TSTP Solution File: ALG213-10 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG213-10 : TPTP v8.1.2. Released v8.1.0.
% 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 : n015.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 : Wed Aug 30 16:42:31 EDT 2023
% Result : Unsatisfiable 69.70s 9.34s
% Output : Proof 70.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG213-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 06:09:39 EDT 2023
% 0.18/0.34 % CPUTime :
% 69.70/9.34 Command-line arguments: --ground-connectedness --complete-subsets
% 69.70/9.34
% 69.70/9.34 % SZS status Unsatisfiable
% 69.70/9.34
% 70.08/9.44 % SZS output start Proof
% 70.08/9.44 Axiom 1 (majority): f(X, X, Y) = X.
% 70.08/9.44 Axiom 2 (permute2): f(X, Y, Z) = f(X, Z, Y).
% 70.08/9.44 Axiom 3 (permute1): f(X, Y, Z) = f(Z, X, Y).
% 70.08/9.44 Axiom 4 (associativity): f(f(X, Y, Z), Y, W) = f(X, Y, f(Z, Y, W)).
% 70.08/9.44
% 70.08/9.44 Lemma 5: f(X, Y, X) = X.
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, X)
% 70.08/9.44 = { by axiom 2 (permute2) R->L }
% 70.08/9.44 f(X, X, Y)
% 70.08/9.44 = { by axiom 1 (majority) }
% 70.08/9.44 X
% 70.08/9.44
% 70.08/9.44 Lemma 6: f(X, Y, Y) = Y.
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, Y)
% 70.08/9.44 = { by axiom 3 (permute1) R->L }
% 70.08/9.44 f(Y, Y, X)
% 70.08/9.44 = { by axiom 1 (majority) }
% 70.08/9.44 Y
% 70.08/9.44
% 70.08/9.44 Lemma 7: f(X, Y, Z) = f(Y, X, Z).
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, Z)
% 70.08/9.44 = { by axiom 3 (permute1) R->L }
% 70.08/9.44 f(Y, Z, X)
% 70.08/9.44 = { by axiom 2 (permute2) }
% 70.08/9.44 f(Y, X, Z)
% 70.08/9.44
% 70.08/9.44 Lemma 8: f(Z, X, f(W, X, Y)) = f(X, Y, f(Z, X, W)).
% 70.08/9.44 Proof:
% 70.08/9.44 f(Z, X, f(W, X, Y))
% 70.08/9.44 = { by axiom 4 (associativity) R->L }
% 70.08/9.44 f(f(Z, X, W), X, Y)
% 70.08/9.44 = { by axiom 3 (permute1) R->L }
% 70.08/9.44 f(X, Y, f(Z, X, W))
% 70.08/9.44
% 70.08/9.44 Lemma 9: f(X, Y, f(X, Y, Z)) = f(X, Y, Z).
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, f(X, Y, Z))
% 70.08/9.44 = { by lemma 8 }
% 70.08/9.44 f(Y, Z, f(X, Y, X))
% 70.08/9.44 = { by lemma 5 }
% 70.08/9.44 f(Y, Z, X)
% 70.08/9.44 = { by axiom 3 (permute1) }
% 70.08/9.44 f(X, Y, Z)
% 70.08/9.44
% 70.08/9.44 Lemma 10: f(Z, Y, f(Y, X, W)) = f(X, Y, f(Z, Y, W)).
% 70.08/9.44 Proof:
% 70.08/9.44 f(Z, Y, f(Y, X, W))
% 70.08/9.44 = { by axiom 3 (permute1) }
% 70.08/9.44 f(Z, Y, f(W, Y, X))
% 70.08/9.44 = { by lemma 8 }
% 70.08/9.44 f(Y, X, f(Z, Y, W))
% 70.08/9.44 = { by axiom 3 (permute1) R->L }
% 70.08/9.44 f(X, f(Z, Y, W), Y)
% 70.08/9.44 = { by axiom 2 (permute2) }
% 70.08/9.44 f(X, Y, f(Z, Y, W))
% 70.08/9.44
% 70.08/9.44 Lemma 11: f(X, Y, f(Y, Z, W)) = f(Z, Y, f(X, W, Y)).
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, f(Y, Z, W))
% 70.08/9.44 = { by lemma 10 }
% 70.08/9.44 f(Z, Y, f(X, Y, W))
% 70.08/9.44 = { by axiom 2 (permute2) }
% 70.08/9.44 f(Z, Y, f(X, W, Y))
% 70.08/9.44
% 70.08/9.44 Lemma 12: f(X, Y, f(Z, Y, W)) = f(Y, W, f(X, Z, Y)).
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, f(Z, Y, W))
% 70.08/9.44 = { by lemma 8 }
% 70.08/9.44 f(Y, W, f(X, Y, Z))
% 70.08/9.44 = { by axiom 2 (permute2) }
% 70.08/9.44 f(Y, W, f(X, Z, Y))
% 70.08/9.44
% 70.08/9.44 Lemma 13: f(X, W, f(Y, X, Z)) = f(X, Y, f(Z, W, X)).
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, W, f(Y, X, Z))
% 70.08/9.44 = { by lemma 7 R->L }
% 70.08/9.44 f(W, X, f(Y, X, Z))
% 70.08/9.44 = { by lemma 8 }
% 70.08/9.44 f(X, Z, f(W, X, Y))
% 70.08/9.44 = { by axiom 2 (permute2) }
% 70.08/9.44 f(X, f(W, X, Y), Z)
% 70.08/9.44 = { by axiom 3 (permute1) R->L }
% 70.08/9.44 f(f(W, X, Y), Z, X)
% 70.08/9.44 = { by axiom 3 (permute1) R->L }
% 70.08/9.44 f(Z, X, f(W, X, Y))
% 70.08/9.44 = { by lemma 12 }
% 70.08/9.44 f(X, Y, f(Z, W, X))
% 70.08/9.44
% 70.08/9.44 Lemma 14: f(X, Y, f(Z, X, W)) = f(X, Z, f(Y, W, X)).
