TSTP Solution File: LAT076-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT076-1 : 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 : n020.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 33.86s 4.89s
% Output : Proof 35.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT076-1 : 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 : n020.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 06:19:30 EDT 2023
% 0.13/0.34 % CPUTime :
% 33.86/4.89 Command-line arguments: --no-flatten-goal
% 33.86/4.89
% 33.86/4.89 % SZS status Unsatisfiable
% 33.86/4.89
% 33.86/4.95 % SZS output start Proof
% 33.86/4.95 Axiom 1 (mol_27B1): f(f(f(f(X, Y), f(Z, Y)), W), f(Y, f(f(f(f(f(f(X, X), Y), Z), Z), Y), X))) = Y.
% 33.86/4.95
% 33.86/4.95 Lemma 2: f(X, f(f(Y, X), f(f(f(f(f(f(f(Z, X), f(Z, X)), f(Y, X)), W), W), f(Y, X)), f(Z, X)))) = f(Y, X).
% 33.86/4.95 Proof:
% 33.86/4.95 f(X, f(f(Y, X), f(f(f(f(f(f(f(Z, X), f(Z, X)), f(Y, X)), W), W), f(Y, X)), f(Z, X))))
% 33.86/4.95 = { by axiom 1 (mol_27B1) R->L }
% 33.86/4.95 f(f(f(f(f(Z, X), f(Y, X)), f(W, f(Y, X))), f(X, f(f(f(f(f(f(Z, Z), X), Y), Y), X), Z))), f(f(Y, X), f(f(f(f(f(f(f(Z, X), f(Z, X)), f(Y, X)), W), W), f(Y, X)), f(Z, X))))
% 33.86/4.95 = { by axiom 1 (mol_27B1) }
% 33.86/4.95 f(Y, X)
% 33.86/4.95
% 33.86/4.95 Lemma 3: f(f(X, f(f(Y, Z), f(W, Z))), f(Z, f(f(f(f(f(f(Y, Y), Z), W), W), Z), Y))) = Z.
% 33.86/4.95 Proof:
% 33.86/4.95 f(f(X, f(f(Y, Z), f(W, Z))), f(Z, f(f(f(f(f(f(Y, Y), Z), W), W), Z), Y)))
% 33.86/4.95 = { by lemma 2 R->L }
% 33.86/4.95 f(f(f(f(Y, Z), f(W, Z)), f(f(X, f(f(Y, Z), f(W, Z))), f(f(f(f(f(f(f(V, f(f(Y, Z), f(W, Z))), f(V, f(f(Y, Z), f(W, Z)))), f(X, f(f(Y, Z), f(W, Z)))), U), U), f(X, f(f(Y, Z), f(W, Z)))), f(V, f(f(Y, Z), f(W, Z)))))), f(Z, f(f(f(f(f(f(Y, Y), Z), W), W), Z), Y)))
% 33.86/4.95 = { by axiom 1 (mol_27B1) }
% 33.86/4.95 Z
% 33.86/4.95
% 33.86/4.95 Lemma 4: f(f(X, Y), f(f(f(Z, Y), f(X, Y)), Y)) = f(f(Z, Y), f(X, Y)).
% 33.86/4.95 Proof:
% 33.86/4.95 f(f(X, Y), f(f(f(Z, Y), f(X, Y)), Y))
% 33.86/4.95 = { by lemma 3 R->L }
% 33.86/4.95 f(f(X, Y), f(f(f(Z, Y), f(X, Y)), f(f(f(f(f(f(f(Y, f(f(f(f(f(f(Z, Z), Y), X), X), Y), Z)), f(Y, f(f(f(f(f(f(Z, Z), Y), X), X), Y), Z))), f(f(Z, Y), f(X, Y))), f(W, f(X, Y))), f(W, f(X, Y))), f(f(Z, Y), f(X, Y))), f(Y, f(f(f(f(f(f(Z, Z), Y), X), X), Y), Z)))))
% 33.86/4.95 = { by lemma 3 R->L }
% 33.86/4.95 f(f(f(f(f(Y, f(f(f(f(f(f(Z, Z), Y), X), X), Y), Z)), f(f(Z, Y), f(X, Y))), f(f(W, f(X, Y)), f(f(Z, Y), f(X, Y)))), f(f(X, Y), f(f(f(f(f(f(W, W), f(X, Y)), f(Z, Y)), f(Z, Y)), f(X, Y)), W))), f(f(f(Z, Y), f(X, Y)), f(f(f(f(f(f(f(Y, f(f(f(f(f(f(Z, Z), Y), X), X), Y), Z)), f(Y, f(f(f(f(f(f(Z, Z), Y), X), X), Y), Z))), f(f(Z, Y), f(X, Y))), f(W, f(X, Y))), f(W, f(X, Y))), f(f(Z, Y), f(X, Y))), f(Y, f(f(f(f(f(f(Z, Z), Y), X), X), Y), Z)))))
% 33.86/4.95 = { by axiom 1 (mol_27B1) }
% 33.86/4.95 f(f(Z, Y), f(X, Y))
% 33.86/4.95
% 33.86/4.95 Lemma 5: f(f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y))) = X.
