TSTP Solution File: ALG212+1 by Twee---2.5.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : ALG212+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n003.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 : Mon Jun 24 04:04:41 EDT 2024
% Result : Theorem 140.74s 18.06s
% Output : Proof 141.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ALG212+1 : TPTP v8.2.0. Released v3.2.0.
% 0.04/0.13 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jun 19 17:30:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 140.74/18.06 Command-line arguments: --ground-connectedness --complete-subsets
% 140.74/18.06
% 140.74/18.06 % SZS status Theorem
% 140.74/18.06
% 141.45/18.15 % SZS output start Proof
% 141.45/18.15 Axiom 1 (majority): f(X, X, Y) = X.
% 141.45/18.15 Axiom 2 (permute2): f(X, Y, Z) = f(X, Z, Y).
% 141.45/18.15 Axiom 3 (permute1): f(X, Y, Z) = f(Z, X, Y).
% 141.45/18.15 Axiom 4 (associativity): f(f(X, Y, Z), Y, W) = f(X, Y, f(Z, Y, W)).
% 141.45/18.15
% 141.45/18.15 Lemma 5: f(X, Y, X) = X.
% 141.45/18.15 Proof:
% 141.45/18.15 f(X, Y, X)
% 141.45/18.15 = { by axiom 2 (permute2) R->L }
% 141.45/18.15 f(X, X, Y)
% 141.45/18.15 = { by axiom 1 (majority) }
% 141.45/18.15 X
% 141.45/18.15
% 141.45/18.15 Lemma 6: f(Y, X, Z) = f(X, Y, Z).
% 141.45/18.15 Proof:
% 141.45/18.15 f(Y, X, Z)
% 141.45/18.15 = { by axiom 3 (permute1) R->L }
% 141.45/18.15 f(X, Z, Y)
% 141.45/18.15 = { by axiom 2 (permute2) }
% 141.45/18.15 f(X, Y, Z)
% 141.45/18.15
% 141.45/18.15 Lemma 7: f(Z, X, f(W, X, Y)) = f(X, Y, f(Z, X, W)).
% 141.45/18.15 Proof:
% 141.45/18.15 f(Z, X, f(W, X, Y))
% 141.45/18.15 = { by axiom 4 (associativity) R->L }
% 141.45/18.15 f(f(Z, X, W), X, Y)
% 141.45/18.15 = { by axiom 3 (permute1) R->L }
% 141.45/18.15 f(X, Y, f(Z, X, W))
% 141.45/18.15
% 141.45/18.15 Lemma 8: f(X, Y, f(X, Y, Z)) = f(X, Y, Z).
% 141.45/18.15 Proof:
% 141.45/18.15 f(X, Y, f(X, Y, Z))
% 141.45/18.15 = { by lemma 7 }
% 141.45/18.15 f(Y, Z, f(X, Y, X))
% 141.45/18.15 = { by lemma 5 }
% 141.45/18.15 f(Y, Z, X)
% 141.45/18.15 = { by axiom 3 (permute1) }
% 141.45/18.16 f(X, Y, Z)
% 141.45/18.16
% 141.45/18.16 Lemma 9: f(X, f(Y, X, Z), W) = f(X, Z, f(W, X, Y)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, f(Y, X, Z), W)
% 141.45/18.16 = { by axiom 3 (permute1) R->L }
% 141.45/18.16 f(f(Y, X, Z), W, X)
% 141.45/18.16 = { by axiom 3 (permute1) R->L }
% 141.45/18.16 f(W, X, f(Y, X, Z))
% 141.45/18.16 = { by lemma 7 }
% 141.45/18.16 f(X, Z, f(W, X, Y))
% 141.45/18.16
% 141.45/18.16 Lemma 10: f(X, f(X, Y, Z), W) = f(X, Y, f(X, W, Z)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, f(X, Y, Z), W)
% 141.45/18.16 = { by axiom 3 (permute1) }
% 141.45/18.16 f(X, f(Z, X, Y), W)
% 141.45/18.16 = { by lemma 9 }
% 141.45/18.16 f(X, Y, f(W, X, Z))
% 141.45/18.16 = { by lemma 6 R->L }
% 141.45/18.16 f(X, Y, f(X, W, Z))
% 141.45/18.16
