22.10 f(f(Y, Z), f(Z, W))
% 169.46/22.10
% 169.46/22.10 Lemma 12: f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z)))) = f(f(X, Y), f(Y, Z)).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z))))
% 169.46/22.10 = { by lemma 11 R->L }
% 169.46/22.10 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(V, f(f(f(X, Y), f(Y, Z)), W)), f(f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), Y)), f(f(X, Y), f(Y, Z))))), f(f(X, Y), f(Y, Z))), f(f(f(X, Y), f(Y, Z)), Y))))
% 169.46/22.10 = { by lemma 4 }
% 169.46/22.10 f(f(X, Y), f(Y, Z))
% 169.46/22.10
% 169.46/22.10 Lemma 13: f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W)))) = f(f(Y, Z), f(Z, W)).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))))
% 169.46/22.10 = { by lemma 11 R->L }
% 169.46/22.10 f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(f(X, f(X, f(f(f(f(f(Y, Z), f(Z, W)), Z), f(f(f(Y, Z), f(Z, W)), Z)), f(f(Y, Z), f(Z, W))))), f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), Z))))
% 169.46/22.10 = { by lemma 5 }
% 169.46/22.10 f(f(Y, Z), f(Z, W))
% 169.46/22.10
% 169.46/22.10 Lemma 14: f(f(f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))))), V), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W)))) = f(f(Y, Z), f(Z, W)).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))))), V), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))))
% 169.46/22.10 = { by lemma 13 R->L }
% 169.46/22.10 f(f(f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))))), V), f(f(f(Y, Z), f(Z, W)), f(f(f(X, f(X, f(f(f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W)))), f(f(Y, Z), f(Z, W))))), f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))))))
% 169.46/22.10 = { by axiom 1 (mol_27B2) }
% 169.46/22.10 f(f(Y, Z), f(Z, W))
% 169.46/22.10
% 169.46/22.10 Lemma 15: f(f(X, f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V)))))), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V)))) = f(f(Z, W), f(W, V)).
% 169.46/22.10 Proof:
% 169.46/22.10 f(f(X, f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V)))))), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V))))
% 169.46/22.10 = { by lemma 6 R->L }
% 169.46/22.11 f(f(f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V))))), f(f(X, f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V)))))), f(f(f(f(U, f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V)))))), f(f(U, f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V)))))), f(f(T, T), f(X, f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V))))))))), f(X, f(f(Y, f(f(Z, W), f(W, V))), f(f(f(Z, W), f(W, V)), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V))))))), T))), f(f(f(Z, W), f(W, V)), f(f(Z, W), f(W, V))))
% 169.46/22.11 = { by lemma 14 }
% 169.46/22.11 f(f(Z, W), f(W, V))
% 169.46/22.11
% 169.46/22.11 Lemma 16: f(f(f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), Y), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X)))) = f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), Y), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))))
% 169.46/22.11 = { by lemma 13 R->L }
% 169.46/22.11 f(f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), Y), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))))
% 169.46/22.11 = { by lemma 15 R->L }
% 169.46/22.11 f(f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), Y), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))), f(X, X))))
% 169.46/22.11 = { by axiom 1 (mol_27B2) }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))
% 169.46/22.11
% 169.46/22.11 Lemma 17: f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, Y)))) = f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, Y))))
% 169.46/22.11 = { by lemma 6 R->L }
% 169.46/22.11 f(f(f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y))), f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(f(f(Z, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(Z, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(W, W), f(X, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y))))))), f(X, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y))))), W))), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, Y))))
% 169.46/22.11 = { by lemma 16 }
% 169.46/22.11 f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))
% 169.46/22.11
% 169.46/22.11 Lemma 18: f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))) = f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X)))
% 169.46/22.11 = { by lemma 2 R->L }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), f(f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X)))), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X)))))), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X)))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))))))
% 169.46/22.11 = { by lemma 17 }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))
% 169.46/22.11 = { by lemma 12 }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))
% 169.46/22.11
% 169.46/22.11 Lemma 19: f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y))) = f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))
% 169.46/22.11 = { by lemma 12 R->L }
% 169.46/22.11 f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))), f(f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.11 = { by lemma 18 R->L }
% 169.46/22.11 f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.11 = { by lemma 17 R->L }
% 169.46/22.11 f(f(X, f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y))), f(f(f(X, f(X, f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, Y))), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, Y)))), f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))))), f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, Y))))))
% 169.46/22.11 = { by lemma 5 }
% 169.46/22.11 f(f(f(Y, Y), f(Y, Y)), f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))
% 169.46/22.11 = { by lemma 18 }
% 169.46/22.11 f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))
% 169.46/22.11
% 169.46/22.11 Lemma 20: f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), Y), f(f(X, X), f(X, X))) = f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), Y), f(f(X, X), f(X, X)))
% 169.46/22.11 = { by lemma 12 R->L }
% 169.46/22.11 f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), Y), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))
% 169.46/22.11 = { by lemma 19 R->L }
% 169.46/22.11 f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), Y), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(f(Z, f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), Y)), f(f(Z, f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), Y)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))), f(f(X, X), f(X, X)))))
% 169.46/22.11 = { by lemma 4 }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))
% 169.46/22.11
% 169.46/22.11 Lemma 21: f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))) = f(X, f(f(X, X), f(X, X))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))
% 169.46/22.11 = { by lemma 20 R->L }
% 169.46/22.11 f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, f(f(f(X, f(X, f(f(X, X), X))), X), X))), f(f(X, X), f(X, X)))
% 169.46/22.11 = { by axiom 1 (mol_27B2) }
% 169.46/22.11 f(X, f(f(X, X), f(X, X)))
% 169.46/22.11
% 169.46/22.11 Lemma 22: f(f(f(X, X), f(X, X)), X) = f(X, f(f(X, X), f(X, X))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(f(X, X), f(X, X)), X)
% 169.46/22.11 = { by lemma 2 R->L }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), X), f(f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(f(f(X, X), f(X, X)), X), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(f(X, X), f(X, X)), X), f(f(f(X, X), f(X, X)), f(X, X)))), f(f(f(X, X), f(X, X)), X)))), f(f(f(X, X), f(X, X)), X)), f(f(f(f(X, X), f(X, X)), X), f(f(f(X, X), f(X, X)), f(X, X))))))
% 169.46/22.11 = { by lemma 10 }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), X), f(f(f(X, X), f(X, X)), X)))
% 169.46/22.11 = { by lemma 8 }
% 169.46/22.11 f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))
% 169.46/22.11 = { by lemma 21 }
% 169.46/22.11 f(X, f(f(X, X), f(X, X)))
% 169.46/22.11
% 169.46/22.11 Lemma 23: f(f(f(X, Y), f(Y, Z)), Y) = f(Y, f(f(X, Y), f(Y, Z))).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(f(X, Y), f(Y, Z)), Y)
% 169.46/22.11 = { by lemma 6 R->L }
% 169.46/22.11 f(Y, f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(f(W, Y), f(f(W, Y), f(f(f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), f(X, Y))), f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), f(X, Y)))), f(f(f(X, Y), f(Y, Z)), Y)))), f(f(f(X, Y), f(Y, Z)), Y)), f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), f(X, Y))))))
% 169.46/22.11 = { by lemma 10 }
% 169.46/22.11 f(Y, f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), Y)))
% 169.46/22.11 = { by lemma 8 }
% 169.46/22.11 f(Y, f(f(X, Y), f(Y, Z)))
% 169.46/22.11
% 169.46/22.11 Lemma 24: f(f(X, f(f(Y, Z), f(Z, W))), f(Z, f(f(Y, Z), f(Z, W)))) = f(f(Y, Z), f(Z, W)).
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(X, f(f(Y, Z), f(Z, W))), f(Z, f(f(Y, Z), f(Z, W))))
% 169.46/22.11 = { by lemma 23 R->L }
% 169.46/22.11 f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(Y, Z), f(Z, W)), Z))
% 169.46/22.11 = { by lemma 11 }
% 169.46/22.11 f(f(Y, Z), f(Z, W))
% 169.46/22.11
% 169.46/22.11 Lemma 25: f(f(f(X, f(X, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y)) = Y.
% 169.46/22.11 Proof:
% 169.46/22.11 f(f(f(X, f(X, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y))
% 169.46/22.11 = { by lemma 22 R->L }
% 169.46/22.11 f(f(f(X, f(X, f(f(f(Y, Y), f(Y, Y)), Y))), Y), f(Y, Y))
% 169.46/22.11 = { by lemma 24 R->L }
% 169.46/22.11 f(f(f(f(X, Y), f(Y, f(Y, Y))), f(f(f(X, f(X, f(f(f(Y, Y), f(Y, Y)), Y))), Y), f(Y, Y))), f(Y, f(f(f(X, f(X, f(f(f(Y, Y), f(Y, Y)), Y))), Y), f(Y, Y))))
% 169.46/22.12 = { by axiom 1 (mol_27B2) }
% 169.46/22.12 Y
% 169.46/22.12
% 169.46/22.12 Lemma 26: f(f(X, Y), f(Y, Y)) = Y.
% 169.46/22.12 Proof:
% 169.46/22.12 f(f(X, Y), f(Y, Y))
% 169.46/22.12 = { by lemma 25 R->L }
% 169.46/22.12 f(f(X, Y), f(Y, f(f(f(X, f(X, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 22 R->L }
% 169.46/22.12 f(f(X, Y), f(Y, f(f(f(X, f(X, f(f(f(Y, Y), f(Y, Y)), Y))), Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 5 }
% 169.46/22.12 Y
% 169.46/22.12
% 169.46/22.12 Lemma 27: f(f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), Z), f(Y, f(f(Y, Y), f(Y, Y)))) = f(f(Y, Y), f(Y, Y)).
% 169.46/22.12 Proof:
% 169.46/22.12 f(f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), Z), f(Y, f(f(Y, Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 21 R->L }
% 169.46/22.12 f(f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))), Z), f(Y, f(f(Y, Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 21 R->L }
% 169.46/22.12 f(f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))), Z), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 13 R->L }
% 169.46/22.12 f(f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))), Z), f(f(f(Y, Y), f(Y, Y)), f(f(f(X, f(X, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))))
% 169.46/22.12 = { by axiom 1 (mol_27B2) }
% 169.46/22.12 f(f(Y, Y), f(Y, Y))
% 169.46/22.12
% 169.46/22.12 Lemma 28: f(f(f(f(X, Y), f(Y, f(Y, Y))), Z), f(Y, Y)) = Y.