% 33.86/4.95 Proof:
% 33.86/4.95 f(f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))
% 33.86/4.95 = { by axiom 1 (mol_27B1) R->L }
% 33.86/4.95 f(f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)), f(f(f(f(f(Y, X), f(Z, X)), f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y))), f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))
% 33.86/4.95 = { by lemma 4 }
% 33.86/4.95 f(f(f(f(Y, X), f(Z, X)), f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))
% 33.86/4.95 = { by axiom 1 (mol_27B1) }
% 33.86/4.95 X
% 33.86/4.95
% 33.86/4.95 Lemma 6: f(f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X)), f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X))) = f(Y, X).
% 33.86/4.95 Proof:
% 33.86/4.95 f(f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X)), f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X)))
% 33.86/4.95 = { by lemma 4 R->L }
% 33.86/4.95 f(f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X)), f(f(Y, X), f(f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X)), X)))
% 33.86/4.95 = { by lemma 4 R->L }
% 33.86/4.95 f(f(f(Y, X), f(f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X)), X)), f(f(Y, X), f(f(f(f(f(f(X, X), f(Y, X)), X), X), f(Y, X)), X)))
% 33.86/4.95 = { by lemma 5 }
% 33.86/4.95 f(Y, X)
% 33.86/4.95
% 33.86/4.95 Lemma 7: f(f(f(f(X, Y), f(Z, Y)), Y), f(f(f(X, Y), f(Z, Y)), Y)) = f(f(X, Y), f(Z, Y)).
% 33.86/4.95 Proof:
% 33.86/4.95 f(f(f(f(X, Y), f(Z, Y)), Y), f(f(f(X, Y), f(Z, Y)), Y))
% 33.86/4.95 = { by lemma 4 R->L }
% 33.86/4.95 f(f(f(f(X, Y), f(Z, Y)), Y), f(f(f(Z, Y), f(f(f(X, Y), f(Z, Y)), Y)), Y))
% 33.86/4.95 = { by lemma 4 }
% 33.86/4.95 f(f(Z, Y), f(f(f(X, Y), f(Z, Y)), Y))
% 33.86/4.95 = { by lemma 4 }
% 33.86/4.95 f(f(X, Y), f(Z, Y))
% 33.86/4.95
% 33.86/4.95 Lemma 8: f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y))) = f(X, Y).
% 33.86/4.95 Proof:
% 33.86/4.95 f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, Y)))
% 33.86/4.95 = { by lemma 6 R->L }
% 33.86/4.95 f(f(f(X, Y), f(X, Y)), f(f(f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y)), f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y))), f(X, Y)))
% 33.86/4.95 = { by lemma 6 R->L }
% 35.34/4.95 f(f(f(f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y)), f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y))), f(X, Y)), f(f(f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y)), f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y))), f(X, Y)))
% 35.34/4.95 = { by lemma 7 }
% 35.34/4.95 f(f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y)), f(f(f(f(f(Y, Y), f(X, Y)), Y), Y), f(X, Y)))
% 35.34/4.95 = { by lemma 6 }
% 35.34/4.95 f(X, Y)
% 35.34/4.96
% 35.34/4.96 Lemma 9: f(f(X, X), f(X, X)) = X.