% 141.45/18.16 Lemma 11: f(X, Y, f(X, Z, W)) = f(X, Z, f(X, Y, W)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, Y, f(X, Z, W))
% 141.45/18.16 = { by axiom 2 (permute2) R->L }
% 141.45/18.16 f(X, f(X, Z, W), Y)
% 141.45/18.16 = { by lemma 10 }
% 141.45/18.16 f(X, Z, f(X, Y, W))
% 141.45/18.16
% 141.45/18.16 Lemma 12: f(X, W, f(X, Y, Z)) = f(X, Y, f(X, Z, W)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, W, f(X, Y, Z))
% 141.45/18.16 = { by axiom 2 (permute2) R->L }
% 141.45/18.16 f(X, W, f(X, Z, Y))
% 141.45/18.16 = { by lemma 10 R->L }
% 141.45/18.16 f(X, f(X, W, Y), Z)
% 141.45/18.16 = { by lemma 6 }
% 141.45/18.16 f(X, f(W, X, Y), Z)
% 141.45/18.16 = { by lemma 9 }
% 141.45/18.16 f(X, Y, f(Z, X, W))
% 141.45/18.16 = { by lemma 6 R->L }
% 141.45/18.16 f(X, Y, f(X, Z, W))
% 141.45/18.16
% 141.45/18.16 Lemma 13: f(X, Y, f(Y, Z, W)) = f(Y, Z, f(Y, W, X)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, Y, f(Y, Z, W))
% 141.45/18.16 = { by lemma 6 }
% 141.45/18.16 f(Y, X, f(Y, Z, W))
% 141.45/18.16 = { by lemma 12 }
% 141.45/18.16 f(Y, Z, f(Y, W, X))
% 141.45/18.16
% 141.45/18.16 Lemma 14: f(Z, Y, f(Y, X, W)) = f(X, Y, f(Z, Y, W)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(Z, Y, f(Y, X, W))
% 141.45/18.16 = { by axiom 3 (permute1) }
% 141.45/18.16 f(Z, Y, f(W, Y, X))
% 141.45/18.16 = { by lemma 7 }
% 141.45/18.16 f(Y, X, f(Z, Y, W))
% 141.45/18.16 = { by axiom 3 (permute1) R->L }
% 141.45/18.16 f(X, f(Z, Y, W), Y)
% 141.45/18.16 = { by axiom 2 (permute2) }
% 141.45/18.16 f(X, Y, f(Z, Y, W))
% 141.45/18.16
% 141.45/18.16 Lemma 15: f(X, Y, f(Y, Z, W)) = f(Z, Y, f(X, W, Y)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, Y, f(Y, Z, W))
% 141.45/18.16 = { by lemma 14 }
% 141.45/18.16 f(Z, Y, f(X, Y, W))
% 141.45/18.16 = { by axiom 2 (permute2) }
% 141.45/18.16 f(Z, Y, f(X, W, Y))
% 141.45/18.16
% 141.45/18.16 Lemma 16: f(X, Y, f(Z, Y, W)) = f(Y, W, f(X, Z, Y)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, Y, f(Z, Y, W))
% 141.45/18.16 = { by lemma 7 }
% 141.45/18.16 f(Y, W, f(X, Y, Z))
% 141.45/18.16 = { by axiom 2 (permute2) }
% 141.45/18.16 f(Y, W, f(X, Z, Y))
% 141.45/18.16
% 141.45/18.16 Lemma 17: f(X, W, f(Y, X, Z)) = f(X, Y, f(Z, W, X)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, W, f(Y, X, Z))
% 141.45/18.16 = { by lemma 6 }
% 141.45/18.16 f(W, X, f(Y, X, Z))
% 141.45/18.16 = { by lemma 7 }
% 141.45/18.16 f(X, Z, f(W, X, Y))
% 141.45/18.16 = { by axiom 2 (permute2) }
% 141.45/18.16 f(X, f(W, X, Y), Z)
% 141.45/18.16 = { by axiom 3 (permute1) R->L }
% 141.45/18.16 f(f(W, X, Y), Z, X)
% 141.45/18.16 = { by axiom 3 (permute1) R->L }
% 141.45/18.16 f(Z, X, f(W, X, Y))
% 141.45/18.16 = { by lemma 16 }
% 141.45/18.16 f(X, Y, f(Z, W, X))
% 141.45/18.16
% 141.45/18.16 Lemma 18: f(X, Y, f(Z, X, W)) = f(X, Z, f(Y, W, X)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, Y, f(Z, X, W))
% 141.45/18.16 = { by lemma 17 }