% 169.46/22.12 Proof:
% 169.46/22.12 f(f(f(f(X, Y), f(Y, f(Y, Y))), Z), f(Y, Y))
% 169.46/22.12 = { by lemma 26 R->L }
% 169.46/22.12 f(f(f(f(X, Y), f(f(f(Y, Y), f(Y, Y)), f(Y, Y))), Z), f(Y, Y))
% 169.46/22.12 = { by lemma 26 R->L }
% 169.46/22.12 f(f(f(f(X, Y), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), Z), f(Y, Y))
% 169.46/22.12 = { by lemma 26 R->L }
% 169.46/22.12 f(f(f(f(X, Y), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), Z), f(Y, f(f(Y, Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 26 R->L }
% 169.46/22.12 f(f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), Z), f(Y, f(f(Y, Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 27 }
% 169.46/22.12 f(f(Y, Y), f(Y, Y))
% 169.46/22.12 = { by lemma 26 }
% 169.46/22.12 Y
% 169.46/22.12
% 169.46/22.12 Lemma 29: f(f(X, f(Y, Y)), Y) = f(Y, Y).
% 169.46/22.12 Proof:
% 169.46/22.12 f(f(X, f(Y, Y)), Y)
% 169.46/22.12 = { by lemma 25 R->L }
% 169.46/22.12 f(f(X, f(Y, Y)), f(f(f(Z, f(Z, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y)))
% 169.46/22.12 = { by lemma 24 R->L }
% 169.46/22.12 f(f(X, f(Y, Y)), f(f(Y, f(f(f(Z, f(Z, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y))), f(Y, f(f(f(Z, f(Z, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y)))))
% 169.46/22.12 = { by lemma 25 R->L }
% 169.46/22.12 f(f(X, f(Y, f(f(f(Z, f(Z, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y)))), f(f(Y, f(f(f(Z, f(Z, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y))), f(Y, f(f(f(Z, f(Z, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y)))))
% 169.46/22.12 = { by lemma 26 }
% 169.46/22.12 f(Y, f(f(f(Z, f(Z, f(Y, f(f(Y, Y), f(Y, Y))))), Y), f(Y, Y)))
% 169.46/22.12 = { by lemma 25 }
% 169.46/22.12 f(Y, Y)
% 169.46/22.12
% 169.46/22.12 Lemma 30: f(f(f(X, f(f(X, X), f(X, X))), Y), f(f(X, X), f(X, X))) = f(X, f(f(X, X), f(X, X))).
% 169.46/22.12 Proof:
% 169.46/22.12 f(f(f(X, f(f(X, X), f(X, X))), Y), f(f(X, X), f(X, X)))
% 169.46/22.12 = { by lemma 21 R->L }
% 169.46/22.12 f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), Y), f(f(X, X), f(X, X)))
% 169.46/22.12 = { by lemma 20 }
% 169.46/22.12 f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))
% 169.46/22.12 = { by lemma 21 }
% 169.46/22.12 f(X, f(f(X, X), f(X, X)))
% 169.46/22.12
% 169.46/22.12 Lemma 31: f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))) = f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))).
% 169.46/22.12 Proof:
% 169.46/22.12 f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 21 R->L }
% 169.46/22.12 f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))))
% 169.46/22.12 = { by lemma 15 R->L }
% 169.46/22.12 f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))), f(f(f(f(Z, f(X, f(f(Y, Y), f(Y, Y)))), f(f(Z, f(X, f(f(Y, Y), f(Y, Y)))), f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))), f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))))))), f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))))))
% 169.46/22.12 = { by lemma 2 }
% 169.46/22.12 f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.12 = { by lemma 21 }
% 169.46/22.12 f(f(X, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y)))))
% 169.46/22.12
% 169.46/22.12 Lemma 32: f(f(f(f(X, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, Y), f(Y, Y))) = f(Y, f(f(Y, Y), f(Y, Y))).
% 169.46/22.12 Proof:
% 169.46/22.12 f(f(f(f(X, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, Y), f(Y, Y)))
% 169.46/22.12 = { by lemma 24 R->L }
% 169.46/22.12 f(f(f(f(X, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, f(f(Y, Y), f(Y, Y))), f(Y, f(f(Y, Y), f(Y, Y)))))
% 169.46/22.12 = { by lemma 21 R->L }
% 169.46/22.12 f(f(f(f(X, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.12 = { by lemma 19 R->L }
% 169.46/22.12 f(f(f(f(X, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.12 = { by lemma 21 }
% 169.46/22.12 f(f(f(f(X, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.12 = { by lemma 30 R->L }
% 169.46/22.13 f(f(f(f(X, f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.13 = { by lemma 30 R->L }
% 169.46/22.13 f(f(f(f(X, f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.13 = { by lemma 30 R->L }
% 169.46/22.13 f(f(f(f(X, f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.13 = { by lemma 30 R->L }
% 169.46/22.13 f(f(f(f(X, f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.13 = { by lemma 21 R->L }
% 169.46/22.13 f(f(f(f(X, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.13 = { by lemma 21 R->L }
% 169.46/22.13 f(f(f(f(X, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.46/22.14 = { by lemma 21 R->L }
% 169.97/22.14 f(f(f(f(X, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.97/22.14 = { by lemma 21 R->L }
% 169.97/22.14 f(f(f(f(X, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.97/22.14 = { by lemma 21 R->L }
% 169.97/22.14 f(f(f(f(X, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))))), f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.97/22.14 = { by lemma 31 R->L }
% 169.97/22.14 f(f(f(f(X, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), Z), f(f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y))), f(f(f(X, f(X, f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))))), f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))), f(f(Y, Y), f(Y, Y)))))
% 169.97/22.14 = { by axiom 1 (mol_27B2) }
% 169.97/22.14 f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))
% 169.97/22.14 = { by lemma 21 }
% 169.97/22.14 f(f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(Y, f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))
% 169.97/22.14 = { by lemma 30 }
% 169.97/22.14 f(Y, f(f(Y, Y), f(Y, Y)))
% 169.97/22.14
% 169.97/22.14 Lemma 33: f(X, f(f(X, X), X)) = f(X, X).
% 169.97/22.14 Proof:
% 169.97/22.14 f(X, f(f(X, X), X))
% 169.97/22.14 = { by lemma 26 R->L }
% 169.97/22.14 f(X, f(f(X, f(f(X, X), f(X, X))), X))
% 169.97/22.14 = { by lemma 26 R->L }
% 169.97/22.14 f(X, f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))
% 169.97/22.15 = { by lemma 26 R->L }
% 169.97/22.15 f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))
% 169.97/22.15 = { by lemma 2 R->L }
% 169.97/22.15 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))), f(f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))), f(f(X, X), f(X, X)))))
% 169.97/22.15 = { by lemma 6 R->L }
% 169.97/22.15 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))), f(f(f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))), f(f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))), f(f(f(f(Z, f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))), f(f(Z, f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))), f(f(W, W), f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))))))), f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))))), W))), f(f(X, X), f(X, X)))))
% 169.97/22.15 = { by lemma 27 R->L }
% 169.97/22.15 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))), f(f(f(f(f(f(f(V, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), U), f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))), f(f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))), f(f(f(f(Z, f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))), f(f(Z, f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))), f(f(W, W), f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))))))), f(f(f(Y, f(f(X, X), f(X, X))), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X))))))), f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))))), W))), f(f(X, X), f(X, X)))))
% 169.97/22.15 = { by lemma 32 }
% 169.97/22.15 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))), f(X, f(f(X, X), f(X, X)))))
% 169.97/22.15 = { by lemma 21 R->L }
% 169.97/22.15 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(X, X), f(X, X)))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))
% 169.97/22.15 = { by lemma 12 }
% 169.97/22.15 f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))
% 169.97/22.15 = { by lemma 21 }
% 169.97/22.15 f(X, f(f(X, X), f(X, X)))
% 169.97/22.15 = { by lemma 26 }
% 169.97/22.15 f(X, X)
% 169.97/22.15
% 169.97/22.15 Lemma 34: f(f(X, Y), f(X, X)) = X.
% 169.97/22.15 Proof:
% 169.97/22.15 f(f(X, Y), f(X, X))
% 169.97/22.15 = { by lemma 25 R->L }
% 169.97/22.15 f(f(X, Y), f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))))
% 169.97/22.15 = { by lemma 23 R->L }
% 169.97/22.15 f(f(X, Y), f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X))
% 169.97/22.15 = { by lemma 25 R->L }
% 169.97/22.15 f(f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), Y), f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X))
% 169.97/22.15 = { by lemma 8 }
% 169.97/22.15 f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))
% 169.97/22.15 = { by lemma 25 }
% 169.97/22.16 X
% 169.97/22.16
% 169.97/22.16 Lemma 35: f(X, f(f(X, X), Y)) = f(X, X).