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, X), f(X, X))
% 35.34/4.96 = { by axiom 1 (mol_27B1) R->L }
% 35.34/4.96 f(f(X, f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))), f(X, X))
% 35.34/4.96 = { by axiom 1 (mol_27B1) R->L }
% 35.34/4.96 f(f(X, f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))), f(f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y))), X))
% 35.34/4.96 = { by axiom 1 (mol_27B1) R->L }
% 35.34/4.96 f(f(X, f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))), f(f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y))), f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))))
% 35.34/4.96 = { by axiom 1 (mol_27B1) R->L }
% 35.34/4.96 f(f(f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y))), f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))), f(f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y))), f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))))
% 35.34/4.96 = { by lemma 8 }
% 35.34/4.96 f(f(f(f(Y, X), f(Z, X)), W), f(X, f(f(f(f(f(f(Y, Y), X), Z), Z), X), Y)))
% 35.34/4.96 = { by axiom 1 (mol_27B1) }
% 35.34/4.96 X
% 35.34/4.96
% 35.34/4.96 Lemma 10: f(f(f(X, f(X, X)), X), f(f(X, f(X, X)), X)) = X.
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(f(X, f(X, X)), X), f(f(X, f(X, X)), X))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(X, X), f(X, X)), f(X, X)), X), f(f(X, f(X, X)), X))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(X, X), f(X, X)), f(X, X)), X), f(f(f(f(X, X), f(X, X)), f(X, X)), X))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(f(f(X, X), f(X, X)), X), f(X, X)), f(X, X)), X), f(f(f(f(X, X), f(X, X)), f(X, X)), X))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(f(f(X, X), f(X, 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(X, X)), X))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(f(f(X, X), f(X, X)), X), f(X, X)), f(X, X)), f(f(X, X), f(X, X))), f(f(f(f(f(f(X, X), f(X, X)), X), f(X, X)), f(X, X)), X))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(f(f(X, X), f(X, X)), X), f(X, X)), f(X, X)), 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(X, X)), f(X, X)), X))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(f(f(X, X), f(X, X)), X), f(X, X)), f(X, X)), 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(X, X)), f(X, X)), f(f(X, X), f(X, X))))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(f(f(f(f(X, X), f(X, X)), f(f(X, X), f(X, X))), f(X, X)), f(X, X)), 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(X, X)), f(X, X)), f(f(X, X), f(X, X))))
% 35.34/4.96 = { by lemma 6 }
% 35.34/4.96 f(f(X, X), f(X, X))
% 35.34/4.96 = { by lemma 9 }
% 35.34/4.96 X
% 35.34/4.96
% 35.34/4.96 Lemma 11: f(f(X, f(X, X)), X) = f(X, X).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, f(X, X)), X)
% 35.34/4.96 = { by lemma 8 R->L }
% 35.34/4.96 f(f(f(f(X, f(X, X)), X), f(f(X, f(X, X)), X)), f(f(f(X, f(X, X)), X), f(f(X, f(X, X)), X)))
% 35.34/4.96 = { by lemma 10 }
% 35.34/4.96 f(X, f(f(f(X, f(X, X)), X), f(f(X, f(X, X)), X)))
% 35.34/4.96 = { by lemma 10 }
% 35.34/4.96 f(X, X)
% 35.34/4.96
% 35.34/4.96 Lemma 12: f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), f(f(X, Y), f(f(Y, f(X, Y)), Y))) = f(X, Y).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), f(f(X, Y), f(f(Y, f(X, Y)), Y)))
% 35.34/4.96 = { by axiom 1 (mol_27B1) R->L }
% 35.34/4.96 f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), f(f(X, Y), f(f(f(f(f(f(Y, Y), f(X, Y)), f(Y, f(f(f(f(f(f(Y, Y), Y), X), X), Y), Y))), f(Y, f(f(f(f(f(f(Y, Y), Y), X), X), Y), Y))), f(X, Y)), Y)))
% 35.34/4.96 = { by axiom 1 (mol_27B1) R->L }
% 35.34/4.96 f(f(f(X, Y), f(f(f(f(f(f(Y, Y), f(X, Y)), f(Y, f(f(f(f(f(f(Y, Y), Y), X), X), Y), Y))), f(Y, f(f(f(f(f(f(Y, Y), Y), X), X), Y), Y))), f(X, Y)), Y)), f(f(X, Y), f(f(f(f(f(f(Y, Y), f(X, Y)), f(Y, f(f(f(f(f(f(Y, Y), Y), X), X), Y), Y))), f(Y, f(f(f(f(f(f(Y, Y), Y), X), X), Y), Y))), f(X, Y)), Y)))
% 35.34/4.96 = { by lemma 5 }
% 35.34/4.96 f(X, Y)
% 35.34/4.96
