TSTP Solution File: LAT393-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT393-1 : TPTP v8.1.2. Released v5.4.0.
% 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 : n025.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 06:29:02 EDT 2023
% Result : Unsatisfiable 32.93s 4.68s
% Output : Proof 36.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT393-1 : TPTP v8.1.2. Released v5.4.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 08:27:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 32.93/4.68 Command-line arguments: --no-flatten-goal
% 32.93/4.68
% 32.93/4.68 % SZS status Unsatisfiable
% 32.93/4.68
% 35.07/4.95 % SZS output start Proof
% 35.07/4.95 Axiom 1 (sos_003): neg(X) = f(X, X).
% 35.07/4.95 Axiom 2 (sos_001): or(X, Y) = f(f(X, X), f(Y, Y)).
% 35.07/4.95 Axiom 3 (sos_002): and(X, Y) = f(f(X, Y), f(X, Y)).
% 35.07/4.95 Axiom 4 (sos): f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z))) = Y.
% 35.07/4.95
% 35.07/4.95 Lemma 5: f(neg(X), neg(Y)) = or(X, Y).
% 35.07/4.95 Proof:
% 35.07/4.95 f(neg(X), neg(Y))
% 35.07/4.95 = { by axiom 1 (sos_003) }
% 35.07/4.95 f(neg(X), f(Y, Y))
% 35.07/4.95 = { by axiom 1 (sos_003) }
% 35.07/4.95 f(f(X, X), f(Y, Y))
% 35.07/4.95 = { by axiom 2 (sos_001) R->L }
% 35.07/4.95 or(X, Y)
% 35.07/4.95
% 35.07/4.95 Lemma 6: neg(neg(X)) = or(X, X).
% 35.07/4.95 Proof:
% 35.07/4.95 neg(neg(X))
% 35.07/4.95 = { by axiom 1 (sos_003) }
% 35.07/4.95 f(neg(X), neg(X))
% 35.07/4.95 = { by lemma 5 }
% 35.07/4.95 or(X, X)
% 35.07/4.95
% 35.07/4.95 Lemma 7: f(or(X, X), neg(Y)) = or(neg(X), Y).
% 35.07/4.95 Proof:
% 35.07/4.95 f(or(X, X), neg(Y))
% 35.07/4.95 = { by lemma 6 R->L }
% 35.07/4.95 f(neg(neg(X)), neg(Y))
% 35.07/4.95 = { by lemma 5 }
% 35.07/4.95 or(neg(X), Y)
% 35.07/4.95
% 35.07/4.95 Lemma 8: f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(neg(X), X)), Z))) = Y.
% 35.07/4.95 Proof:
% 35.07/4.95 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(neg(X), X)), Z)))
% 35.07/4.95 = { by axiom 1 (sos_003) }
% 35.07/4.95 f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z)))
% 35.07/4.95 = { by axiom 4 (sos) }
% 35.07/4.95 Y
% 35.07/4.95
% 35.07/4.95 Lemma 9: neg(f(X, Y)) = and(X, Y).
% 35.07/4.95 Proof:
% 35.07/4.95 neg(f(X, Y))
% 35.07/4.95 = { by axiom 1 (sos_003) }
% 35.07/4.95 f(f(X, Y), f(X, Y))
% 35.07/4.95 = { by axiom 3 (sos_002) R->L }
% 35.07/4.96 and(X, Y)
% 35.07/4.96
% 35.07/4.96 Lemma 10: f(X, f(f(X, Y), f(f(f(X, Y), f(and(Z, X), f(Z, X))), W))) = f(X, Y).
% 35.07/4.96 Proof:
% 35.07/4.96 f(X, f(f(X, Y), f(f(f(X, Y), f(and(Z, X), f(Z, X))), W)))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 f(X, f(f(X, Y), f(f(f(X, Y), f(neg(f(Z, X)), f(Z, X))), W)))
% 35.07/4.96 = { by lemma 8 R->L }
% 35.07/4.96 f(f(f(f(f(Z, X), f(X, Y)), f(f(X, Y), W)), f(X, f(f(X, f(neg(Z), Z)), Y))), f(f(X, Y), f(f(f(X, Y), f(neg(f(Z, X)), f(Z, X))), W)))
% 35.07/4.96 = { by lemma 8 }
% 35.07/4.96 f(X, Y)
% 35.07/4.96
% 35.07/4.96 Lemma 11: f(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y)) = f(f(X, Y), f(Y, Z)).
% 35.07/4.96 Proof:
% 35.07/4.96 f(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y))
% 35.07/4.96 = { by lemma 8 R->L }
% 35.07/4.96 f(f(X, Y), f(f(f(X, Y), f(Y, Z)), f(f(f(f(X, Y), f(Y, Z)), f(and(W, f(X, Y)), f(W, f(X, Y)))), f(Y, f(f(Y, f(neg(X), X)), Z)))))
% 35.07/4.96 = { by lemma 10 }
% 35.07/4.96 f(f(X, Y), f(Y, Z))
% 35.07/4.96
% 35.07/4.96 Lemma 12: f(f(f(f(X, Y), f(Y, Z)), Y), neg(Y)) = Y.
% 35.07/4.96 Proof:
% 35.07/4.96 f(f(f(f(X, Y), f(Y, Z)), Y), neg(Y))
% 35.07/4.96 = { by axiom 1 (sos_003) }
% 35.07/4.96 f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, Y))
% 35.07/4.96 = { by lemma 8 R->L }
% 35.07/4.96 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(neg(X), X)), Z))), Y))
% 35.07/4.96 = { by lemma 11 }
% 35.07/4.96 f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, f(f(Y, f(neg(X), X)), Z)))
% 35.07/4.96 = { by lemma 8 }
% 35.07/4.96 Y
% 35.07/4.96
% 35.07/4.96 Lemma 13: or(X, X) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 or(X, X)
% 35.07/4.96 = { by lemma 5 R->L }
% 35.07/4.96 f(neg(X), neg(X))
% 35.07/4.96 = { by axiom 1 (sos_003) }
% 35.07/4.96 f(f(X, X), neg(X))
% 35.07/4.96 = { by lemma 8 R->L }
% 35.07/4.96 f(f(f(f(f(f(Y, X), f(X, Z)), X), f(X, f(f(X, f(neg(Y), Y)), Z))), X), neg(X))
% 35.07/4.96 = { by lemma 12 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 14: or(neg(X), neg(Y)) = f(X, Y).
% 35.07/4.96 Proof:
% 35.07/4.96 or(neg(X), neg(Y))
% 35.07/4.96 = { by lemma 7 R->L }
% 35.07/4.96 f(or(X, X), neg(neg(Y)))
% 35.07/4.96 = { by lemma 6 }
% 35.07/4.96 f(or(X, X), or(Y, Y))
% 35.07/4.96 = { by lemma 13 }
% 35.07/4.96 f(X, or(Y, Y))
% 35.07/4.96 = { by lemma 13 }
% 35.07/4.96 f(X, Y)
% 35.07/4.96
% 35.07/4.96 Lemma 15: f(neg(X), Y) = or(X, neg(Y)).
% 35.07/4.96 Proof:
% 35.07/4.96 f(neg(X), Y)
% 35.07/4.96 = { by lemma 13 R->L }
% 35.07/4.96 f(neg(X), or(Y, Y))
% 35.07/4.96 = { by lemma 6 R->L }
% 35.07/4.96 f(neg(X), neg(neg(Y)))
% 35.07/4.96 = { by lemma 5 }
% 35.07/4.96 or(X, neg(Y))
% 35.07/4.96
% 35.07/4.96 Lemma 16: f(X, neg(Y)) = or(neg(X), Y).
% 35.07/4.96 Proof:
% 35.07/4.96 f(X, neg(Y))
% 35.07/4.96 = { by lemma 13 R->L }
% 35.07/4.96 f(or(X, X), neg(Y))
% 35.07/4.96 = { by lemma 7 }
% 35.07/4.96 or(neg(X), Y)
% 35.07/4.96
% 35.07/4.96 Lemma 17: or(and(or(and(X, Y), Y), Y), Y) = Y.
% 35.07/4.96 Proof:
% 35.07/4.96 or(and(or(and(X, Y), Y), Y), Y)
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 or(and(or(neg(f(X, Y)), Y), Y), Y)
% 35.07/4.96 = { by lemma 16 R->L }
% 35.07/4.96 or(and(f(f(X, Y), neg(Y)), Y), Y)
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 or(neg(f(f(f(X, Y), neg(Y)), Y)), Y)
% 35.07/4.96 = { by lemma 16 R->L }
% 35.07/4.96 f(f(f(f(X, Y), neg(Y)), Y), neg(Y))
% 35.07/4.96 = { by axiom 1 (sos_003) }
% 35.07/4.96 f(f(f(f(X, Y), f(Y, Y)), Y), neg(Y))
% 35.07/4.96 = { by lemma 12 }
% 35.07/4.96 Y
% 35.07/4.96
% 35.07/4.96 Lemma 18: and(neg(X), neg(Y)) = neg(or(X, Y)).
% 35.07/4.96 Proof:
% 35.07/4.96 and(neg(X), neg(Y))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 neg(f(neg(X), neg(Y)))
% 35.07/4.96 = { by lemma 5 }
% 35.07/4.96 neg(or(X, Y))
% 35.07/4.96
% 35.07/4.96 Lemma 19: or(and(X, Y), neg(Z)) = f(f(X, Y), Z).
% 35.07/4.96 Proof:
% 35.07/4.96 or(and(X, Y), neg(Z))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 or(neg(f(X, Y)), neg(Z))
% 35.07/4.96 = { by lemma 14 }
% 35.07/4.96 f(f(X, Y), Z)
% 35.07/4.96
% 35.07/4.96 Lemma 20: and(or(X, X), neg(Y)) = neg(or(neg(X), Y)).
% 35.07/4.96 Proof:
% 35.07/4.96 and(or(X, X), neg(Y))
% 35.07/4.96 = { by lemma 6 R->L }
% 35.07/4.96 and(neg(neg(X)), neg(Y))
% 35.07/4.96 = { by lemma 18 }
% 35.07/4.96 neg(or(neg(X), Y))
% 35.07/4.96
% 35.07/4.96 Lemma 21: neg(or(neg(X), Y)) = and(X, neg(Y)).
% 35.07/4.96 Proof:
% 35.07/4.96 neg(or(neg(X), Y))
% 35.07/4.96 = { by lemma 20 R->L }
% 35.07/4.96 and(or(X, X), neg(Y))
% 35.07/4.96 = { by lemma 13 }
% 35.07/4.96 and(X, neg(Y))
% 35.07/4.96
% 35.07/4.96 Lemma 22: neg(neg(X)) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 neg(neg(X))
% 35.07/4.96 = { by lemma 6 }
% 35.07/4.96 or(X, X)
% 35.07/4.96 = { by lemma 13 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 23: and(X, X) = or(X, X).
% 35.07/4.96 Proof:
% 35.07/4.96 and(X, X)
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 neg(f(X, X))
% 35.07/4.96 = { by axiom 1 (sos_003) R->L }
% 35.07/4.96 neg(neg(X))
% 35.07/4.96 = { by lemma 6 }
% 35.07/4.96 or(X, X)
% 35.07/4.96
% 35.07/4.96 Lemma 24: f(f(or(X, X), Y), f(X, f(f(X, f(neg(X), X)), X))) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 f(f(or(X, X), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 23 R->L }
% 35.07/4.96 f(f(and(X, X), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 f(f(neg(f(X, X)), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by axiom 1 (sos_003) }
% 35.07/4.96 f(f(f(f(X, X), f(X, X)), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 8 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 25: f(or(neg(X), Y), f(X, f(f(X, f(neg(X), X)), X))) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 f(or(neg(X), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 7 R->L }
% 35.07/4.96 f(f(or(X, X), neg(Y)), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 24 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 26: and(or(neg(X), Y), f(X, f(f(X, f(neg(X), X)), X))) = neg(X).
% 35.07/4.96 Proof:
% 35.07/4.96 and(or(neg(X), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 neg(f(or(neg(X), Y), f(X, f(f(X, f(neg(X), X)), X))))
% 35.07/4.96 = { by lemma 25 }
% 35.07/4.96 neg(X)
% 35.07/4.96
% 35.07/4.96 Lemma 27: and(X, f(f(X, or(X, neg(X))), X)) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 and(X, f(f(X, or(X, neg(X))), X))
% 35.07/4.96 = { by lemma 15 R->L }
% 35.07/4.96 and(X, f(f(X, f(neg(X), X)), X))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 neg(f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 17 R->L }
% 35.07/4.96 or(and(or(and(neg(neg(X)), neg(f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X))))
% 35.07/4.96 = { by lemma 18 }
% 35.07/4.96 or(and(or(neg(or(neg(X), f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X))))
% 35.07/4.96 = { by lemma 19 }
% 35.07/4.96 f(f(or(neg(or(neg(X), f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X)))), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 16 }
% 35.07/4.96 f(or(neg(or(neg(or(neg(X), f(X, f(f(X, f(neg(X), X)), X)))), neg(f(X, f(f(X, f(neg(X), X)), X))))), f(X, f(f(X, f(neg(X), X)), X))), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 21 }
% 35.07/4.96 f(or(and(or(neg(X), f(X, f(f(X, f(neg(X), X)), X))), neg(neg(f(X, f(f(X, f(neg(X), X)), X))))), f(X, f(f(X, f(neg(X), X)), X))), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 22 }
% 35.07/4.96 f(or(and(or(neg(X), f(X, f(f(X, f(neg(X), X)), X))), f(X, f(f(X, f(neg(X), X)), X))), f(X, f(f(X, f(neg(X), X)), X))), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 26 }
% 35.07/4.96 f(or(neg(X), f(X, f(f(X, f(neg(X), X)), X))), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 25 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 28: or(neg(X), and(Y, Z)) = f(X, f(Y, Z)).