% 169.97/22.16 Proof:
% 169.97/22.16 f(X, f(f(X, X), Y))
% 169.97/22.16 = { by lemma 2 R->L }
% 169.97/22.16 f(X, f(f(X, f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), X)))
% 170.17/22.16 = { by lemma 6 R->L }
% 170.17/22.16 f(X, f(f(X, f(f(X, X), Y)), f(f(f(X, f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), X)))
% 170.17/22.17 = { by lemma 26 R->L }
% 170.17/22.17 f(X, f(f(X, f(f(X, X), Y)), f(f(f(X, f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(X, X)))))
% 170.17/22.17 = { by lemma 29 R->L }
% 170.17/22.18 f(X, f(f(X, f(f(X, X), Y)), f(f(f(X, f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(f(f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(X, X), f(X, X)))), f(X, X)), X)))))
% 170.17/22.18 = { by lemma 3 R->L }
% 170.17/22.18 f(X, f(f(X, f(f(X, X), Y)), f(f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, f(f(f(f(f(X2, f(X, X)), f(f(f(T, X), f(X, S)), f(X, X))), f(f(f(X2, f(X, X)), f(f(f(T, X), f(X, S)), f(X, X))), f(f(X, X), X))), X), X))), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(f(f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(X, X), f(X, X)))), f(X, X)), X)))))
% 170.17/22.19 = { by lemma 6 R->L }
% 170.17/22.19 f(X, f(f(X, f(f(X, X), Y)), f(f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, f(f(f(f(f(X2, f(X, X)), f(f(X, X), f(f(f(f(T, X), f(X, S)), f(X, X)), f(f(f(f(Y2, f(X, X)), f(f(Y2, f(X, X)), f(f(Z2, Z2), f(f(f(T, X), f(X, S)), f(X, X))))), f(f(f(T, X), f(X, S)), f(X, X))), Z2)))), f(f(f(X2, f(X, X)), f(f(f(T, X), f(X, S)), f(X, X))), f(f(X, X), X))), X), X))), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(f(f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(X, X), f(X, X)))), f(X, X)), X)))))
% 170.17/22.19 = { by lemma 26 R->L }
% 170.17/22.20 f(X, f(f(X, f(f(X, X), Y)), f(f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, f(f(f(f(f(X2, f(X, X)), f(f(X, X), f(f(f(f(T, X), f(X, S)), f(X, X)), f(f(f(f(Y2, f(X, X)), f(f(Y2, f(X, X)), f(f(Z2, Z2), f(f(f(T, X), f(X, S)), f(X, X))))), f(f(f(T, X), f(X, S)), f(X, X))), Z2)))), f(f(f(X2, f(X, X)), f(f(f(T, X), f(X, S)), f(X, X))), f(f(X, X), X))), f(f(X, X), f(X, X))), X))), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(f(f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(X, X), f(X, X)))), f(X, X)), X)))))
% 170.17/22.20 = { by lemma 29 R->L }
% 170.17/22.20 f(X, f(f(X, f(f(X, X), Y)), f(f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, f(f(f(f(f(X2, f(X, X)), f(f(X, X), f(f(f(f(T, X), f(X, S)), f(X, X)), f(f(f(f(Y2, f(X, X)), f(f(Y2, f(X, X)), f(f(Z2, Z2), f(f(f(T, X), f(X, S)), f(X, X))))), f(f(f(T, X), f(X, S)), f(X, X))), Z2)))), f(f(f(X2, f(X, X)), f(f(f(T, X), f(X, S)), f(X, X))), f(f(X, X), X))), f(f(X, X), f(f(f(f(W2, f(f(f(X2, f(X, X)), f(f(X, X), f(f(f(f(T, X), f(X, S)), f(X, X)), f(f(f(f(Y2, f(X, X)), f(f(Y2, f(X, X)), f(f(Z2, Z2), f(f(f(T, X), f(X, S)), f(X, X))))), f(f(f(T, X), f(X, S)), f(X, X))), Z2)))), f(f(f(X2, f(X, X)), f(f(f(T, X), f(X, S)), f(X, X))), f(f(X, X), X)))), f(f(W2, f(f(f(X2, f(X, X)), f(f(X, X), f(f(f(f(T, X), f(X, S)), f(X, X)), f(f(f(f(Y2, f(X, X)), f(f(Y2, f(X, X)), f(f(Z2, Z2), f(f(f(T, X), f(X, S)), f(X, X))))), f(f(f(T, X), f(X, S)), f(X, X))), Z2)))), f(f(f(X2, f(X, X)), f(f(f(T, X), f(X, S)), f(X, X))), f(f(X, X), X)))), f(f(X, X), f(X, X)))), f(X, X)), X))), X))), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(f(f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(X, X), f(X, X)))), f(X, X)), X)))))
% 170.17/22.20 = { by lemma 3 }
% 170.17/22.21 f(X, f(f(X, f(f(X, X), Y)), f(f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, f(f(X, X), X))), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(f(f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(X, X), f(X, X)))), f(X, X)), X)))))
% 170.17/22.21 = { by lemma 33 }
% 170.17/22.21 f(X, f(f(X, f(f(X, X), Y)), f(f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V))), f(f(X, X), f(f(f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(U, f(f(f(f(f(f(T, X), f(X, S)), f(X, X)), f(X, X)), f(f(X, X), Y)), f(f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y))), f(f(f(f(W, f(X, f(f(X, X), Y))), f(f(W, f(X, f(f(X, X), Y))), f(f(V, V), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))))), f(f(f(Z, X), f(f(Z, X), f(f(X, X), f(X, f(f(X, X), Y))))), f(X, f(f(X, X), Y)))), V)))), f(f(X, X), f(X, X)))), f(X, X)), X)))))
% 170.17/22.21 = { by lemma 3 }
% 170.17/22.21 f(X, f(f(X, f(f(X, X), Y)), f(X, X)))
% 170.17/22.21 = { by lemma 34 }
% 170.17/22.21 f(X, X)
% 170.17/22.21
% 170.17/22.21 Lemma 36: f(X, f(Y, f(X, X))) = f(X, X).
% 170.17/22.21 Proof:
% 170.17/22.21 f(X, f(Y, f(X, X)))
% 170.17/22.21 = { by lemma 6 R->L }
% 170.17/22.21 f(X, f(f(X, X), f(f(Y, f(X, X)), f(f(f(f(Z, f(X, X)), f(f(Z, f(X, X)), f(f(W, W), f(Y, f(X, X))))), f(Y, f(X, X))), W))))
% 170.17/22.21 = { by lemma 35 }
% 170.17/22.21 f(X, X)
% 170.17/22.21
% 170.17/22.21 Lemma 37: f(X, f(f(X, f(X, X)), f(f(X, X), X))) = f(X, f(X, X)).
% 170.17/22.21 Proof:
% 170.17/22.21 f(X, f(f(X, f(X, X)), f(f(X, X), X)))
% 170.17/22.21 = { by lemma 36 R->L }
% 170.17/22.21 f(X, f(f(X, f(X, X)), f(f(X, f(X, f(X, X))), X)))
% 170.17/22.21 = { by lemma 26 R->L }
% 170.17/22.21 f(X, f(f(f(f(X, X), f(X, X)), f(X, X)), f(f(X, f(X, f(X, X))), X)))
% 170.17/22.21 = { by lemma 26 R->L }
% 170.17/22.21 f(X, f(f(f(f(X, X), f(X, X)), f(X, X)), f(f(f(f(X, X), f(X, X)), f(X, f(X, X))), X)))
% 170.17/22.21 = { by lemma 26 R->L }
% 170.17/22.21 f(X, f(f(f(f(X, X), f(X, X)), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(X, X))), X)))
% 170.17/22.21 = { by lemma 26 R->L }
% 170.17/22.21 f(X, f(f(f(f(X, X), f(X, X)), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(X, X))), f(f(X, X), f(X, X)))))
% 170.17/22.21 = { by lemma 26 R->L }
% 170.17/22.21 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(X, X))), f(f(X, X), f(X, X)))))
% 170.17/22.21 = { by lemma 13 R->L }
% 170.17/22.21 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(X, X)), f(f(f(f(f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(X, X), f(X, X)), f(X, X))), f(f(X, X), f(X, X)))))
% 170.17/22.21 = { by lemma 16 R->L }
% 170.17/22.22 f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(X, X)), f(f(f(f(f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), f(f(X, X), f(X, X))), f(f(f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X))), f(f(X, X), f(X, X))), f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))))), f(f(f(X, X), f(X, X)), f(X, X))), f(f(X, X), f(X, X)))))
% 170.17/22.22 = { by lemma 2 }
% 170.17/22.22 f(f(f(X, X), f(X, X)), f(X, X))
% 170.17/22.22 = { by lemma 26 }
% 170.17/22.22 f(X, f(X, X))
% 170.17/22.22
% 170.17/22.22 Lemma 38: f(f(X, f(X, X)), f(f(X, X), f(X, Y))) = f(X, X).
% 170.17/22.22 Proof:
% 170.17/22.22 f(f(X, f(X, X)), f(f(X, X), f(X, Y)))
% 170.17/22.22 = { by lemma 25 R->L }
% 170.17/22.22 f(f(X, f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), f(f(X, X), f(X, Y)))
% 170.17/22.22 = { by lemma 25 R->L }
% 170.17/22.22 f(f(X, f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), f(f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(X, Y)))
% 170.17/22.22 = { by lemma 25 R->L }
% 170.17/22.22 f(f(X, f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), f(f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), Y)))
% 170.17/22.22 = { by lemma 23 R->L }
% 170.17/22.22 f(f(X, f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), Y)))
% 170.17/22.22 = { by lemma 23 R->L }
% 170.17/22.22 f(f(X, f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X), f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), Y)))
% 170.17/22.22 = { by lemma 25 R->L }
% 170.17/22.22 f(f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X), f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), Y)))
% 170.17/22.22 = { by lemma 9 }
% 170.17/22.22 f(f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)
% 170.17/22.22 = { by lemma 23 }
% 170.17/22.22 f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))
% 170.17/22.22 = { by lemma 25 }
% 170.63/22.22 f(X, X)
% 170.63/22.22
% 170.63/22.22 Lemma 39: f(f(f(X, X), X), f(X, f(X, X))) = f(f(X, f(X, X)), f(f(X, X), X)).