% 141.45/18.16 f(X, Z, f(W, Y, X))
% 141.45/18.16 = { by lemma 6 R->L }
% 141.45/18.16 f(X, Z, f(Y, W, X))
% 141.45/18.16
% 141.45/18.16 Lemma 19: f(Y, Z, f(X, Y, W)) = f(X, Y, f(Y, Z, W)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(Y, Z, f(X, Y, W))
% 141.45/18.16 = { by lemma 6 }
% 141.45/18.16 f(Z, Y, f(X, Y, W))
% 141.45/18.16 = { by lemma 14 R->L }
% 141.45/18.16 f(X, Y, f(Y, Z, W))
% 141.45/18.16
% 141.45/18.16 Lemma 20: f(X, Y, f(Z, X, W)) = f(Z, f(X, Y, W), X).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, Y, f(Z, X, W))
% 141.45/18.16 = { by lemma 19 }
% 141.45/18.16 f(Z, X, f(X, Y, W))
% 141.45/18.16 = { by axiom 2 (permute2) }
% 141.45/18.16 f(Z, f(X, Y, W), X)
% 141.45/18.16
% 141.45/18.16 Lemma 21: f(X, Y, f(Z, Y, W)) = f(Y, Z, f(W, Y, X)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(X, Y, f(Z, Y, W))
% 141.45/18.16 = { by lemma 16 }
% 141.45/18.16 f(Y, W, f(X, Z, Y))
% 141.45/18.16 = { by lemma 17 R->L }
% 141.45/18.16 f(Y, Z, f(W, Y, X))
% 141.45/18.16
% 141.45/18.16 Lemma 22: f(Z, f(X, Y, W), Y) = f(X, Y, f(Z, Y, W)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(Z, f(X, Y, W), Y)
% 141.45/18.16 = { by axiom 3 (permute1) R->L }
% 141.45/18.16 f(f(X, Y, W), Y, Z)
% 141.45/18.16 = { by axiom 3 (permute1) R->L }
% 141.45/18.16 f(Y, Z, f(X, Y, W))
% 141.45/18.16 = { by lemma 7 R->L }
% 141.45/18.16 f(X, Y, f(W, Y, Z))
% 141.45/18.16 = { by lemma 6 R->L }
% 141.45/18.16 f(X, Y, f(Y, W, Z))
% 141.45/18.16 = { by axiom 3 (permute1) }
% 141.45/18.16 f(X, Y, f(Z, Y, W))
% 141.45/18.16
% 141.45/18.16 Lemma 23: f(W, f(X, Y, Z), Y) = f(X, Y, f(Y, Z, W)).
% 141.45/18.16 Proof:
% 141.45/18.16 f(W, f(X, Y, Z), Y)
% 141.45/18.16 = { by lemma 22 }
% 141.45/18.16 f(X, Y, f(W, Y, Z))
% 141.66/18.16 = { by axiom 3 (permute1) R->L }
% 141.66/18.16 f(Y, f(W, Y, Z), X)
% 141.66/18.16 = { by lemma 9 }
% 141.66/18.16 f(Y, Z, f(X, Y, W))
% 141.66/18.16 = { by lemma 19 }
% 141.66/18.16 f(X, Y, f(Y, Z, W))
% 141.66/18.16
% 141.66/18.16 Lemma 24: f(f(X, Y, Z), X, Y) = f(X, Y, Z).
% 141.66/18.16 Proof:
% 141.66/18.16 f(f(X, Y, Z), X, Y)
% 141.66/18.16 = { by axiom 3 (permute1) R->L }
% 141.66/18.16 f(X, Y, f(X, Y, Z))
% 141.66/18.16 = { by lemma 8 }
% 141.66/18.16 f(X, Y, Z)
% 141.66/18.16
% 141.66/18.16 Lemma 25: f(f(X, Y, Z), X, Z) = f(X, Y, Z).
% 141.66/18.16 Proof:
% 141.66/18.16 f(f(X, Y, Z), X, Z)
% 141.66/18.16 = { by axiom 3 (permute1) R->L }
% 141.66/18.16 f(X, Z, f(X, Y, Z))
% 141.66/18.16 = { by axiom 2 (permute2) R->L }
% 141.66/18.16 f(X, Z, f(X, Z, Y))
% 141.66/18.16 = { by lemma 7 }
% 141.66/18.16 f(Z, Y, f(X, Z, X))
% 141.66/18.16 = { by lemma 5 }
% 141.66/18.16 f(Z, Y, X)
% 141.66/18.16 = { by axiom 3 (permute1) }
% 141.66/18.16 f(X, Z, Y)
% 141.66/18.16 = { by axiom 2 (permute2) }
% 141.66/18.16 f(X, Y, Z)
% 141.66/18.16
% 141.66/18.16 Lemma 26: f(X, Y, f(X, Z, f(Y, Z, W))) = f(X, Y, Z).