% 35.34/4.96 Lemma 13: f(f(f(X, Y), f(Z, Y)), f(f(X, Y), f(Z, Y))) = f(f(f(X, Y), f(Z, Y)), Y).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(f(X, Y), f(Z, Y)), f(f(X, Y), f(Z, Y)))
% 35.34/4.96 = { by lemma 7 R->L }
% 35.34/4.96 f(f(f(X, Y), f(Z, Y)), f(f(f(f(X, Y), f(Z, Y)), Y), f(f(f(X, Y), f(Z, Y)), Y)))
% 35.34/4.96 = { by lemma 7 R->L }
% 35.34/4.96 f(f(f(f(f(X, Y), f(Z, Y)), Y), f(f(f(X, Y), f(Z, Y)), Y)), f(f(f(f(X, Y), f(Z, Y)), Y), f(f(f(X, Y), f(Z, Y)), Y)))
% 35.34/4.96 = { by lemma 8 }
% 35.34/4.96 f(f(f(X, Y), f(Z, Y)), Y)
% 35.34/4.96
% 35.34/4.96 Lemma 14: f(f(f(X, Y), f(X, Y)), Y) = f(X, Y).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(f(X, Y), f(X, Y)), Y)
% 35.34/4.96 = { by lemma 12 R->L }
% 35.34/4.96 f(f(f(X, Y), f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), f(f(X, Y), f(f(Y, f(X, Y)), Y)))), Y)
% 35.34/4.96 = { by lemma 12 R->L }
% 35.34/4.96 f(f(f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), f(f(X, Y), f(f(Y, f(X, Y)), Y))), f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), f(f(X, Y), f(f(Y, f(X, Y)), Y)))), Y)
% 35.34/4.96 = { by lemma 8 }
% 35.34/4.96 f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), Y)
% 35.34/4.96 = { by lemma 13 R->L }
% 35.34/4.96 f(f(f(X, Y), f(f(Y, f(X, Y)), Y)), f(f(X, Y), f(f(Y, f(X, Y)), Y)))
% 35.34/4.96 = { by lemma 12 }
% 35.34/4.96 f(X, Y)
% 35.34/4.96
% 35.34/4.96 Lemma 15: f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(Y, Y)) = Y.
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(Y, Y))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(Y, f(f(Y, Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 11 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(Y, f(f(f(Y, f(Y, Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(Y, Y), Y))), f(Y, f(f(f(f(f(Y, Y), f(Y, Y)), f(Y, Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 14 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(f(f(Y, Y), f(Y, Y)), Y), Y))), f(Y, f(f(f(f(f(Y, Y), f(Y, Y)), f(Y, Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 14 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(f(f(Y, Y), f(Y, Y)), Y), Y))), f(Y, f(f(f(f(f(f(f(Y, Y), f(Y, Y)), Y), f(Y, Y)), f(Y, Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 14 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(f(f(Y, Y), f(Y, Y)), Y), Y))), f(Y, f(f(f(f(f(f(f(Y, Y), f(Y, Y)), Y), f(Y, Y)), f(f(f(Y, Y), f(Y, Y)), Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(f(f(Y, Y), f(Y, Y)), Y), Y))), f(Y, f(f(f(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)), Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 13 R->L }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(f(f(Y, Y), f(Y, Y)), Y), Y))), f(Y, f(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(f(Y, Y), f(Y, Y)))), f(f(f(Y, Y), f(Y, Y)), Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 9 }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(f(f(Y, Y), f(Y, Y)), Y), Y))), f(Y, f(f(f(f(f(f(f(Y, Y), f(Y, 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)), Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 9 }
% 35.34/4.96 f(f(X, f(f(f(Y, Y), Y), f(f(f(f(Y, Y), f(Y, Y)), Y), Y))), f(Y, f(f(f(f(f(f(f(Y, Y), f(Y, Y)), Y), f(f(f(Y, Y), f(Y, Y)), Y)), f(f(f(Y, Y), f(Y, Y)), Y)), Y), f(Y, Y))))
% 35.34/4.96 = { by lemma 3 }
% 35.34/4.96 Y
% 35.34/4.96
% 35.34/4.96 Lemma 16: f(f(f(X, X), f(X, Y)), f(f(X, X), f(X, Y))) = f(X, X).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(f(X, X), f(X, Y)), f(f(X, X), f(X, Y)))
% 35.34/4.96 = { by lemma 15 R->L }
% 35.34/4.96 f(f(f(X, X), f(X, Y)), f(f(X, X), f(f(f(f(f(f(Y, Y), f(X, X)), f(f(f(X, X), X), f(f(X, X), X))), f(f(f(X, X), X), f(f(X, X), X))), f(X, X)), Y)))
% 35.34/4.96 = { by lemma 15 R->L }
% 35.34/4.96 f(f(f(X, X), f(f(f(f(f(f(Y, Y), f(X, X)), f(f(f(X, X), X), f(f(X, X), X))), f(f(f(X, X), X), f(f(X, X), X))), f(X, X)), Y)), f(f(X, X), f(f(f(f(f(f(Y, Y), f(X, X)), f(f(f(X, X), X), f(f(X, X), X))), f(f(f(X, X), X), f(f(X, X), X))), f(X, X)), Y)))
% 35.34/4.96 = { by lemma 5 }
% 35.34/4.96 f(X, X)
% 35.34/4.96
% 35.34/4.96 Lemma 17: f(f(X, X), f(X, Y)) = X.