% 170.63/22.22 Proof:
% 170.63/22.22 f(f(f(X, X), X), f(X, f(X, X)))
% 170.63/22.22 = { by lemma 4 R->L }
% 170.63/22.22 f(f(f(X, X), X), f(f(f(X, f(X, X)), f(f(X, X), X)), f(f(X, f(X, X)), f(f(f(f(X, f(f(X, f(X, X)), f(f(X, X), X))), f(f(X, f(f(X, f(X, X)), f(f(X, X), X))), f(f(X, X), f(X, f(X, X))))), f(X, f(X, X))), X))))
% 170.63/22.22 = { by lemma 37 }
% 170.63/22.22 f(f(f(X, X), X), f(f(f(X, f(X, X)), f(f(X, X), X)), f(f(X, f(X, X)), f(f(f(f(X, f(X, X)), f(f(X, f(f(X, f(X, X)), f(f(X, X), X))), f(f(X, X), f(X, f(X, X))))), f(X, f(X, X))), X))))
% 170.63/22.22 = { by lemma 37 }
% 170.63/22.22 f(f(f(X, X), X), f(f(f(X, f(X, X)), f(f(X, X), X)), f(f(X, f(X, X)), f(f(f(f(X, f(X, X)), f(f(X, f(X, X)), f(f(X, X), f(X, f(X, X))))), f(X, f(X, X))), X))))
% 170.63/22.22 = { by lemma 38 }
% 170.63/22.22 f(f(f(X, X), X), f(f(f(X, f(X, X)), f(f(X, X), X)), f(f(X, f(X, X)), f(f(f(f(X, f(X, X)), f(X, X)), f(X, f(X, X))), X))))
% 170.63/22.22 = { by lemma 34 }
% 170.63/22.22 f(f(f(X, X), X), f(f(f(X, f(X, X)), f(f(X, X), X)), f(f(X, f(X, X)), f(f(X, f(X, f(X, X))), X))))
% 170.63/22.22 = { by lemma 36 }
% 170.63/22.22 f(f(f(X, X), X), f(f(f(X, f(X, X)), f(f(X, X), X)), f(f(X, f(X, X)), f(f(X, X), X))))
% 170.63/22.22 = { by lemma 26 R->L }
% 170.63/22.22 f(f(f(X, X), f(f(Y, X), f(X, X))), f(f(f(X, f(X, X)), f(f(X, X), X)), f(f(X, f(X, X)), f(f(X, X), X))))
% 170.63/22.22 = { by lemma 26 R->L }
% 170.63/22.22 f(f(f(X, X), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, X), X)), f(f(X, f(X, X)), f(f(X, X), X))))
% 170.63/22.22 = { by lemma 26 R->L }
% 170.63/22.22 f(f(f(X, X), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), X)), f(f(X, f(X, X)), f(f(X, X), X))))
% 170.63/22.22 = { by lemma 26 R->L }
% 170.63/22.22 f(f(f(X, X), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(X, f(X, X)), f(f(X, X), X))))
% 170.63/22.22 = { by lemma 26 R->L }
% 170.63/22.23 f(f(f(X, X), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, X), X))))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(f(X, X), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), X))))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(f(X, X), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))))))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))))))
% 170.63/22.23 = { by lemma 11 R->L }
% 170.63/22.23 f(f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(f(f(Z, f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(Z, f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(f(f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(X, f(f(X, X), f(X, X)))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(X, f(f(X, X), f(X, X))))), f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))))))), f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))))), f(f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X)))), f(X, f(f(X, X), f(X, X)))))))
% 170.63/22.23 = { by lemma 6 }
% 170.63/22.23 f(f(X, f(X, f(f(X, X), f(X, X)))), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))))
% 170.63/22.23 = { by lemma 35 }
% 170.63/22.23 f(f(X, f(X, X)), f(f(X, f(f(X, X), f(X, X))), f(f(Y, X), f(X, X))))
% 170.63/22.23 = { by lemma 35 }
% 170.63/22.23 f(f(X, f(X, X)), f(f(X, X), f(f(Y, X), f(X, X))))
% 170.63/22.23 = { by lemma 26 }
% 170.63/22.23 f(f(X, f(X, X)), f(f(X, X), X))
% 170.63/22.23
% 170.63/22.23 Lemma 40: f(f(X, X), X) = f(X, f(X, X)).
% 170.63/22.23 Proof:
% 170.63/22.23 f(f(X, X), X)
% 170.63/22.23 = { by lemma 2 R->L }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(f(f(f(f(Y, X), f(X, f(X, X))), Z), f(X, X)), f(f(f(f(f(Y, X), f(X, f(X, X))), Z), f(X, X)), f(f(X, X), f(f(X, X), X)))), f(f(X, X), X)), X)))
% 170.63/22.23 = { by lemma 28 }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(X, f(f(f(f(f(Y, X), f(X, f(X, X))), Z), f(X, X)), f(f(X, X), f(f(X, X), X)))), f(f(X, X), X)), X)))
% 170.63/22.23 = { by lemma 28 }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(X, f(X, f(f(X, X), f(f(X, X), X)))), f(f(X, X), X)), X)))
% 170.63/22.23 = { by lemma 35 }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(X, f(X, X)), f(f(X, X), X)), X)))
% 170.63/22.23 = { by lemma 39 R->L }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, X), X), f(X, f(X, X))), X)))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(X, f(X, X))), X)))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))), X)))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), X)))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), f(f(X, X), f(X, X)))))
% 170.63/22.23 = { by lemma 26 R->L }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), f(f(X, X), f(X, X)))))
% 170.63/22.23 = { by lemma 31 }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))))
% 170.63/22.23 = { by lemma 26 }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))))
% 170.63/22.23 = { by lemma 26 }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(X, f(X, f(f(X, X), f(X, X))))))
% 170.63/22.23 = { by lemma 26 }
% 170.63/22.23 f(f(X, X), f(f(f(X, X), X), f(X, f(X, X))))
% 170.63/22.23 = { by lemma 39 }
% 170.63/22.23 f(f(X, X), f(f(X, f(X, X)), f(f(X, X), X)))
% 170.63/22.23 = { by lemma 36 R->L }
% 170.63/22.23 f(f(X, X), f(f(X, f(X, X)), f(f(X, f(X, f(X, X))), X)))
% 170.63/22.23 = { by lemma 34 R->L }
% 170.63/22.23 f(f(X, X), f(f(X, f(X, X)), f(f(f(f(X, f(X, X)), f(X, X)), f(X, f(X, X))), X)))
% 170.63/22.23 = { by lemma 38 R->L }
% 170.63/22.23 f(f(X, X), f(f(X, f(X, X)), f(f(f(f(X, f(X, X)), f(f(X, f(X, X)), f(f(X, X), f(X, f(X, X))))), f(X, f(X, X))), X)))
% 170.63/22.23 = { by lemma 6 }
% 170.63/22.23 f(X, f(X, X))
% 170.63/22.23
% 170.63/22.23 Lemma 41: f(f(X, Y), f(X, f(f(f(Z, f(Z, f(f(Y, Y), X))), X), Y))) = X.
% 170.63/22.23 Proof:
% 170.63/22.23 f(f(X, Y), f(X, f(f(f(Z, f(Z, f(f(Y, Y), X))), X), Y)))
% 170.63/22.23 = { by lemma 5 R->L }
% 170.63/22.23 f(f(f(f(Z, X), f(X, Y)), f(f(X, Y), f(f(f(f(Z, X), f(f(Z, X), f(f(W, W), f(X, Y)))), f(X, Y)), W))), f(X, f(f(f(Z, f(Z, f(f(Y, Y), X))), X), Y)))
% 170.63/22.23 = { by axiom 1 (mol_27B2) }
% 170.63/22.24 X
% 170.63/22.24
% 170.63/22.24 Lemma 42: f(f(f(f(X, X), X), f(f(X, X), X)), Y) = f(f(X, X), X).
% 170.63/22.24 Proof:
% 170.63/22.24 f(f(f(f(X, X), X), f(f(X, X), X)), Y)
% 170.63/22.24 = { by lemma 41 R->L }
% 170.63/22.24 f(f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), X), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(X, f(X, f(f(X, X), f(f(f(f(X, X), X), f(f(X, X), X)), Y)))), f(f(f(f(X, X), X), f(f(X, X), X)), Y)), X)))
% 170.63/22.24 = { by lemma 35 }
% 170.63/22.24 f(f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), X), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(X, f(X, X)), f(f(f(f(X, X), X), f(f(X, X), X)), Y)), X)))
% 170.63/22.24 = { by lemma 40 R->L }
% 170.63/22.24 f(f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), X), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(f(X, X), X), f(f(f(f(X, X), X), f(f(X, X), X)), Y)), X)))
% 170.63/22.24 = { by lemma 35 }
% 170.63/22.24 f(f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), X), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(f(X, X), X), f(f(X, X), X)), X)))
% 170.63/22.24 = { by lemma 26 R->L }
% 170.63/22.24 f(f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(X, X), f(X, X))), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(f(X, X), X), f(f(X, X), X)), X)))
% 170.63/22.24 = { by lemma 29 R->L }
% 170.63/22.24 f(f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(X, X), f(f(f(f(Z, f(f(f(X, f(X, X)), f(f(X, X), X)), Y)), f(f(Z, f(f(f(X, f(X, X)), f(f(X, X), X)), Y)), f(f(X, X), f(X, X)))), f(X, X)), X))), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(f(X, X), X), f(f(X, X), X)), X)))
% 170.63/22.24 = { by lemma 40 }
% 170.63/22.24 f(f(f(f(f(X, f(X, X)), f(f(X, X), X)), Y), f(f(X, X), f(f(f(f(Z, f(f(f(X, f(X, X)), f(f(X, X), X)), Y)), f(f(Z, f(f(f(X, f(X, X)), f(f(X, X), X)), Y)), f(f(X, X), f(X, X)))), f(X, X)), X))), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(f(X, X), X), f(f(X, X), X)), X)))
% 170.63/22.24 = { by lemma 3 }
% 170.63/22.24 f(f(X, X), f(f(f(f(f(X, X), X), f(f(X, X), X)), Y), f(f(f(f(X, X), X), f(f(X, X), X)), X)))
% 170.63/22.24 = { by lemma 40 }
% 170.63/22.24 f(f(X, X), f(f(f(f(f(X, X), X), f(X, f(X, X))), Y), f(f(f(f(X, X), X), f(f(X, X), X)), X)))
% 170.63/22.24 = { by lemma 40 }
% 170.63/22.24 f(f(X, X), f(f(f(f(f(X, X), X), f(X, f(X, X))), Y), f(f(f(f(X, X), X), f(X, f(X, X))), X)))
% 170.63/22.24 = { by lemma 26 R->L }
% 170.63/22.24 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(X, f(X, X))), Y), f(f(f(f(X, X), X), f(X, f(X, X))), X)))
% 170.63/22.24 = { by lemma 26 R->L }
% 170.63/22.24 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))), Y), f(f(f(f(X, X), X), f(X, f(X, X))), X)))
% 170.63/22.24 = { by lemma 26 R->L }
% 170.63/22.24 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), X), f(X, f(X, X))), X)))
% 170.63/22.24 = { by lemma 26 R->L }
% 170.63/22.24 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(X, f(X, X))), X)))
% 170.63/22.24 = { by lemma 26 R->L }
% 170.63/22.25 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, X))), X)))
% 170.63/22.25 = { by lemma 26 R->L }
% 170.63/22.25 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), X)))
% 170.63/22.25 = { by lemma 26 R->L }
% 170.63/22.25 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), f(f(X, X), f(X, X)))))
% 170.92/22.26 = { by lemma 14 R->L }
% 170.92/22.26 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))))), f(f(f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(f(X, f(f(X, X), f(X, X))), f(X, f(f(X, X), f(X, X)))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X)))))))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))), f(f(f(f(V, f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))), f(f(V, f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))), f(f(U, U), f(f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(f(X, f(f(X, X), f(X, X))), f(X, f(f(X, X), f(X, X)))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X)))))))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))))))))), f(f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(f(X, f(f(X, X), f(X, X))), f(X, f(f(X, X), f(X, X)))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X)))))))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))))))), U))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))))
% 170.92/22.26 = { by lemma 6 }
% 170.92/22.26 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), f(f(f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(f(X, f(f(X, X), f(X, X))), f(X, f(f(X, X), f(X, X)))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X)))))))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))))
% 170.92/22.26 = { by lemma 21 }
% 170.92/22.26 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), f(f(f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(f(X, f(f(X, X), f(X, X))), f(X, f(f(X, X), f(X, X)))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X)))))))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X)))))), f(X, f(f(X, X), f(X, X)))))))
% 170.92/22.26 = { by lemma 21 }
% 170.92/22.26 f(f(X, X), f(f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), f(f(f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(W, f(f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))), Y)), f(f(f(X, f(f(X, X), f(X, X))), f(X, f(f(X, X), f(X, X)))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X)))))))), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X)))))), f(X, f(f(X, X), f(X, X)))))))
% 170.92/22.26 = { by lemma 4 }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))))
% 170.92/22.26 = { by lemma 26 }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(f(f(X, X), f(X, X)), f(X, f(f(X, X), f(X, X))))))
% 170.92/22.26 = { by lemma 26 }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(X, f(X, f(f(X, X), f(X, X))))))
% 170.92/22.26 = { by lemma 26 }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(X, f(X, X))))
% 170.92/22.26 = { by lemma 40 R->L }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(f(X, X), X)))
% 170.92/22.26 = { by lemma 33 R->L }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(f(X, f(f(X, X), X)), X)))
% 170.92/22.26 = { by lemma 34 R->L }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(X, X)), f(f(X, X), X)), X)))
% 170.92/22.26 = { by lemma 25 R->L }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(X, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), f(f(X, X), X)), X)))
% 170.92/22.26 = { by lemma 23 R->L }
% 170.92/22.26 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(X, X), X)), X)))
% 170.92/22.26 = { by lemma 9 R->L }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X), f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), f(f(f(X, X), f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(f(f(S, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(S, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(X2, X2), f(f(X, X), f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))))), f(f(X, X), f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), X2)))))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 6 }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X), f(f(X, X), f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 25 }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(X, f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X), f(f(X, X), f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 23 }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(X, f(f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)), X)), f(f(X, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(X, X), f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 23 }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(X, f(X, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), f(f(X, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(X, X), f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 25 }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(X, f(X, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), f(f(X, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(f(X, X), X)))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 25 }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(X, f(X, f(f(f(T, f(T, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))), f(f(X, X), f(f(X, X), X)))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 25 }
% 170.92/22.27 f(f(X, X), f(f(f(X, X), X), f(f(f(f(X, f(X, X)), f(f(X, f(X, X)), f(f(X, X), f(f(X, X), X)))), f(f(X, X), X)), X)))
% 170.92/22.27 = { by lemma 2 }
% 170.92/22.27 f(f(X, X), X)
% 170.92/22.27
% 170.92/22.27 Lemma 43: f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))) = f(f(Y, Y), Y).