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, f(Z, X, W))
% 70.08/9.44 = { by lemma 13 }
% 70.08/9.44 f(X, Z, f(W, Y, X))
% 70.08/9.44 = { by lemma 7 }
% 70.08/9.44 f(X, Z, f(Y, W, X))
% 70.08/9.44
% 70.08/9.44 Lemma 15: f(X, Y, f(Z, Y, W)) = f(Y, Z, f(W, Y, X)).
% 70.08/9.44 Proof:
% 70.08/9.44 f(X, Y, f(Z, Y, W))
% 70.08/9.44 = { by lemma 12 }
% 70.67/9.44 f(Y, W, f(X, Z, Y))
% 70.67/9.44 = { by lemma 13 R->L }
% 70.67/9.44 f(Y, Z, f(W, Y, X))
% 70.67/9.44
% 70.67/9.44 Lemma 16: f(X, f(Y, X, Z), W) = f(X, Z, f(W, X, Y)).
% 70.67/9.44 Proof:
% 70.67/9.44 f(X, f(Y, X, Z), W)
% 70.67/9.44 = { by axiom 3 (permute1) R->L }
% 70.67/9.44 f(f(Y, X, Z), W, X)
% 70.67/9.44 = { by axiom 3 (permute1) R->L }
% 70.67/9.44 f(W, X, f(Y, X, Z))
% 70.67/9.44 = { by lemma 8 }
% 70.67/9.44 f(X, Z, f(W, X, Y))
% 70.67/9.44
% 70.67/9.44 Lemma 17: f(X, f(X, Y, Z), W) = f(X, Y, f(X, W, Z)).
% 70.67/9.44 Proof:
% 70.67/9.44 f(X, f(X, Y, Z), W)
% 70.67/9.44 = { by axiom 3 (permute1) }
% 70.67/9.45 f(X, f(Z, X, Y), W)
% 70.67/9.45 = { by lemma 16 }
% 70.67/9.45 f(X, Y, f(W, X, Z))
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, Y, f(X, W, Z))
% 70.67/9.45
% 70.67/9.45 Lemma 18: f(X, Z, f(X, Y, W)) = f(X, Y, f(X, Z, W)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Z, f(X, Y, W))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(X, f(X, Y, W), Z)
% 70.67/9.45 = { by lemma 17 }
% 70.67/9.45 f(X, Y, f(X, Z, W))
% 70.67/9.45
% 70.67/9.45 Lemma 19: f(X, W, f(X, Y, Z)) = f(X, Y, f(X, Z, W)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, W, f(X, Y, Z))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(X, W, f(X, Z, Y))
% 70.67/9.45 = { by lemma 17 R->L }
% 70.67/9.45 f(X, f(X, W, Y), Z)
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(X, f(W, X, Y), Z)
% 70.67/9.45 = { by lemma 16 }
% 70.67/9.45 f(X, Y, f(Z, X, W))
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, Y, f(X, Z, W))
% 70.67/9.45
% 70.67/9.45 Lemma 20: f(X, f(Y, Z, X), W) = f(X, Z, f(W, X, Y)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, f(Y, Z, X), W)
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(X, W, f(Y, Z, X))
% 70.67/9.45 = { by lemma 13 R->L }
% 70.67/9.45 f(X, Z, f(W, X, Y))
% 70.67/9.45
% 70.67/9.45 Lemma 21: f(Y, Z, f(X, Y, W)) = f(X, Y, f(Y, Z, W)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(Y, Z, f(X, Y, W))
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(Z, Y, f(X, Y, W))
% 70.67/9.45 = { by lemma 10 R->L }
% 70.67/9.45 f(X, Y, f(Y, Z, W))
% 70.67/9.45
% 70.67/9.45 Lemma 22: f(Y, Z, f(Y, W, X)) = f(X, Y, f(Y, Z, W)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(Y, Z, f(Y, W, X))
% 70.67/9.45 = { by lemma 19 R->L }
% 70.67/9.45 f(Y, X, f(Y, Z, W))
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, Y, f(Y, Z, W))
% 70.67/9.45
% 70.67/9.45 Lemma 23: f(Z, f(X, Y, W), Y) = f(X, Y, f(Z, Y, W)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(Z, f(X, Y, W), Y)
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(f(X, Y, W), Y, Z)
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(Y, Z, f(X, Y, W))
% 70.67/9.45 = { by lemma 8 R->L }
% 70.67/9.45 f(X, Y, f(W, Y, Z))
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, Y, f(Y, W, Z))
% 70.67/9.45 = { by axiom 3 (permute1) }
% 70.67/9.45 f(X, Y, f(Z, Y, W))
% 70.67/9.45
% 70.67/9.45 Lemma 24: f(Z, f(W, X, Y), Y) = f(X, Y, f(Z, Y, W)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(Z, f(W, X, Y), Y)
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(f(W, X, Y), Y, Z)
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(Y, Z, f(W, X, Y))
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(Y, Z, f(X, Y, W))
% 70.67/9.45 = { by lemma 8 R->L }
% 70.67/9.45 f(X, Y, f(W, Y, Z))
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, Y, f(Y, W, Z))
% 70.67/9.45 = { by axiom 3 (permute1) }
% 70.67/9.45 f(X, Y, f(Z, Y, W))
% 70.67/9.45
% 70.67/9.45 Lemma 25: f(W, f(X, Y, Z), Y) = f(X, Y, f(Y, Z, W)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(W, f(X, Y, Z), Y)
% 70.67/9.45 = { by lemma 23 }
% 70.67/9.45 f(X, Y, f(W, Y, Z))
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(Y, f(W, Y, Z), X)
% 70.67/9.45 = { by lemma 16 }
% 70.67/9.45 f(Y, Z, f(X, Y, W))
% 70.67/9.45 = { by lemma 21 }
% 70.67/9.45 f(X, Y, f(Y, Z, W))
% 70.67/9.45
% 70.67/9.45 Lemma 26: f(f(X, Y, Z), X, Y) = f(X, Y, Z).
