TSTP Solution File: LAT070-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT070-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:27:20 EDT 2023
% Result : Unsatisfiable 24.91s 3.59s
% Output : Proof 24.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT070-1 : 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
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Thu Aug 24 08:28:17 EDT 2023
% 0.19/0.34 % CPUTime :
% 24.91/3.59 Command-line arguments: --no-flatten-goal
% 24.91/3.59
% 24.91/3.59 % SZS status Unsatisfiable
% 24.91/3.59
% 24.91/3.66 % SZS output start Proof
% 24.91/3.66 Axiom 1 (ol_23A): f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z))) = Y.
% 24.91/3.66
% 24.91/3.66 Lemma 2: f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), W))) = f(X, Y).
% 24.91/3.66 Proof:
% 24.91/3.66 f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), W)))
% 24.91/3.66 = { by axiom 1 (ol_23A) R->L }
% 24.91/3.66 f(f(f(f(f(Z, X), f(X, Y)), f(f(X, Y), W)), f(X, f(f(X, f(f(Z, Z), Z)), Y))), f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), W)))
% 24.91/3.66 = { by axiom 1 (ol_23A) }
% 24.91/3.66 f(X, Y)
% 24.91/3.66
% 24.91/3.66 Lemma 3: f(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y)) = f(f(X, Y), f(Y, Z)).
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y))
% 24.91/3.66 = { by axiom 1 (ol_23A) R->L }
% 24.91/3.66 f(f(X, Y), f(f(f(X, Y), f(Y, Z)), f(f(f(f(X, Y), f(Y, Z)), f(f(f(W, f(X, Y)), f(W, f(X, Y))), f(W, f(X, Y)))), f(Y, f(f(Y, f(f(X, X), X)), Z)))))
% 24.91/3.66 = { by lemma 2 }
% 24.91/3.66 f(f(X, Y), f(Y, Z))
% 24.91/3.66
% 24.91/3.66 Lemma 4: f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, Y)) = Y.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, Y))
% 24.91/3.66 = { by axiom 1 (ol_23A) R->L }
% 24.91/3.66 f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, f(f(Y, f(f(X, X), X)), Z))), Y))
% 24.91/3.66 = { by lemma 3 }
% 24.91/3.66 f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, f(f(Y, f(f(X, X), X)), Z)))
% 24.91/3.66 = { by axiom 1 (ol_23A) }
% 24.91/3.66 Y
% 24.91/3.66
% 24.91/3.66 Lemma 5: f(f(X, X), f(X, X)) = X.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(X, X), f(X, X))
% 24.91/3.66 = { by axiom 1 (ol_23A) R->L }
% 24.91/3.66 f(f(f(f(f(f(Y, X), f(X, Z)), X), f(X, f(f(X, f(f(Y, Y), Y)), Z))), X), f(X, X))
% 24.91/3.66 = { by lemma 4 }
% 24.91/3.66 X
% 24.91/3.66
% 24.91/3.66 Lemma 6: f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))) = X.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))
% 24.91/3.66 = { by lemma 5 R->L }
% 24.91/3.66 f(f(f(f(X, X), f(X, X)), Y), f(X, f(f(X, f(f(X, X), X)), X)))
% 24.91/3.66 = { by axiom 1 (ol_23A) }
% 24.91/3.66 X
% 24.91/3.66
% 24.91/3.66 Lemma 7: f(X, f(f(X, Y), f(X, Y))) = f(X, Y).
% 24.91/3.66 Proof:
% 24.91/3.66 f(X, f(f(X, Y), f(X, Y)))
% 24.91/3.66 = { by lemma 6 R->L }
% 24.91/3.66 f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(X, Y), f(f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))), f(X, Y))))))
% 24.91/3.66 = { by lemma 2 }
% 24.91/3.66 f(X, Y)
% 24.91/3.66
% 24.91/3.66 Lemma 8: f(f(f(f(X, Y), f(Y, Z)), W), f(Y, Y)) = Y.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, Y))
% 24.91/3.66 = { by axiom 1 (ol_23A) R->L }
% 24.91/3.66 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(Y, f(f(X, X), X)), Z)))))
% 24.91/3.66 = { by axiom 1 (ol_23A) R->L }
% 24.91/3.66 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(Y, f(f(X, X), X)), Z))), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z)))))
% 24.91/3.66 = { by lemma 7 }
% 24.91/3.66 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z)))
% 24.91/3.66 = { by axiom 1 (ol_23A) }
% 24.91/3.66 Y
% 24.91/3.66
% 24.91/3.66 Lemma 9: f(f(X, Y), f(Y, Y)) = Y.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(X, Y), f(Y, Y))
% 24.91/3.66 = { by lemma 6 R->L }
% 24.91/3.66 f(f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))), f(X, Y)))), f(Y, Y))
% 24.91/3.66 = { by lemma 8 }
% 24.91/3.66 Y
% 24.91/3.66
% 24.91/3.66 Lemma 10: f(X, f(f(X, f(f(X, X), Y)), f(X, X))) = f(X, f(f(X, X), Y)).