% 170.92/22.27 Proof:
% 170.92/22.27 f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y)))
% 170.92/22.27 = { by lemma 6 R->L }
% 170.92/22.27 f(f(f(f(Y, Y), Y), f(f(Y, Y), Y)), f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(f(f(f(Z, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(f(Z, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(f(W, W), f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y)))))), f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y)))), W)))
% 170.92/22.27 = { by lemma 42 }
% 170.92/22.27 f(f(Y, Y), Y)
% 170.92/22.27
% 170.92/22.27 Lemma 44: f(f(X, Y), f(Y, f(f(Z, Z), Z))) = Y.
% 170.92/22.27 Proof:
% 170.92/22.27 f(f(X, Y), f(Y, f(f(Z, Z), Z)))
% 170.92/22.27 = { by lemma 43 R->L }
% 170.92/22.27 f(f(X, Y), f(Y, f(f(f(X, f(X, f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Z, Z), Z), f(f(Z, Z), Z))), Y))), Y), f(f(f(Z, Z), Z), f(f(Z, Z), Z)))))
% 170.92/22.27 = { by lemma 5 }
% 170.92/22.27 Y
% 170.92/22.27
% 170.92/22.27 Lemma 45: f(X, f(f(X, Y), f(X, Y))) = f(X, Y).
% 170.92/22.27 Proof:
% 170.92/22.27 f(X, f(f(X, Y), f(X, Y)))
% 170.92/22.27 = { by lemma 44 R->L }
% 170.92/22.27 f(X, f(f(X, Y), f(f(f(f(Z, X), f(f(Z, X), f(f(f(f(X, Y), f(f(W, W), W)), f(f(X, Y), f(f(W, W), W))), f(X, Y)))), f(X, Y)), f(f(X, Y), f(f(W, W), W)))))
% 170.92/22.27 = { by lemma 2 }
% 170.92/22.27 f(X, Y)
% 170.92/22.27
% 170.92/22.27 Lemma 46: f(f(f(Y, Y), Y), X) = f(X, X).
% 170.92/22.27 Proof:
% 170.92/22.27 f(f(f(Y, Y), Y), X)
% 170.92/22.27 = { by lemma 42 R->L }
% 170.92/22.27 f(f(f(f(f(Y, Y), Y), f(f(Y, Y), Y)), f(X, X)), X)
% 170.92/22.27 = { by lemma 29 }
% 170.92/22.27 f(X, X)
% 170.92/22.27
% 170.92/22.27 Lemma 47: f(f(f(Z, Z), Z), X) = f(X, f(f(Y, Y), Y)).
% 170.92/22.27 Proof:
% 170.92/22.27 f(f(f(Z, Z), Z), X)
% 170.92/22.27 = { by lemma 41 R->L }
% 170.92/22.27 f(f(f(Z, Z), Z), f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(X, f(f(f(W, f(W, f(f(f(f(f(Y, Y), Y), f(f(Y, Y), Y)), f(f(f(Y, Y), Y), f(f(Y, Y), Y))), X))), X), f(f(f(Y, Y), Y), f(f(Y, Y), Y))))))
% 170.92/22.27 = { by lemma 43 }
% 170.92/22.27 f(f(f(Z, Z), Z), f(f(f(Y, Y), Y), f(X, f(f(f(W, f(W, f(f(f(f(f(Y, Y), Y), f(f(Y, Y), Y)), f(f(f(Y, Y), Y), f(f(Y, Y), Y))), X))), X), f(f(f(Y, Y), Y), f(f(Y, Y), Y))))))
% 170.92/22.27 = { by lemma 43 }
% 170.92/22.27 f(f(f(Z, Z), Z), f(f(f(Y, Y), Y), f(X, f(f(Y, Y), Y))))
% 170.92/22.27 = { by lemma 46 }
% 170.92/22.27 f(f(f(Z, Z), Z), f(f(X, f(f(Y, Y), Y)), f(X, f(f(Y, Y), Y))))
% 170.92/22.27 = { by lemma 42 R->L }
% 170.92/22.27 f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(X, f(f(Y, Y), Y))), f(f(X, f(f(Y, Y), Y)), f(X, f(f(Y, Y), Y))))
% 170.92/22.27 = { by lemma 26 }
% 170.92/22.27 f(X, f(f(Y, Y), Y))
% 170.92/22.27
% 170.92/22.27 Lemma 48: f(X, f(f(Y, Y), Y)) = f(X, X).
% 170.92/22.27 Proof:
% 170.92/22.27 f(X, f(f(Y, Y), Y))
% 170.92/22.27 = { by lemma 45 R->L }
% 170.92/22.27 f(X, f(f(X, f(f(Y, Y), Y)), f(X, f(f(Y, Y), Y))))
% 170.92/22.27 = { by lemma 47 R->L }
% 170.92/22.27 f(X, f(f(f(f(Z, Z), Z), X), f(X, f(f(Y, Y), Y))))
% 170.92/22.27 = { by lemma 44 }
% 170.92/22.27 f(X, X)
% 170.92/22.27
% 170.92/22.27 Lemma 49: f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), Y) = f(Y, Y).
% 170.92/22.27 Proof:
% 170.92/22.27 f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), Y)
% 170.92/22.27 = { by lemma 40 }
% 170.92/22.27 f(f(X, f(f(Y, f(Y, Y)), f(f(Y, Y), Y))), Y)
% 170.92/22.27 = { by lemma 26 R->L }
% 170.92/22.27 f(f(X, f(f(Y, f(Y, Y)), f(f(Y, Y), f(f(Y, Y), f(Y, Y))))), Y)
% 170.92/22.27 = { by lemma 26 R->L }
% 170.92/22.27 f(f(X, f(f(Y, f(Y, Y)), f(f(Y, Y), f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))
% 170.92/22.27 = { by lemma 35 R->L }
% 170.92/22.27 f(f(X, f(f(Y, f(Y, Y)), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))
% 170.92/22.27 = { by lemma 26 R->L }
% 170.92/22.27 f(f(X, f(f(Y, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y))))), f(f(Y, Y), f(Y, Y)))
% 170.92/22.27 = { by lemma 6 R->L }
% 170.92/22.27 f(f(f(f(Y, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))), f(f(X, f(f(Y, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y))))), f(f(f(f(Z, f(f(Y, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y))))), f(f(Z, f(f(Y, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y))))), f(f(W, W), f(X, f(f(Y, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))))))), f(X, f(f(Y, f(Y, f(f(Y, Y), f(Y, Y)))), f(f(Y, f(f(Y, Y), f(Y, Y))), f(f(Y, Y), f(Y, Y)))))), W))), f(f(Y, Y), f(Y, Y)))
% 170.92/22.27 = { by lemma 32 }
% 170.92/22.27 f(Y, f(f(Y, Y), f(Y, Y)))
% 170.92/22.27 = { by lemma 35 }
% 170.92/22.27 f(Y, Y)
% 170.92/22.27
% 170.92/22.27 Lemma 50: f(f(X, f(f(Y, Z), f(Z, W))), f(Z, Z)) = Z.