% 35.07/4.96 Proof:
% 35.07/4.96 or(neg(X), and(Y, Z))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 or(neg(X), neg(f(Y, Z)))
% 35.07/4.96 = { by lemma 14 }
% 35.07/4.96 f(X, f(Y, Z))
% 35.07/4.96
% 35.07/4.96 Lemma 29: or(and(X, neg(Y)), X) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 or(and(X, neg(Y)), X)
% 35.07/4.96 = { by lemma 27 R->L }
% 35.07/4.96 or(and(X, neg(Y)), and(X, f(f(X, or(X, neg(X))), X)))
% 35.07/4.96 = { by lemma 15 R->L }
% 35.07/4.96 or(and(X, neg(Y)), and(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 21 R->L }
% 35.07/4.96 or(neg(or(neg(X), Y)), and(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 28 }
% 35.07/4.96 f(or(neg(X), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 25 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 30: or(and(X, Y), X) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 or(and(X, Y), X)
% 35.07/4.96 = { by lemma 13 R->L }
% 35.07/4.96 or(and(X, or(Y, Y)), X)
% 35.07/4.96 = { by lemma 6 R->L }
% 35.07/4.96 or(and(X, neg(neg(Y))), X)
% 35.07/4.96 = { by lemma 29 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 31: neg(and(X, Y)) = f(X, Y).
% 35.07/4.96 Proof:
% 35.07/4.96 neg(and(X, Y))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 neg(neg(f(X, Y)))
% 35.07/4.96 = { by lemma 22 }
% 35.07/4.96 f(X, Y)
% 35.07/4.96
% 35.07/4.96 Lemma 32: f(f(X, Y), or(neg(Z), W)) = or(and(X, Y), and(Z, neg(W))).
% 35.07/4.96 Proof:
% 35.07/4.96 f(f(X, Y), or(neg(Z), W))
% 35.07/4.96 = { by lemma 19 R->L }
% 35.07/4.96 or(and(X, Y), neg(or(neg(Z), W)))
% 35.07/4.96 = { by lemma 21 }
% 35.07/4.96 or(and(X, Y), and(Z, neg(W)))
% 35.07/4.96
% 35.07/4.96 Lemma 33: f(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 f(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 6 }
% 35.07/4.96 f(f(or(X, X), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 24 }
% 35.07/4.96 X
% 35.07/4.96
% 35.07/4.96 Lemma 34: and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))) = neg(X).
% 35.07/4.96 Proof:
% 35.07/4.96 and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 neg(f(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))))
% 35.07/4.96 = { by lemma 33 }
% 35.07/4.96 neg(X)
% 35.07/4.96
% 35.07/4.96 Lemma 35: f(f(X, Y), f(Z, W)) = or(and(X, Y), and(Z, W)).
% 35.07/4.96 Proof:
% 35.07/4.96 f(f(X, Y), f(Z, W))
% 35.07/4.96 = { by lemma 19 R->L }
% 35.07/4.96 or(and(X, Y), neg(f(Z, W)))
% 35.07/4.96 = { by lemma 9 }
% 35.07/4.96 or(and(X, Y), and(Z, W))
% 35.07/4.96
% 35.07/4.96 Lemma 36: f(X, or(and(X, Y), and(and(Z, X), f(Z, X)))) = f(X, Y).
% 35.07/4.96 Proof:
% 35.07/4.96 f(X, or(and(X, Y), and(and(Z, X), f(Z, X))))
% 35.07/4.96 = { by lemma 35 R->L }
% 35.07/4.96 f(X, f(f(X, Y), f(and(Z, X), f(Z, X))))
% 35.07/4.96 = { by lemma 10 R->L }
% 35.07/4.96 f(X, f(f(X, Y), f(f(f(X, Y), f(and(Z, X), f(Z, X))), f(f(f(f(X, Y), f(and(Z, X), f(Z, X))), f(and(W, f(X, Y)), f(W, f(X, Y)))), V))))
% 35.07/4.96 = { by lemma 10 }
% 35.07/4.96 f(X, Y)
% 35.07/4.96
% 35.07/4.96 Lemma 37: f(X, or(and(X, Y), and(X, neg(X)))) = f(X, Y).
% 35.07/4.96 Proof:
% 35.07/4.96 f(X, or(and(X, Y), and(X, neg(X))))
% 35.07/4.96 = { by lemma 32 R->L }
% 35.07/4.96 f(X, f(f(X, Y), or(neg(X), X)))
% 35.07/4.96 = { by lemma 19 R->L }
% 35.07/4.96 f(X, or(and(X, Y), neg(or(neg(X), X))))
% 35.07/4.96 = { by lemma 20 R->L }
% 35.07/4.96 f(X, or(and(X, Y), and(or(X, X), neg(X))))
% 35.07/4.96 = { by lemma 23 R->L }
% 35.07/4.96 f(X, or(and(X, Y), and(and(X, X), neg(X))))
% 35.07/4.96 = { by axiom 1 (sos_003) }
% 35.07/4.96 f(X, or(and(X, Y), and(and(X, X), f(X, X))))
% 35.07/4.96 = { by lemma 36 }
% 35.07/4.96 f(X, Y)
% 35.07/4.96
% 35.07/4.96 Lemma 38: and(or(X, Y), or(X, and(or(X, Y), neg(or(X, Y))))) = X.
% 35.07/4.96 Proof:
% 35.07/4.96 and(or(X, Y), or(X, and(or(X, Y), neg(or(X, Y)))))
% 35.07/4.96 = { by lemma 9 R->L }
% 35.07/4.96 neg(f(or(X, Y), or(X, and(or(X, Y), neg(or(X, Y))))))
% 35.07/4.96 = { by lemma 21 R->L }
% 35.07/4.96 neg(f(or(X, Y), or(X, neg(or(neg(or(X, Y)), or(X, Y))))))
% 35.07/4.96 = { by lemma 15 R->L }
% 35.07/4.96 neg(f(or(X, Y), f(neg(X), or(neg(or(X, Y)), or(X, Y)))))
% 35.07/4.96 = { by lemma 28 R->L }
% 35.07/4.97 neg(or(neg(or(X, Y)), and(neg(X), or(neg(or(X, Y)), or(X, Y)))))
% 35.07/4.97 = { by lemma 18 R->L }
% 35.07/4.97 neg(or(and(neg(X), neg(Y)), and(neg(X), or(neg(or(X, Y)), or(X, Y)))))
% 35.07/4.97 = { by lemma 18 R->L }
% 35.07/4.97 neg(or(and(neg(X), neg(Y)), and(neg(X), or(and(neg(X), neg(Y)), or(X, Y)))))
% 35.07/4.97 = { by lemma 5 R->L }
% 35.07/4.97 neg(or(and(neg(X), neg(Y)), and(neg(X), or(and(neg(X), neg(Y)), f(neg(X), neg(Y))))))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 neg(or(and(neg(X), neg(Y)), and(neg(X), or(neg(f(neg(X), neg(Y))), f(neg(X), neg(Y))))))
% 35.07/4.97 = { by lemma 16 R->L }
% 35.07/4.97 neg(or(and(neg(X), neg(Y)), and(neg(X), f(f(neg(X), neg(Y)), neg(f(neg(X), neg(Y)))))))
% 35.07/4.97 = { by lemma 31 R->L }
% 35.07/4.97 neg(or(and(neg(X), neg(Y)), and(neg(X), neg(and(f(neg(X), neg(Y)), neg(f(neg(X), neg(Y))))))))
% 35.07/4.97 = { by lemma 22 R->L }
% 35.07/4.97 neg(or(and(neg(neg(neg(X))), neg(Y)), and(neg(X), neg(and(f(neg(X), neg(Y)), neg(f(neg(X), neg(Y))))))))
% 35.07/4.97 = { by lemma 22 R->L }
% 35.07/4.97 neg(or(and(neg(neg(neg(X))), neg(Y)), and(neg(X), neg(and(f(neg(neg(neg(X))), neg(Y)), neg(f(neg(X), neg(Y))))))))
% 35.07/4.97 = { by lemma 22 R->L }
% 35.07/4.97 neg(or(and(neg(neg(neg(X))), neg(Y)), and(neg(X), neg(and(f(neg(neg(neg(X))), neg(Y)), neg(f(neg(neg(neg(X))), neg(Y))))))))
% 35.07/4.97 = { by lemma 32 R->L }
% 35.07/4.97 neg(f(f(neg(neg(neg(X))), neg(Y)), or(neg(neg(X)), and(f(neg(neg(neg(X))), neg(Y)), neg(f(neg(neg(neg(X))), neg(Y)))))))
% 35.07/4.97 = { by lemma 34 R->L }
% 35.07/4.97 neg(f(f(neg(neg(neg(X))), neg(Y)), or(and(f(neg(neg(neg(X))), neg(Y)), f(neg(X), f(f(neg(X), f(neg(neg(X)), neg(X))), neg(X)))), and(f(neg(neg(neg(X))), neg(Y)), neg(f(neg(neg(neg(X))), neg(Y)))))))
% 35.07/4.97 = { by lemma 37 }
% 35.07/4.97 neg(f(f(neg(neg(neg(X))), neg(Y)), f(neg(X), f(f(neg(X), f(neg(neg(X)), neg(X))), neg(X)))))
% 35.07/4.97 = { by lemma 33 }
% 35.07/4.97 neg(neg(X))
% 35.07/4.97 = { by lemma 22 }
% 35.07/4.97 X
% 35.07/4.97
% 35.07/4.97 Lemma 39: f(and(X, Y), neg(Z)) = or(f(X, Y), Z).
% 35.07/4.97 Proof:
% 35.07/4.97 f(and(X, Y), neg(Z))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 f(neg(f(X, Y)), neg(Z))
% 35.07/4.97 = { by lemma 5 }
% 35.07/4.97 or(f(X, Y), Z)
% 35.07/4.97
% 35.07/4.97 Lemma 40: f(and(X, Y), and(Z, W)) = or(f(X, Y), f(Z, W)).
% 35.07/4.97 Proof:
% 35.07/4.97 f(and(X, Y), and(Z, W))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 f(and(X, Y), neg(f(Z, W)))
% 35.07/4.97 = { by lemma 39 }
% 35.07/4.97 or(f(X, Y), f(Z, W))
% 35.07/4.97
% 35.07/4.97 Lemma 41: f(neg(X), and(Y, Z)) = or(X, f(Y, Z)).
% 35.07/4.97 Proof:
% 35.07/4.97 f(neg(X), and(Y, Z))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 f(neg(X), neg(f(Y, Z)))
% 35.07/4.97 = { by lemma 5 }
% 35.07/4.97 or(X, f(Y, Z))
% 35.07/4.97
% 35.07/4.97 Lemma 42: f(or(X, X), and(Y, Z)) = or(neg(X), f(Y, Z)).
% 35.07/4.97 Proof:
% 35.07/4.97 f(or(X, X), and(Y, Z))
% 35.07/4.97 = { by lemma 6 R->L }
% 35.07/4.97 f(neg(neg(X)), and(Y, Z))
% 35.07/4.97 = { by lemma 41 }
% 35.07/4.97 or(neg(X), f(Y, Z))
% 35.07/4.97
% 35.07/4.97 Lemma 43: or(neg(X), f(Y, Z)) = f(X, and(Y, Z)).
% 35.07/4.97 Proof:
% 35.07/4.97 or(neg(X), f(Y, Z))
% 35.07/4.97 = { by lemma 42 R->L }
% 35.07/4.97 f(or(X, X), and(Y, Z))
% 35.07/4.97 = { by lemma 13 }
% 35.07/4.97 f(X, and(Y, Z))
% 35.07/4.97
% 35.07/4.97 Lemma 44: f(neg(and(X, Y)), or(neg(and(X, Y)), f(X, Y))) = neg(neg(and(X, Y))).
% 35.07/4.97 Proof:
% 35.07/4.97 f(neg(and(X, Y)), or(neg(and(X, Y)), f(X, Y)))
% 35.07/4.97 = { by lemma 42 R->L }
% 35.07/4.97 f(neg(and(X, Y)), f(or(and(X, Y), and(X, Y)), and(X, Y)))
% 35.07/4.97 = { by lemma 6 R->L }
% 35.07/4.97 f(neg(and(X, Y)), f(neg(neg(and(X, Y))), and(X, Y)))
% 35.07/4.97 = { by axiom 1 (sos_003) }
% 35.07/4.97 f(f(and(X, Y), and(X, Y)), f(neg(neg(and(X, Y))), and(X, Y)))
% 35.07/4.97 = { by axiom 1 (sos_003) }
% 35.07/4.97 f(f(and(X, Y), and(X, Y)), f(neg(f(and(X, Y), and(X, Y))), and(X, Y)))
% 35.07/4.97 = { by axiom 1 (sos_003) }
% 35.07/4.97 f(f(and(X, Y), and(X, Y)), f(f(f(and(X, Y), and(X, Y)), f(and(X, Y), and(X, Y))), and(X, Y)))
% 35.07/4.97 = { by lemma 11 }
% 35.07/4.97 f(f(and(X, Y), and(X, Y)), f(and(X, Y), and(X, Y)))
% 35.07/4.97 = { by axiom 1 (sos_003) R->L }
% 35.07/4.97 neg(f(and(X, Y), and(X, Y)))
% 35.07/4.97 = { by lemma 9 }
% 35.07/4.97 and(and(X, Y), and(X, Y))
% 35.07/4.97 = { by lemma 23 }
% 35.07/4.97 or(and(X, Y), and(X, Y))
% 35.07/4.97 = { by lemma 6 R->L }
% 35.07/4.97 neg(neg(and(X, Y)))
% 35.07/4.97
% 35.07/4.97 Lemma 45: and(f(X, Y), f(or(and(X, Y), and(Y, Z)), Y)) = and(f(X, Y), f(Y, Z)).