% 24.91/3.66 Proof:
% 24.91/3.66 f(X, f(f(X, f(f(X, X), Y)), f(X, X)))
% 24.91/3.66 = { by lemma 4 R->L }
% 24.91/3.66 f(X, f(f(f(f(f(f(Z, X), f(X, W)), X), f(X, X)), f(f(X, X), Y)), f(X, X)))
% 24.91/3.66 = { by lemma 4 R->L }
% 24.91/3.66 f(f(f(f(f(Z, X), f(X, W)), X), f(X, X)), f(f(f(f(f(f(Z, X), f(X, W)), X), f(X, X)), f(f(X, X), Y)), f(X, X)))
% 24.91/3.66 = { by lemma 3 }
% 24.91/3.66 f(f(f(f(f(Z, X), f(X, W)), X), f(X, X)), f(f(X, X), Y))
% 24.91/3.66 = { by lemma 4 }
% 24.91/3.66 f(X, f(f(X, X), Y))
% 24.91/3.66
% 24.91/3.66 Lemma 11: f(f(X, Y), f(X, X)) = X.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(X, Y), f(X, X))
% 24.91/3.66 = { by lemma 6 R->L }
% 24.91/3.66 f(f(X, Y), f(X, f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))))
% 24.91/3.66 = { by lemma 6 R->L }
% 24.91/3.66 f(f(X, Y), f(f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))))
% 24.91/3.66 = { by lemma 7 }
% 24.91/3.66 f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))
% 24.91/3.66 = { by lemma 6 }
% 24.91/3.66 X
% 24.91/3.66
% 24.91/3.66 Lemma 12: f(f(X, X), f(X, Y)) = X.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(X, X), f(X, Y))
% 24.91/3.66 = { by lemma 5 R->L }
% 24.91/3.66 f(f(X, X), f(f(f(X, X), f(X, X)), Y))
% 24.91/3.66 = { by lemma 10 R->L }
% 24.91/3.66 f(f(X, X), f(f(f(X, X), f(f(f(X, X), f(X, X)), Y)), f(f(X, X), f(X, X))))
% 24.91/3.66 = { by lemma 11 }
% 24.91/3.66 f(f(X, X), f(f(f(X, X), f(X, Y)), f(f(X, X), f(X, X))))
% 24.91/3.66 = { by lemma 11 }
% 24.91/3.66 f(f(X, X), f(X, X))
% 24.91/3.66 = { by lemma 5 }
% 24.91/3.66 X
% 24.91/3.66
% 24.91/3.66 Lemma 13: f(f(f(X, Y), f(X, Y)), X) = f(X, Y).
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(f(X, Y), f(X, Y)), X)
% 24.91/3.66 = { by lemma 6 R->L }
% 24.91/3.66 f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))
% 24.91/3.66 = { by lemma 12 }
% 24.91/3.66 f(X, Y)
% 24.91/3.66
% 24.91/3.66 Lemma 14: f(f(X, X), f(Y, X)) = X.
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(X, X), f(Y, X))
% 24.91/3.66 = { by lemma 9 R->L }
% 24.91/3.66 f(f(X, f(f(Y, X), f(X, X))), f(Y, X))
% 24.91/3.66 = { by lemma 9 R->L }
% 24.91/3.66 f(f(f(f(Y, X), f(X, X)), f(f(Y, X), f(X, X))), f(Y, X))
% 24.91/3.66 = { by lemma 13 }
% 24.91/3.66 f(f(Y, X), f(X, X))
% 24.91/3.66 = { by lemma 9 }
% 24.91/3.66 X
% 24.91/3.66
% 24.91/3.66 Lemma 15: f(f(f(X, X), Y), X) = f(X, X).