% 170.92/22.27 Proof:
% 170.92/22.27 f(f(X, f(f(Y, Z), f(Z, W))), f(Z, Z))
% 170.92/22.28 = { by lemma 6 R->L }
% 170.92/22.28 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, Z))
% 170.92/22.29 = { by lemma 33 R->L }
% 170.92/22.29 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, f(f(Z, Z), Z)))
% 170.92/22.29 = { by lemma 49 R->L }
% 170.92/22.29 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, f(f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))), Z), Z)))
% 170.92/22.30 = { by lemma 4 R->L }
% 170.92/22.30 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, f(f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z)), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z)))))), Z), Z)))
% 170.92/22.30 = { by lemma 49 R->L }
% 170.92/22.31 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, f(f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z)), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z)), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))))), f(f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(T, f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))))), f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z)), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(Z, Z))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))))), f(f(Z, Z), f(f(f(Z, Z), Z), f(f(Z, Z), Z))))), f(f(f(Z, Z), Z), f(f(Z, Z), Z))), Z)))))), Z), Z)))
% 170.92/22.31 = { by lemma 5 }
% 170.92/22.31 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, f(f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Z, Z), Z), f(f(Z, Z), Z))))), Z), Z)))
% 170.92/22.31 = { by lemma 34 }
% 170.92/22.31 f(f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U))), f(Z, f(f(f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(f(f(f(Z, Z), Z), f(f(Z, Z), Z)), f(f(f(Y, Z), f(Z, W)), f(f(X, f(f(Y, Z), f(Z, W))), f(f(f(f(V, f(f(Y, Z), f(Z, W))), f(f(V, f(f(Y, Z), f(Z, W))), f(f(U, U), f(X, f(f(Y, Z), f(Z, W)))))), f(X, f(f(Y, Z), f(Z, W)))), U)))), f(f(Z, Z), Z))), Z), Z)))
% 170.92/22.31 = { by lemma 3 }
% 170.92/22.31 Z
% 170.92/22.31
% 170.92/22.31 Lemma 51: f(f(f(X, X), Y), X) = f(X, X).
% 170.92/22.31 Proof:
% 170.92/22.31 f(f(f(X, X), Y), X)
% 170.92/22.31 = { by lemma 25 R->L }
% 170.92/22.31 f(f(f(X, X), Y), f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))
% 170.92/22.31 = { by lemma 24 R->L }
% 170.92/22.31 f(f(f(X, X), Y), f(f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))))
% 170.92/22.31 = { by lemma 25 R->L }
% 170.92/22.32 f(f(f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), Y), f(f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X))), f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))))
% 170.92/22.32 = { by lemma 34 }
% 170.92/22.32 f(X, f(f(f(Z, f(Z, f(X, f(f(X, X), f(X, X))))), X), f(X, X)))
% 170.92/22.32 = { by lemma 25 }
% 170.92/22.32 f(X, X)
% 170.92/22.32
% 170.92/22.32 Lemma 52: f(f(X, X), f(X, Y)) = X.
% 170.92/22.32 Proof:
% 170.92/22.32 f(f(X, X), f(X, Y))
% 170.92/22.32 = { by lemma 2 R->L }
% 170.92/22.32 f(f(X, X), f(f(f(X, X), f(X, Y)), f(f(f(f(Z, f(X, X)), f(f(Z, f(X, X)), f(f(f(X, X), f(X, X)), f(f(X, X), f(X, Y))))), f(f(X, X), f(X, Y))), f(X, X))))
% 170.92/22.32 = { by lemma 50 }
% 170.92/22.32 f(f(X, X), f(f(f(X, X), f(X, Y)), X))
% 170.92/22.32 = { by lemma 51 }
% 170.92/22.32 f(f(X, X), f(X, X))
% 170.92/22.32 = { by lemma 26 }
% 170.92/22.32 X
% 170.92/22.32
% 170.92/22.32 Lemma 53: f(f(f(X, Y), f(X, Y)), X) = f(X, Y).
% 170.92/22.32 Proof:
% 170.92/22.32 f(f(f(X, Y), f(X, Y)), X)
% 170.92/22.32 = { by lemma 4 R->L }
% 170.92/22.32 f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, f(f(f(f(Z, f(X, Y)), f(f(Z, f(X, Y)), f(f(W, W), X))), X), W))))
% 170.92/22.32 = { by lemma 52 }
% 170.92/22.32 f(X, Y)
% 170.92/22.32
% 170.92/22.32 Lemma 54: f(f(f(f(X, Y), f(Z, Y)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Z, Y)), W)), f(f(V, f(f(f(X, Y), f(Z, Y)), W)), f(f(U, U), Y))), Y), U))) = Y.
% 170.92/22.32 Proof:
% 170.92/22.32 f(f(f(f(X, Y), f(Z, Y)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Z, Y)), W)), f(f(V, f(f(f(X, Y), f(Z, Y)), W)), f(f(U, U), Y))), Y), U)))
% 170.92/22.32 = { by lemma 6 R->L }
% 170.92/22.32 f(f(f(f(X, Y), f(Z, Y)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Y, f(f(Z, Y), f(f(f(f(T, Y), f(f(T, Y), f(f(S, S), f(Z, Y)))), f(Z, Y)), S)))), W)), f(f(V, f(f(f(X, Y), f(Z, Y)), W)), f(f(U, U), Y))), Y), U)))
% 170.92/22.32 = { by lemma 6 R->L }
% 170.92/22.32 f(f(f(f(X, Y), f(Z, Y)), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Y, f(f(Z, Y), f(f(f(f(T, Y), f(f(T, Y), f(f(S, S), f(Z, Y)))), f(Z, Y)), S)))), W)), f(f(V, f(f(f(X, Y), f(Y, f(f(Z, Y), f(f(f(f(T, Y), f(f(T, Y), f(f(S, S), f(Z, Y)))), f(Z, Y)), S)))), W)), f(f(U, U), Y))), Y), U)))
% 170.92/22.32 = { by lemma 6 R->L }
% 170.92/22.32 f(f(f(f(X, Y), f(Y, f(f(Z, Y), f(f(f(f(T, Y), f(f(T, Y), f(f(S, S), f(Z, Y)))), f(Z, Y)), S)))), W), f(Y, f(f(f(f(V, f(f(f(X, Y), f(Y, f(f(Z, Y), f(f(f(f(T, Y), f(f(T, Y), f(f(S, S), f(Z, Y)))), f(Z, Y)), S)))), W)), f(f(V, f(f(f(X, Y), f(Y, f(f(Z, Y), f(f(f(f(T, Y), f(f(T, Y), f(f(S, S), f(Z, Y)))), f(Z, Y)), S)))), W)), f(f(U, U), Y))), Y), U)))
% 170.92/22.32 = { by lemma 3 }
% 170.92/22.32 Y
% 170.92/22.32
% 170.92/22.32 Lemma 55: f(f(f(X, X), Y), f(f(Z, X), f(Z, X))) = f(Z, X).
% 170.92/22.32 Proof:
% 170.92/22.32 f(f(f(X, X), Y), f(f(Z, X), f(Z, X)))
% 170.92/22.32 = { by lemma 48 R->L }
% 170.92/22.32 f(f(f(X, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(Z, X)))), Y), f(f(Z, X), f(Z, X)))
% 170.92/22.32 = { by lemma 26 R->L }
% 170.92/22.32 f(f(f(X, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), Y), f(f(Z, X), f(Z, X)))
% 170.92/22.33 = { by lemma 26 R->L }
% 170.92/22.33 f(f(f(X, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), Y), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))
% 170.92/22.33 = { by lemma 52 R->L }
% 170.92/22.33 f(f(f(f(f(X, X), f(X, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(f(f(W, X), f(f(W, X), f(f(V, V), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), V)))), f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), Y), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))
% 170.92/22.33 = { by lemma 54 R->L }
% 170.92/22.33 f(f(f(f(f(X, X), f(X, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(f(f(W, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(X, f(f(f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(T, T), X))), X), T)))), f(f(W, X), f(f(V, V), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), V)))), f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), Y), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))
% 170.92/22.33 = { by lemma 54 R->L }
% 170.92/22.33 f(f(f(f(f(X, X), f(X, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(f(f(W, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(X, f(f(f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(T, T), X))), X), T)))), f(f(W, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(X, f(f(f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(T, T), X))), X), T)))), f(f(V, V), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), V)))), f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), Y), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))
% 170.92/22.33 = { by lemma 54 R->L }
% 171.53/22.33 f(f(f(f(f(X, X), f(f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(X, f(f(f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(T, T), X))), X), T))), f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(f(f(W, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(X, f(f(f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(T, T), X))), X), T)))), f(f(W, f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(X, f(f(f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(U, f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(T, T), X))), X), T)))), f(f(V, V), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), V)))), f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), Y), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))
% 171.53/22.33 = { by lemma 4 }
% 171.53/22.33 f(f(f(f(f(X, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))), f(f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X))), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))), Y), f(f(Z, X), f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))))
% 171.53/22.33 = { by lemma 27 }
% 171.53/22.33 f(f(f(Z, X), f(Z, X)), f(f(Z, X), f(Z, X)))
% 171.53/22.33 = { by lemma 26 }
% 171.53/22.33 f(Z, X)
% 171.53/22.33
% 171.53/22.33 Lemma 56: f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, Y)) = Y.
% 171.53/22.33 Proof:
% 171.53/22.33 f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, Y))
% 171.53/22.33 = { by lemma 6 R->L }
% 171.53/22.33 f(f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, Y))
% 171.53/22.33 = { by lemma 35 R->L }
% 171.53/22.33 f(f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, f(f(Y, Y), Z)))
% 171.53/22.34 = { by lemma 46 R->L }
% 171.53/22.34 f(f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, f(f(f(f(f(Y, Z), f(Y, Z)), f(Y, Z)), Y), Z)))
% 171.53/22.34 = { by lemma 51 R->L }
% 171.53/22.34 f(f(f(f(f(f(Y, Z), f(Y, Z)), Y), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, f(f(f(f(f(Y, Z), f(Y, Z)), f(Y, Z)), Y), Z)))
% 171.53/22.34 = { by lemma 55 R->L }
% 171.53/22.34 f(f(f(f(f(f(Y, Z), f(Y, Z)), Y), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, f(f(f(f(f(Y, Z), f(Y, Z)), f(f(f(Z, Z), Y), f(f(Y, Z), f(Y, Z)))), Y), Z)))
% 171.53/22.34 = { by lemma 53 R->L }
% 171.53/22.34 f(f(f(f(f(f(Y, Z), f(Y, Z)), Y), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, f(f(f(f(f(Y, Z), f(Y, Z)), f(f(f(f(f(Z, Z), Y), f(f(Y, Z), f(Y, Z))), f(f(f(Z, Z), Y), f(f(Y, Z), f(Y, Z)))), f(f(Z, Z), Y))), Y), Z)))
% 171.53/22.34 = { by lemma 55 }
% 171.53/22.34 f(f(f(f(f(f(Y, Z), f(Y, Z)), Y), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, f(f(f(f(f(Y, Z), f(Y, Z)), f(f(f(Y, Z), f(f(f(Z, Z), Y), f(f(Y, Z), f(Y, Z)))), f(f(Z, Z), Y))), Y), Z)))
% 171.53/22.34 = { by lemma 36 }
% 171.53/22.34 f(f(f(f(f(f(Y, Z), f(Y, Z)), Y), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(W, f(f(Y, Z), f(Y, Z))), f(f(V, V), f(X, f(f(Y, Z), f(Y, Z)))))), f(X, f(f(Y, Z), f(Y, Z)))), V))), f(Y, f(f(f(f(f(Y, Z), f(Y, Z)), f(f(f(Y, Z), f(Y, Z)), f(f(Z, Z), Y))), Y), Z)))
% 171.53/22.34 = { by axiom 1 (mol_27B2) }
% 171.53/22.34 Y
% 171.53/22.34
% 171.53/22.34 Lemma 57: f(f(X, X), f(Y, f(f(X, Z), f(X, Z)))) = X.