% 35.07/4.97 Proof:
% 35.07/4.97 and(f(X, Y), f(or(and(X, Y), and(Y, Z)), Y))
% 35.07/4.97 = { by lemma 35 R->L }
% 35.07/4.97 and(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 neg(f(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y)))
% 35.07/4.97 = { by lemma 11 }
% 35.07/4.97 neg(f(f(X, Y), f(Y, Z)))
% 35.07/4.97 = { by lemma 9 }
% 35.07/4.97 and(f(X, Y), f(Y, Z))
% 35.07/4.97
% 35.07/4.97 Lemma 46: f(f(or(X, X), X), neg(X)) = X.
% 35.07/4.97 Proof:
% 35.07/4.97 f(f(or(X, X), X), neg(X))
% 35.07/4.97 = { by lemma 6 R->L }
% 35.07/4.97 f(f(neg(neg(X)), X), neg(X))
% 35.07/4.97 = { by axiom 1 (sos_003) }
% 35.07/4.97 f(f(neg(neg(X)), X), f(X, X))
% 35.07/4.97 = { by lemma 33 R->L }
% 35.07/4.97 f(f(neg(neg(X)), X), f(f(f(neg(neg(X)), X), f(X, f(f(X, f(neg(X), X)), X))), X))
% 35.07/4.97 = { by lemma 11 }
% 35.07/4.97 f(f(neg(neg(X)), X), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.97 = { by lemma 6 }
% 35.07/4.97 f(f(or(X, X), X), f(X, f(f(X, f(neg(X), X)), X)))
% 35.07/4.97 = { by lemma 24 }
% 35.07/4.97 X
% 35.07/4.97
% 35.07/4.97 Lemma 47: f(X, or(and(X, or(X, neg(Y))), X)) = f(X, or(X, neg(Y))).
% 35.07/4.97 Proof:
% 35.07/4.97 f(X, or(and(X, or(X, neg(Y))), X))
% 35.07/4.97 = { by lemma 15 R->L }
% 35.07/4.97 f(X, or(and(X, f(neg(X), Y)), X))
% 35.07/4.97 = { by lemma 46 R->L }
% 35.07/4.97 f(X, or(and(f(f(or(X, X), X), neg(X)), f(neg(X), Y)), X))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 f(X, or(neg(f(f(f(or(X, X), X), neg(X)), f(neg(X), Y))), X))
% 35.07/4.97 = { by lemma 16 R->L }
% 35.07/4.97 f(X, f(f(f(f(or(X, X), X), neg(X)), f(neg(X), Y)), neg(X)))
% 35.07/4.97 = { by lemma 46 R->L }
% 35.07/4.97 f(f(f(or(X, X), X), neg(X)), f(f(f(f(or(X, X), X), neg(X)), f(neg(X), Y)), neg(X)))
% 35.07/4.97 = { by lemma 11 }
% 35.07/4.97 f(f(f(or(X, X), X), neg(X)), f(neg(X), Y))
% 35.07/4.97 = { by lemma 35 }
% 35.07/4.97 or(and(f(or(X, X), X), neg(X)), and(neg(X), Y))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 or(neg(f(f(or(X, X), X), neg(X))), and(neg(X), Y))
% 35.07/4.97 = { by lemma 46 }
% 35.07/4.97 or(neg(X), and(neg(X), Y))
% 35.07/4.97 = { by lemma 28 }
% 35.07/4.97 f(X, f(neg(X), Y))
% 35.07/4.97 = { by lemma 15 }
% 35.07/4.97 f(X, or(X, neg(Y)))
% 35.07/4.97
% 35.07/4.97 Lemma 48: and(X, or(X, Y)) = X.
% 35.07/4.97 Proof:
% 35.07/4.97 and(X, or(X, Y))
% 35.07/4.97 = { by lemma 9 R->L }
% 35.07/4.97 neg(f(X, or(X, Y)))
% 35.07/4.97 = { by lemma 22 R->L }
% 35.07/4.97 neg(f(X, or(X, neg(neg(Y)))))
% 35.07/4.97 = { by lemma 47 R->L }
% 35.07/4.97 neg(f(X, or(and(X, or(X, neg(neg(Y)))), X)))
% 35.07/4.97 = { by lemma 6 }
% 35.77/4.97 neg(f(X, or(and(X, or(X, or(Y, Y))), X)))
% 35.77/4.97 = { by lemma 13 }
% 35.77/4.97 neg(f(X, or(and(X, or(X, Y)), X)))
% 35.77/4.97 = { by lemma 9 }
% 35.77/4.97 and(X, or(and(X, or(X, Y)), X))
% 35.77/4.97 = { by lemma 30 }
% 35.77/4.97 and(X, X)
% 35.77/4.97 = { by lemma 23 }
% 35.77/4.97 or(X, X)
% 35.77/4.97 = { by lemma 13 }
% 35.77/4.97 X
% 35.77/4.97
% 35.77/4.97 Lemma 49: and(and(or(and(X, Y), and(Y, Z)), W), Y) = and(or(and(X, Y), and(Y, Z)), W).
% 35.77/4.97 Proof:
% 35.77/4.97 and(and(or(and(X, Y), and(Y, Z)), W), Y)
% 35.77/4.97 = { by lemma 35 R->L }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), Y)
% 35.77/4.97 = { by lemma 8 R->L }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(neg(X), X)), Z))))
% 35.77/4.97 = { by lemma 13 R->L }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), f(or(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z))))
% 35.77/4.97 = { by lemma 40 R->L }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), f(f(and(f(f(X, Y), f(Y, Z)), W), and(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z))))
% 35.77/4.97 = { by lemma 43 R->L }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), f(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z))))
% 35.77/4.97 = { by lemma 22 R->L }
% 35.77/4.97 and(neg(neg(and(f(f(X, Y), f(Y, Z)), W))), f(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z))))
% 35.77/4.97 = { by lemma 44 R->L }
% 35.77/4.97 and(f(neg(and(f(f(X, Y), f(Y, Z)), W)), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))), f(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z))))
% 35.77/4.97 = { by lemma 45 R->L }
% 35.77/4.97 and(f(neg(and(f(f(X, Y), f(Y, Z)), W)), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))), f(or(and(neg(and(f(f(X, Y), f(Y, Z)), W)), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))), and(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))))
% 35.77/4.97 = { by lemma 44 }
% 35.77/4.97 and(neg(neg(and(f(f(X, Y), f(Y, Z)), W))), f(or(and(neg(and(f(f(X, Y), f(Y, Z)), W)), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))), and(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))))
% 35.77/4.97 = { by lemma 22 }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), f(or(and(neg(and(f(f(X, Y), f(Y, Z)), W)), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))), and(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))))
% 35.77/4.97 = { by lemma 48 }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), f(or(neg(and(f(f(X, Y), f(Y, Z)), W)), and(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))))
% 35.77/4.97 = { by lemma 28 }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), f(f(and(f(f(X, Y), f(Y, Z)), W), f(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W))))
% 35.77/4.97 = { by lemma 32 }
% 35.77/4.97 and(and(f(f(X, Y), f(Y, Z)), W), or(and(and(f(f(X, Y), f(Y, Z)), W), f(or(neg(and(f(f(X, Y), f(Y, Z)), W)), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), and(and(f(f(X, Y), f(Y, Z)), W), neg(f(f(f(X, Y), f(Y, Z)), W)))))
% 35.77/4.97 = { by lemma 43 }
% 35.77/4.98 and(and(f(f(X, Y), f(Y, Z)), W), or(and(and(f(f(X, Y), f(Y, Z)), W), f(f(and(f(f(X, Y), f(Y, Z)), W), and(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), and(and(f(f(X, Y), f(Y, Z)), W), neg(f(f(f(X, Y), f(Y, Z)), W)))))
% 35.77/4.98 = { by lemma 40 }
% 35.77/4.98 and(and(f(f(X, Y), f(Y, Z)), W), or(and(and(f(f(X, Y), f(Y, Z)), W), f(or(f(f(f(X, Y), f(Y, Z)), W), f(f(f(X, Y), f(Y, Z)), W)), f(Y, f(f(Y, f(neg(X), X)), Z)))), and(and(f(f(X, Y), f(Y, Z)), W), neg(f(f(f(X, Y), f(Y, Z)), W)))))
% 35.77/4.98 = { by lemma 13 }
% 35.77/4.98 and(and(f(f(X, Y), f(Y, Z)), W), or(and(and(f(f(X, Y), f(Y, Z)), W), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(neg(X), X)), Z)))), and(and(f(f(X, Y), f(Y, Z)), W), neg(f(f(f(X, Y), f(Y, Z)), W)))))
% 35.77/4.98 = { by lemma 9 }
% 35.77/4.98 and(and(f(f(X, Y), f(Y, Z)), W), or(and(and(f(f(X, Y), f(Y, Z)), W), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(neg(X), X)), Z)))), and(and(f(f(X, Y), f(Y, Z)), W), and(f(f(X, Y), f(Y, Z)), W))))
% 35.77/4.98 = { by lemma 23 }
% 35.77/4.98 and(and(f(f(X, Y), f(Y, Z)), W), or(and(and(f(f(X, Y), f(Y, Z)), W), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(neg(X), X)), Z)))), or(and(f(f(X, Y), f(Y, Z)), W), and(f(f(X, Y), f(Y, Z)), W))))
% 35.77/4.98 = { by lemma 13 }
% 35.77/4.98 and(and(f(f(X, Y), f(Y, Z)), W), or(and(and(f(f(X, Y), f(Y, Z)), W), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(neg(X), X)), Z)))), and(f(f(X, Y), f(Y, Z)), W)))
% 35.77/4.98 = { by lemma 30 }
% 35.77/4.98 and(and(f(f(X, Y), f(Y, Z)), W), and(f(f(X, Y), f(Y, Z)), W))
% 35.77/4.98 = { by lemma 23 }
% 35.77/4.98 or(and(f(f(X, Y), f(Y, Z)), W), and(f(f(X, Y), f(Y, Z)), W))
% 35.77/4.98 = { by lemma 13 }
% 35.77/4.98 and(f(f(X, Y), f(Y, Z)), W)
% 35.77/4.98 = { by lemma 35 }
% 35.77/4.98 and(or(and(X, Y), and(Y, Z)), W)
% 35.77/4.98
% 35.77/4.98 Lemma 50: and(or(and(X, Y), and(Y, Z)), Y) = or(and(X, Y), and(Y, Z)).
% 35.77/4.98 Proof:
% 35.77/4.98 and(or(and(X, Y), and(Y, Z)), Y)
% 35.77/4.98 = { by lemma 13 R->L }
% 35.77/4.98 and(or(or(and(X, Y), and(Y, Z)), or(and(X, Y), and(Y, Z))), Y)
% 35.77/4.98 = { by lemma 23 R->L }
% 35.77/4.98 and(and(or(and(X, Y), and(Y, Z)), or(and(X, Y), and(Y, Z))), Y)
% 35.77/4.98 = { by lemma 49 }
% 35.77/4.98 and(or(and(X, Y), and(Y, Z)), or(and(X, Y), and(Y, Z)))
% 35.77/4.98 = { by lemma 23 }
% 35.77/4.98 or(or(and(X, Y), and(Y, Z)), or(and(X, Y), and(Y, Z)))
% 35.77/4.98 = { by lemma 13 }
% 35.77/4.98 or(and(X, Y), and(Y, Z))
% 35.77/4.98
% 35.77/4.98 Lemma 51: and(or(and(X, Y), Y), Y) = or(and(X, Y), Y).
% 35.77/4.98 Proof:
% 35.77/4.98 and(or(and(X, Y), Y), Y)
% 35.77/4.98 = { by lemma 13 R->L }
% 35.77/4.98 and(or(and(X, Y), or(Y, Y)), Y)
% 35.77/4.98 = { by lemma 23 R->L }
% 35.77/4.98 and(or(and(X, Y), and(Y, Y)), Y)
% 35.77/4.98 = { by lemma 50 }
% 35.77/4.98 or(and(X, Y), and(Y, Y))
% 35.77/4.98 = { by lemma 23 }
% 35.77/4.98 or(and(X, Y), or(Y, Y))
% 35.77/4.98 = { by lemma 13 }
% 35.77/4.98 or(and(X, Y), Y)
% 35.77/4.98
% 35.77/4.98 Lemma 52: or(and(X, Y), Y) = Y.
% 35.77/4.98 Proof:
% 35.77/4.98 or(and(X, Y), Y)
% 35.77/4.98 = { by lemma 5 R->L }
% 35.77/4.98 f(neg(and(X, Y)), neg(Y))
% 35.77/4.98 = { by lemma 31 R->L }
% 35.77/4.98 neg(and(neg(and(X, Y)), neg(Y)))
% 35.77/4.98 = { by lemma 38 R->L }
% 35.77/4.98 neg(and(or(and(neg(and(X, Y)), neg(Y)), and(neg(Y), Z)), or(and(neg(and(X, Y)), neg(Y)), and(or(and(neg(and(X, Y)), neg(Y)), and(neg(Y), Z)), neg(or(and(neg(and(X, Y)), neg(Y)), and(neg(Y), Z)))))))
% 35.77/4.98 = { by lemma 49 R->L }
% 35.77/4.98 neg(and(and(or(and(neg(and(X, Y)), neg(Y)), and(neg(Y), Z)), or(and(neg(and(X, Y)), neg(Y)), and(or(and(neg(and(X, Y)), neg(Y)), and(neg(Y), Z)), neg(or(and(neg(and(X, Y)), neg(Y)), and(neg(Y), Z)))))), neg(Y)))
% 35.77/4.98 = { by lemma 38 }
% 35.77/4.98 neg(and(and(neg(and(X, Y)), neg(Y)), neg(Y)))
% 35.77/4.98 = { by lemma 31 }
% 35.77/4.98 f(and(neg(and(X, Y)), neg(Y)), neg(Y))
% 35.77/4.98 = { by lemma 18 }
% 35.77/4.98 f(neg(or(and(X, Y), Y)), neg(Y))
% 35.77/4.98 = { by lemma 5 }
% 35.77/4.98 or(or(and(X, Y), Y), Y)
% 35.77/4.98 = { by lemma 51 R->L }
% 35.77/4.98 or(and(or(and(X, Y), Y), Y), Y)
% 35.77/4.98 = { by lemma 17 }
% 35.77/4.98 Y
% 35.77/4.98
% 35.77/4.98 Lemma 53: and(or(X, Y), Y) = Y.