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(f(X, X), Y), X)
% 24.91/3.66 = { by lemma 5 R->L }
% 24.91/3.66 f(f(f(X, X), Y), f(f(X, X), f(X, X)))
% 24.91/3.66 = { by lemma 11 }
% 24.91/3.66 f(X, X)
% 24.91/3.66
% 24.91/3.66 Lemma 16: f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z))) = f(Y, f(f(X, Y), f(Y, Z))).
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z)))
% 24.91/3.66 = { by lemma 15 R->L }
% 24.91/3.66 f(f(f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z))), f(Y, f(f(Y, f(f(X, X), X)), Z))), f(f(X, Y), f(Y, Z)))
% 24.91/3.66 = { by axiom 1 (ol_23A) }
% 24.91/3.66 f(Y, f(f(X, Y), f(Y, Z)))
% 24.91/3.66
% 24.91/3.66 Lemma 17: f(f(Y, X), f(Y, X)) = f(f(X, Y), f(Y, X)).
% 24.91/3.66 Proof:
% 24.91/3.66 f(f(Y, X), f(Y, X))
% 24.91/3.66 = { by lemma 14 R->L }
% 24.91/3.66 f(f(Y, X), f(f(f(Y, Y), f(X, Y)), X))
% 24.91/3.66 = { by lemma 14 R->L }
% 24.91/3.66 f(f(f(f(Y, Y), f(X, Y)), X), f(f(f(Y, Y), f(X, Y)), X))
% 24.91/3.66 = { by lemma 6 R->L }
% 24.91/3.66 f(f(f(f(Y, Y), f(X, Y)), X), f(f(f(Y, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))))
% 24.91/3.66 = { by lemma 6 R->L }
% 24.91/3.66 f(f(f(f(Y, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))), f(f(f(Y, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))))
% 24.91/3.66 = { by lemma 16 }
% 24.91/3.66 f(f(X, Y), f(f(f(Y, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))))
% 24.91/3.66 = { by lemma 6 }
% 24.91/3.66 f(f(X, Y), f(f(f(Y, Y), f(X, Y)), X))
% 24.91/3.66 = { by lemma 14 }
% 24.91/3.66 f(f(X, Y), f(Y, X))
% 24.91/3.67
% 24.91/3.67 Lemma 18: f(X, f(f(X, X), Y)) = f(X, X).
% 24.91/3.67 Proof:
% 24.91/3.67 f(X, f(f(X, X), Y))
% 24.91/3.67 = { by lemma 10 R->L }
% 24.91/3.67 f(X, f(f(X, f(f(X, X), Y)), f(X, X)))
% 24.91/3.67 = { by lemma 11 }
% 24.91/3.67 f(X, X)
% 24.91/3.67
% 24.91/3.67 Lemma 19: f(Y, X) = f(X, Y).
% 24.91/3.67 Proof:
% 24.91/3.67 f(Y, X)
% 24.91/3.67 = { by lemma 14 R->L }
% 24.91/3.67 f(f(f(Y, Y), f(X, Y)), X)
% 24.91/3.67 = { by lemma 6 R->L }
% 24.91/3.67 f(f(f(Y, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))
% 24.91/3.67 = { by lemma 3 R->L }
% 24.91/3.67 f(f(f(Y, Y), f(X, Y)), f(f(f(f(Y, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))), f(X, Y)))
% 24.91/3.67 = { by lemma 6 }
% 24.91/3.67 f(f(f(Y, Y), f(X, Y)), f(f(f(f(Y, Y), f(X, Y)), X), f(X, Y)))
% 24.91/3.67 = { by lemma 14 }
% 24.91/3.67 f(Y, f(f(f(f(Y, Y), f(X, Y)), X), f(X, Y)))
% 24.91/3.67 = { by lemma 14 }
% 24.91/3.67 f(Y, f(f(Y, X), f(X, Y)))
% 24.91/3.67 = { by lemma 17 R->L }
% 24.91/3.67 f(Y, f(f(X, Y), f(X, Y)))
% 24.91/3.67 = { by lemma 18 R->L }
% 24.91/3.67 f(Y, f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))))
% 24.91/3.67 = { by lemma 18 R->L }
% 24.91/3.67 f(Y, f(f(X, Y), f(f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))), f(X, Y))))
% 24.91/3.67 = { by lemma 9 R->L }
% 24.91/3.67 f(f(f(X, Y), f(Y, Y)), f(f(X, Y), f(f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))), f(X, Y))))
% 24.91/3.67 = { by lemma 6 }
% 24.91/3.67 f(X, Y)
% 24.91/3.67
% 24.91/3.67 Lemma 20: f(f(X, f(Y, Y)), Y) = f(Y, Y).