% 70.67/9.45 Proof:
% 70.67/9.45 f(f(X, Y, Z), X, Y)
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(X, Y, f(X, Y, Z))
% 70.67/9.45 = { by lemma 9 }
% 70.67/9.45 f(X, Y, Z)
% 70.67/9.45
% 70.67/9.45 Lemma 27: f(X, Y, f(X, Z, f(Y, Z, W))) = f(X, Y, Z).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Y, f(X, Z, f(Y, Z, W)))
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(X, Y, f(X, Z, f(Z, Y, W)))
% 70.67/9.45 = { by lemma 9 R->L }
% 70.67/9.45 f(X, Y, f(X, Y, f(X, Z, f(Z, Y, W))))
% 70.67/9.45 = { by lemma 18 }
% 70.67/9.45 f(X, Y, f(X, Z, f(X, Y, f(Z, Y, W))))
% 70.67/9.45 = { by lemma 15 }
% 70.67/9.45 f(X, Y, f(X, Z, f(Y, Z, f(W, Y, X))))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(X, Y, f(X, f(Y, Z, f(W, Y, X)), Z))
% 70.67/9.45 = { by lemma 16 R->L }
% 70.67/9.45 f(X, Y, f(X, f(Y, f(X, Y, Z), W), Z))
% 70.67/9.45 = { by lemma 17 R->L }
% 70.67/9.45 f(X, f(X, Y, Z), f(Y, f(X, Y, Z), W))
% 70.67/9.45 = { by lemma 12 }
% 70.67/9.45 f(f(X, Y, Z), W, f(X, Y, f(X, Y, Z)))
% 70.67/9.45 = { by lemma 9 }
% 70.67/9.45 f(f(X, Y, Z), W, f(X, Y, Z))
% 70.67/9.45 = { by lemma 5 }
% 70.67/9.45 f(X, Y, Z)
% 70.67/9.45
% 70.67/9.45 Lemma 28: f(Z, Y, f(W, X, f(Y, X, V))) = f(X, Y, f(Z, Y, f(X, W, V))).
% 70.67/9.45 Proof:
% 70.67/9.45 f(Z, Y, f(W, X, f(Y, X, V)))
% 70.67/9.45 = { by lemma 10 R->L }
% 70.67/9.45 f(Z, Y, f(Y, X, f(X, W, V)))
% 70.67/9.45 = { by lemma 10 }
% 70.67/9.45 f(X, Y, f(Z, Y, f(X, W, V)))
% 70.67/9.45
% 70.67/9.45 Lemma 29: f(X, Y, f(f(Z, X, W), Y, V)) = f(Y, V, f(Z, X, f(W, X, Y))).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Y, f(f(Z, X, W), Y, V))
% 70.67/9.45 = { by lemma 8 }
% 70.67/9.45 f(Y, V, f(X, Y, f(Z, X, W)))
% 70.67/9.45 = { by lemma 8 R->L }
% 70.67/9.45 f(Y, V, f(Z, X, f(W, X, Y)))
% 70.67/9.45
% 70.67/9.45 Lemma 30: f(X, Y, f(f(Z, X, W), Y, V)) = f(Y, V, f(Z, X, f(X, W, Y))).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Y, f(f(Z, X, W), Y, V))
% 70.67/9.45 = { by lemma 29 }
% 70.67/9.45 f(Y, V, f(Z, X, f(W, X, Y)))
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(Y, V, f(Z, X, f(X, W, Y)))
% 70.67/9.45
% 70.67/9.45 Lemma 31: f(X, Y, f(f(Z, X, W), Y, Z)) = f(X, Z, Y).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Y, f(f(Z, X, W), Y, Z))
% 70.67/9.45 = { by lemma 30 }
% 70.67/9.45 f(Y, Z, f(Z, X, f(X, W, Y)))
% 70.67/9.45 = { by lemma 11 }
% 70.67/9.45 f(X, Z, f(Y, f(X, W, Y), Z))
% 70.67/9.45 = { by lemma 20 }
% 70.67/9.45 f(X, Z, f(Y, W, f(Z, Y, X)))
% 70.67/9.45 = { by lemma 16 R->L }
% 70.67/9.45 f(X, Z, f(Y, f(X, Y, W), Z))
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(X, Z, f(f(X, Y, W), Y, Z))
% 70.67/9.45 = { by lemma 11 R->L }
% 70.67/9.45 f(f(X, Y, W), Z, f(Z, X, Y))
% 70.67/9.45 = { by lemma 22 R->L }
% 70.67/9.45 f(Z, X, f(Z, Y, f(X, Y, W)))
% 70.67/9.45 = { by lemma 27 }
% 70.67/9.45 f(Z, X, Y)
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, Z, Y)
% 70.67/9.45
% 70.67/9.45 Lemma 32: f(X, Y, f(Z, W, f(Y, W, X))) = f(X, Y, W).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Y, f(Z, W, f(Y, W, X)))
% 70.67/9.45 = { by lemma 28 }
% 70.67/9.45 f(W, Y, f(X, Y, f(W, Z, X)))
% 70.67/9.45 = { by lemma 14 R->L }
% 70.67/9.45 f(W, Y, f(X, W, f(Y, X, Z)))
% 70.67/9.45 = { by lemma 21 }
% 70.67/9.45 f(W, Y, f(Y, X, f(X, W, Z)))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(W, Y, f(Y, f(X, W, Z), X))
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(W, Y, f(f(X, W, Z), Y, X))
% 70.67/9.45 = { by lemma 31 }
% 70.67/9.45 f(W, X, Y)
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, W, Y)
% 70.67/9.45 = { by axiom 2 (permute2) }
% 70.67/9.45 f(X, Y, W)
% 70.67/9.45
% 70.67/9.45 Lemma 33: f(f(X, Y, Z), X, f(X, Y, W)) = f(W, f(X, Y, Z), X).