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, X), f(X, Y))
% 35.34/4.96 = { by lemma 8 R->L }
% 35.34/4.96 f(f(f(f(X, X), f(X, Y)), f(f(X, X), f(X, Y))), f(f(f(X, X), f(X, Y)), f(f(X, X), f(X, Y))))
% 35.34/4.96 = { by lemma 16 }
% 35.34/4.96 f(f(X, X), f(f(f(X, X), f(X, Y)), f(f(X, X), f(X, Y))))
% 35.34/4.96 = { by lemma 16 }
% 35.34/4.96 f(f(X, X), f(X, X))
% 35.34/4.96 = { by lemma 9 }
% 35.34/4.96 X
% 35.34/4.96
% 35.34/4.96 Lemma 18: f(f(X, X), f(Y, X)) = X.
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, X), f(Y, X))
% 35.34/4.96 = { by lemma 2 R->L }
% 35.34/4.96 f(f(X, X), f(X, f(f(Y, X), f(f(f(f(f(f(f(Z, X), f(Z, X)), f(Y, X)), W), W), f(Y, X)), f(Z, X)))))
% 35.34/4.96 = { by lemma 17 }
% 35.34/4.96 X
% 35.34/4.96
% 35.34/4.96 Lemma 19: f(f(f(X, Y), f(X, Y)), X) = f(X, Y).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(f(X, Y), f(X, Y)), X)
% 35.34/4.96 = { by lemma 17 R->L }
% 35.34/4.96 f(f(f(X, Y), f(X, Y)), f(f(X, X), f(X, Y)))
% 35.34/4.96 = { by lemma 18 }
% 35.34/4.96 f(X, Y)
% 35.34/4.96
% 35.34/4.96 Lemma 20: f(X, f(f(X, X), Y)) = f(X, X).
% 35.34/4.96 Proof:
% 35.34/4.96 f(X, f(f(X, X), Y))
% 35.34/4.96 = { by lemma 9 R->L }
% 35.34/4.96 f(f(f(X, X), f(X, X)), f(f(X, X), Y))
% 35.34/4.96 = { by lemma 17 }
% 35.34/4.96 f(X, X)
% 35.34/4.96
% 35.34/4.96 Lemma 21: f(f(X, Y), f(Y, Y)) = Y.
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, Y), f(Y, Y))
% 35.34/4.96 = { by lemma 4 R->L }
% 35.34/4.96 f(f(Y, Y), f(f(f(X, Y), f(Y, Y)), Y))
% 35.34/4.96 = { by lemma 18 }
% 35.34/4.96 Y
% 35.34/4.96
% 35.34/4.96 Lemma 22: f(X, f(f(Y, X), f(Y, X))) = f(Y, X).