% 35.77/4.98 Proof:
% 35.77/4.98 and(or(X, Y), Y)
% 35.77/4.98 = { by lemma 9 R->L }
% 35.77/4.98 neg(f(or(X, Y), Y))
% 35.77/4.98 = { by lemma 14 R->L }
% 35.77/4.98 neg(or(neg(or(X, Y)), neg(Y)))
% 35.77/4.98 = { by lemma 18 R->L }
% 35.77/4.98 neg(or(and(neg(X), neg(Y)), neg(Y)))
% 35.77/4.98 = { by lemma 52 }
% 35.77/4.98 neg(neg(Y))
% 35.77/4.98 = { by lemma 22 }
% 35.77/4.98 Y
% 35.77/4.98
% 35.77/4.98 Lemma 54: or(f(X, Y), neg(Z)) = f(and(X, Y), Z).
% 35.77/4.98 Proof:
% 35.77/4.98 or(f(X, Y), neg(Z))
% 35.77/4.98 = { by lemma 39 R->L }
% 35.77/4.98 f(and(X, Y), neg(neg(Z)))
% 35.77/4.98 = { by lemma 6 }
% 35.77/4.98 f(and(X, Y), or(Z, Z))
% 35.77/4.98 = { by lemma 13 }
% 35.77/4.98 f(and(X, Y), Z)
% 35.77/4.98
% 35.77/4.98 Lemma 55: and(neg(X), f(or(X, and(X, Y)), X)) = and(neg(X), f(X, Y)).
% 35.77/4.98 Proof:
% 35.77/4.98 and(neg(X), f(or(X, and(X, Y)), X))
% 35.77/4.98 = { by lemma 9 R->L }
% 35.77/4.98 and(neg(X), f(or(X, neg(f(X, Y))), X))
% 35.77/4.98 = { by lemma 15 R->L }
% 35.77/4.98 and(neg(X), f(f(neg(X), f(X, Y)), X))
% 35.77/4.98 = { by lemma 9 R->L }
% 35.77/4.98 neg(f(neg(X), f(f(neg(X), f(X, Y)), X)))
% 35.77/4.98 = { by axiom 1 (sos_003) }
% 35.77/4.98 neg(f(neg(X), f(f(f(X, X), f(X, Y)), X)))
% 35.77/4.98 = { by axiom 1 (sos_003) }
% 35.77/4.98 neg(f(f(X, X), f(f(f(X, X), f(X, Y)), X)))
% 35.77/4.98 = { by lemma 11 }
% 35.77/4.98 neg(f(f(X, X), f(X, Y)))
% 35.77/4.98 = { by axiom 1 (sos_003) R->L }
% 35.77/4.98 neg(f(neg(X), f(X, Y)))
% 35.77/4.98 = { by lemma 9 }
% 35.77/4.98 and(neg(X), f(X, Y))
% 35.77/4.98
% 35.77/4.98 Lemma 56: and(and(X, Y), or(and(and(X, Y), X), and(X, Y))) = and(and(X, Y), or(and(X, Y), X)).
% 35.77/4.98 Proof:
% 35.77/4.98 and(and(X, Y), or(and(and(X, Y), X), and(X, Y)))
% 35.77/4.98 = { by lemma 35 R->L }
% 35.77/4.98 and(and(X, Y), f(f(and(X, Y), X), f(X, Y)))
% 35.77/4.98 = { by lemma 54 R->L }
% 35.77/4.98 and(and(X, Y), f(or(f(X, Y), neg(X)), f(X, Y)))
% 35.77/4.98 = { by lemma 22 R->L }
% 35.77/4.98 and(and(neg(neg(X)), Y), f(or(f(X, Y), neg(X)), f(X, Y)))
% 35.77/4.98 = { by lemma 22 R->L }
% 35.77/4.98 and(and(neg(neg(X)), Y), f(or(f(neg(neg(X)), Y), neg(X)), f(X, Y)))
% 35.77/4.98 = { by lemma 22 R->L }
% 35.77/4.98 and(and(neg(neg(X)), Y), f(or(f(neg(neg(X)), Y), neg(X)), f(neg(neg(X)), Y)))
% 35.77/4.98 = { by lemma 9 R->L }
% 35.77/4.98 and(neg(f(neg(neg(X)), Y)), f(or(f(neg(neg(X)), Y), neg(X)), f(neg(neg(X)), Y)))
% 35.77/4.98 = { by lemma 34 R->L }
% 35.77/4.98 and(neg(f(neg(neg(X)), Y)), f(or(f(neg(neg(X)), Y), and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X)))), f(neg(neg(X)), Y)))
% 35.77/4.98 = { by lemma 55 }
% 35.77/4.98 and(neg(f(neg(neg(X)), Y)), f(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))))
% 35.77/4.98 = { by lemma 9 }
% 35.77/4.98 and(and(neg(neg(X)), Y), f(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))))
% 35.77/4.98 = { by lemma 22 }
% 35.77/4.98 and(and(X, Y), f(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))))
% 35.77/4.98 = { by lemma 22 }
% 35.77/4.98 and(and(X, Y), f(f(X, Y), f(X, f(f(X, f(neg(X), X)), X))))
% 35.77/4.98 = { by lemma 35 }
% 35.77/4.98 and(and(X, Y), or(and(X, Y), and(X, f(f(X, f(neg(X), X)), X))))
% 35.77/4.98 = { by lemma 15 }
% 35.77/4.98 and(and(X, Y), or(and(X, Y), and(X, f(f(X, or(X, neg(X))), X))))
% 35.77/4.98 = { by lemma 27 }
% 35.77/4.98 and(and(X, Y), or(and(X, Y), X))
% 35.77/4.98
% 35.77/4.98 Lemma 57: and(X, or(Y, X)) = X.
% 35.77/4.98 Proof:
% 35.77/4.98 and(X, or(Y, X))
% 35.77/4.98 = { by lemma 30 R->L }
% 35.77/4.98 and(X, or(and(or(Y, X), X), or(Y, X)))
% 35.77/4.98 = { by lemma 53 R->L }
% 35.77/4.98 and(and(or(Y, X), X), or(and(or(Y, X), X), or(Y, X)))
% 35.77/4.98 = { by lemma 56 R->L }
% 35.77/4.98 and(and(or(Y, X), X), or(and(and(or(Y, X), X), or(Y, X)), and(or(Y, X), X)))
% 35.77/4.98 = { by lemma 30 }
% 35.77/4.98 and(and(or(Y, X), X), and(or(Y, X), X))
% 35.77/4.98 = { by lemma 23 }
% 35.77/4.98 or(and(or(Y, X), X), and(or(Y, X), X))
% 35.77/4.98 = { by lemma 13 }
% 35.77/4.98 and(or(Y, X), X)
% 35.77/4.98 = { by lemma 53 }
% 35.77/4.98 X
% 35.77/4.98
% 35.77/4.98 Lemma 58: or(and(X, Y), and(or(and(X, Y), Y), Y)) = or(and(X, Y), Y).
% 35.77/4.98 Proof:
% 35.77/4.98 or(and(X, Y), and(or(and(X, Y), Y), Y))
% 35.77/4.98 = { by lemma 35 R->L }
% 35.77/4.98 f(f(X, Y), f(or(and(X, Y), Y), Y))
% 35.77/4.98 = { by lemma 31 R->L }
% 35.77/4.98 neg(and(f(X, Y), f(or(and(X, Y), Y), Y)))
% 35.77/4.98 = { by lemma 9 R->L }
% 35.77/4.98 neg(and(f(X, Y), f(or(neg(f(X, Y)), Y), Y)))
% 35.77/4.98 = { by lemma 16 R->L }
% 35.77/4.98 neg(and(f(X, Y), f(f(f(X, Y), neg(Y)), Y)))
% 35.77/4.98 = { by lemma 9 R->L }
% 35.77/4.98 neg(neg(f(f(X, Y), f(f(f(X, Y), neg(Y)), Y))))
% 35.77/4.98 = { by axiom 1 (sos_003) }
% 35.77/4.98 neg(neg(f(f(X, Y), f(f(f(X, Y), f(Y, Y)), Y))))
% 35.77/4.98 = { by lemma 11 }
% 35.77/4.98 neg(neg(f(f(X, Y), f(Y, Y))))
% 35.77/4.98 = { by axiom 1 (sos_003) R->L }
% 35.77/4.98 neg(neg(f(f(X, Y), neg(Y))))
% 35.77/4.98 = { by lemma 9 }
% 35.77/4.98 neg(and(f(X, Y), neg(Y)))
% 35.77/4.98 = { by lemma 31 }
% 35.77/4.98 f(f(X, Y), neg(Y))
% 35.77/4.98 = { by lemma 16 }
% 35.77/4.98 or(neg(f(X, Y)), Y)
% 35.77/4.98 = { by lemma 9 }
% 35.77/4.98 or(and(X, Y), Y)
% 35.77/4.98
% 35.77/4.98 Lemma 59: or(or(X, Y), or(Y, X)) = or(Y, X).
% 35.77/4.98 Proof:
% 35.77/4.98 or(or(X, Y), or(Y, X))
% 35.77/4.98 = { by lemma 57 R->L }
% 35.77/4.98 or(or(and(X, or(Y, X)), Y), or(Y, X))
% 35.77/4.98 = { by lemma 38 R->L }
% 35.77/4.98 or(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), or(Y, X))
% 35.77/4.98 = { by lemma 52 R->L }
% 35.77/4.98 or(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), or(and(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), or(Y, X)), or(Y, X)))
% 35.77/4.98 = { by lemma 51 R->L }
% 35.77/4.98 or(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), and(or(and(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), or(Y, X)), or(Y, X)), or(Y, X)))
% 35.77/4.98 = { by lemma 50 R->L }
% 35.77/4.98 or(and(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), or(Y, X)), and(or(and(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), or(Y, X)), or(Y, X)), or(Y, X)))
% 35.77/4.98 = { by lemma 58 }
% 35.77/4.98 or(and(or(and(X, or(Y, X)), and(or(Y, X), or(Y, and(or(Y, X), neg(or(Y, X)))))), or(Y, X)), or(Y, X))
% 35.77/4.98 = { by lemma 52 }
% 35.77/4.98 or(Y, X)
% 35.77/4.98
% 35.77/4.98 Lemma 60: and(neg(X), f(X, and(X, Y))) = and(neg(X), f(X, Y)).
% 35.77/4.98 Proof:
% 35.77/4.98 and(neg(X), f(X, and(X, Y)))
% 35.77/4.98 = { by lemma 22 R->L }
% 35.77/4.98 and(neg(X), f(X, and(neg(neg(X)), Y)))
% 35.77/4.98 = { by lemma 43 R->L }
% 35.77/4.98 and(neg(X), or(neg(X), f(neg(neg(X)), Y)))
% 35.89/4.98 = { by lemma 34 R->L }
% 35.89/4.98 and(and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))), or(neg(X), f(neg(neg(X)), Y)))
% 35.89/4.98 = { by lemma 34 R->L }
% 35.89/4.98 and(and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))), or(and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))), f(neg(neg(X)), Y)))
% 35.89/4.98 = { by lemma 56 R->L }
% 35.89/4.98 and(and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))), or(and(and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))), f(neg(neg(X)), Y)), and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X)))))
% 35.89/4.98 = { by lemma 34 }
% 35.89/4.98 and(neg(X), or(and(and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))), f(neg(neg(X)), Y)), and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X)))))
% 35.89/4.99 = { by lemma 34 }
% 35.89/4.99 and(neg(X), or(and(neg(X), f(neg(neg(X)), Y)), and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X)))))
% 35.89/4.99 = { by lemma 34 }
% 35.89/4.99 and(neg(X), or(and(neg(X), f(neg(neg(X)), Y)), neg(X)))
% 35.89/4.99 = { by lemma 19 }
% 35.89/4.99 and(neg(X), f(f(neg(X), f(neg(neg(X)), Y)), X))
% 35.89/4.99 = { by lemma 15 }
% 35.89/4.99 and(neg(X), f(or(X, neg(f(neg(neg(X)), Y))), X))
% 35.89/4.99 = { by lemma 9 }
% 35.89/4.99 and(neg(X), f(or(X, and(neg(neg(X)), Y)), X))
% 35.89/4.99 = { by lemma 22 }
% 35.89/4.99 and(neg(X), f(or(X, and(X, Y)), X))
% 35.89/4.99 = { by lemma 55 }
% 35.89/4.99 and(neg(X), f(X, Y))
% 35.89/4.99
% 35.89/4.99 Lemma 61: neg(or(and(X, Y), Z)) = and(f(X, Y), neg(Z)).
% 35.89/4.99 Proof:
% 35.89/4.99 neg(or(and(X, Y), Z))
% 35.89/4.99 = { by lemma 9 R->L }
% 35.89/4.99 neg(or(neg(f(X, Y)), Z))
% 35.89/4.99 = { by lemma 21 }
% 35.89/4.99 and(f(X, Y), neg(Z))
% 35.89/4.99
% 35.89/4.99 Lemma 62: neg(or(X, neg(Y))) = and(neg(X), Y).
% 35.89/4.99 Proof:
% 35.89/4.99 neg(or(X, neg(Y)))
% 35.89/4.99 = { by lemma 18 R->L }
% 35.89/4.99 and(neg(X), neg(neg(Y)))
% 35.89/4.99 = { by lemma 6 }
% 35.89/4.99 and(neg(X), or(Y, Y))
% 35.89/4.99 = { by lemma 13 }
% 35.89/4.99 and(neg(X), Y)
% 35.89/4.99
% 35.89/4.99 Lemma 63: and(or(X, Y), X) = X.