% 141.66/18.16 Proof:
% 141.66/18.16 f(X, Y, f(X, Z, f(Y, Z, W)))
% 141.66/18.16 = { by lemma 6 }
% 141.66/18.16 f(X, Y, f(X, Z, f(Z, Y, W)))
% 141.66/18.16 = { by lemma 15 }
% 141.66/18.16 f(X, Y, f(Y, Z, f(X, W, Z)))
% 141.66/18.16 = { by lemma 6 }
% 141.66/18.16 f(X, Y, f(Y, Z, f(W, X, Z)))
% 141.66/18.16 = { by lemma 8 R->L }
% 141.66/18.16 f(X, Y, f(X, Y, f(Y, Z, f(W, X, Z))))
% 141.66/18.16 = { by lemma 19 R->L }
% 141.66/18.16 f(X, Y, f(Y, Z, f(X, Y, f(W, X, Z))))
% 141.66/18.16 = { by lemma 19 }
% 141.66/18.16 f(X, Y, f(Y, Z, f(W, X, f(X, Y, Z))))
% 141.66/18.16 = { by lemma 6 }
% 141.66/18.16 f(Y, X, f(Y, Z, f(W, X, f(X, Y, Z))))
% 141.66/18.16 = { by lemma 11 R->L }
% 141.66/18.16 f(Y, Z, f(Y, X, f(W, X, f(X, Y, Z))))
% 141.66/18.16 = { by axiom 2 (permute2) R->L }
% 141.66/18.16 f(Y, Z, f(Y, X, f(W, f(X, Y, Z), X)))
% 141.66/18.16 = { by axiom 2 (permute2) R->L }
% 141.66/18.16 f(Y, Z, f(Y, f(W, f(X, Y, Z), X), X))
% 141.66/18.16 = { by lemma 6 }
% 141.66/18.16 f(Y, Z, f(f(W, f(X, Y, Z), X), Y, X))
% 141.66/18.16 = { by lemma 9 R->L }
% 141.66/18.16 f(Y, f(X, Y, Z), f(W, f(X, Y, Z), X))
% 141.66/18.16 = { by lemma 6 }
% 141.66/18.16 f(f(X, Y, Z), Y, f(W, f(X, Y, Z), X))
% 141.66/18.16 = { by lemma 17 }
% 141.66/18.16 f(f(X, Y, Z), W, f(X, Y, f(X, Y, Z)))
% 141.66/18.16 = { by axiom 2 (permute2) }
% 141.66/18.16 f(f(X, Y, Z), f(X, Y, f(X, Y, Z)), W)
% 141.66/18.16 = { by lemma 8 }
% 141.66/18.16 f(f(X, Y, Z), f(X, Y, Z), W)
% 141.66/18.16 = { by axiom 1 (majority) }
% 141.66/18.16 f(X, Y, Z)
% 141.66/18.16
% 141.66/18.16 Lemma 27: f(Z, Y, f(W, X, f(X, Y, V))) = f(X, Y, f(Z, Y, f(W, X, V))).
% 141.66/18.16 Proof:
% 141.66/18.16 f(Z, Y, f(W, X, f(X, Y, V)))
% 141.66/18.16 = { by lemma 14 }
% 141.66/18.16 f(Z, Y, f(Y, X, f(W, X, V)))
% 141.66/18.16 = { by lemma 14 }
% 141.66/18.16 f(X, Y, f(Z, Y, f(W, X, V)))
% 141.66/18.16
% 141.66/18.16 Lemma 28: f(X, Y, f(Z, Y, f(Z, X, W))) = f(Z, X, Y).
% 141.66/18.16 Proof:
% 141.66/18.16 f(X, Y, f(Z, Y, f(Z, X, W)))
% 141.66/18.16 = { by lemma 27 R->L }
% 141.66/18.16 f(Z, Y, f(Z, X, f(X, Y, W)))
% 141.66/18.16 = { by lemma 11 }
% 141.66/18.16 f(Z, X, f(Z, Y, f(X, Y, W)))
% 141.66/18.16 = { by lemma 26 }
% 141.66/18.16 f(Z, X, Y)
% 141.66/18.16
% 141.66/18.16 Lemma 29: f(X, Y, f(Z, W, f(W, Y, X))) = f(W, X, Y).