% 35.34/4.96 Proof:
% 35.34/4.96 f(X, f(f(Y, X), f(Y, X)))
% 35.34/4.96 = { by lemma 20 R->L }
% 35.34/4.96 f(X, f(f(Y, X), f(f(f(Y, X), f(Y, X)), f(Z, X))))
% 35.34/4.96 = { by lemma 11 R->L }
% 35.34/4.96 f(X, f(f(Y, X), f(f(f(f(Y, X), f(f(Y, X), f(Y, X))), f(Y, X)), f(Z, X))))
% 35.34/4.96 = { by lemma 21 R->L }
% 35.34/4.96 f(X, f(f(Y, X), f(f(f(f(f(f(f(Z, X), f(Z, X)), f(Y, X)), f(f(Y, X), f(Y, X))), f(f(Y, X), f(Y, X))), f(Y, X)), f(Z, X))))
% 35.34/4.96 = { by lemma 2 }
% 35.34/4.96 f(Y, X)
% 35.34/4.96
% 35.34/4.96 Lemma 23: f(f(X, Y), f(Y, X)) = f(f(X, Y), f(X, Y)).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, Y), f(Y, X))
% 35.34/4.96 = { by lemma 18 R->L }
% 35.34/4.96 f(f(f(f(X, X), f(Y, X)), Y), f(Y, X))
% 35.34/4.96 = { by lemma 17 R->L }
% 35.34/4.96 f(f(f(f(X, X), f(Y, X)), f(f(Y, Y), f(Y, X))), f(Y, X))
% 35.34/4.96 = { by lemma 13 R->L }
% 35.34/4.96 f(f(f(f(X, X), f(Y, X)), f(f(Y, Y), f(Y, X))), f(f(f(X, X), f(Y, X)), f(f(Y, Y), f(Y, X))))
% 35.34/4.96 = { by lemma 17 }
% 35.34/4.96 f(f(f(f(X, X), f(Y, X)), Y), f(f(f(X, X), f(Y, X)), f(f(Y, Y), f(Y, X))))
% 35.34/4.96 = { by lemma 17 }
% 35.34/4.96 f(f(f(f(X, X), f(Y, X)), Y), f(f(f(X, X), f(Y, X)), Y))
% 35.34/4.96 = { by lemma 18 }
% 35.34/4.96 f(f(X, Y), f(f(f(X, X), f(Y, X)), Y))
% 35.34/4.96 = { by lemma 18 }
% 35.34/4.96 f(f(X, Y), f(X, Y))
% 35.34/4.96
% 35.34/4.96 Lemma 24: f(f(X, Y), f(Y, X)) = f(f(Y, X), f(Y, X)).
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, Y), f(Y, X))
% 35.34/4.96 = { by lemma 22 R->L }
% 35.34/4.96 f(f(Y, X), f(f(f(X, Y), f(Y, X)), f(f(X, Y), f(Y, X))))
% 35.34/4.96 = { by lemma 23 }
% 35.34/4.96 f(f(Y, X), f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(Y, X))))
% 35.34/4.96 = { by lemma 17 }
% 35.34/4.96 f(f(Y, X), f(X, Y))
% 35.34/4.96 = { by lemma 23 }
% 35.34/4.96 f(f(Y, X), f(Y, X))
% 35.34/4.96
% 35.34/4.96 Lemma 25: f(Y, X) = f(X, Y).
% 35.34/4.96 Proof:
% 35.34/4.96 f(Y, X)
% 35.34/4.96 = { by lemma 19 R->L }
% 35.34/4.96 f(f(f(Y, X), f(Y, X)), Y)
% 35.34/4.96 = { by lemma 24 R->L }
% 35.34/4.96 f(f(f(X, Y), f(Y, X)), Y)
% 35.34/4.96 = { by lemma 23 }
% 35.34/4.96 f(f(f(X, Y), f(X, Y)), Y)
% 35.34/4.96 = { by lemma 14 }
% 35.34/4.96 f(X, Y)
% 35.34/4.96
% 35.34/4.96 Lemma 26: f(f(X, X), f(Y, f(f(X, Z), f(X, Z)))) = X.