% 70.67/9.45 Proof:
% 70.67/9.45 f(f(X, Y, Z), X, f(X, Y, W))
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(f(X, Y, Z), X, f(Y, X, W))
% 70.67/9.45 = { by lemma 15 }
% 70.67/9.45 f(X, Y, f(W, X, f(X, Y, Z)))
% 70.67/9.45 = { by lemma 8 R->L }
% 70.67/9.45 f(W, X, f(f(X, Y, Z), X, Y))
% 70.67/9.45 = { by lemma 26 }
% 70.67/9.45 f(W, X, f(X, Y, Z))
% 70.67/9.45 = { by axiom 2 (permute2) }
% 70.67/9.45 f(W, f(X, Y, Z), X)
% 70.67/9.45
% 70.67/9.45 Lemma 34: f(f(X, Y, Z), X, f(X, Z, W)) = f(W, f(X, Y, Z), X).
% 70.67/9.45 Proof:
% 70.67/9.45 f(f(X, Y, Z), X, f(X, Z, W))
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(f(X, Y, Z), X, f(Z, X, W))
% 70.67/9.45 = { by lemma 15 }
% 70.67/9.45 f(X, Z, f(W, X, f(X, Y, Z)))
% 70.67/9.45 = { by lemma 8 R->L }
% 70.67/9.45 f(W, X, f(f(X, Y, Z), X, Z))
% 70.67/9.45 = { by axiom 3 (permute1) R->L }
% 70.67/9.45 f(W, X, f(X, Z, f(X, Y, Z)))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(W, X, f(X, Z, f(X, Z, Y)))
% 70.67/9.45 = { by lemma 8 }
% 70.67/9.45 f(W, X, f(Z, Y, f(X, Z, X)))
% 70.67/9.45 = { by lemma 5 }
% 70.67/9.45 f(W, X, f(Z, Y, X))
% 70.67/9.45 = { by axiom 3 (permute1) }
% 70.67/9.45 f(W, X, f(X, Z, Y))
% 70.67/9.45 = { by axiom 2 (permute2) }
% 70.67/9.45 f(W, X, f(X, Y, Z))
% 70.67/9.45 = { by axiom 2 (permute2) }
% 70.67/9.45 f(W, f(X, Y, Z), X)
% 70.67/9.45
% 70.67/9.45 Lemma 35: f(f(X, Y, Z), X, f(W, Y, Z)) = f(X, Y, Z).
% 70.67/9.45 Proof:
% 70.67/9.45 f(f(X, Y, Z), X, f(W, Y, Z))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(f(X, Y, Z), f(W, Y, Z), X)
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(f(W, Y, Z), f(X, Y, Z), X)
% 70.67/9.45 = { by lemma 33 R->L }
% 70.67/9.45 f(f(X, Y, Z), X, f(X, Y, f(W, Y, Z)))
% 70.67/9.45 = { by lemma 23 R->L }
% 70.67/9.45 f(f(X, Y, Z), X, f(W, f(X, Y, Z), Y))
% 70.67/9.45 = { by lemma 21 }
% 70.67/9.45 f(W, f(X, Y, Z), f(f(X, Y, Z), X, Y))
% 70.67/9.45 = { by lemma 26 }
% 70.67/9.45 f(W, f(X, Y, Z), f(X, Y, Z))
% 70.67/9.45 = { by lemma 6 }
% 70.67/9.45 f(X, Y, Z)
% 70.67/9.45
% 70.67/9.45 Lemma 36: f(X, Y, f(X, Z, f(W, f(V, Y, Z), Z))) = f(X, Y, Z).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Y, f(X, Z, f(W, f(V, Y, Z), Z)))
% 70.67/9.45 = { by lemma 24 }
% 70.67/9.45 f(X, Y, f(X, Z, f(Y, Z, f(W, Z, V))))
% 70.67/9.45 = { by lemma 27 }
% 70.67/9.45 f(X, Y, Z)
% 70.67/9.45
% 70.67/9.45 Lemma 37: f(X, Y, f(X, f(Z, W, V), f(Y, W, V))) = f(X, Y, f(Z, W, V)).