% 35.89/4.99 Proof:
% 35.89/4.99 and(or(X, Y), X)
% 35.89/4.99 = { by lemma 5 R->L }
% 35.89/4.99 and(f(neg(X), neg(Y)), X)
% 35.89/4.99 = { by lemma 31 R->L }
% 35.89/4.99 and(neg(and(neg(X), neg(Y))), X)
% 35.89/4.99 = { by lemma 62 R->L }
% 35.89/4.99 neg(or(and(neg(X), neg(Y)), neg(X)))
% 35.89/4.99 = { by lemma 29 }
% 35.89/4.99 neg(neg(X))
% 35.89/4.99 = { by lemma 22 }
% 35.89/4.99 X
% 35.89/4.99
% 35.89/4.99 Lemma 64: or(or(X, Y), X) = or(X, Y).
% 35.89/4.99 Proof:
% 35.89/4.99 or(or(X, Y), X)
% 35.89/4.99 = { by lemma 5 R->L }
% 35.89/4.99 or(f(neg(X), neg(Y)), X)
% 35.89/4.99 = { by lemma 39 R->L }
% 35.89/4.99 f(and(neg(X), neg(Y)), neg(X))
% 35.89/4.99 = { by lemma 31 R->L }
% 35.89/4.99 neg(and(and(neg(X), neg(Y)), neg(X)))
% 35.89/4.99 = { by lemma 22 R->L }
% 35.89/4.99 neg(and(and(neg(X), neg(neg(neg(Y)))), neg(X)))
% 35.89/4.99 = { by lemma 25 R->L }
% 35.89/4.99 neg(and(and(neg(X), neg(neg(neg(Y)))), f(or(neg(neg(X)), neg(neg(Y))), f(neg(X), f(f(neg(X), f(neg(neg(X)), neg(X))), neg(X))))))
% 35.89/4.99 = { by lemma 21 R->L }
% 35.89/4.99 neg(and(neg(or(neg(neg(X)), neg(neg(Y)))), f(or(neg(neg(X)), neg(neg(Y))), f(neg(X), f(f(neg(X), f(neg(neg(X)), neg(X))), neg(X))))))
% 35.89/4.99 = { by lemma 60 R->L }
% 35.89/4.99 neg(and(neg(or(neg(neg(X)), neg(neg(Y)))), f(or(neg(neg(X)), neg(neg(Y))), and(or(neg(neg(X)), neg(neg(Y))), f(neg(X), f(f(neg(X), f(neg(neg(X)), neg(X))), neg(X)))))))
% 35.89/4.99 = { by lemma 26 }
% 35.89/4.99 neg(and(neg(or(neg(neg(X)), neg(neg(Y)))), f(or(neg(neg(X)), neg(neg(Y))), neg(neg(X)))))
% 35.89/4.99 = { by lemma 21 }
% 35.89/4.99 neg(and(and(neg(X), neg(neg(neg(Y)))), f(or(neg(neg(X)), neg(neg(Y))), neg(neg(X)))))
% 35.89/4.99 = { by lemma 16 }
% 35.89/4.99 neg(and(and(neg(X), neg(neg(neg(Y)))), or(neg(or(neg(neg(X)), neg(neg(Y)))), neg(X))))
% 35.89/4.99 = { by lemma 21 }
% 35.89/4.99 neg(and(and(neg(X), neg(neg(neg(Y)))), or(and(neg(X), neg(neg(neg(Y)))), neg(X))))
% 35.89/4.99 = { by lemma 6 }
% 35.89/4.99 neg(and(and(neg(X), or(neg(Y), neg(Y))), or(and(neg(X), neg(neg(neg(Y)))), neg(X))))
% 35.89/4.99 = { by lemma 13 }
% 35.89/4.99 neg(and(and(neg(X), neg(Y)), or(and(neg(X), neg(neg(neg(Y)))), neg(X))))
% 35.89/4.99 = { by lemma 22 }
% 35.89/4.99 neg(and(and(neg(X), neg(Y)), or(and(neg(X), neg(Y)), neg(X))))
% 35.89/4.99 = { by lemma 31 }
% 35.89/4.99 f(and(neg(X), neg(Y)), or(and(neg(X), neg(Y)), neg(X)))
% 35.89/4.99 = { by lemma 47 R->L }
% 35.89/4.99 f(and(neg(X), neg(Y)), or(and(and(neg(X), neg(Y)), or(and(neg(X), neg(Y)), neg(X))), and(neg(X), neg(Y))))
% 35.89/4.99 = { by lemma 29 }
% 35.89/4.99 f(and(neg(X), neg(Y)), or(and(and(neg(X), neg(Y)), neg(X)), and(neg(X), neg(Y))))
% 35.89/4.99 = { by lemma 18 }
% 35.89/4.99 f(neg(or(X, Y)), or(and(and(neg(X), neg(Y)), neg(X)), and(neg(X), neg(Y))))
% 35.89/4.99 = { by lemma 18 }
% 35.89/4.99 f(neg(or(X, Y)), or(and(neg(or(X, Y)), neg(X)), and(neg(X), neg(Y))))
% 35.89/4.99 = { by lemma 18 }
% 35.89/4.99 f(neg(or(X, Y)), or(and(neg(or(X, Y)), neg(X)), neg(or(X, Y))))
% 35.89/4.99 = { by lemma 15 }
% 35.89/4.99 or(or(X, Y), neg(or(and(neg(or(X, Y)), neg(X)), neg(or(X, Y)))))
% 35.89/4.99 = { by lemma 61 }
% 35.89/4.99 or(or(X, Y), and(f(neg(or(X, Y)), neg(X)), neg(neg(or(X, Y)))))
% 35.89/4.99 = { by lemma 5 }
% 35.89/4.99 or(or(X, Y), and(or(or(X, Y), X), neg(neg(or(X, Y)))))
% 35.89/4.99 = { by lemma 22 }
% 35.89/4.99 or(or(X, Y), and(or(or(X, Y), X), or(X, Y)))
% 35.89/4.99 = { by lemma 63 }
% 35.89/4.99 or(or(X, Y), or(X, Y))
% 35.89/4.99 = { by lemma 13 }
% 35.89/4.99 or(X, Y)
% 35.89/4.99
% 35.89/4.99 Lemma 65: or(X, Y) = or(Y, X).
% 35.89/4.99 Proof:
% 35.89/4.99 or(X, Y)
% 35.89/4.99 = { by lemma 59 R->L }
% 35.89/4.99 or(or(Y, X), or(X, Y))
% 35.89/4.99 = { by lemma 64 R->L }
% 35.89/4.99 or(or(or(Y, X), or(X, Y)), or(Y, X))
% 35.89/4.99 = { by lemma 59 }
% 35.89/4.99 or(or(X, Y), or(Y, X))
% 35.89/4.99 = { by lemma 59 }
% 35.89/4.99 or(Y, X)
% 35.89/4.99
% 35.89/4.99 Lemma 66: f(Y, X) = f(X, Y).
% 35.89/4.99 Proof:
% 35.89/4.99 f(Y, X)
% 35.89/4.99 = { by lemma 14 R->L }
% 35.89/4.99 or(neg(Y), neg(X))
% 35.89/4.99 = { by lemma 65 R->L }
% 35.89/4.99 or(neg(X), neg(Y))
% 35.89/4.99 = { by lemma 14 }
% 35.89/4.99 f(X, Y)
% 35.89/4.99
% 35.89/4.99 Lemma 67: and(Y, X) = and(X, Y).
% 35.89/4.99 Proof:
% 35.89/4.99 and(Y, X)
% 35.89/4.99 = { by lemma 9 R->L }
% 35.89/4.99 neg(f(Y, X))
% 35.89/4.99 = { by lemma 66 }
% 35.89/4.99 neg(f(X, Y))
% 35.89/4.99 = { by lemma 9 }
% 35.89/4.99 and(X, Y)
% 35.89/4.99
% 35.89/4.99 Lemma 68: f(or(X, Y), X) = neg(X).
% 35.89/4.99 Proof:
% 35.89/4.99 f(or(X, Y), X)
% 35.89/4.99 = { by lemma 14 R->L }
% 35.89/4.99 or(neg(or(X, Y)), neg(X))
% 35.89/4.99 = { by lemma 18 R->L }
% 35.89/4.99 or(and(neg(X), neg(Y)), neg(X))
% 35.89/4.99 = { by lemma 29 }
% 35.89/4.99 neg(X)
% 35.89/4.99
% 35.89/4.99 Lemma 69: or(X, or(X, Y)) = or(X, Y).
% 35.89/4.99 Proof:
% 35.89/4.99 or(X, or(X, Y))
% 35.89/4.99 = { by lemma 63 R->L }
% 35.89/4.99 or(and(or(X, Y), X), or(X, Y))
% 35.89/4.99 = { by lemma 30 }
% 35.89/4.99 or(X, Y)
% 35.89/4.99
% 35.89/4.99 Lemma 70: or(X, and(Y, X)) = X.
% 35.89/4.99 Proof:
% 35.89/4.99 or(X, and(Y, X))
% 35.89/4.99 = { by lemma 52 R->L }
% 35.89/4.99 or(or(and(Y, X), X), and(Y, X))
% 35.89/4.99 = { by lemma 64 }
% 35.89/4.99 or(and(Y, X), X)
% 35.89/4.99 = { by lemma 52 }
% 35.89/4.99 X
% 35.89/4.99
% 35.89/4.99 Lemma 71: neg(or(f(X, Y), Z)) = and(and(X, Y), neg(Z)).
% 35.89/4.99 Proof:
% 35.89/4.99 neg(or(f(X, Y), Z))
% 35.89/4.99 = { by lemma 18 R->L }
% 35.89/4.99 and(neg(f(X, Y)), neg(Z))
% 35.89/4.99 = { by lemma 9 }
% 35.89/4.99 and(and(X, Y), neg(Z))
% 35.89/4.99
% 35.89/4.99 Lemma 72: f(and(X, Y), f(Z, W)) = or(f(X, Y), and(Z, W)).
% 35.89/4.99 Proof:
% 35.89/4.99 f(and(X, Y), f(Z, W))
% 35.89/4.99 = { by lemma 54 R->L }
% 35.89/4.99 or(f(X, Y), neg(f(Z, W)))
% 35.89/4.99 = { by lemma 9 }
% 35.89/4.99 or(f(X, Y), and(Z, W))
% 35.89/4.99
% 35.89/4.99 Lemma 73: f(and(X, Y), or(Y, Z)) = f(X, Y).
% 35.89/4.99 Proof:
% 35.89/4.99 f(and(X, Y), or(Y, Z))
% 35.89/4.99 = { by lemma 63 R->L }
% 35.89/4.99 f(and(or(and(X, Y), Y), and(X, Y)), or(Y, Z))
% 35.89/4.99 = { by lemma 52 }
% 35.89/4.99 f(and(Y, and(X, Y)), or(Y, Z))
% 35.89/4.99 = { by lemma 31 R->L }
% 35.89/4.99 neg(and(and(Y, and(X, Y)), or(Y, Z)))
% 35.89/4.99 = { by lemma 63 R->L }
% 35.89/4.99 neg(and(and(and(or(Y, Z), Y), and(X, Y)), or(Y, Z)))
% 35.89/4.99 = { by lemma 30 R->L }
% 35.89/4.99 neg(and(and(or(and(and(or(Y, Z), Y), or(Y, Z)), and(or(Y, Z), Y)), and(X, Y)), or(Y, Z)))
% 35.89/4.99 = { by lemma 49 }
% 35.89/4.99 neg(and(or(and(and(or(Y, Z), Y), or(Y, Z)), and(or(Y, Z), Y)), and(X, Y)))
% 35.89/4.99 = { by lemma 30 }
% 35.89/4.99 neg(and(and(or(Y, Z), Y), and(X, Y)))
% 35.89/4.99 = { by lemma 63 }
% 35.89/4.99 neg(and(Y, and(X, Y)))
% 35.89/4.99 = { by lemma 31 }
% 35.89/4.99 f(Y, and(X, Y))
% 35.89/4.99 = { by lemma 52 R->L }
% 35.89/4.99 f(or(and(X, Y), Y), and(X, Y))
% 35.89/4.99 = { by lemma 68 }
% 35.89/4.99 neg(and(X, Y))
% 35.89/4.99 = { by lemma 31 }
% 35.89/4.99 f(X, Y)
% 35.89/4.99
% 35.89/4.99 Lemma 74: or(X, and(or(X, neg(Y)), or(or(Z, X), neg(or(Z, X))))) = or(X, neg(Y)).
% 35.89/4.99 Proof:
% 35.89/4.99 or(X, and(or(X, neg(Y)), or(or(Z, X), neg(or(Z, X)))))
% 35.89/4.99 = { by lemma 15 R->L }
% 35.89/4.99 or(X, and(or(X, neg(Y)), f(neg(or(Z, X)), or(Z, X))))
% 35.89/4.99 = { by lemma 18 R->L }
% 35.89/4.99 or(X, and(or(X, neg(Y)), f(and(neg(Z), neg(X)), or(Z, X))))
% 35.89/4.99 = { by lemma 31 R->L }
% 35.89/4.99 or(X, and(or(X, neg(Y)), neg(and(and(neg(Z), neg(X)), or(Z, X)))))
% 35.89/4.99 = { by lemma 15 R->L }
% 35.89/4.99 or(X, and(f(neg(X), Y), neg(and(and(neg(Z), neg(X)), or(Z, X)))))
% 35.89/4.99 = { by lemma 61 R->L }
% 35.89/4.99 or(X, neg(or(and(neg(X), Y), and(and(neg(Z), neg(X)), or(Z, X)))))
% 35.89/4.99 = { by lemma 15 R->L }
% 35.89/4.99 f(neg(X), or(and(neg(X), Y), and(and(neg(Z), neg(X)), or(Z, X))))
% 35.89/4.99 = { by lemma 5 R->L }
% 35.89/4.99 f(neg(X), or(and(neg(X), Y), and(and(neg(Z), neg(X)), f(neg(Z), neg(X)))))
% 35.89/4.99 = { by lemma 36 }
% 35.89/4.99 f(neg(X), Y)
% 35.89/4.99 = { by lemma 15 }
% 35.89/4.99 or(X, neg(Y))
% 35.89/4.99
% 35.89/4.99 Lemma 75: or(X, and(or(X, Y), or(X, neg(X)))) = or(X, Y).