% 35.34/4.96 Proof:
% 35.34/4.96 f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))
% 35.34/4.96 = { by lemma 23 R->L }
% 35.34/4.96 f(f(X, X), f(Y, f(f(X, Z), f(Z, X))))
% 35.34/4.96 = { by lemma 24 }
% 35.34/4.96 f(f(X, X), f(Y, f(f(Z, X), f(Z, X))))
% 35.34/4.97 = { by lemma 6 R->L }
% 35.34/4.97 f(f(X, X), f(Y, f(f(Z, X), f(f(f(f(f(f(X, X), f(Z, X)), X), X), f(Z, X)), f(f(f(f(f(X, X), f(Z, X)), X), X), f(Z, X))))))
% 35.34/4.97 = { by lemma 22 }
% 35.34/4.97 f(f(X, X), f(Y, f(f(f(f(f(X, X), f(Z, X)), X), X), f(Z, X))))
% 35.34/4.97 = { by lemma 9 R->L }
% 35.34/4.97 f(f(X, X), f(Y, f(f(f(f(f(X, X), f(Z, X)), f(f(X, X), f(X, X))), X), f(Z, X))))
% 35.34/4.97 = { by lemma 19 R->L }
% 35.34/4.97 f(f(X, X), f(Y, f(f(f(f(f(f(f(X, X), f(Z, X)), f(f(X, X), f(Z, X))), f(X, X)), f(f(X, X), f(X, X))), X), f(Z, X))))
% 35.34/4.97 = { by lemma 21 }
% 35.34/4.97 f(f(X, X), f(Y, f(f(f(X, X), X), f(Z, X))))
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 f(f(X, X), f(Y, f(f(X, f(X, X)), f(Z, X))))
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 f(f(X, X), f(Y, f(f(Z, X), f(X, f(X, X)))))
% 35.34/4.97 = { by lemma 25 }
% 35.34/4.97 f(f(X, X), f(f(f(Z, X), f(X, f(X, X))), Y))
% 35.34/4.97 = { by lemma 25 }
% 35.34/4.97 f(f(f(f(Z, X), f(X, f(X, X))), Y), f(X, X))
% 35.34/4.97 = { by lemma 20 R->L }
% 35.34/4.97 f(f(f(f(Z, X), f(X, f(X, X))), Y), f(X, f(f(X, X), Z)))
% 35.34/4.97 = { by lemma 19 R->L }
% 35.34/4.97 f(f(f(f(Z, X), f(f(f(X, f(X, X)), f(X, f(X, X))), X)), Y), f(X, f(f(X, X), Z)))
% 35.34/4.97 = { by lemma 3 R->L }
% 35.34/4.97 f(f(f(f(Z, X), f(f(f(X, f(X, X)), f(X, f(X, X))), X)), Y), f(X, f(f(f(f(f(f(Z, Z), X), f(f(X, f(X, X)), f(X, f(X, X)))), f(f(X, f(X, X)), f(X, f(X, X)))), f(f(X, X), f(f(f(f(f(f(X, X), f(X, X)), X), X), f(X, X)), X))), Z)))
% 35.34/4.97 = { by lemma 14 }
% 35.34/4.97 f(f(f(f(Z, X), f(f(f(X, f(X, X)), f(X, f(X, X))), X)), Y), f(X, f(f(f(f(f(f(Z, Z), X), f(f(X, f(X, X)), f(X, f(X, X)))), f(f(X, f(X, X)), f(X, f(X, X)))), f(f(X, X), f(f(f(f(X, X), X), f(X, X)), X))), Z)))
% 35.34/4.97 = { by lemma 18 }
% 35.34/4.97 f(f(f(f(Z, X), f(f(f(X, f(X, X)), f(X, f(X, X))), X)), Y), f(X, f(f(f(f(f(f(Z, Z), X), f(f(X, f(X, X)), f(X, f(X, X)))), f(f(X, f(X, X)), f(X, f(X, X)))), X), Z)))
% 35.34/4.97 = { by axiom 1 (mol_27B1) }
% 35.34/4.97 X
% 35.34/4.97
% 35.34/4.97 Lemma 27: f(f(X, Y), f(Y, f(f(X, Z), f(X, Z)))) = f(f(Y, X), f(Y, X)).