% 24.91/3.67 Proof:
% 24.91/3.67 f(f(X, f(Y, Y)), Y)
% 24.91/3.67 = { by lemma 5 R->L }
% 24.91/3.67 f(f(X, f(Y, Y)), f(f(Y, Y), f(Y, Y)))
% 24.91/3.67 = { by lemma 9 }
% 24.91/3.67 f(Y, Y)
% 24.91/3.67
% 24.91/3.67 Lemma 21: f(X, f(Y, f(X, X))) = f(X, X).
% 24.91/3.67 Proof:
% 24.91/3.67 f(X, f(Y, f(X, X)))
% 24.91/3.67 = { by lemma 14 R->L }
% 24.91/3.67 f(f(f(X, X), f(f(Y, f(X, X)), X)), f(Y, f(X, X)))
% 24.91/3.67 = { by lemma 20 R->L }
% 24.91/3.67 f(f(f(f(Y, f(X, X)), X), f(f(Y, f(X, X)), X)), f(Y, f(X, X)))
% 24.91/3.67 = { by lemma 13 }
% 24.91/3.67 f(f(Y, f(X, X)), X)
% 24.91/3.67 = { by lemma 20 }
% 24.91/3.67 f(X, X)
% 24.91/3.67
% 24.91/3.67 Lemma 22: f(f(Z, X), f(X, X)) = f(f(X, X), f(X, Y)).
% 24.91/3.67 Proof:
% 24.91/3.67 f(f(Z, X), f(X, X))
% 24.91/3.67 = { by lemma 19 }
% 24.91/3.67 f(f(X, Z), f(X, X))
% 24.91/3.67 = { by lemma 19 }
% 24.91/3.67 f(f(X, X), f(X, Z))
% 24.91/3.67 = { by lemma 19 }
% 24.91/3.67 f(f(X, X), f(Z, X))
% 24.91/3.67 = { by lemma 12 R->L }
% 24.91/3.67 f(f(X, X), f(Z, f(f(X, X), f(X, X))))
% 24.91/3.67 = { by lemma 21 }
% 24.91/3.67 f(f(X, X), f(X, X))
% 24.91/3.67 = { by lemma 21 R->L }
% 24.91/3.67 f(f(X, X), f(f(f(Y, X), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(Y, f(f(X, X), f(X, X)))), f(U, f(T, S)))), f(f(X, X), f(X, X))))
% 24.91/3.67 = { by lemma 12 }
% 24.91/3.67 f(f(X, X), f(f(f(Y, X), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(Y, f(f(X, X), f(X, X)))), f(U, f(T, S)))), X))
% 24.91/3.67 = { by lemma 19 R->L }
% 24.91/3.67 f(f(X, X), f(X, f(f(Y, X), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(Y, f(f(X, X), f(X, X)))), f(U, f(T, S))))))
% 24.91/3.67 = { by lemma 5 R->L }
% 24.91/3.67 f(f(X, X), f(X, f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(Y, f(f(X, X), f(X, X)))), f(U, f(T, S))))))
% 24.91/3.67 = { by lemma 5 R->L }
% 24.91/3.67 f(f(X, X), f(X, f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(Y, f(f(X, X), f(X, X)))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 5 R->L }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(Y, f(f(X, X), f(X, X))), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(Y, f(f(X, X), f(X, X)))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 19 }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), Y), f(f(f(f(X, X), f(f(X, X), f(X, X))), f(Y, f(f(X, X), f(X, X)))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 19 }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(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)), Y)), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 19 }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), Y), f(f(f(f(f(X, X), f(X, X)), Y), f(f(X, X), f(f(X, X), f(X, X)))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 19 }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), Y), f(f(f(f(f(X, X), f(X, X)), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 4 R->L }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), Y), f(f(f(f(f(X, X), f(X, X)), Y), f(f(f(X, X), f(X, X)), f(f(f(f(W, f(X, X)), f(f(X, X), V)), f(X, X)), f(f(X, X), f(X, X))))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 21 R->L }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), Y), f(f(f(f(f(X, X), f(X, X)), Y), f(f(f(X, X), f(f(f(f(W, f(X, X)), f(f(X, X), V)), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(f(W, f(X, X)), f(f(X, X), V)), f(X, X)), f(f(X, X), f(X, X))))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 4 R->L }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), Y), f(f(f(f(f(X, X), f(X, X)), Y), f(f(f(f(f(f(W, f(X, X)), f(f(X, X), V)), f(X, X)), f(f(X, X), f(X, X))), f(f(f(f(W, f(X, X)), f(f(X, X), V)), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(f(W, f(X, X)), f(f(X, X), V)), f(X, X)), f(f(X, X), f(X, X))))), f(U, f(T, f(f(S, S), f(S, S))))))))