% 70.67/9.45 Proof:
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(Y, W, V)))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(Y, V, W)))
% 70.67/9.45 = { by lemma 31 R->L }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(Y, W, f(f(V, Y, Z), W, V))))
% 70.67/9.45 = { by lemma 30 }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(W, V, f(V, Y, f(Y, Z, W)))))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(W, V, f(V, f(Y, Z, W), Y))))
% 70.67/9.45 = { by axiom 2 (permute2) R->L }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(W, V, f(V, f(Y, W, Z), Y))))
% 70.67/9.45 = { by lemma 7 R->L }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(W, V, f(f(Y, W, Z), V, Y))))
% 70.67/9.45 = { by lemma 29 }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(V, Y, f(Y, W, f(Z, W, V)))))
% 70.67/9.45 = { by axiom 2 (permute2) }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(V, Y, f(Y, f(Z, W, V), W))))
% 70.67/9.45 = { by lemma 7 }
% 70.67/9.45 f(X, Y, f(X, f(Z, W, V), f(Y, V, f(Y, f(Z, W, V), W))))
% 70.67/9.46 = { by lemma 18 R->L }
% 70.67/9.46 f(X, Y, f(X, f(Z, W, V), f(Y, f(Z, W, V), f(Y, V, W))))
% 70.67/9.46 = { by axiom 2 (permute2) }
% 70.67/9.46 f(X, Y, f(X, f(Z, W, V), f(Y, f(Z, W, V), f(Y, W, V))))
% 70.67/9.46 = { by lemma 27 }
% 70.67/9.46 f(X, Y, f(Z, W, V))
% 70.67/9.46
% 70.67/9.46 Lemma 38: f(f(X, Y, Z), X, f(X, f(W, Y, Z), V)) = f(V, f(X, Y, Z), X).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(X, Y, Z), X, f(X, f(W, Y, Z), V))
% 70.67/9.46 = { by lemma 7 R->L }
% 70.67/9.46 f(f(X, Y, Z), X, f(f(W, Y, Z), X, V))
% 70.67/9.46 = { by lemma 15 }
% 70.67/9.46 f(X, f(W, Y, Z), f(V, X, f(X, Y, Z)))
% 70.67/9.46 = { by lemma 8 R->L }
% 70.67/9.46 f(V, X, f(f(X, Y, Z), X, f(W, Y, Z)))
% 70.67/9.46 = { by lemma 35 }
% 70.67/9.46 f(V, X, f(X, Y, Z))
% 70.67/9.46 = { by axiom 2 (permute2) }
% 70.67/9.46 f(V, f(X, Y, Z), X)
% 70.67/9.46
% 70.67/9.46 Lemma 39: f(f(X, Y, Z), W, f(f(V, W, U), f(U, Y, Z), W)) = f(f(X, Y, Z), f(V, W, U), W).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(X, Y, Z), W, f(f(V, W, U), f(U, Y, Z), W))
% 70.67/9.46 = { by lemma 11 R->L }
% 70.67/9.46 f(f(V, W, U), W, f(W, f(X, Y, Z), f(U, Y, Z)))
% 70.67/9.46 = { by axiom 2 (permute2) R->L }
% 70.67/9.46 f(f(V, W, U), f(W, f(X, Y, Z), f(U, Y, Z)), W)
% 70.67/9.46 = { by lemma 7 R->L }
% 70.67/9.46 f(f(W, f(X, Y, Z), f(U, Y, Z)), f(V, W, U), W)
% 70.67/9.46 = { by lemma 25 }
% 70.67/9.46 f(V, W, f(W, U, f(W, f(X, Y, Z), f(U, Y, Z))))
% 70.67/9.46 = { by lemma 37 }
% 70.67/9.46 f(V, W, f(W, U, f(X, Y, Z)))
% 70.67/9.46 = { by lemma 25 R->L }
% 70.67/9.46 f(f(X, Y, Z), f(V, W, U), W)
% 70.67/9.46
% 70.67/9.46 Lemma 40: f(f(f(X, Y, Z), W, V), f(X, Y, Z), Y) = f(f(X, Y, Z), f(Z, W, V), Y).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(f(X, Y, Z), W, V), f(X, Y, Z), Y)
% 70.67/9.46 = { by axiom 2 (permute2) R->L }
% 70.67/9.46 f(f(f(X, Y, Z), W, V), Y, f(X, Y, Z))
% 70.67/9.46 = { by lemma 7 R->L }
% 70.67/9.46 f(Y, f(f(X, Y, Z), W, V), f(X, Y, Z))
% 70.67/9.46 = { by lemma 38 R->L }
% 70.67/9.46 f(f(f(X, Y, Z), W, V), f(X, Y, Z), f(f(X, Y, Z), f(Z, W, V), Y))
% 70.67/9.46 = { by lemma 10 }
% 70.67/9.46 f(f(Z, W, V), f(X, Y, Z), f(f(f(X, Y, Z), W, V), f(X, Y, Z), Y))
% 70.67/9.46 = { by lemma 39 R->L }
% 70.67/9.46 f(f(Z, W, V), f(X, Y, Z), f(f(f(X, Y, Z), W, V), Y, f(f(X, Y, Z), f(Z, W, V), Y)))
% 70.67/9.46 = { by axiom 2 (permute2) R->L }
% 70.67/9.46 f(f(Z, W, V), f(X, Y, Z), f(f(f(X, Y, Z), W, V), Y, f(f(X, Y, Z), Y, f(Z, W, V))))
% 70.67/9.46 = { by lemma 32 }
% 70.67/9.46 f(f(Z, W, V), f(X, Y, Z), Y)
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(X, Y, Z), f(Z, W, V), Y)
% 70.67/9.46
% 70.67/9.46 Lemma 41: f(f(X, f(W, V, U), f(Z, V, U)), f(X, Y, Z), X) = f(f(X, Y, Z), f(W, V, U), X).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(X, f(W, V, U), f(Z, V, U)), f(X, Y, Z), X)
% 70.67/9.46 = { by lemma 34 R->L }
% 70.67/9.46 f(f(X, Y, Z), X, f(X, Z, f(X, f(W, V, U), f(Z, V, U))))
% 70.67/9.46 = { by lemma 37 }
% 70.67/9.46 f(f(X, Y, Z), X, f(X, Z, f(W, V, U)))
% 70.67/9.46 = { by lemma 34 }
% 70.67/9.46 f(f(W, V, U), f(X, Y, Z), X)
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(X, Y, Z), f(W, V, U), X)
% 70.67/9.46
% 70.67/9.46 Lemma 42: f(f(X, Y, Z), W, f(f(V, f(X, Y, Z), f(U, Y, Z)), f(V, T, U), V)) = f(f(V, f(X, Y, Z), W), f(V, T, U), f(X, Y, Z)).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(X, Y, Z), W, f(f(V, f(X, Y, Z), f(U, Y, Z)), f(V, T, U), V))
% 70.67/9.46 = { by lemma 41 }
% 70.67/9.46 f(f(X, Y, Z), W, f(f(V, T, U), f(X, Y, Z), V))
% 70.67/9.46 = { by lemma 21 }
% 70.67/9.46 f(f(V, T, U), f(X, Y, Z), f(f(X, Y, Z), W, V))
% 70.67/9.46 = { by axiom 3 (permute1) }
% 70.67/9.46 f(f(V, T, U), f(X, Y, Z), f(V, f(X, Y, Z), W))
% 70.67/9.46 = { by axiom 2 (permute2) }
% 70.67/9.46 f(f(V, T, U), f(V, f(X, Y, Z), W), f(X, Y, Z))
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(V, f(X, Y, Z), W), f(V, T, U), f(X, Y, Z))
% 70.67/9.46
% 70.67/9.46 Lemma 43: f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, U, V), f(Y, Z, W)) = f(X, f(Y, Z, W), f(V, Z, W)).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, U, V), f(Y, Z, W))