% 35.34/4.97 Proof:
% 35.34/4.97 f(f(X, Y), f(Y, f(f(X, Z), f(X, Z))))
% 35.34/4.97 = { by lemma 25 }
% 35.34/4.97 f(f(Y, X), f(Y, f(f(X, Z), f(X, Z))))
% 35.34/4.97 = { by lemma 26 R->L }
% 35.34/4.97 f(f(Y, f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))), f(Y, f(f(X, Z), f(X, Z))))
% 35.34/4.97 = { by lemma 17 R->L }
% 35.34/4.97 f(f(f(f(Y, Y), f(Y, f(f(X, Z), f(X, Z)))), f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))), f(Y, f(f(X, Z), f(X, Z))))
% 35.34/4.97 = { by lemma 13 R->L }
% 35.34/4.97 f(f(f(f(Y, Y), f(Y, f(f(X, Z), f(X, Z)))), f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))), f(f(f(Y, Y), f(Y, f(f(X, Z), f(X, Z)))), f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))))
% 35.34/4.97 = { by lemma 17 }
% 35.34/4.97 f(f(Y, f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))), f(f(f(Y, Y), f(Y, f(f(X, Z), f(X, Z)))), f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))))
% 35.34/4.97 = { by lemma 17 }
% 35.34/4.97 f(f(Y, f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))), f(Y, f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))))
% 35.34/4.97 = { by lemma 26 }
% 35.34/4.97 f(f(Y, X), f(Y, f(f(X, X), f(Y, f(f(X, Z), f(X, Z))))))
% 35.34/4.97 = { by lemma 26 }
% 35.34/4.97 f(f(Y, X), f(Y, X))
% 35.34/4.97
% 35.34/4.97 Lemma 28: f(f(f(X, Y), f(X, Y)), f(f(X, Z), f(X, Z))) = f(Z, f(f(X, Y), f(X, Y))).
% 35.34/4.97 Proof:
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(X, Z), f(X, Z)))
% 35.34/4.97 = { by lemma 25 }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(X, Z)))
% 35.34/4.97 = { by lemma 25 }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(Z, X), f(Z, X)))
% 35.34/4.97 = { by lemma 27 R->L }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(X, Z), f(Z, f(f(X, Y), f(X, Y)))))
% 35.34/4.97 = { by lemma 25 }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(X, Z), f(f(f(X, Y), f(X, Y)), Z)))
% 35.34/4.97 = { by lemma 25 }
% 35.34/4.97 f(f(f(X, Z), f(f(f(X, Y), f(X, Y)), Z)), f(f(X, Y), f(X, Y)))
% 35.34/4.97 = { by lemma 17 R->L }
% 35.34/4.97 f(f(f(X, Z), f(f(f(X, Y), f(X, Y)), Z)), 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)))
% 35.34/4.97 = { by lemma 4 R->L }
% 35.34/4.97 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, Z), f(f(f(X, Y), f(X, Y)), Z)), 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(X, Y), f(X, Y)), Z)))
% 35.34/4.97 = { by lemma 17 }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Z), f(f(f(X, Y), f(X, Y)), Z)), 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(X, Y), f(X, Y)), Z)))
% 35.34/4.97 = { by lemma 17 }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Z), f(f(f(X, Y), f(X, Y)), Z)), f(f(X, Y), f(X, Y))), f(f(f(X, Y), f(X, Y)), Z)))
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), f(f(f(f(X, Y), f(X, Y)), Z), f(f(f(X, Z), f(f(f(X, Y), f(X, Y)), Z)), f(f(X, Y), f(X, Y)))))
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 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(X, Z), f(f(f(X, Y), f(X, Y)), Z)))))
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 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(X, Z), f(Z, f(f(X, Y), f(X, Y)))))))
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 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(X, Z), f(Z, f(f(X, Y), f(X, Y)))))))
% 35.34/4.97 = { by lemma 27 }
% 35.34/4.97 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)))))
% 35.34/4.97 = { by lemma 27 }
% 35.34/4.97 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)))
% 35.34/4.97 = { by lemma 17 R->L }
% 35.34/4.97 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(f(f(X, Y), f(X, Y)), Z)))
% 35.34/4.97 = { by lemma 21 }
% 35.34/4.97 f(f(f(X, Y), f(X, Y)), Z)
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 f(Z, f(f(X, Y), f(X, Y)))
% 35.34/4.97
% 35.34/4.97 Goal 1 (associativity): f(a, f(f(b, c), f(b, c))) = f(c, f(f(b, a), f(b, a))).
% 35.34/4.97 Proof:
% 35.34/4.97 f(a, f(f(b, c), f(b, c)))
% 35.34/4.97 = { by lemma 28 R->L }
% 35.34/4.97 f(f(f(b, c), f(b, c)), f(f(b, a), f(b, a)))
% 35.34/4.97 = { by lemma 25 R->L }
% 35.34/4.97 f(f(f(b, a), f(b, a)), f(f(b, c), f(b, c)))
% 35.34/4.97 = { by lemma 28 }
% 35.34/4.97 f(c, f(f(b, a), f(b, a)))
% 35.34/4.97 % SZS output end Proof
% 35.34/4.97
% 35.34/4.97 RESULT: Unsatisfiable (the axioms are contradictory).
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