TSTP Solution File: LAT072-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT072-1 : 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 : n008.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 06:27:20 EDT 2023
% Result : Unsatisfiable 6.57s 1.24s
% Output : Proof 7.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT072-1 : 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
% 0.18/0.34 % Computer : n008.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Thu Aug 24 09:39:02 EDT 2023
% 0.18/0.35 % CPUTime :
% 6.57/1.24 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 6.57/1.24
% 6.57/1.24 % SZS status Unsatisfiable
% 6.57/1.24
% 7.44/1.31 % SZS output start Proof
% 7.44/1.31 Axiom 1 (oml_23A): f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))) = Y.
% 7.44/1.31
% 7.44/1.31 Lemma 2: f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z)))) = X.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))
% 7.44/1.31 = { by axiom 1 (oml_23A) R->L }
% 7.44/1.31 f(f(f(f(f(f(W, X), f(X, Z)), X), f(X, f(f(Z, f(f(X, X), Z)), Z))), Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))
% 7.44/1.31 = { by axiom 1 (oml_23A) }
% 7.44/1.31 X
% 7.44/1.31
% 7.44/1.31 Lemma 3: f(f(X, Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))) = Y.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))
% 7.44/1.31 = { by lemma 2 R->L }
% 7.44/1.31 f(f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W)))), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))
% 7.44/1.31 = { by axiom 1 (oml_23A) }
% 7.44/1.31 Y
% 7.44/1.31
% 7.44/1.31 Lemma 4: f(X, f(f(X, Y), f(f(Z, f(f(f(X, Y), f(X, Y)), Z)), Z))) = f(X, Y).
% 7.44/1.31 Proof:
% 7.44/1.31 f(X, f(f(X, Y), f(f(Z, f(f(f(X, Y), f(X, Y)), Z)), Z)))
% 7.44/1.31 = { by axiom 1 (oml_23A) R->L }
% 7.44/1.31 f(f(f(f(f(W, X), f(X, Y)), f(f(X, Y), Z)), f(X, f(f(Y, f(f(X, X), Y)), Y))), f(f(X, Y), f(f(Z, f(f(f(X, Y), f(X, Y)), Z)), Z)))
% 7.44/1.31 = { by axiom 1 (oml_23A) }
% 7.44/1.31 f(X, Y)
% 7.44/1.31
% 7.44/1.31 Lemma 5: f(X, f(f(X, Y), f(X, Y))) = f(X, Y).
% 7.44/1.31 Proof:
% 7.44/1.31 f(X, f(f(X, Y), f(X, Y)))
% 7.44/1.31 = { by lemma 4 R->L }
% 7.44/1.31 f(X, f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(X, Y), f(X, Y)))), f(f(X, Y), f(X, Y))))))
% 7.44/1.31 = { by lemma 3 R->L }
% 7.44/1.31 f(X, f(f(X, Y), f(f(f(f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(X, Y), f(X, Y)))), f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(X, Y), f(X, Y)))), f(f(X, Y), f(X, Y))))), f(f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(X, Y), f(X, Y)))), f(f(X, Y), f(X, Y))))))
% 7.44/1.31 = { by lemma 4 }
% 7.44/1.31 f(X, Y)
% 7.44/1.31
% 7.44/1.31 Lemma 6: f(f(X, Y), f(X, X)) = X.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, Y), f(X, X))
% 7.44/1.31 = { by lemma 2 R->L }
% 7.44/1.31 f(f(X, Y), f(X, f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))))
% 7.44/1.31 = { by lemma 2 R->L }
% 7.44/1.31 f(f(X, Y), f(f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z)))), f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))))
% 7.44/1.31 = { by lemma 5 }
% 7.44/1.31 f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))
% 7.44/1.31 = { by lemma 2 }
% 7.44/1.31 X
% 7.44/1.31
% 7.44/1.31 Lemma 7: f(X, f(f(Y, X), f(Y, X))) = f(Y, X).