% 171.53/22.34 Proof:
% 171.53/22.34 f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))
% 171.53/22.34 = { by lemma 36 R->L }
% 171.53/22.34 f(f(X, f(f(Y, f(f(X, Z), f(X, Z))), f(X, X))), f(Y, f(f(X, Z), f(X, Z))))
% 171.53/22.34 = { by lemma 56 R->L }
% 171.53/22.34 f(f(f(f(Y, f(f(X, Z), f(X, Z))), f(X, X)), f(f(Y, f(f(X, Z), f(X, Z))), f(X, X))), f(Y, f(f(X, Z), f(X, Z))))
% 171.53/22.34 = { by lemma 53 }
% 171.53/22.34 f(f(Y, f(f(X, Z), f(X, Z))), f(X, X))
% 171.53/22.34 = { by lemma 56 }
% 171.53/22.34 X
% 171.53/22.34
% 171.53/22.34 Lemma 58: f(f(X, f(f(Y, Z), f(W, Z))), f(Z, f(f(f(f(V, f(X, f(f(Y, Z), f(W, Z)))), f(f(V, f(X, f(f(Y, Z), f(W, Z)))), f(f(U, U), Z))), Z), U))) = Z.
% 171.53/22.34 Proof:
% 171.53/22.34 f(f(X, f(f(Y, Z), f(W, Z))), f(Z, f(f(f(f(V, f(X, f(f(Y, Z), f(W, Z)))), f(f(V, f(X, f(f(Y, Z), f(W, Z)))), f(f(U, U), Z))), Z), U)))
% 171.53/22.34 = { by lemma 6 R->L }
% 171.53/22.34 f(f(X, f(f(Y, Z), f(W, Z))), f(Z, f(f(f(f(V, f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(f(f(f(T, f(f(Y, Z), f(W, Z))), f(f(T, f(f(Y, Z), f(W, Z))), f(f(S, S), f(X, f(f(Y, Z), f(W, Z)))))), f(X, f(f(Y, Z), f(W, Z)))), S)))), f(f(V, f(X, f(f(Y, Z), f(W, Z)))), f(f(U, U), Z))), Z), U)))
% 171.53/22.34 = { by lemma 6 R->L }
% 171.53/22.34 f(f(X, f(f(Y, Z), f(W, Z))), f(Z, f(f(f(f(V, f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(f(f(f(T, f(f(Y, Z), f(W, Z))), f(f(T, f(f(Y, Z), f(W, Z))), f(f(S, S), f(X, f(f(Y, Z), f(W, Z)))))), f(X, f(f(Y, Z), f(W, Z)))), S)))), f(f(V, f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(f(f(f(T, f(f(Y, Z), f(W, Z))), f(f(T, f(f(Y, Z), f(W, Z))), f(f(S, S), f(X, f(f(Y, Z), f(W, Z)))))), f(X, f(f(Y, Z), f(W, Z)))), S)))), f(f(U, U), Z))), Z), U)))
% 171.53/22.34 = { by lemma 6 R->L }
% 171.53/22.34 f(f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(f(f(f(T, f(f(Y, Z), f(W, Z))), f(f(T, f(f(Y, Z), f(W, Z))), f(f(S, S), f(X, f(f(Y, Z), f(W, Z)))))), f(X, f(f(Y, Z), f(W, Z)))), S))), f(Z, f(f(f(f(V, f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(f(f(f(T, f(f(Y, Z), f(W, Z))), f(f(T, f(f(Y, Z), f(W, Z))), f(f(S, S), f(X, f(f(Y, Z), f(W, Z)))))), f(X, f(f(Y, Z), f(W, Z)))), S)))), f(f(V, f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(f(f(f(T, f(f(Y, Z), f(W, Z))), f(f(T, f(f(Y, Z), f(W, Z))), f(f(S, S), f(X, f(f(Y, Z), f(W, Z)))))), f(X, f(f(Y, Z), f(W, Z)))), S)))), f(f(U, U), Z))), Z), U)))
% 171.53/22.34 = { by lemma 54 }
% 171.53/22.35 Z
% 171.53/22.35
% 171.53/22.35 Lemma 59: f(X, f(f(Y, f(f(Z, X), f(W, X))), f(f(f(f(V, X), f(f(V, X), f(f(U, U), f(Y, f(f(Z, X), f(W, X)))))), f(Y, f(f(Z, X), f(W, X)))), U))) = f(Y, f(f(Z, X), f(W, X))).
% 171.53/22.35 Proof:
% 171.53/22.35 f(X, f(f(Y, f(f(Z, X), f(W, X))), f(f(f(f(V, X), f(f(V, X), f(f(U, U), f(Y, f(f(Z, X), f(W, X)))))), f(Y, f(f(Z, X), f(W, X)))), U)))
% 171.53/22.35 = { by lemma 58 R->L }
% 171.53/22.35 f(X, f(f(Y, f(f(Z, X), f(W, X))), f(f(f(f(V, f(f(Y, f(f(Z, X), f(W, X))), f(X, f(f(f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(S, S), X))), X), S)))), f(f(V, X), f(f(U, U), f(Y, f(f(Z, X), f(W, X)))))), f(Y, f(f(Z, X), f(W, X)))), U)))
% 171.53/22.35 = { by lemma 58 R->L }
% 171.53/22.35 f(X, f(f(Y, f(f(Z, X), f(W, X))), f(f(f(f(V, f(f(Y, f(f(Z, X), f(W, X))), f(X, f(f(f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(S, S), X))), X), S)))), f(f(V, f(f(Y, f(f(Z, X), f(W, X))), f(X, f(f(f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(S, S), X))), X), S)))), f(f(U, U), f(Y, f(f(Z, X), f(W, X)))))), f(Y, f(f(Z, X), f(W, X)))), U)))
% 171.53/22.35 = { by lemma 58 R->L }
% 171.53/22.35 f(f(f(Y, f(f(Z, X), f(W, X))), f(X, f(f(f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(S, S), X))), X), S))), f(f(Y, f(f(Z, X), f(W, X))), f(f(f(f(V, f(f(Y, f(f(Z, X), f(W, X))), f(X, f(f(f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(S, S), X))), X), S)))), f(f(V, f(f(Y, f(f(Z, X), f(W, X))), f(X, f(f(f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(T, f(Y, f(f(Z, X), f(W, X)))), f(f(S, S), X))), X), S)))), f(f(U, U), f(Y, f(f(Z, X), f(W, X)))))), f(Y, f(f(Z, X), f(W, X)))), U)))
% 171.53/22.35 = { by lemma 4 }
% 171.53/22.35 f(Y, f(f(Z, X), f(W, X)))
% 171.53/22.35
% 171.53/22.35 Lemma 60: f(f(X, X), f(Y, f(f(Z, X), f(W, X)))) = X.
% 171.53/22.35 Proof:
% 171.53/22.35 f(f(X, X), f(Y, f(f(Z, X), f(W, X))))
% 171.53/22.35 = { by lemma 59 R->L }
% 171.53/22.35 f(f(X, X), f(X, f(f(Y, f(f(Z, X), f(W, X))), f(f(f(f(V, X), f(f(V, X), f(f(U, U), f(Y, f(f(Z, X), f(W, X)))))), f(Y, f(f(Z, X), f(W, X)))), U))))
% 171.53/22.35 = { by lemma 52 }
% 171.53/22.35 X
% 171.53/22.35
% 171.53/22.35 Lemma 61: f(f(f(X, X), X), f(f(Y, Z), f(Z, W))) = f(Z, f(f(Y, Z), f(Z, W))).
% 171.53/22.35 Proof:
% 171.53/22.35 f(f(f(X, X), X), f(f(Y, Z), f(Z, W)))
% 171.53/22.35 = { by lemma 47 }
% 171.53/22.35 f(f(f(Y, Z), f(Z, W)), f(f(V, V), V))
% 171.53/22.35 = { by lemma 48 }
% 171.53/22.35 f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W)))
% 171.53/22.35 = { by lemma 51 R->L }
% 171.53/22.35 f(f(f(f(f(Y, Z), f(Z, W)), f(f(Y, Z), f(Z, W))), f(Z, f(f(f(Y, f(Y, f(f(W, W), Z))), Z), W))), f(f(Y, Z), f(Z, W)))
% 171.53/22.35 = { by axiom 1 (mol_27B2) }
% 171.53/22.35 f(Z, f(f(Y, Z), f(Z, W)))
% 171.53/22.35
% 171.53/22.35 Lemma 62: f(f(X, Y), f(f(f(Z, X), f(X, Y)), X)) = f(f(Z, X), f(X, Y)).
% 171.53/22.35 Proof:
% 171.53/22.35 f(f(X, Y), f(f(f(Z, X), f(X, Y)), X))
% 171.53/22.35 = { by lemma 50 R->L }
% 171.53/22.35 f(f(X, Y), f(f(f(Z, X), f(X, Y)), f(f(f(f(W, f(X, Y)), f(f(W, f(X, Y)), f(f(f(X, X), f(X, X)), f(f(Z, X), f(X, Y))))), f(f(Z, X), f(X, Y))), f(X, X))))
% 171.53/22.35 = { by lemma 6 }
% 171.53/22.35 f(f(Z, X), f(X, Y))
% 171.53/22.35
% 171.53/22.35 Lemma 63: f(f(X, Y), f(X, f(f(Z, X), f(X, Y)))) = f(f(Z, X), f(X, Y)).