% 24.91/3.67 = { by lemma 2 }
% 24.91/3.67 f(f(X, X), f(f(f(X, X), f(X, X)), Y))
% 24.91/3.67 = { by lemma 19 R->L }
% 24.91/3.67 f(f(X, X), f(Y, f(f(X, X), f(X, X))))
% 24.91/3.67 = { by lemma 5 }
% 24.91/3.67 f(f(X, X), f(Y, X))
% 24.91/3.67 = { by lemma 19 R->L }
% 24.91/3.67 f(f(X, X), f(X, Y))
% 24.91/3.67
% 24.91/3.67 Lemma 23: f(X, f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X)))) = f(X, Y).
% 24.91/3.67 Proof:
% 24.91/3.67 f(X, f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))))
% 24.91/3.67 = { by lemma 2 R->L }
% 24.91/3.67 f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(W, f(X, Y)), f(W, f(X, Y))), f(W, f(X, Y)))), V))))
% 24.91/3.67 = { by lemma 2 }
% 24.91/3.67 f(X, Y)
% 24.91/3.67
% 24.91/3.67 Lemma 24: f(f(f(f(X, Y), f(X, Y)), Z), f(X, X)) = X.
% 24.91/3.67 Proof:
% 24.91/3.67 f(f(f(f(X, Y), f(X, Y)), Z), f(X, X))
% 24.91/3.67 = { by lemma 15 R->L }
% 24.91/3.67 f(f(f(f(f(f(X, Y), f(X, Y)), X), f(X, Y)), Z), f(X, X))
% 24.91/3.67 = { by lemma 8 }
% 24.91/3.67 X
% 24.91/3.67
% 24.91/3.67 Lemma 25: f(f(X, f(X, X)), Y) = f(Y, Y).
% 24.91/3.67 Proof:
% 24.91/3.67 f(f(X, f(X, X)), Y)
% 24.91/3.67 = { by lemma 23 R->L }
% 24.91/3.67 f(f(X, f(f(X, f(X, X)), f(f(f(X, X), f(X, X)), f(X, X)))), Y)
% 24.91/3.67 = { by lemma 5 }
% 24.91/3.67 f(f(X, f(f(X, f(X, X)), f(X, f(X, X)))), Y)
% 24.91/3.67 = { by lemma 24 R->L }
% 24.91/3.67 f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(X, f(X, X)), f(X, f(X, X)))), Y)
% 24.91/3.67 = { by lemma 15 R->L }
% 24.91/3.67 f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, f(X, X)))), Y)
% 24.91/3.67 = { by lemma 21 R->L }
% 24.91/3.67 f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)))))), Y)
% 24.91/3.68 = { by lemma 12 R->L }
% 24.91/3.68 f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(X, X), f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)))), f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)))))), Y)
% 24.91/3.68 = { by lemma 21 R->L }
% 24.91/3.68 f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X))), f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)))), f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)))))), Y)
% 24.91/3.68 = { by lemma 6 R->L }
% 24.91/3.68 f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y))), f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)))), f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y))))), f(f(f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X))), f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)))), f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)))))), Y)
% 24.91/3.68 = { by lemma 23 }
% 24.91/3.68 f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y))), f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)))), f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y))))), Y)
% 24.91/3.68 = { by lemma 6 }
% 24.91/3.68 f(f(f(f(X, f(X, X)), f(X, f(X, X))), f(Y, Y)), Y)
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(f(Y, Y), f(f(X, f(X, X)), f(X, f(X, X)))), Y)
% 24.91/3.68 = { by lemma 15 }
% 24.91/3.68 f(Y, Y)
% 24.91/3.68
% 24.91/3.68 Lemma 26: f(f(X, X), f(Y, f(f(X, Z), f(X, Z)))) = X.