% 7.44/1.31 Proof:
% 7.44/1.31 f(X, f(f(Y, X), f(Y, X)))
% 7.44/1.31 = { by lemma 3 R->L }
% 7.44/1.31 f(f(f(Y, X), f(X, f(f(Z, f(f(X, X), Z)), Z))), f(f(Y, X), f(Y, X)))
% 7.44/1.31 = { by lemma 6 }
% 7.44/1.31 f(Y, X)
% 7.44/1.31
% 7.44/1.31 Lemma 8: f(f(X, Y), f(X, f(f(Z, f(f(X, X), Z)), Z))) = X.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, Y), f(X, f(f(Z, f(f(X, X), Z)), Z)))
% 7.44/1.31 = { by lemma 2 R->L }
% 7.44/1.31 f(f(X, Y), f(X, f(f(Z, f(f(f(f(X, Y), f(X, f(f(f(f(W, f(f(X, X), W)), W), f(f(X, X), f(f(W, f(f(X, X), W)), W))), f(f(W, f(f(X, X), W)), W)))), X), Z)), Z)))
% 7.44/1.31 = { by lemma 2 R->L }
% 7.44/1.31 f(f(X, Y), f(X, f(f(Z, f(f(f(f(X, Y), f(X, f(f(f(f(W, f(f(X, X), W)), W), f(f(X, X), f(f(W, f(f(X, X), W)), W))), f(f(W, f(f(X, X), W)), W)))), f(f(X, Y), f(X, f(f(f(f(W, f(f(X, X), W)), W), f(f(X, X), f(f(W, f(f(X, X), W)), W))), f(f(W, f(f(X, X), W)), W))))), Z)), Z)))
% 7.44/1.31 = { by lemma 2 R->L }
% 7.44/1.31 f(f(X, Y), f(f(f(X, Y), f(X, f(f(f(f(W, f(f(X, X), W)), W), f(f(X, X), f(f(W, f(f(X, X), W)), W))), f(f(W, f(f(X, X), W)), W)))), f(f(Z, f(f(f(f(X, Y), f(X, f(f(f(f(W, f(f(X, X), W)), W), f(f(X, X), f(f(W, f(f(X, X), W)), W))), f(f(W, f(f(X, X), W)), W)))), f(f(X, Y), f(X, f(f(f(f(W, f(f(X, X), W)), W), f(f(X, X), f(f(W, f(f(X, X), W)), W))), f(f(W, f(f(X, X), W)), W))))), Z)), Z)))
% 7.44/1.31 = { by lemma 4 }
% 7.44/1.31 f(f(X, Y), f(X, f(f(f(f(W, f(f(X, X), W)), W), f(f(X, X), f(f(W, f(f(X, X), W)), W))), f(f(W, f(f(X, X), W)), W))))
% 7.44/1.31 = { by lemma 2 }
% 7.44/1.31 X
% 7.44/1.31
% 7.44/1.31 Lemma 9: f(f(X, Y), f(X, f(f(X, X), Z))) = X.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, Y), f(X, f(f(X, X), Z)))
% 7.44/1.31 = { by lemma 3 R->L }
% 7.44/1.31 f(f(X, Y), f(X, f(f(f(f(f(X, X), Z), f(f(W, f(f(f(f(X, X), Z), f(f(X, X), Z)), W)), W)), f(f(X, X), Z)), f(f(f(X, X), Z), f(f(W, f(f(f(f(X, X), Z), f(f(X, X), Z)), W)), W)))))
% 7.44/1.31 = { by lemma 4 R->L }
% 7.44/1.31 f(f(X, Y), f(X, f(f(f(f(f(X, X), Z), f(f(W, f(f(f(f(X, X), Z), f(f(X, X), Z)), W)), W)), f(f(X, X), f(f(f(X, X), Z), f(f(W, f(f(f(f(X, X), Z), f(f(X, X), Z)), W)), W)))), f(f(f(X, X), Z), f(f(W, f(f(f(f(X, X), Z), f(f(X, X), Z)), W)), W)))))
% 7.44/1.31 = { by lemma 8 }
% 7.44/1.31 X
% 7.44/1.31
% 7.44/1.31 Lemma 10: f(X, f(f(X, X), Y)) = f(X, X).
% 7.44/1.31 Proof:
% 7.44/1.31 f(X, f(f(X, X), Y))
% 7.44/1.31 = { by lemma 5 R->L }
% 7.44/1.31 f(X, f(f(X, f(f(X, X), Y)), f(X, f(f(X, X), Y))))
% 7.44/1.31 = { by lemma 9 }
% 7.44/1.31 f(X, X)
% 7.44/1.31
% 7.44/1.31 Lemma 11: f(X, f(Y, f(X, X))) = f(X, X).