% 171.53/22.35 Proof:
% 171.53/22.35 f(f(X, Y), f(X, f(f(Z, X), f(X, Y))))
% 171.53/22.35 = { by lemma 61 R->L }
% 171.53/22.35 f(f(X, Y), f(f(f(W, W), W), f(f(Z, X), f(X, Y))))
% 171.53/22.35 = { by lemma 62 R->L }
% 171.53/22.35 f(f(X, Y), f(f(f(W, W), W), f(f(X, Y), f(f(f(Z, X), f(X, Y)), X))))
% 171.53/22.35 = { by lemma 46 }
% 171.53/22.35 f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(X, Y)), X)), f(f(X, Y), f(f(f(Z, X), f(X, Y)), X))))
% 171.53/22.35 = { by lemma 45 }
% 171.53/22.35 f(f(X, Y), f(f(f(Z, X), f(X, Y)), X))
% 171.53/22.35 = { by lemma 62 }
% 171.53/22.35 f(f(Z, X), f(X, Y))
% 171.53/22.35
% 171.53/22.35 Lemma 64: f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, X)) = f(f(Y, X), f(Y, X)).
% 171.53/22.35 Proof:
% 171.53/22.35 f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, X))
% 171.53/22.35 = { by lemma 57 R->L }
% 171.53/22.35 f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), X))
% 171.53/22.35 = { by lemma 41 R->L }
% 171.53/22.35 f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(f(W, f(W, f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), X))), X), f(f(Y, Z), f(Y, Z)))))))
% 171.53/22.35 = { by lemma 61 R->L }
% 171.53/22.35 f(f(f(f(Y, X), f(Y, X)), f(Y, X)), f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(f(W, f(W, f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), X))), X), f(f(Y, Z), f(Y, Z)))))))
% 171.53/22.35 = { by lemma 41 }
% 171.53/22.35 f(f(f(f(Y, X), f(Y, X)), f(Y, X)), f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), X))
% 171.53/22.35 = { by lemma 57 }
% 171.53/22.35 f(f(f(f(Y, X), f(Y, X)), f(Y, X)), f(Y, X))
% 171.53/22.35 = { by lemma 51 }
% 171.53/22.36 f(f(Y, X), f(Y, X))
% 171.53/22.36
% 171.53/22.36 Lemma 65: f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))) = f(f(X, Y), f(X, Y)).
% 171.53/22.36 Proof:
% 171.53/22.36 f(f(X, Y), f(Y, f(f(X, Z), f(X, Z))))
% 171.53/22.36 = { by lemma 52 R->L }
% 171.53/22.36 f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(f(f(Y, f(f(X, Z), f(X, Z))), f(X, Y)), f(f(f(f(W, f(X, Y)), f(f(W, f(X, Y)), f(f(V, V), f(f(Y, f(f(X, Z), f(X, Z))), f(X, Y))))), f(f(Y, f(f(X, Z), f(X, Z))), f(X, Y))), V)))), f(Y, f(f(X, Z), f(X, Z))))
% 171.53/22.36 = { by lemma 6 }
% 171.53/22.36 f(f(f(f(X, Y), f(X, Y)), f(f(Y, f(f(X, Z), f(X, Z))), f(X, Y))), f(Y, f(f(X, Z), f(X, Z))))
% 171.53/22.36 = { by lemma 64 R->L }
% 171.53/22.36 f(f(f(f(Y, f(f(X, Z), f(X, Z))), f(X, Y)), f(f(Y, f(f(X, Z), f(X, Z))), f(X, Y))), f(Y, f(f(X, Z), f(X, Z))))
% 171.53/22.36 = { by lemma 53 }
% 171.53/22.36 f(f(Y, f(f(X, Z), f(X, Z))), f(X, Y))
% 171.53/22.36 = { by lemma 64 }
% 171.53/22.36 f(f(X, Y), f(X, Y))
% 171.53/22.36
% 171.53/22.36 Lemma 66: f(f(Z, f(f(W, Y), f(V, Y))), f(Y, f(f(Z, f(f(W, Y), f(V, Y))), U))) = f(f(f(X, X), X), f(Y, f(f(Z, f(f(W, Y), f(V, Y))), U))).
% 171.53/22.36 Proof:
% 171.53/22.36 f(f(Z, f(f(W, Y), f(V, Y))), f(Y, f(f(Z, f(f(W, Y), f(V, Y))), U)))
% 171.53/22.36 = { by lemma 60 R->L }
% 171.53/22.36 f(f(Z, f(f(W, Y), f(V, Y))), f(f(f(Y, Y), f(Z, f(f(W, Y), f(V, Y)))), f(f(Z, f(f(W, Y), f(V, Y))), U)))
% 171.53/22.36 = { by lemma 61 R->L }
% 171.53/22.36 f(f(f(X, X), X), f(f(f(Y, Y), f(Z, f(f(W, Y), f(V, Y)))), f(f(Z, f(f(W, Y), f(V, Y))), U)))
% 171.53/22.36 = { by lemma 60 }
% 171.53/22.36 f(f(f(X, X), X), f(Y, f(f(Z, f(f(W, Y), f(V, Y))), U)))
% 171.53/22.36
% 171.53/22.36 Goal 1 (associativity): f(a, f(f(b, c), f(b, c))) = f(c, f(f(b, a), f(b, a))).
% 171.53/22.36 Proof:
% 171.53/22.36 f(a, f(f(b, c), f(b, c)))
% 171.53/22.36 = { by lemma 59 R->L }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(f(f(f(X, c), f(f(X, c), f(f(f(f(a, f(f(b, c), f(b, c))), f(f(Y, Y), Y)), f(f(a, f(f(b, c), f(b, c))), f(f(Y, Y), Y))), f(a, f(f(b, c), f(b, c)))))), f(a, f(f(b, c), f(b, c)))), f(f(a, f(f(b, c), f(b, c))), f(f(Y, Y), Y)))))
% 171.53/22.36 = { by lemma 44 }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(a, f(f(b, c), f(b, c)))))
% 171.53/22.36 = { by lemma 48 R->L }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(f(Z, Z), Z)))
% 171.53/22.36 = { by lemma 47 R->L }
% 171.53/22.36 f(c, f(f(f(W, W), W), f(a, f(f(b, c), f(b, c)))))
% 171.53/22.36 = { by lemma 65 R->L }
% 171.53/22.36 f(c, f(f(f(W, W), W), f(a, f(f(b, c), f(c, f(f(b, a), f(b, a)))))))
% 171.53/22.36 = { by lemma 63 R->L }
% 171.53/22.36 f(c, f(f(f(W, W), W), f(a, f(f(c, f(f(b, a), f(b, a))), f(c, f(f(b, c), f(c, f(f(b, a), f(b, a)))))))))
% 171.53/22.36 = { by lemma 66 R->L }
% 171.53/22.36 f(c, f(f(c, f(f(b, a), f(b, a))), f(a, f(f(c, f(f(b, a), f(b, a))), f(c, f(f(b, c), f(c, f(f(b, a), f(b, a)))))))))
% 171.53/22.36 = { by lemma 63 }
% 171.53/22.36 f(c, f(f(c, f(f(b, a), f(b, a))), f(a, f(f(b, c), f(c, f(f(b, a), f(b, a)))))))
% 171.53/22.36 = { by lemma 65 }
% 171.53/22.36 f(c, f(f(c, f(f(b, a), f(b, a))), f(a, f(f(b, c), f(b, c)))))
% 171.53/22.36 = { by lemma 60 R->L }
% 171.53/22.36 f(c, f(f(f(f(c, c), f(a, f(f(b, c), f(b, c)))), f(f(b, a), f(b, a))), f(a, f(f(b, c), f(b, c)))))
% 171.53/22.36 = { by lemma 65 R->L }
% 171.53/22.36 f(c, f(f(f(f(c, c), f(a, f(f(b, c), f(b, c)))), f(f(b, a), f(a, f(f(b, c), f(b, c))))), f(a, f(f(b, c), f(b, c)))))
% 171.53/22.36 = { by lemma 62 R->L }
% 171.53/22.36 f(c, f(f(f(f(c, c), f(a, f(f(b, c), f(b, c)))), f(f(a, f(f(b, c), f(b, c))), f(f(f(b, a), f(a, f(f(b, c), f(b, c)))), a))), f(a, f(f(b, c), f(b, c)))))
% 171.53/22.36 = { by lemma 23 }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(f(f(c, c), f(a, f(f(b, c), f(b, c)))), f(f(a, f(f(b, c), f(b, c))), f(f(f(b, a), f(a, f(f(b, c), f(b, c)))), a)))))
% 171.53/22.36 = { by lemma 62 }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(f(f(c, c), f(a, f(f(b, c), f(b, c)))), f(f(b, a), f(a, f(f(b, c), f(b, c)))))))
% 171.53/22.36 = { by lemma 65 }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(f(f(c, c), f(a, f(f(b, c), f(b, c)))), f(f(b, a), f(b, a)))))
% 171.53/22.36 = { by lemma 60 }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(c, f(f(b, a), f(b, a)))))
% 171.53/22.36 = { by lemma 64 R->L }
% 171.53/22.36 f(c, f(f(a, f(f(b, c), f(b, c))), f(c, f(f(a, f(f(b, c), f(b, c))), f(b, a)))))
% 171.53/22.36 = { by lemma 66 }
% 171.53/22.36 f(c, f(f(f(V, V), V), f(c, f(f(a, f(f(b, c), f(b, c))), f(b, a)))))
% 171.53/22.36 = { by lemma 64 }
% 171.53/22.36 f(c, f(f(f(V, V), V), f(c, f(f(b, a), f(b, a)))))
% 171.53/22.36 = { by lemma 47 }
% 171.53/22.36 f(c, f(f(c, f(f(b, a), f(b, a))), f(f(U, U), U)))
% 171.53/22.36 = { by lemma 48 }
% 171.53/22.36 f(c, f(f(c, f(f(b, a), f(b, a))), f(c, f(f(b, a), f(b, a)))))
% 171.53/22.36 = { by lemma 45 }
% 171.53/22.36 f(c, f(f(b, a), f(b, a)))
% 171.53/22.36 % SZS output end Proof
% 171.53/22.36
% 171.53/22.36 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------