% 70.67/9.46 = { by lemma 42 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, U, V), X))
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, U, V), f(X, f(Y, Z, W), f(V, Z, W)), X))
% 70.67/9.46 = { by axiom 3 (permute1) R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, f(Y, Z, W), f(V, Z, W)), X, f(X, U, V)))
% 70.67/9.46 = { by axiom 3 (permute1) R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, U, V), f(X, f(Y, Z, W), f(V, Z, W))))
% 70.67/9.46 = { by axiom 3 (permute1) R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, U, V), f(f(Y, Z, W), f(V, Z, W), X)))
% 70.67/9.46 = { by lemma 12 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(Y, Z, W), X, f(f(V, Z, W), X, f(X, U, V))))
% 70.67/9.46 = { by lemma 27 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), X)
% 70.67/9.46 = { by axiom 3 (permute1) }
% 70.67/9.46 f(X, f(Y, Z, W), f(V, Z, W))
% 70.67/9.46
% 70.67/9.46 Lemma 44: f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, Y, V), f(V, Z, W)) = f(X, f(Y, Z, W), f(V, Z, W)).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, Y, V), f(V, Z, W))
% 70.67/9.46 = { by lemma 7 R->L }
% 70.67/9.46 f(f(X, Y, V), f(X, f(Y, Z, W), f(V, Z, W)), f(V, Z, W))
% 70.67/9.46 = { by lemma 24 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, Y, V), f(V, Z, W), X))
% 70.67/9.46 = { by lemma 7 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(V, Z, W), f(X, Y, V), X))
% 70.67/9.46 = { by lemma 33 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, Y, V), X, f(X, Y, f(V, Z, W))))
% 70.67/9.46 = { by lemma 37 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, Y, V), X, f(X, Y, f(X, f(V, Z, W), f(Y, Z, W)))))
% 70.67/9.46 = { by lemma 33 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, f(V, Z, W), f(Y, Z, W)), f(X, Y, V), X))
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, Y, V), f(X, f(V, Z, W), f(Y, Z, W)), X))
% 70.67/9.46 = { by axiom 2 (permute2) }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, Y, V), X, f(X, f(V, Z, W), f(Y, Z, W))))
% 70.67/9.46 = { by lemma 11 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(V, Z, W), X, f(f(X, Y, V), f(Y, Z, W), X)))
% 70.67/9.46 = { by lemma 41 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(V, Z, W), X, f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, Y, V), X)))
% 70.67/9.46 = { by lemma 11 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, f(Y, Z, W), f(V, Z, W)), X, f(X, f(V, Z, W), f(X, Y, V))))
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, f(Y, Z, W), f(V, Z, W)), X, f(f(V, Z, W), X, f(X, Y, V))))
% 70.67/9.46 = { by lemma 12 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, Y, V), f(f(X, f(Y, Z, W), f(V, Z, W)), f(V, Z, W), X)))
% 70.67/9.46 = { by axiom 3 (permute1) R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, Y, V), f(f(V, Z, W), X, f(X, f(Y, Z, W), f(V, Z, W)))))
% 70.67/9.46 = { by axiom 3 (permute1) R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, Y, V), f(f(V, Z, W), X, f(f(Y, Z, W), f(V, Z, W), X))))
% 70.67/9.46 = { by lemma 8 R->L }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, Y, V), f(f(Y, Z, W), f(V, Z, W), f(X, f(V, Z, W), X))))
% 70.67/9.46 = { by lemma 5 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, Y, V), f(f(Y, Z, W), f(V, Z, W), X)))
% 70.67/9.46 = { by axiom 3 (permute1) }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(X, f(X, Y, V), f(X, f(Y, Z, W), f(V, Z, W))))
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, Y, V), X, f(X, f(Y, Z, W), f(V, Z, W))))
% 70.67/9.46 = { by axiom 2 (permute2) }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, Y, V), f(X, f(Y, Z, W), f(V, Z, W)), X))
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(Y, Z, W), f(V, Z, W), f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, Y, V), X))
% 70.67/9.46 = { by lemma 42 }
% 70.67/9.46 f(f(X, f(Y, Z, W), f(V, Z, W)), f(X, Y, V), f(Y, Z, W))
% 70.67/9.46 = { by lemma 43 }
% 70.67/9.46 f(X, f(Y, Z, W), f(V, Z, W))
% 70.67/9.46
% 70.67/9.46 Lemma 45: f(f(X, Y, Z), f(Z, W, V), f(U, f(X, f(Y, W, V), f(Z, W, V)), f(Z, W, V))) = f(U, f(X, f(Y, W, V), f(Z, W, V)), f(Z, W, V)).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(X, Y, Z), f(Z, W, V), f(U, f(X, f(Y, W, V), f(Z, W, V)), f(Z, W, V)))
% 70.67/9.46 = { by axiom 2 (permute2) R->L }
% 70.67/9.46 f(f(X, Y, Z), f(Z, W, V), f(U, f(Z, W, V), f(X, f(Y, W, V), f(Z, W, V))))
% 70.67/9.46 = { by lemma 7 R->L }
% 70.67/9.46 f(f(Z, W, V), f(X, Y, Z), f(U, f(Z, W, V), f(X, f(Y, W, V), f(Z, W, V))))
% 70.67/9.46 = { by lemma 20 R->L }
% 70.67/9.46 f(f(Z, W, V), f(f(X, f(Y, W, V), f(Z, W, V)), f(X, Y, Z), f(Z, W, V)), U)
% 70.67/9.46 = { by lemma 44 }
% 70.67/9.46 f(f(Z, W, V), f(X, f(Y, W, V), f(Z, W, V)), U)
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(f(X, f(Y, W, V), f(Z, W, V)), f(Z, W, V), U)
% 70.67/9.46 = { by axiom 2 (permute2) }
% 70.67/9.46 f(f(X, f(Y, W, V), f(Z, W, V)), U, f(Z, W, V))
% 70.67/9.46 = { by lemma 7 }
% 70.67/9.46 f(U, f(X, f(Y, W, V), f(Z, W, V)), f(Z, W, V))
% 70.67/9.46
% 70.67/9.46 Goal 1 (dist_long): f(f(x, y, z), u, w) = f(x, f(y, u, w), f(z, u, w)).