% 7.44/1.31 Proof:
% 7.44/1.31 f(X, f(Y, f(X, X)))
% 7.44/1.31 = { by lemma 7 R->L }
% 7.44/1.31 f(X, f(f(X, X), f(f(Y, f(X, X)), f(Y, f(X, X)))))
% 7.44/1.31 = { by lemma 10 }
% 7.44/1.31 f(X, X)
% 7.44/1.31
% 7.44/1.31 Lemma 12: f(f(X, X), f(X, Y)) = X.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, X), f(X, Y))
% 7.44/1.31 = { by lemma 10 R->L }
% 7.44/1.31 f(f(X, f(f(X, X), Z)), f(X, Y))
% 7.44/1.31 = { by lemma 9 R->L }
% 7.44/1.31 f(f(X, f(f(X, X), Z)), f(f(f(X, f(f(X, X), Z)), f(X, f(f(X, X), Z))), Y))
% 7.44/1.31 = { by lemma 10 }
% 7.44/1.31 f(f(X, f(f(X, X), Z)), f(X, f(f(X, X), Z)))
% 7.44/1.31 = { by lemma 9 }
% 7.44/1.31 X
% 7.44/1.31
% 7.44/1.31 Lemma 13: f(f(X, X), f(Y, X)) = X.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, X), f(Y, X))
% 7.44/1.31 = { by lemma 7 R->L }
% 7.44/1.31 f(f(X, X), f(X, f(f(Y, X), f(Y, X))))
% 7.44/1.31 = { by lemma 12 }
% 7.44/1.31 X
% 7.44/1.31
% 7.44/1.31 Lemma 14: f(f(X, Y), f(Y, Y)) = Y.
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(X, Y), f(Y, Y))
% 7.44/1.31 = { by lemma 3 R->L }
% 7.44/1.31 f(f(X, Y), f(Y, f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))
% 7.44/1.31 = { by lemma 3 R->L }
% 7.44/1.31 f(f(X, Y), f(Y, f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), f(f(Y, Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))
% 7.44/1.31 = { by lemma 3 }
% 7.44/1.31 Y
% 7.44/1.31
% 7.44/1.31 Lemma 15: f(X, f(f(Y, f(f(X, X), Y)), Y)) = f(X, X).
% 7.44/1.31 Proof:
% 7.44/1.31 f(X, f(f(Y, f(f(X, X), Y)), Y))
% 7.44/1.31 = { by lemma 5 R->L }
% 7.44/1.31 f(X, f(f(X, f(f(Y, f(f(X, X), Y)), Y)), f(X, f(f(Y, f(f(X, X), Y)), Y))))
% 7.44/1.31 = { by lemma 8 }
% 7.44/1.31 f(X, X)
% 7.44/1.31
% 7.44/1.31 Lemma 16: f(f(f(X, Y), f(X, Y)), X) = f(X, Y).
% 7.44/1.31 Proof:
% 7.44/1.31 f(f(f(X, Y), f(X, Y)), X)
% 7.44/1.31 = { by lemma 3 R->L }
% 7.44/1.32 f(f(f(X, Y), f(X, Y)), f(f(f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))), X), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z)))))
% 7.44/1.32 = { by lemma 2 R->L }
% 7.44/1.32 f(f(f(X, Y), f(X, Y)), f(f(f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))), f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z)))))
% 7.44/1.32 = { by lemma 15 R->L }
% 7.44/1.32 f(f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))), f(f(X, Y), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z)))))
% 7.44/1.32 = { by lemma 2 R->L }
% 7.44/1.32 f(f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))), f(f(f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W)))), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z))))), f(X, f(f(f(f(Z, f(f(X, X), Z)), Z), f(f(X, X), f(f(Z, f(f(X, X), Z)), Z))), f(f(Z, f(f(X, X), Z)), Z)))))
% 7.44/1.32 = { by lemma 15 }
% 7.44/1.32 f(f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))))
% 7.44/1.32 = { by lemma 2 }
% 7.44/1.32 f(X, Y)
% 7.44/1.32
% 7.44/1.32 Lemma 17: f(f(f(f(X, Y), f(Y, Z)), W), f(Y, Y)) = Y.