% 35.89/4.99 Proof:
% 35.89/4.99 or(X, and(or(X, Y), or(X, neg(X))))
% 35.89/4.99 = { by lemma 5 R->L }
% 35.89/4.99 or(X, and(or(X, Y), f(neg(X), neg(neg(X)))))
% 35.89/4.99 = { by lemma 31 R->L }
% 35.89/4.99 or(X, and(or(X, Y), neg(and(neg(X), neg(neg(X))))))
% 35.89/4.99 = { by lemma 21 R->L }
% 35.89/4.99 or(X, neg(or(neg(or(X, Y)), and(neg(X), neg(neg(X))))))
% 35.89/4.99 = { by lemma 15 R->L }
% 35.89/4.99 f(neg(X), or(neg(or(X, Y)), and(neg(X), neg(neg(X)))))
% 35.89/4.99 = { by lemma 18 R->L }
% 35.89/4.99 f(neg(X), or(and(neg(X), neg(Y)), and(neg(X), neg(neg(X)))))
% 35.89/4.99 = { by lemma 37 }
% 35.89/4.99 f(neg(X), neg(Y))
% 35.89/4.99 = { by lemma 5 }
% 35.89/4.99 or(X, Y)
% 35.89/4.99
% 35.89/4.99 Lemma 76: and(X, or(X, or(X, Y))) = and(X, or(X, Y)).
% 35.89/4.99 Proof:
% 35.89/4.99 and(X, or(X, or(X, Y)))
% 35.89/4.99 = { by lemma 5 R->L }
% 35.89/4.99 and(X, f(neg(X), neg(or(X, Y))))
% 35.89/4.99 = { by lemma 22 R->L }
% 35.89/4.99 and(neg(neg(X)), f(neg(X), neg(or(X, Y))))
% 35.89/4.99 = { by lemma 18 R->L }
% 35.89/4.99 and(neg(neg(X)), f(neg(X), and(neg(X), neg(Y))))
% 35.89/4.99 = { by lemma 60 }
% 35.89/4.99 and(neg(neg(X)), f(neg(X), neg(Y)))
% 35.89/4.99 = { by lemma 22 }
% 35.89/4.99 and(X, f(neg(X), neg(Y)))
% 35.89/4.99 = { by lemma 5 }
% 35.89/4.99 and(X, or(X, Y))
% 35.89/4.99
% 35.89/4.99 Lemma 77: and(or(X, Y), or(X, and(Z, or(X, Y)))) = or(X, and(Z, or(X, Y))).
% 35.89/4.99 Proof:
% 35.89/4.99 and(or(X, Y), or(X, and(Z, or(X, Y))))
% 35.89/4.99 = { by lemma 67 }
% 35.89/4.99 and(or(X, Y), or(X, and(or(X, Y), Z)))
% 35.89/4.99 = { by lemma 67 }
% 35.89/4.99 and(or(X, and(or(X, Y), Z)), or(X, Y))
% 35.89/4.99 = { by lemma 69 R->L }
% 35.89/4.99 and(or(X, and(or(X, or(X, Y)), Z)), or(X, Y))
% 35.89/4.99 = { by lemma 69 R->L }
% 35.89/4.99 and(or(X, and(or(X, or(X, Y)), Z)), or(X, or(X, Y)))
% 35.89/4.99 = { by lemma 48 R->L }
% 35.89/4.99 and(or(and(X, or(X, Y)), and(or(X, or(X, Y)), Z)), or(X, or(X, Y)))
% 35.89/4.99 = { by lemma 76 R->L }
% 35.89/4.99 and(or(and(X, or(X, or(X, Y))), and(or(X, or(X, Y)), Z)), or(X, or(X, Y)))
% 35.89/4.99 = { by lemma 50 }
% 35.89/4.99 or(and(X, or(X, or(X, Y))), and(or(X, or(X, Y)), Z))
% 35.89/4.99 = { by lemma 76 }
% 35.89/4.99 or(and(X, or(X, Y)), and(or(X, or(X, Y)), Z))
% 35.89/4.99 = { by lemma 48 }
% 35.89/4.99 or(X, and(or(X, or(X, Y)), Z))
% 35.89/4.99 = { by lemma 69 }
% 35.89/4.99 or(X, and(or(X, Y), Z))
% 35.89/4.99 = { by lemma 67 R->L }
% 35.89/4.99 or(X, and(Z, or(X, Y)))
% 35.89/4.99
% 35.89/4.99 Lemma 78: or(or(X, Y), or(X, neg(X))) = or(X, neg(X)).
% 35.89/4.99 Proof:
% 35.89/4.99 or(or(X, Y), or(X, neg(X)))
% 35.89/4.99 = { by lemma 52 R->L }
% 35.89/4.99 or(or(X, Y), or(and(or(X, Y), or(X, neg(X))), or(X, neg(X))))
% 35.89/4.99 = { by lemma 51 R->L }
% 35.89/4.99 or(or(X, Y), and(or(and(or(X, Y), or(X, neg(X))), or(X, neg(X))), or(X, neg(X))))
% 35.89/5.00 = { by lemma 75 R->L }
% 35.89/5.00 or(or(X, and(or(X, Y), or(X, neg(X)))), and(or(and(or(X, Y), or(X, neg(X))), or(X, neg(X))), or(X, neg(X))))
% 35.89/5.00 = { by lemma 77 R->L }
% 35.89/5.00 or(and(or(X, neg(X)), or(X, and(or(X, Y), or(X, neg(X))))), and(or(and(or(X, Y), or(X, neg(X))), or(X, neg(X))), or(X, neg(X))))
% 35.89/5.00 = { by lemma 75 }
% 35.89/5.00 or(and(or(X, neg(X)), or(X, Y)), and(or(and(or(X, Y), or(X, neg(X))), or(X, neg(X))), or(X, neg(X))))
% 35.89/5.00 = { by lemma 67 R->L }
% 35.89/5.00 or(and(or(X, Y), or(X, neg(X))), and(or(and(or(X, Y), or(X, neg(X))), or(X, neg(X))), or(X, neg(X))))
% 35.89/5.00 = { by lemma 58 }
% 35.89/5.00 or(and(or(X, Y), or(X, neg(X))), or(X, neg(X)))
% 35.89/5.00 = { by lemma 52 }
% 35.89/5.00 or(X, neg(X))
% 35.89/5.00
% 35.89/5.00 Lemma 79: or(or(X, neg(Y)), neg(Z)) = f(and(neg(X), Y), Z).
% 35.89/5.00 Proof:
% 35.89/5.00 or(or(X, neg(Y)), neg(Z))
% 35.89/5.00 = { by lemma 15 R->L }
% 35.89/5.00 f(neg(or(X, neg(Y))), Z)
% 35.89/5.00 = { by lemma 62 }
% 35.89/5.00 f(and(neg(X), Y), Z)
% 35.89/5.00
% 35.89/5.00 Lemma 80: or(X, and(or(and(Y, X), and(X, Z)), W)) = X.
% 35.89/5.00 Proof:
% 35.89/5.00 or(X, and(or(and(Y, X), and(X, Z)), W))
% 35.89/5.00 = { by lemma 65 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), X)
% 35.89/5.00 = { by lemma 48 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, or(X, neg(Z))))
% 35.89/5.00 = { by lemma 15 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(neg(X), Z)))
% 35.89/5.00 = { by lemma 68 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(X, or(Y, neg(Y))), X), Z)))
% 35.89/5.00 = { by lemma 65 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), X), X), Z)))
% 35.89/5.00 = { by lemma 22 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), neg(neg(X))), X), Z)))
% 35.89/5.00 = { by lemma 74 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), neg(neg(X))), or(or(or(Y, V), or(Y, neg(Y))), neg(or(or(Y, V), or(Y, neg(Y))))))), X), Z)))
% 35.89/5.00 = { by lemma 6 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), or(X, X)), or(or(or(Y, V), or(Y, neg(Y))), neg(or(or(Y, V), or(Y, neg(Y))))))), X), Z)))
% 35.89/5.00 = { by lemma 13 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), X), or(or(or(Y, V), or(Y, neg(Y))), neg(or(or(Y, V), or(Y, neg(Y))))))), X), Z)))
% 35.89/5.00 = { by lemma 78 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), X), or(or(Y, neg(Y)), neg(or(or(Y, V), or(Y, neg(Y))))))), X), Z)))
% 35.89/5.00 = { by lemma 79 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), X), f(and(neg(Y), Y), or(or(Y, V), or(Y, neg(Y)))))), X), Z)))
% 35.89/5.00 = { by lemma 78 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), X), f(and(neg(Y), Y), or(Y, neg(Y))))), X), Z)))
% 35.89/5.00 = { by lemma 73 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), X), f(neg(Y), Y))), X), Z)))
% 35.89/5.00 = { by lemma 15 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(or(Y, neg(Y)), and(or(or(Y, neg(Y)), X), or(Y, neg(Y)))), X), Z)))
% 35.89/5.00 = { by lemma 70 }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(or(Y, neg(Y)), X), Z)))
% 35.89/5.00 = { by lemma 66 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(X, or(Y, neg(Y))), Z)))
% 35.89/5.00 = { by lemma 15 R->L }
% 35.89/5.00 or(and(or(and(Y, X), and(X, Z)), W), and(X, f(f(X, f(neg(Y), Y)), Z)))
% 35.89/5.00 = { by lemma 35 R->L }
% 35.89/5.00 or(and(f(f(Y, X), f(X, Z)), W), and(X, f(f(X, f(neg(Y), Y)), Z)))
% 35.89/5.00 = { by lemma 35 R->L }
% 35.89/5.00 f(f(f(f(Y, X), f(X, Z)), W), f(X, f(f(X, f(neg(Y), Y)), Z)))
% 35.89/5.00 = { by axiom 1 (sos_003) }
% 35.89/5.00 f(f(f(f(Y, X), f(X, Z)), W), f(X, f(f(X, f(f(Y, Y), Y)), Z)))
% 35.89/5.00 = { by axiom 4 (sos) }
% 35.89/5.00 X
% 35.89/5.00
% 35.89/5.00 Lemma 81: and(X, or(and(X, Y), and(and(Z, X), f(Z, X)))) = and(X, Y).
% 35.89/5.00 Proof:
% 35.89/5.00 and(X, or(and(X, Y), and(and(Z, X), f(Z, X))))
% 35.89/5.00 = { by lemma 9 R->L }
% 35.89/5.00 neg(f(X, or(and(X, Y), and(and(Z, X), f(Z, X)))))
% 35.89/5.00 = { by lemma 36 }
% 35.89/5.00 neg(f(X, Y))
% 35.89/5.00 = { by lemma 9 }
% 35.89/5.00 and(X, Y)
% 35.89/5.00
% 35.89/5.00 Lemma 82: and(or(X, Y), or(X, and(and(Z, or(X, Y)), f(Z, or(X, Y))))) = X.
% 35.89/5.00 Proof:
% 35.89/5.00 and(or(X, Y), or(X, and(and(Z, or(X, Y)), f(Z, or(X, Y)))))
% 35.89/5.00 = { by lemma 31 R->L }
% 35.89/5.00 and(or(X, Y), or(X, and(and(Z, or(X, Y)), neg(and(Z, or(X, Y))))))
% 35.89/5.00 = { by lemma 5 R->L }
% 35.89/5.00 and(or(X, Y), or(X, and(and(Z, f(neg(X), neg(Y))), neg(and(Z, or(X, Y))))))
% 35.89/5.00 = { by lemma 5 R->L }
% 35.89/5.00 and(or(X, Y), or(X, and(and(Z, f(neg(X), neg(Y))), neg(and(Z, f(neg(X), neg(Y)))))))
% 35.89/5.00 = { by lemma 71 R->L }
% 35.89/5.00 and(or(X, Y), or(X, neg(or(f(Z, f(neg(X), neg(Y))), and(Z, f(neg(X), neg(Y)))))))
% 35.89/5.00 = { by lemma 15 R->L }
% 35.89/5.00 and(or(X, Y), f(neg(X), or(f(Z, f(neg(X), neg(Y))), and(Z, f(neg(X), neg(Y))))))
% 35.89/5.00 = { by lemma 5 R->L }
% 35.89/5.00 and(f(neg(X), neg(Y)), f(neg(X), or(f(Z, f(neg(X), neg(Y))), and(Z, f(neg(X), neg(Y))))))
% 35.89/5.00 = { by lemma 72 R->L }
% 35.89/5.00 and(f(neg(X), neg(Y)), f(neg(X), f(and(Z, f(neg(X), neg(Y))), f(Z, f(neg(X), neg(Y))))))
% 35.89/5.00 = { by lemma 28 R->L }
% 35.89/5.00 and(f(neg(X), neg(Y)), or(neg(neg(X)), and(and(Z, f(neg(X), neg(Y))), f(Z, f(neg(X), neg(Y))))))
% 35.89/5.00 = { by lemma 14 R->L }
% 35.89/5.00 and(or(neg(neg(X)), neg(neg(Y))), or(neg(neg(X)), and(and(Z, f(neg(X), neg(Y))), f(Z, f(neg(X), neg(Y))))))
% 35.89/5.00 = { by lemma 14 R->L }
% 35.89/5.00 and(or(neg(neg(X)), neg(neg(Y))), or(neg(neg(X)), and(and(Z, or(neg(neg(X)), neg(neg(Y)))), f(Z, f(neg(X), neg(Y))))))
% 35.89/5.00 = { by lemma 14 R->L }
% 35.89/5.00 and(or(neg(neg(X)), neg(neg(Y))), or(neg(neg(X)), and(and(Z, or(neg(neg(X)), neg(neg(Y)))), f(Z, or(neg(neg(X)), neg(neg(Y)))))))
% 35.89/5.00 = { by lemma 15 R->L }
% 35.89/5.00 and(f(neg(neg(neg(X))), neg(Y)), or(neg(neg(X)), and(and(Z, or(neg(neg(X)), neg(neg(Y)))), f(Z, or(neg(neg(X)), neg(neg(Y)))))))
% 35.89/5.00 = { by lemma 15 R->L }
% 35.89/5.00 and(f(neg(neg(neg(X))), neg(Y)), or(neg(neg(X)), and(and(Z, f(neg(neg(neg(X))), neg(Y))), f(Z, or(neg(neg(X)), neg(neg(Y)))))))
% 35.89/5.00 = { by lemma 15 R->L }
% 35.89/5.00 and(f(neg(neg(neg(X))), neg(Y)), or(neg(neg(X)), and(and(Z, f(neg(neg(neg(X))), neg(Y))), f(Z, f(neg(neg(neg(X))), neg(Y))))))
% 35.89/5.00 = { by lemma 34 R->L }
% 35.89/5.00 and(f(neg(neg(neg(X))), neg(Y)), or(and(f(neg(neg(neg(X))), neg(Y)), f(neg(X), f(f(neg(X), f(neg(neg(X)), neg(X))), neg(X)))), and(and(Z, f(neg(neg(neg(X))), neg(Y))), f(Z, f(neg(neg(neg(X))), neg(Y))))))
% 35.89/5.00 = { by lemma 81 }
% 35.89/5.00 and(f(neg(neg(neg(X))), neg(Y)), f(neg(X), f(f(neg(X), f(neg(neg(X)), neg(X))), neg(X))))
% 35.89/5.00 = { by lemma 34 }
% 35.89/5.00 neg(neg(X))
% 35.89/5.00 = { by lemma 22 }
% 35.89/5.00 X
% 35.89/5.00
% 35.89/5.00 Lemma 83: or(or(X, Y), and(X, Z)) = or(X, Y).