% 70.67/9.46 Proof:
% 70.67/9.46 f(f(x, y, z), u, w)
% 70.67/9.46 = { by lemma 5 R->L }
% 70.67/9.46 f(f(f(x, y, z), u, w), y, f(f(x, y, z), u, w))
% 70.67/9.46 = { by lemma 35 R->L }
% 70.67/9.46 f(f(f(x, y, z), u, w), y, f(f(f(x, y, z), u, w), f(x, y, z), f(z, u, w)))
% 70.67/9.46 = { by lemma 19 R->L }
% 70.67/9.46 f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), y, f(x, y, z)))
% 70.67/9.46 = { by lemma 19 R->L }
% 70.67/9.46 f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, y, z), u, w), f(z, u, w), y))
% 70.67/9.46 = { by lemma 18 }
% 70.67/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, y, z), y))
% 70.67/9.47 = { by lemma 40 }
% 70.67/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(z, u, w), y))
% 70.67/9.47 = { by lemma 6 R->L }
% 70.67/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(z, u, w), f(f(z, u, w), y, y)))
% 70.67/9.47 = { by lemma 10 }
% 70.67/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(y, f(z, u, w), f(f(x, y, z), f(z, u, w), y)))
% 70.67/9.47 = { by lemma 40 R->L }
% 70.67/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(y, f(z, u, w), f(f(f(x, y, z), u, w), f(x, y, z), y)))
% 70.67/9.47 = { by lemma 28 R->L }
% 70.67/9.47 f(y, f(z, u, w), f(f(x, y, z), f(f(x, y, z), u, w), f(f(z, u, w), f(f(x, y, z), u, w), y)))
% 70.67/9.47 = { by lemma 32 }
% 70.67/9.47 f(y, f(z, u, w), f(f(x, y, z), u, w))
% 70.67/9.47 = { by axiom 2 (permute2) }
% 70.67/9.47 f(y, f(f(x, y, z), u, w), f(z, u, w))
% 70.67/9.47 = { by lemma 7 }
% 70.67/9.47 f(f(f(x, y, z), u, w), y, f(z, u, w))
% 70.67/9.47 = { by lemma 32 R->L }
% 70.67/9.47 f(f(f(x, y, z), u, w), y, f(f(x, y, z), f(z, u, w), f(y, f(z, u, w), f(f(x, y, z), u, w))))
% 70.67/9.47 = { by lemma 29 R->L }
% 70.67/9.47 f(f(z, u, w), f(f(x, y, z), u, w), f(f(f(x, y, z), f(z, u, w), y), f(f(x, y, z), u, w), y))
% 70.67/9.47 = { by lemma 7 }
% 70.67/9.47 f(f(z, u, w), f(f(x, y, z), u, w), f(f(f(x, y, z), u, w), f(f(x, y, z), f(z, u, w), y), y))
% 70.67/9.47 = { by axiom 2 (permute2) }
% 70.67/9.47 f(f(z, u, w), f(f(x, y, z), u, w), f(f(f(x, y, z), u, w), y, f(f(x, y, z), f(z, u, w), y)))
% 70.67/9.47 = { by lemma 39 }
% 70.67/9.47 f(f(z, u, w), f(f(x, y, z), u, w), f(f(f(x, y, z), u, w), f(x, y, z), y))
% 70.67/9.47 = { by lemma 40 }
% 70.67/9.47 f(f(z, u, w), f(f(x, y, z), u, w), f(f(x, y, z), f(z, u, w), y))
% 70.67/9.47 = { by lemma 14 }
% 70.67/9.47 f(f(z, u, w), f(x, y, z), f(f(f(x, y, z), u, w), y, f(z, u, w)))
% 70.67/9.47 = { by lemma 7 }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), y, f(z, u, w)))
% 70.67/9.47 = { by lemma 37 R->L }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), y, f(f(f(x, y, z), u, w), f(z, u, w), f(y, u, w))))
% 70.67/9.47 = { by lemma 18 R->L }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), y, f(y, u, w))))
% 70.67/9.47 = { by axiom 2 (permute2) }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(y, u, w), y)))
% 70.67/9.47 = { by lemma 18 R->L }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), y)))
% 70.67/9.47 = { by lemma 17 R->L }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), f(f(f(x, y, z), u, w), f(y, u, w), y), f(z, u, w)))
% 70.67/9.47 = { by lemma 7 R->L }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), f(f(y, u, w), f(f(x, y, z), u, w), y), f(z, u, w)))
% 70.67/9.47 = { by axiom 2 (permute2) R->L }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), f(f(y, u, w), y, f(f(x, y, z), u, w)), f(z, u, w)))
% 70.67/9.47 = { by lemma 35 }
% 70.67/9.47 f(f(x, y, z), f(z, u, w), f(f(f(x, y, z), u, w), f(y, u, w), f(z, u, w)))
% 70.67/9.47 = { by lemma 11 R->L }
% 70.67/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(z, u, w), f(x, y, z), f(y, u, w)))
% 70.67/9.47 = { by lemma 7 }
% 70.67/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(z, u, w), f(y, u, w)))
% 70.85/9.47 = { by axiom 2 (permute2) }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(y, u, w), f(z, u, w)))