% 7.44/1.32 Proof:
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, Y))
% 7.44/1.32 = { by axiom 1 (oml_23A) R->L }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))
% 7.44/1.32 = { by axiom 1 (oml_23A) R->L }
% 7.44/1.32 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(Z, f(f(Y, Y), Z)), Z))), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))
% 7.44/1.32 = { by lemma 5 }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))
% 7.44/1.32 = { by axiom 1 (oml_23A) }
% 7.44/1.32 Y
% 7.44/1.32
% 7.44/1.32 Lemma 18: 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)).
% 7.44/1.32 Proof:
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), Y))
% 7.44/1.32 = { by lemma 17 R->L }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, Y))))
% 7.44/1.32 = { by lemma 15 R->L }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Z, f(f(Y, Y), Z)), Z)), f(f(Y, Y), f(f(f(Y, Y), f(Y, Y)), f(f(Z, f(f(Y, Y), Z)), Z)))), f(f(f(Y, Y), f(Y, Y)), f(f(Z, f(f(Y, Y), Z)), Z)))))))
% 7.44/1.32 = { by lemma 10 }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Z, f(f(Y, Y), Z)), Z)), f(f(Y, Y), f(Y, Y))), f(f(f(Y, Y), f(Y, Y)), f(f(Z, f(f(Y, Y), Z)), Z)))))))
% 7.44/1.32 = { by lemma 12 }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Z, f(f(Y, Y), Z)), Z)), f(f(Y, Y), f(Y, Y))), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))))
% 7.44/1.32 = { by lemma 12 }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, f(f(f(f(f(Y, Y), f(Y, Y)), f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))))
% 7.44/1.32 = { by lemma 12 }
% 7.44/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z))), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))))
% 7.44/1.32 = { by lemma 13 }
% 7.63/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), Y), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))
% 7.63/1.32 = { by axiom 1 (oml_23A) R->L }
% 7.63/1.32 f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), f(f(f(Y, f(f(Z, f(f(Y, Y), Z)), Z)), f(f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z))), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))), f(Y, f(f(Z, f(f(Y, Y), Z)), Z)))))
% 7.63/1.32 = { by lemma 8 }
% 7.63/1.32 f(f(X, Y), f(Y, Z))
% 7.63/1.32
% 7.63/1.32 Lemma 19: f(f(f(X, Y), f(Y, Z)), Y) = f(Y, f(f(X, Y), f(Y, Z))).
% 7.63/1.32 Proof:
% 7.63/1.32 f(f(f(X, Y), f(Y, Z)), Y)
% 7.63/1.32 = { by lemma 7 R->L }
% 7.63/1.32 f(Y, f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(X, Y), f(Y, Z)), Y)))
% 7.63/1.32 = { by lemma 18 }
% 7.63/1.32 f(Y, f(f(X, Y), f(Y, Z)))
% 7.63/1.32
% 7.63/1.32 Lemma 20: f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, Y)) = Y.
% 7.63/1.32 Proof:
% 7.63/1.32 f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, Y))
% 7.63/1.32 = { by lemma 7 R->L }
% 7.63/1.32 f(f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z))))), f(Y, Y))
% 7.63/1.32 = { by axiom 1 (oml_23A) R->L }
% 7.63/1.32 f(f(f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(f(f(Y, Z), f(Y, Z)), f(f(V, f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), V)), V))), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z))))), f(Y, Y))
% 7.63/1.32 = { by lemma 5 R->L }
% 7.63/1.32 f(f(f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(f(f(Y, Z), f(Y, Z)), f(f(V, f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), V)), V))), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(f(f(Y, Z), f(Y, Z)), f(f(V, f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), V)), V))))), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z))))), f(Y, Y))
% 7.63/1.32 = { by axiom 1 (oml_23A) }
% 7.63/1.32 f(f(f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(f(f(Y, Z), f(Y, Z)), f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(f(f(Y, Z), f(Y, Z)), f(f(V, f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), V)), V))))), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z))))), f(Y, Y))
% 7.63/1.32 = { by axiom 1 (oml_23A) }
% 7.63/1.32 f(f(f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z)))), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z))))), f(Y, Y))
% 7.63/1.32 = { by lemma 14 }
% 7.63/1.32 f(f(f(f(f(f(W, f(f(Y, Z), f(Y, Z))), f(f(f(Y, Z), f(Y, Z)), V)), Y), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z))))), f(Y, Y))
% 7.63/1.32 = { by lemma 17 }
% 7.63/1.32 Y
% 7.63/1.32
% 7.63/1.32 Lemma 21: f(f(X, X), f(Y, f(f(X, Z), f(X, Z)))) = X.