% 24.91/3.68 Proof:
% 24.91/3.68 f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(Y, f(f(X, Z), f(X, Z))), f(X, X))
% 24.91/3.68 = { by lemma 21 R->L }
% 24.91/3.68 f(f(Y, f(f(X, Z), f(X, Z))), f(X, f(f(W, X), f(X, X))))
% 24.91/3.68 = { by lemma 22 }
% 24.91/3.68 f(f(Y, f(f(X, Z), f(X, Z))), f(X, f(f(X, X), f(X, Z))))
% 24.91/3.68 = { by lemma 9 R->L }
% 24.91/3.68 f(f(Y, f(f(X, Z), f(X, Z))), f(f(f(V, X), f(X, X)), f(f(X, X), f(X, Z))))
% 24.91/3.68 = { by lemma 22 }
% 24.91/3.68 f(f(Y, f(f(X, Z), f(X, Z))), f(f(f(X, X), f(X, Z)), f(f(X, X), f(X, Z))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(Y, f(f(X, Z), f(X, Z))), f(f(f(X, X), f(X, Z)), f(f(X, Z), f(X, X))))
% 24.91/3.68 = { by lemma 17 R->L }
% 24.91/3.68 f(f(Y, f(f(X, Z), f(X, Z))), f(f(f(X, Z), f(X, X)), f(f(X, Z), f(X, X))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(f(f(X, Z), f(X, Z)), Y), f(f(f(X, Z), f(X, X)), f(f(X, Z), f(X, X))))
% 24.91/3.68 = { by lemma 6 R->L }
% 24.91/3.68 f(f(f(f(X, Z), f(f(f(X, Z), f(X, X)), f(f(X, Z), f(f(f(X, Z), f(f(f(X, Z), f(X, Z)), f(X, Z))), f(X, Z))))), Y), f(f(f(X, Z), f(X, X)), f(f(X, Z), f(X, X))))
% 24.91/3.68 = { by lemma 6 R->L }
% 24.91/3.68 f(f(f(f(f(f(X, Z), f(X, X)), f(f(X, Z), f(f(f(X, Z), f(f(f(X, Z), f(X, Z)), f(X, Z))), f(X, Z)))), f(f(f(X, Z), f(X, X)), f(f(X, Z), f(f(f(X, Z), f(f(f(X, Z), f(X, Z)), f(X, Z))), f(X, Z))))), Y), f(f(f(X, Z), f(X, X)), f(f(X, Z), f(X, X))))
% 24.91/3.68 = { by lemma 24 }
% 24.91/3.68 f(f(X, Z), f(X, X))
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(X, X), f(X, Z))
% 24.91/3.68 = { by lemma 22 R->L }
% 24.91/3.68 f(f(U, X), f(X, X))
% 24.91/3.68 = { by lemma 9 }
% 24.91/3.68 X
% 24.91/3.68
% 24.91/3.68 Lemma 27: f(f(X, Y), f(X, f(f(Y, Z), f(Y, Z)))) = f(f(X, Y), f(X, Y)).