% 35.89/5.00 Proof:
% 35.89/5.00 or(or(X, Y), and(X, Z))
% 35.89/5.00 = { by lemma 67 }
% 35.89/5.00 or(or(X, Y), and(Z, X))
% 35.89/5.00 = { by lemma 80 R->L }
% 35.89/5.00 or(or(X, Y), and(Z, or(X, and(or(and(W, X), and(X, V)), or(X, Y)))))
% 35.89/5.00 = { by lemma 67 }
% 35.89/5.00 or(or(X, Y), and(or(X, and(or(and(W, X), and(X, V)), or(X, Y))), Z))
% 35.89/5.00 = { by lemma 65 R->L }
% 35.89/5.00 or(or(X, Y), and(or(and(or(and(W, X), and(X, V)), or(X, Y)), X), Z))
% 35.89/5.00 = { by lemma 82 R->L }
% 35.89/5.00 or(or(X, Y), and(or(and(or(and(W, X), and(X, V)), or(X, Y)), and(or(X, Y), or(X, and(and(U, or(X, Y)), f(U, or(X, Y)))))), Z))
% 35.89/5.00 = { by lemma 80 }
% 35.89/5.00 or(X, Y)
% 35.89/5.00
% 35.89/5.00 Lemma 84: or(or(X, neg(Y)), f(Y, f(Z, or(X, neg(Y))))) = or(X, neg(Y)).
% 35.89/5.00 Proof:
% 35.89/5.00 or(or(X, neg(Y)), f(Y, f(Z, or(X, neg(Y)))))
% 35.89/5.00 = { by lemma 13 R->L }
% 35.89/5.00 or(or(X, neg(Y)), or(f(Y, f(Z, or(X, neg(Y)))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 6 R->L }
% 35.89/5.00 or(or(X, neg(Y)), neg(neg(f(Y, f(Z, or(X, neg(Y)))))))
% 35.89/5.00 = { by axiom 1 (sos_003) }
% 35.89/5.00 or(or(X, neg(Y)), neg(f(f(Y, f(Z, or(X, neg(Y)))), f(Y, f(Z, or(X, neg(Y)))))))
% 35.89/5.00 = { by lemma 9 }
% 35.89/5.00 or(or(X, neg(Y)), and(f(Y, f(Z, or(X, neg(Y)))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 65 R->L }
% 35.89/5.00 or(or(X, neg(Y)), and(f(Y, f(Z, or(neg(Y), X))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 66 }
% 35.89/5.00 or(or(X, neg(Y)), and(f(f(Z, or(neg(Y), X)), Y), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 19 R->L }
% 35.89/5.00 or(or(X, neg(Y)), and(or(and(Z, or(neg(Y), X)), neg(Y)), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 26 R->L }
% 35.89/5.00 or(or(X, neg(Y)), and(or(and(Z, or(neg(Y), X)), and(or(neg(Y), X), f(Y, f(f(Y, f(neg(Y), Y)), Y)))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 35 R->L }
% 35.89/5.00 or(or(X, neg(Y)), and(f(f(Z, or(neg(Y), X)), f(or(neg(Y), X), f(Y, f(f(Y, f(neg(Y), Y)), Y)))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 11 R->L }
% 35.89/5.00 or(or(X, neg(Y)), and(f(f(Z, or(neg(Y), X)), f(f(f(Z, or(neg(Y), X)), f(or(neg(Y), X), f(Y, f(f(Y, f(neg(Y), Y)), Y)))), or(neg(Y), X))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 25 }
% 35.89/5.00 or(or(X, neg(Y)), and(f(f(Z, or(neg(Y), X)), f(f(f(Z, or(neg(Y), X)), Y), or(neg(Y), X))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.00 = { by lemma 35 }
% 35.89/5.00 or(or(X, neg(Y)), and(or(and(Z, or(neg(Y), X)), and(f(f(Z, or(neg(Y), X)), Y), or(neg(Y), X))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.01 = { by lemma 67 R->L }
% 35.89/5.01 or(or(X, neg(Y)), and(or(and(Z, or(neg(Y), X)), and(or(neg(Y), X), f(f(Z, or(neg(Y), X)), Y))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.01 = { by lemma 66 R->L }
% 35.89/5.01 or(or(X, neg(Y)), and(or(and(Z, or(neg(Y), X)), and(or(neg(Y), X), f(Y, f(Z, or(neg(Y), X))))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.01 = { by lemma 65 }
% 35.89/5.01 or(or(X, neg(Y)), and(or(and(Z, or(neg(Y), X)), and(or(neg(Y), X), f(Y, f(Z, or(X, neg(Y)))))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.01 = { by lemma 65 }
% 35.89/5.01 or(or(X, neg(Y)), and(or(and(Z, or(neg(Y), X)), and(or(X, neg(Y)), f(Y, f(Z, or(X, neg(Y)))))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.01 = { by lemma 65 }
% 35.89/5.01 or(or(X, neg(Y)), and(or(and(Z, or(X, neg(Y))), and(or(X, neg(Y)), f(Y, f(Z, or(X, neg(Y)))))), f(Y, f(Z, or(X, neg(Y))))))
% 35.89/5.01 = { by lemma 80 }
% 35.89/5.01 or(X, neg(Y))
% 35.89/5.01
% 35.89/5.01 Lemma 85: f(f(neg(and(X, Y)), f(X, Y)), and(X, Y)) = f(X, Y).
% 35.89/5.01 Proof:
% 35.89/5.01 f(f(neg(and(X, Y)), f(X, Y)), and(X, Y))
% 35.89/5.01 = { by lemma 9 R->L }
% 35.89/5.01 f(f(neg(and(X, Y)), f(X, Y)), neg(f(X, Y)))
% 35.89/5.01 = { by lemma 9 R->L }
% 35.89/5.01 f(f(neg(neg(f(X, Y))), f(X, Y)), neg(f(X, Y)))
% 35.89/5.01 = { by lemma 6 }
% 35.89/5.01 f(f(or(f(X, Y), f(X, Y)), f(X, Y)), neg(f(X, Y)))
% 35.89/5.01 = { by lemma 46 }
% 35.89/5.01 f(X, Y)
% 35.89/5.01
% 35.89/5.01 Lemma 86: and(f(X, Y), f(X, or(and(Z, f(X, Y)), f(Z, f(X, Y))))) = neg(X).
% 35.89/5.01 Proof:
% 35.89/5.01 and(f(X, Y), f(X, or(and(Z, f(X, Y)), f(Z, f(X, Y)))))
% 35.89/5.01 = { by lemma 65 R->L }
% 35.89/5.01 and(f(X, Y), f(X, or(f(Z, f(X, Y)), and(Z, f(X, Y)))))
% 35.89/5.01 = { by lemma 72 R->L }
% 35.89/5.01 and(f(X, Y), f(X, f(and(Z, f(X, Y)), f(Z, f(X, Y)))))
% 35.89/5.01 = { by lemma 28 R->L }
% 35.89/5.01 and(f(X, Y), or(neg(X), and(and(Z, f(X, Y)), f(Z, f(X, Y)))))
% 35.89/5.01 = { by lemma 14 R->L }
% 35.89/5.01 and(or(neg(X), neg(Y)), or(neg(X), and(and(Z, f(X, Y)), f(Z, f(X, Y)))))
% 35.89/5.01 = { by lemma 14 R->L }
% 35.89/5.01 and(or(neg(X), neg(Y)), or(neg(X), and(and(Z, or(neg(X), neg(Y))), f(Z, f(X, Y)))))
% 35.89/5.01 = { by lemma 14 R->L }
% 35.89/5.01 and(or(neg(X), neg(Y)), or(neg(X), and(and(Z, or(neg(X), neg(Y))), f(Z, or(neg(X), neg(Y))))))
% 35.89/5.01 = { by lemma 15 R->L }
% 35.89/5.01 and(f(neg(neg(X)), Y), or(neg(X), and(and(Z, or(neg(X), neg(Y))), f(Z, or(neg(X), neg(Y))))))
% 35.89/5.01 = { by lemma 15 R->L }
% 35.89/5.01 and(f(neg(neg(X)), Y), or(neg(X), and(and(Z, f(neg(neg(X)), Y)), f(Z, or(neg(X), neg(Y))))))
% 35.89/5.01 = { by lemma 15 R->L }
% 35.89/5.01 and(f(neg(neg(X)), Y), or(neg(X), and(and(Z, f(neg(neg(X)), Y)), f(Z, f(neg(neg(X)), Y)))))
% 35.89/5.01 = { by lemma 34 R->L }
% 35.89/5.01 and(f(neg(neg(X)), Y), or(and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X))), and(and(Z, f(neg(neg(X)), Y)), f(Z, f(neg(neg(X)), Y)))))
% 35.89/5.01 = { by lemma 81 }
% 35.89/5.01 and(f(neg(neg(X)), Y), f(X, f(f(X, f(neg(X), X)), X)))
% 35.89/5.01 = { by lemma 34 }
% 35.89/5.01 neg(X)
% 35.89/5.01
% 35.89/5.01 Lemma 87: and(neg(X), or(Y, f(X, Z))) = neg(X).
% 35.89/5.01 Proof:
% 35.89/5.01 and(neg(X), or(Y, f(X, Z)))
% 35.89/5.01 = { by lemma 65 R->L }
% 35.89/5.01 and(neg(X), or(f(X, Z), Y))
% 35.89/5.01 = { by lemma 67 }
% 35.89/5.01 and(or(f(X, Z), Y), neg(X))
% 35.89/5.01 = { by lemma 86 R->L }
% 35.89/5.01 and(or(f(X, Z), Y), and(f(X, Z), f(X, or(and(W, f(X, Z)), f(W, f(X, Z))))))
% 35.89/5.01 = { by lemma 67 }
% 35.89/5.01 and(or(f(X, Z), Y), and(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))), f(X, Z)))
% 35.89/5.01 = { by lemma 22 R->L }
% 35.89/5.01 and(or(f(X, Z), Y), and(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))), neg(neg(f(X, Z)))))
% 35.89/5.01 = { by lemma 22 R->L }
% 35.89/5.01 and(neg(neg(or(f(X, Z), Y))), and(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))), neg(neg(f(X, Z)))))
% 35.89/5.01 = { by lemma 67 }
% 35.89/5.01 and(and(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))), neg(neg(f(X, Z)))), neg(neg(or(f(X, Z), Y))))
% 35.89/5.01 = { by lemma 71 R->L }
% 35.89/5.01 neg(or(f(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))), neg(neg(f(X, Z)))), neg(or(f(X, Z), Y))))
% 35.89/5.01 = { by lemma 16 }
% 35.89/5.01 neg(or(or(neg(f(X, or(and(W, f(X, Z)), f(W, f(X, Z))))), neg(f(X, Z))), neg(or(f(X, Z), Y))))
% 35.89/5.01 = { by lemma 65 R->L }
% 35.89/5.01 neg(or(or(neg(f(X, Z)), neg(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))))), neg(or(f(X, Z), Y))))
% 35.89/5.01 = { by lemma 18 R->L }
% 35.89/5.01 neg(or(or(neg(f(X, Z)), neg(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))))), and(neg(f(X, Z)), neg(Y))))
% 35.89/5.01 = { by lemma 83 }
% 35.89/5.01 neg(or(neg(f(X, Z)), neg(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))))))
% 35.89/5.01 = { by lemma 65 }
% 35.89/5.01 neg(or(neg(f(X, or(and(W, f(X, Z)), f(W, f(X, Z))))), neg(f(X, Z))))
% 35.89/5.01 = { by lemma 21 }
% 35.89/5.01 and(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))), neg(neg(f(X, Z))))
% 35.89/5.01 = { by lemma 22 }
% 35.89/5.01 and(f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))), f(X, Z))
% 35.89/5.01 = { by lemma 67 R->L }
% 35.89/5.01 and(f(X, Z), f(X, or(and(W, f(X, Z)), f(W, f(X, Z)))))
% 35.89/5.01 = { by lemma 86 }
% 36.10/5.01 neg(X)
% 36.10/5.01
% 36.10/5.01 Lemma 88: or(f(X, Y), f(X, Z)) = f(Z, and(X, Y)).