% 7.63/1.32 Proof:
% 7.63/1.32 f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))
% 7.63/1.32 = { by lemma 11 R->L }
% 7.63/1.32 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))))
% 7.63/1.32 = { by lemma 20 R->L }
% 7.63/1.32 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))))
% 7.63/1.32 = { by lemma 16 }
% 7.63/1.32 f(f(Y, f(f(X, Z), f(X, Z))), f(X, X))
% 7.63/1.32 = { by lemma 20 }
% 7.63/1.33 X
% 7.63/1.33
% 7.63/1.33 Lemma 22: f(f(X, f(f(Y, Z), f(W, Z))), f(Z, Z)) = Z.
% 7.63/1.33 Proof:
% 7.63/1.33 f(f(X, f(f(Y, Z), f(W, Z))), f(Z, Z))
% 7.63/1.33 = { by lemma 7 R->L }
% 7.63/1.33 f(f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(X, f(f(Y, Z), f(W, Z))))), f(Z, Z))
% 7.63/1.33 = { by lemma 8 R->L }
% 7.63/1.33 f(f(f(f(Y, Z), f(f(f(W, Z), f(Z, f(f(V, f(f(Z, Z), V)), V))), f(f(W, Z), f(f(U, f(f(f(W, Z), f(W, Z)), U)), U)))), f(f(X, f(f(Y, Z), f(W, Z))), f(X, f(f(Y, Z), f(W, Z))))), f(Z, Z))
% 7.63/1.33 = { by lemma 3 }
% 7.63/1.33 f(f(f(f(Y, Z), f(Z, f(f(W, Z), f(f(U, f(f(f(W, Z), f(W, Z)), U)), U)))), f(f(X, f(f(Y, Z), f(W, Z))), f(X, f(f(Y, Z), f(W, Z))))), f(Z, Z))
% 7.63/1.33 = { by lemma 17 }
% 7.63/1.33 Z
% 7.63/1.33
% 7.63/1.33 Lemma 23: f(f(X, X), f(Y, f(f(Z, X), f(W, X)))) = X.
% 7.63/1.33 Proof:
% 7.63/1.33 f(f(X, X), f(Y, f(f(Z, X), f(W, X))))
% 7.63/1.33 = { by lemma 11 R->L }
% 7.63/1.33 f(f(X, f(f(Y, f(f(Z, X), f(W, X))), f(X, X))), f(Y, f(f(Z, X), f(W, X))))
% 7.63/1.33 = { by lemma 22 R->L }
% 7.63/1.33 f(f(f(f(Y, f(f(Z, X), f(W, X))), f(X, X)), f(f(Y, f(f(Z, X), f(W, X))), f(X, X))), f(Y, f(f(Z, X), f(W, X))))
% 7.63/1.33 = { by lemma 16 }
% 7.63/1.33 f(f(Y, f(f(Z, X), f(W, X))), f(X, X))
% 7.63/1.33 = { by lemma 22 }
% 7.63/1.33 X
% 7.63/1.33
% 7.63/1.33 Lemma 24: f(X, f(f(Y, X), f(X, f(f(Y, Z), f(Y, Z))))) = f(Y, X).