% 70.85/9.47 = { by lemma 36 R->L }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(y, u, w), f(f(x, y, z), f(z, u, w), f(f(x, f(y, u, w), f(z, u, w)), f(x, f(y, u, w), f(z, u, w)), f(z, u, w)))))
% 70.85/9.47 = { by lemma 45 }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(y, u, w), f(f(x, f(y, u, w), f(z, u, w)), f(x, f(y, u, w), f(z, u, w)), f(z, u, w))))
% 70.85/9.47 = { by axiom 1 (majority) }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(y, u, w), f(x, f(y, u, w), f(z, u, w))))
% 70.85/9.47 = { by axiom 2 (permute2) }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(y, u, w)))
% 70.85/9.47 = { by lemma 7 }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, f(y, u, w), f(z, u, w)), f(x, y, z), f(y, u, w)))
% 70.85/9.47 = { by lemma 43 }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(z, u, w), f(x, f(y, u, w), f(z, u, w)))
% 70.85/9.47 = { by axiom 2 (permute2) }
% 70.85/9.47 f(f(f(x, y, z), u, w), f(x, f(y, u, w), f(z, u, w)), f(z, u, w))
% 70.85/9.47 = { by lemma 7 R->L }
% 70.85/9.47 f(f(x, f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w), f(z, u, w))
% 70.85/9.47 = { by axiom 2 (permute2) R->L }
% 70.85/9.47 f(f(x, f(y, u, w), f(z, u, w)), f(z, u, w), f(f(x, y, z), u, w))
% 70.85/9.47 = { by lemma 7 R->L }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w))
% 70.85/9.47 = { by lemma 35 R->L }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(z, u, w)))
% 70.85/9.47 = { by axiom 2 (permute2) R->L }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(z, u, w), f(x, y, z)))
% 70.85/9.47 = { by lemma 7 R->L }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(z, u, w), f(f(x, y, z), u, w), f(x, y, z)))
% 70.85/9.47 = { by lemma 38 R->L }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(x, y, z), f(y, u, w), f(z, u, w))))
% 70.85/9.47 = { by lemma 36 R->L }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(x, y, z), f(y, u, w), f(f(x, y, z), f(z, u, w), f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(z, u, w))))))
% 70.85/9.47 = { by lemma 38 }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), f(z, u, w), f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(z, u, w))), f(f(x, y, z), u, w), f(x, y, z)))
% 70.85/9.47 = { by lemma 45 }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(z, u, w)), f(f(x, y, z), u, w), f(x, y, z)))
% 70.85/9.47 = { by lemma 7 }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(z, u, w)), f(x, y, z)))
% 70.85/9.47 = { by axiom 2 (permute2) }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(z, u, w))))
% 70.85/9.47 = { by lemma 22 R->L }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(f(x, y, z), f(z, u, w), f(f(x, y, z), u, w))))
% 70.85/9.47 = { by lemma 10 R->L }
% 70.85/9.47 f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(f(x, f(y, u, w), f(z, u, w)), f(z, u, w), f(f(x, y, z), f(z, u, w), f(f(x, y, z), u, w))))
% 70.85/9.47 = { by lemma 10 R->L }
% 70.85/9.47 f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(f(x, y, z), f(z, u, w), f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w))))
% 70.85/9.47 = { by lemma 18 R->L }
% 70.85/9.47 f(f(x, y, z), f(z, u, w), f(f(x, y, z), f(x, f(y, u, w), f(z, u, w)), f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w))))
% 70.85/9.47 = { by lemma 27 }
% 70.85/9.47 f(f(x, y, z), f(z, u, w), f(x, f(y, u, w), f(z, u, w)))
% 70.85/9.47 = { by lemma 7 }
% 70.85/9.47 f(f(z, u, w), f(x, y, z), f(x, f(y, u, w), f(z, u, w)))
% 70.85/9.47 = { by axiom 2 (permute2) }
% 70.85/9.47 f(f(z, u, w), f(x, f(y, u, w), f(z, u, w)), f(x, y, z))
% 70.85/9.47 = { by lemma 7 }
% 70.85/9.47 f(f(x, f(y, u, w), f(z, u, w)), f(z, u, w), f(x, y, z))
% 70.85/9.47 = { by axiom 2 (permute2) }
% 70.85/9.47 f(f(x, f(y, u, w), f(z, u, w)), f(x, y, z), f(z, u, w))
% 70.85/9.47 = { by lemma 44 }
% 70.85/9.47 f(x, f(y, u, w), f(z, u, w))
% 70.85/9.47 % SZS output end Proof
% 70.85/9.47
% 70.85/9.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------