% 36.10/5.01 Proof:
% 36.10/5.01 or(f(X, Y), f(X, Z))
% 36.10/5.01 = { by lemma 66 }
% 36.10/5.01 or(f(X, Y), f(Z, X))
% 36.10/5.01 = { by lemma 66 }
% 36.10/5.01 or(f(Y, X), f(Z, X))
% 36.10/5.01 = { by lemma 14 R->L }
% 36.10/5.01 or(f(Y, X), or(neg(Z), neg(X)))
% 36.10/5.01 = { by lemma 66 }
% 36.10/5.01 or(f(X, Y), or(neg(Z), neg(X)))
% 36.10/5.01 = { by lemma 65 R->L }
% 36.10/5.01 or(or(neg(Z), neg(X)), f(X, Y))
% 36.10/5.01 = { by lemma 22 R->L }
% 36.10/5.01 or(or(neg(Z), neg(X)), neg(neg(f(X, Y))))
% 36.10/5.01 = { by lemma 83 R->L }
% 36.10/5.01 or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))
% 36.10/5.01 = { by lemma 9 R->L }
% 36.10/5.01 or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), neg(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))
% 36.10/5.01 = { by lemma 84 R->L }
% 36.10/5.01 or(or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), neg(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))), f(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(neg(neg(f(X, Y))), or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), neg(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))))))
% 36.10/5.01 = { by lemma 9 }
% 36.10/5.02 or(or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), f(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(neg(neg(f(X, Y))), or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), neg(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))))))
% 36.10/5.02 = { by lemma 35 }
% 36.10/5.02 or(or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(neg(neg(f(X, Y))), or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), neg(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))))))
% 36.10/5.02 = { by lemma 9 }
% 36.10/5.02 or(or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(neg(neg(f(X, Y))), or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.10/5.02 = { by lemma 83 }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(neg(neg(f(X, Y))), or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.10/5.02 = { by lemma 83 }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(neg(neg(f(X, Y))), or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))))))
% 36.10/5.02 = { by lemma 57 }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), neg(neg(f(X, Y)))))
% 36.10/5.02 = { by lemma 65 }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), or(neg(neg(f(X, Y))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))
% 36.10/5.02 = { by lemma 28 }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), neg(neg(f(X, Y)))), f(neg(f(X, Y)), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))
% 36.10/5.02 = { by lemma 22 }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))
% 36.10/5.02 = { by lemma 13 R->L }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), or(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))))
% 36.10/5.02 = { by lemma 23 R->L }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))))
% 36.10/5.02 = { by lemma 31 R->L }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), neg(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.10/5.02 = { by lemma 68 R->L }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.10/5.02 = { by lemma 63 R->L }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(or(and(or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), neg(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), and(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.10/5.02 = { by lemma 15 R->L }
% 36.10/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(or(and(f(neg(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), and(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.10/5.02 = { by lemma 85 R->L }
% 36.18/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(f(neg(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), f(or(and(f(neg(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), and(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.18/5.02 = { by lemma 45 }
% 36.18/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(f(neg(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))), f(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.18/5.02 = { by lemma 85 }
% 36.18/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), f(neg(f(X, Y)), and(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.18/5.02 = { by lemma 41 }
% 36.18/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), or(f(X, Y), f(f(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), f(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.18/5.02 = { by lemma 35 }
% 36.18/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), or(f(X, Y), or(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X)))))), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))))
% 36.18/5.02 = { by lemma 70 }
% 36.18/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), or(f(X, Y), and(or(neg(Z), neg(X)), or(neg(Z), and(and(W, or(neg(Z), neg(X))), f(W, or(neg(Z), neg(X))))))))
% 36.18/5.02 = { by lemma 82 }
% 36.18/5.02 or(or(or(neg(Z), neg(X)), f(X, Y)), or(f(X, Y), neg(Z)))
% 36.18/5.02 = { by lemma 65 }
% 36.18/5.02 or(or(f(X, Y), neg(Z)), or(or(neg(Z), neg(X)), f(X, Y)))
% 36.18/5.02 = { by lemma 65 }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(or(neg(Z), neg(X)), f(X, Y)))
% 36.18/5.02 = { by lemma 65 }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(f(X, Y), or(neg(Z), neg(X))))
% 36.18/5.02 = { by lemma 87 R->L }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(f(X, Y), or(neg(Z), and(neg(X), or(neg(Z), f(X, Y))))))
% 36.18/5.02 = { by lemma 77 R->L }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(f(X, Y), and(or(neg(Z), f(X, Y)), or(neg(Z), and(neg(X), or(neg(Z), f(X, Y)))))))
% 36.18/5.02 = { by lemma 87 }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(f(X, Y), and(or(neg(Z), f(X, Y)), or(neg(Z), neg(X)))))
% 36.18/5.02 = { by lemma 67 R->L }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(f(X, Y), and(or(neg(Z), neg(X)), or(neg(Z), f(X, Y)))))
% 36.18/5.02 = { by lemma 65 R->L }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(and(or(neg(Z), neg(X)), or(neg(Z), f(X, Y))), f(X, Y)))
% 36.18/5.02 = { by lemma 31 R->L }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(and(or(neg(Z), neg(X)), or(neg(Z), neg(and(X, Y)))), f(X, Y)))
% 36.18/5.02 = { by lemma 65 R->L }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(f(X, Y), and(or(neg(Z), neg(X)), or(neg(Z), neg(and(X, Y))))))
% 36.18/5.02 = { by lemma 9 R->L }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), or(f(X, Y), neg(f(or(neg(Z), neg(X)), or(neg(Z), neg(and(X, Y)))))))
% 36.18/5.02 = { by lemma 54 }
% 36.18/5.02 or(or(neg(Z), f(X, Y)), f(and(X, Y), f(or(neg(Z), neg(X)), or(neg(Z), neg(and(X, Y))))))
% 36.18/5.02 = { by lemma 31 R->L }
% 36.18/5.02 or(or(neg(Z), neg(and(X, Y))), f(and(X, Y), f(or(neg(Z), neg(X)), or(neg(Z), neg(and(X, Y))))))
% 36.18/5.02 = { by lemma 84 }
% 36.18/5.02 or(neg(Z), neg(and(X, Y)))
% 36.18/5.02 = { by lemma 31 }
% 36.18/5.02 or(neg(Z), f(X, Y))
% 36.18/5.02 = { by lemma 66 R->L }
% 36.18/5.02 or(neg(Z), f(Y, X))
% 36.18/5.02 = { by lemma 43 }
% 36.18/5.02 f(Z, and(Y, X))
% 36.18/5.02 = { by lemma 67 R->L }
% 36.18/5.03 f(Z, and(X, Y))
% 36.18/5.03
% 36.18/5.03 Goal 1 (goals): f(x0, f(f(x1, x2), f(x1, x2))) = f(x1, f(f(x0, x2), f(x0, x2))).
% 36.18/5.03 Proof:
% 36.18/5.03 f(x0, f(f(x1, x2), f(x1, x2)))
% 36.18/5.03 = { by axiom 1 (sos_003) R->L }
% 36.18/5.03 f(x0, neg(f(x1, x2)))
% 36.18/5.03 = { by lemma 9 }
% 36.18/5.03 f(x0, and(x1, x2))
% 36.18/5.03 = { by lemma 67 }
% 36.18/5.03 f(x0, and(x2, x1))
% 36.18/5.03 = { by lemma 88 R->L }
% 36.18/5.03 or(f(x2, x1), f(x2, x0))
% 36.18/5.03 = { by lemma 8 R->L }
% 36.18/5.03 or(f(x2, x1), f(f(f(f(f(X, x2), f(x2, x0)), f(f(x2, x0), or(and(x2, x0), and(and(Y, Z), f(Y, Z))))), f(x2, f(f(x2, f(neg(X), X)), x0))), f(f(x2, x0), f(f(f(x2, x0), f(neg(f(X, x2)), f(X, x2))), or(and(x2, x0), and(and(Y, Z), f(Y, Z)))))))
% 36.18/5.03 = { by lemma 8 }
% 36.18/5.03 or(f(x2, x1), f(x2, f(f(x2, x0), f(f(f(x2, x0), f(neg(f(X, x2)), f(X, x2))), or(and(x2, x0), and(and(Y, Z), f(Y, Z)))))))
% 36.18/5.03 = { by lemma 9 }
% 36.18/5.03 or(f(x2, x1), f(x2, f(f(x2, x0), f(f(f(x2, x0), f(and(X, x2), f(X, x2))), or(and(x2, x0), and(and(Y, Z), f(Y, Z)))))))
% 36.18/5.03 = { by lemma 35 }
% 36.18/5.03 or(f(x2, x1), f(x2, or(and(x2, x0), and(f(f(x2, x0), f(and(X, x2), f(X, x2))), or(and(x2, x0), and(and(Y, Z), f(Y, Z)))))))
% 36.18/5.03 = { by lemma 35 }
% 36.18/5.03 or(f(x2, x1), f(x2, or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(x2, x0), and(and(Y, Z), f(Y, Z)))))))
% 36.18/5.03 = { by lemma 88 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(x2, x0), and(and(Y, Z), f(Y, Z))))), and(x2, x1))
% 36.18/5.03 = { by lemma 67 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(x2, x0), and(f(Y, Z), and(Y, Z))))), and(x2, x1))
% 36.18/5.03 = { by lemma 31 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(x2, x0), and(neg(and(Y, Z)), and(Y, Z))))), and(x2, x1))
% 36.18/5.03 = { by lemma 67 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(x2, x0), and(and(Y, Z), neg(and(Y, Z)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 65 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(and(Y, Z), neg(and(Y, Z))), and(x2, x0)))), and(x2, x1))
% 36.18/5.03 = { by lemma 67 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(neg(and(Y, Z)), and(Y, Z)), and(x2, x0)))), and(x2, x1))
% 36.18/5.03 = { by lemma 27 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(neg(and(Y, Z)), and(Y, Z)), and(and(x2, x0), f(f(and(x2, x0), or(and(x2, x0), neg(and(x2, x0)))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 15 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(and(neg(and(Y, Z)), and(Y, Z)), and(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 62 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), or(neg(or(and(Y, Z), neg(and(Y, Z)))), and(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 28 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(and(Y, Z), neg(and(Y, Z))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 78 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), or(and(Y, Z), neg(and(Y, Z)))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 15 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), f(neg(and(Y, Z)), and(Y, Z))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 31 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), neg(and(neg(and(Y, Z)), and(Y, Z)))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 30 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), neg(or(and(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0))), and(neg(and(Y, Z)), and(Y, Z))))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 9 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), neg(or(and(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0))), neg(f(neg(and(Y, Z)), and(Y, Z)))))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 62 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), and(neg(and(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0)))), f(neg(and(Y, Z)), and(Y, Z)))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 31 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), and(f(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0))), f(neg(and(Y, Z)), and(Y, Z)))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 73 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), and(f(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0))), f(and(neg(and(Y, Z)), and(Y, Z)), or(and(Y, Z), neg(and(Y, Z)))))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 78 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), and(f(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0))), f(and(neg(and(Y, Z)), and(Y, Z)), or(or(and(Y, Z), W), or(and(Y, Z), neg(and(Y, Z))))))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 79 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), and(f(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0))), or(or(and(Y, Z), neg(and(Y, Z))), neg(or(or(and(Y, Z), W), or(and(Y, Z), neg(and(Y, Z)))))))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 79 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), and(or(or(and(Y, Z), neg(and(Y, Z))), neg(or(and(x2, x0), and(x2, x0)))), or(or(and(Y, Z), neg(and(Y, Z))), neg(or(or(and(Y, Z), W), or(and(Y, Z), neg(and(Y, Z)))))))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 78 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), and(or(or(and(Y, Z), neg(and(Y, Z))), neg(or(and(x2, x0), and(x2, x0)))), or(or(or(and(Y, Z), W), or(and(Y, Z), neg(and(Y, Z)))), neg(or(or(and(Y, Z), W), or(and(Y, Z), neg(and(Y, Z)))))))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 74 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(or(or(and(Y, Z), neg(and(Y, Z))), neg(or(and(x2, x0), and(x2, x0)))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 79 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(f(and(neg(and(Y, Z)), and(Y, Z)), or(and(x2, x0), and(x2, x0))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 67 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(f(and(and(Y, Z), neg(and(Y, Z))), or(and(x2, x0), and(x2, x0))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 66 R->L }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), f(f(or(and(x2, x0), and(x2, x0)), and(and(Y, Z), neg(and(Y, Z)))), f(and(x2, x0), f(f(and(x2, x0), f(neg(and(x2, x0)), and(x2, x0))), and(x2, x0)))))), and(x2, x1))
% 36.18/5.03 = { by lemma 24 }
% 36.18/5.03 f(or(and(x2, x0), and(or(and(x2, x0), and(and(X, x2), f(X, x2))), and(x2, x0))), and(x2, x1))
% 36.18/5.03 = { by lemma 70 }
% 36.18/5.03 f(and(x2, x0), and(x2, x1))
% 36.18/5.03 = { by lemma 40 }
% 36.18/5.03 or(f(x2, x0), f(x2, x1))
% 36.18/5.03 = { by lemma 88 }
% 36.18/5.03 f(x1, and(x2, x0))
% 36.18/5.03 = { by lemma 67 R->L }
% 36.18/5.03 f(x1, and(x0, x2))
% 36.18/5.03 = { by lemma 9 R->L }
% 36.18/5.03 f(x1, neg(f(x0, x2)))
% 36.18/5.03 = { by axiom 1 (sos_003) }
% 36.18/5.03 f(x1, f(f(x0, x2), f(x0, x2)))
% 36.18/5.03 % SZS output end Proof
% 36.18/5.03
% 36.18/5.03 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------