% 7.63/1.33 Proof:
% 7.63/1.33 f(X, f(f(Y, X), f(X, f(f(Y, Z), f(Y, Z)))))
% 7.63/1.33 = { by lemma 21 R->L }
% 7.63/1.33 f(X, f(f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), X), f(X, f(f(Y, Z), f(Y, Z)))))
% 7.63/1.33 = { by lemma 3 R->L }
% 7.63/1.33 f(f(f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), X), f(X, f(f(W, f(f(X, X), W)), W))), f(f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), X), f(X, f(f(Y, Z), f(Y, Z)))))
% 7.63/1.33 = { by lemma 8 R->L }
% 7.63/1.33 f(f(f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), X), f(X, f(f(W, f(f(X, X), W)), W))), f(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(V, f(f(X, X), V)), V)))), f(X, f(f(Y, Z), f(Y, Z)))))
% 7.63/1.33 = { by lemma 8 R->L }
% 7.63/1.33 f(f(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(V, f(f(X, X), V)), V)))), f(X, f(f(W, f(f(X, X), W)), W))), f(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(V, f(f(X, X), V)), V)))), f(X, f(f(Y, Z), f(Y, Z)))))
% 7.63/1.33 = { by lemma 18 }
% 7.63/1.33 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(V, f(f(X, X), V)), V))))
% 7.63/1.33 = { by lemma 8 }
% 7.63/1.33 f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z)))), X)
% 7.63/1.33 = { by lemma 21 }
% 7.63/1.33 f(Y, X)
% 7.63/1.33
% 7.63/1.33 Lemma 25: f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))) = f(f(X, Y), f(X, Y)).
% 7.63/1.33 Proof:
% 7.63/1.33 f(f(X, Y), f(Y, f(f(X, Z), f(X, Z))))
% 7.63/1.33 = { by lemma 18 R->L }
% 7.63/1.33 f(f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), Y), f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), Y))
% 7.63/1.33 = { by lemma 10 R->L }
% 7.63/1.33 f(f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), Y), f(f(f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), Y), f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), Y)), f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W)))))
% 7.63/1.33 = { by lemma 18 }
% 7.63/1.33 f(f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), Y), f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), f(f(X, Y), f(f(f(f(W, f(f(f(X, Y), f(X, Y)), W)), W), f(f(f(X, Y), f(X, Y)), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W)))))
% 7.63/1.33 = { by lemma 2 }
% 7.63/1.33 f(f(f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))), Y), f(X, Y))
% 7.63/1.33 = { by lemma 19 }
% 7.63/1.33 f(f(Y, f(f(X, Y), f(Y, f(f(X, Z), f(X, Z))))), f(X, Y))
% 7.63/1.33 = { by lemma 24 }
% 7.63/1.33 f(f(X, Y), f(X, Y))
% 7.63/1.33
% 7.63/1.33 Lemma 26: f(f(X, Y), f(f(f(Z, X), f(X, Y)), X)) = f(f(Z, X), f(X, Y)).
% 7.63/1.33 Proof:
% 7.63/1.33 f(f(X, Y), f(f(f(Z, X), f(X, Y)), X))
% 7.63/1.33 = { by lemma 3 R->L }
% 7.63/1.33 f(f(f(f(Z, X), f(X, Y)), f(f(X, Y), f(f(W, f(f(f(X, Y), f(X, Y)), W)), W))), f(f(f(Z, X), f(X, Y)), X))
% 7.63/1.33 = { by lemma 18 }
% 7.63/1.33 f(f(Z, X), f(X, Y))
% 7.63/1.33
% 7.63/1.33 Lemma 27: f(f(X, f(f(Y, Z), f(Y, Z))), f(Z, f(f(Y, X), f(Y, X)))) = f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z)))).