% 24.91/3.68 Proof:
% 24.91/3.68 f(f(X, Y), f(X, f(f(Y, Z), f(Y, Z))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(X, f(f(Y, Z), f(Y, Z))), f(X, Y))
% 24.91/3.68 = { by lemma 26 R->L }
% 24.91/3.68 f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z))))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, Y))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(X, f(f(Y, Z), f(Y, Z))), f(Y, Y))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))))
% 24.91/3.68 = { by lemma 14 R->L }
% 24.91/3.68 f(f(f(f(Y, Z), f(Y, Z)), X), f(f(f(X, X), f(f(f(Y, Z), f(Y, Z)), X)), f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))))
% 24.91/3.68 = { by lemma 16 R->L }
% 24.91/3.68 f(f(f(f(X, X), f(f(f(Y, Z), f(Y, Z)), X)), f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))), f(f(f(X, X), f(f(f(Y, Z), f(Y, Z)), X)), f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))))
% 24.91/3.68 = { by lemma 14 }
% 24.91/3.68 f(f(X, f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))), f(f(f(X, X), f(f(f(Y, Z), f(Y, Z)), X)), f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))))
% 24.91/3.68 = { by lemma 14 }
% 24.91/3.68 f(f(X, f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))), f(X, f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))))
% 24.91/3.68 = { by lemma 25 R->L }
% 24.91/3.68 f(f(W, f(W, W)), f(X, f(f(f(f(Y, Z), f(Y, Z)), X), f(Y, Y))))
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(W, f(W, W)), f(X, f(f(Y, Y), f(f(f(Y, Z), f(Y, Z)), X))))
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(W, f(W, W)), f(X, f(f(Y, Y), f(X, f(f(Y, Z), f(Y, Z))))))
% 24.91/3.68 = { by lemma 26 }
% 24.91/3.68 f(f(W, f(W, W)), f(X, Y))
% 24.91/3.68 = { by lemma 25 }
% 24.91/3.68 f(f(X, Y), f(X, Y))
% 24.91/3.68
% 24.91/3.68 Lemma 28: f(f(X, Y), f(f(f(Y, Z), f(Y, Z)), X)) = f(f(X, Y), f(X, Y)).
% 24.91/3.68 Proof:
% 24.91/3.68 f(f(X, Y), f(f(f(Y, Z), f(Y, Z)), X))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(X, Y), f(X, f(f(Y, Z), f(Y, Z))))
% 24.91/3.68 = { by lemma 27 }
% 24.91/3.68 f(f(X, Y), f(X, Y))
% 24.91/3.68
% 24.91/3.68 Lemma 29: f(f(f(X, Y), f(X, Y)), f(f(X, Z), f(X, Z))) = f(Z, f(f(X, Y), f(X, Y))).
% 24.91/3.68 Proof:
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(X, Z), f(X, Z)))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(X, Z)))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(Z, X)))
% 24.91/3.68 = { by lemma 28 R->L }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(f(f(X, Y), f(X, Y)), Z)))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(Z, X)))
% 24.91/3.68 = { by lemma 12 R->L }
% 24.91/3.68 f(f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), Z)), f(f(f(f(X, Y), f(X, Y)), Z), f(Z, X)))
% 24.91/3.68 = { by lemma 3 R->L }
% 24.91/3.68 f(f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), Z)), f(f(f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), Z)), f(f(f(f(X, Y), f(X, Y)), Z), f(Z, X))), f(f(f(X, Y), f(X, Y)), Z)))
% 24.91/3.68 = { by lemma 12 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), Z)), f(f(f(f(X, Y), f(X, Y)), Z), f(Z, X))), f(f(f(X, Y), f(X, Y)), Z)))
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(f(f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), Z)), f(f(f(f(X, Y), f(X, Y)), Z), f(Z, X)))))
% 24.91/3.68 = { by lemma 12 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(Z, X)))))
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(f(f(X, Y), f(X, Y)), Z)))))
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(Z, f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(f(f(X, Y), f(X, Y)), Z)))))
% 24.91/3.68 = { by lemma 28 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(Z, f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(Z, X)))))
% 24.91/3.68 = { by lemma 19 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(Z, X)))))
% 24.91/3.68 = { by lemma 27 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(f(f(X, Y), f(X, Y)), Z)))
% 24.91/3.68 = { by lemma 7 }
% 24.91/3.68 f(f(f(X, Y), f(X, Y)), Z)
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(Z, f(f(X, Y), f(X, Y)))
% 24.91/3.68
% 24.91/3.68 Goal 1 (associativity): f(a, f(f(b, c), f(b, c))) = f(c, f(f(b, a), f(b, a))).
% 24.91/3.68 Proof:
% 24.91/3.68 f(a, f(f(b, c), f(b, c)))
% 24.91/3.68 = { by lemma 29 R->L }
% 24.91/3.68 f(f(f(b, c), f(b, c)), f(f(b, a), f(b, a)))
% 24.91/3.68 = { by lemma 19 R->L }
% 24.91/3.68 f(f(f(b, a), f(b, a)), f(f(b, c), f(b, c)))
% 24.91/3.68 = { by lemma 29 }
% 24.91/3.68 f(c, f(f(b, a), f(b, a)))
% 24.91/3.68 % SZS output end Proof
% 24.91/3.68
% 24.91/3.68 RESULT: Unsatisfiable (the axioms are contradictory).
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