% 7.63/1.33 Proof:
% 7.63/1.33 f(f(X, f(f(Y, Z), f(Y, Z))), f(Z, f(f(Y, X), f(Y, X))))
% 7.63/1.33 = { by lemma 23 R->L }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(Z, f(f(Y, X), f(Y, X))))
% 7.63/1.33 = { by lemma 25 R->L }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X))))), f(Z, f(f(Y, X), f(Y, X))))
% 7.63/1.33 = { by lemma 26 R->L }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z))), f(Z, f(f(Y, X), f(Y, X))))
% 7.63/1.33 = { by lemma 5 R->L }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z))), f(f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z))), f(Z, f(f(Y, X), f(Y, X)))), f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z))), f(Z, f(f(Y, X), f(Y, X))))))
% 7.63/1.33 = { by lemma 18 }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z))))
% 7.63/1.33 = { by lemma 26 }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X))))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z))))
% 7.63/1.33 = { by lemma 25 }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X))))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Y, Z)), Z))))
% 7.63/1.33 = { by lemma 25 }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Y, Z)), Z))))
% 7.63/1.33 = { by lemma 3 R->L }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Z, f(f(W, f(f(Z, Z), W)), W)))))))
% 7.63/1.33 = { by lemma 12 }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(Y, Z))))
% 7.63/1.33 = { by lemma 17 R->L }
% 7.63/1.33 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(f(f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), f(f(Z, f(f(Y, X), f(Y, X))), f(Z, f(f(V, f(f(Z, Z), V)), V)))), f(f(f(Y, Z), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z)), f(f(Y, Z), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z)))), f(f(Z, f(f(Y, X), f(Y, X))), f(Z, f(f(Y, X), f(Y, X))))), f(Y, Z))))
% 7.63/1.34 = { by lemma 8 }
% 7.63/1.34 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(f(f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z), f(f(f(Y, Z), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z)), f(f(Y, Z), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z)))), f(f(Z, f(f(Y, X), f(Y, X))), f(Z, f(f(Y, X), f(Y, X))))), f(Y, Z))))
% 7.63/1.34 = { by lemma 7 }
% 7.63/1.34 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(f(f(Y, Z), f(f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))), Z)), f(f(Z, f(f(Y, X), f(Y, X))), f(Z, f(f(Y, X), f(Y, X))))), f(Y, Z))))
% 7.63/1.34 = { by lemma 19 }
% 7.63/1.34 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(f(f(Y, Z), f(Z, f(f(Y, Z), f(Z, f(f(Y, X), f(Y, X)))))), f(f(Z, f(f(Y, X), f(Y, X))), f(Z, f(f(Y, X), f(Y, X))))), f(Y, Z))))
% 7.63/1.34 = { by lemma 24 }
% 7.63/1.34 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Z, f(f(Y, X), f(Y, X))), f(Z, f(f(Y, X), f(Y, X))))), f(Y, Z))))
% 7.63/1.34 = { by lemma 14 R->L }
% 7.63/1.34 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Z, f(f(Y, X), f(Y, X))), f(Z, f(f(Y, X), f(Y, X))))), f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))))))
% 7.63/1.34 = { by lemma 6 }
% 7.63/1.34 f(f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))))
% 7.63/1.34 = { by lemma 23 }
% 7.63/1.34 f(f(X, f(f(Y, Z), f(Y, Z))), f(f(f(X, X), f(Z, f(f(Y, X), f(Y, X)))), f(f(Y, Z), f(Y, Z))))
% 7.63/1.34 = { by lemma 23 }
% 7.63/1.34 f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(Y, Z))))
% 7.63/1.34
% 7.63/1.34 Goal 1 (associativity): f(a, f(f(b, c), f(b, c))) = f(c, f(f(b, a), f(b, a))).
% 7.63/1.34 Proof:
% 7.63/1.34 f(a, f(f(b, c), f(b, c)))
% 7.63/1.34 = { by lemma 13 R->L }
% 7.63/1.34 f(f(f(a, f(f(b, c), f(b, c))), f(a, f(f(b, c), f(b, c)))), f(f(c, f(f(b, a), f(b, a))), f(a, f(f(b, c), f(b, c)))))
% 7.63/1.34 = { by lemma 27 }
% 7.63/1.34 f(f(f(a, f(f(b, c), f(b, c))), f(a, f(f(b, c), f(b, c)))), f(f(c, f(f(b, a), f(b, a))), f(c, f(f(b, a), f(b, a)))))
% 7.63/1.34 = { by lemma 15 R->L }
% 7.63/1.34 f(f(f(a, f(f(b, c), f(b, c))), f(a, f(f(b, c), f(b, c)))), f(f(c, f(f(b, a), f(b, a))), f(f(X, f(f(f(c, f(f(b, a), f(b, a))), f(c, f(f(b, a), f(b, a)))), X)), X)))
% 7.63/1.34 = { by lemma 27 R->L }
% 7.63/1.34 f(f(f(a, f(f(b, c), f(b, c))), f(c, f(f(b, a), f(b, a)))), f(f(c, f(f(b, a), f(b, a))), f(f(X, f(f(f(c, f(f(b, a), f(b, a))), f(c, f(f(b, a), f(b, a)))), X)), X)))
% 7.63/1.34 = { by lemma 3 }
% 7.63/1.34 f(c, f(f(b, a), f(b, a)))
% 7.63/1.34 % SZS output end Proof
% 7.63/1.34
% 7.63/1.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------