% 141.66/18.16 Proof:
% 141.66/18.16 f(X, Y, f(Z, W, f(W, Y, X)))
% 141.66/18.16 = { by lemma 13 }
% 141.66/18.16 f(X, Y, f(W, Y, f(W, X, Z)))
% 141.66/18.16 = { by lemma 28 }
% 141.66/18.16 f(W, X, Y)
% 141.66/18.16
% 141.66/18.16 Lemma 30: f(X, f(Y, Z, W), f(X, Z, W)) = f(X, Z, W).
% 141.66/18.16 Proof:
% 141.66/18.16 f(X, f(Y, Z, W), f(X, Z, W))
% 141.66/18.16 = { by axiom 2 (permute2) R->L }
% 141.66/18.16 f(X, f(Y, Z, W), f(X, W, Z))
% 141.66/18.16 = { by lemma 11 R->L }
% 141.66/18.16 f(X, W, f(X, f(Y, Z, W), Z))
% 141.66/18.16 = { by lemma 23 }
% 141.66/18.16 f(X, W, f(Y, Z, f(Z, W, X)))
% 141.66/18.16 = { by lemma 29 }
% 141.66/18.16 f(Z, X, W)
% 141.66/18.16 = { by lemma 6 R->L }
% 141.66/18.16 f(X, Z, W)
% 141.66/18.16
% 141.66/18.16 Lemma 31: f(f(X, Y, Z), X, f(X, Y, W)) = f(W, f(X, Y, Z), X).
% 141.66/18.16 Proof:
% 141.66/18.16 f(f(X, Y, Z), X, f(X, Y, W))
% 141.66/18.16 = { by lemma 6 }
% 141.66/18.16 f(f(X, Y, Z), X, f(Y, X, W))
% 141.66/18.16 = { by lemma 21 }
% 141.66/18.16 f(X, Y, f(W, X, f(X, Y, Z)))
% 141.66/18.16 = { by lemma 7 R->L }
% 141.66/18.16 f(W, X, f(f(X, Y, Z), X, Y))
% 141.66/18.16 = { by lemma 24 }
% 141.66/18.16 f(W, X, f(X, Y, Z))
% 141.66/18.16 = { by axiom 2 (permute2) }
% 141.66/18.16 f(W, f(X, Y, Z), X)
% 141.66/18.16
% 141.66/18.16 Lemma 32: f(f(X, Y, Z), X, f(W, Y, Z)) = f(X, Y, Z).
% 141.66/18.16 Proof:
% 141.66/18.16 f(f(X, Y, Z), X, f(W, Y, Z))
% 141.66/18.16 = { by axiom 2 (permute2) R->L }
% 141.66/18.16 f(f(X, Y, Z), f(W, Y, Z), X)
% 141.66/18.16 = { by lemma 6 }
% 141.66/18.16 f(f(W, Y, Z), f(X, Y, Z), X)
% 141.66/18.16 = { by lemma 31 R->L }
% 141.66/18.16 f(f(X, Y, Z), X, f(X, Y, f(W, Y, Z)))
% 141.66/18.16 = { by lemma 22 R->L }
% 141.66/18.16 f(f(X, Y, Z), X, f(W, f(X, Y, Z), Y))
% 141.66/18.16 = { by lemma 19 }
% 141.66/18.16 f(W, f(X, Y, Z), f(f(X, Y, Z), X, Y))
% 141.66/18.16 = { by lemma 24 }
% 141.66/18.16 f(W, f(X, Y, Z), f(X, Y, Z))
% 141.66/18.16 = { by axiom 3 (permute1) R->L }
% 141.66/18.16 f(f(X, Y, Z), f(X, Y, Z), W)
% 141.66/18.16 = { by axiom 1 (majority) }
% 141.66/18.16 f(X, Y, Z)
% 141.66/18.16
% 141.66/18.16 Lemma 33: f(f(X, Y, Z), f(W, Y, Z), X) = f(X, Y, Z).
% 141.66/18.16 Proof:
% 141.66/18.16 f(f(X, Y, Z), f(W, Y, Z), X)
% 141.66/18.16 = { by axiom 2 (permute2) R->L }
% 141.66/18.16 f(f(X, Y, Z), X, f(W, Y, Z))
% 141.66/18.16 = { by lemma 32 }
% 141.66/18.16 f(X, Y, Z)
% 141.66/18.16
% 141.66/18.16 Lemma 34: f(f(X, Y, Z), f(W, Y, Z), W) = f(W, Y, Z).
% 141.66/18.16 Proof:
% 141.66/18.17 f(f(X, Y, Z), f(W, Y, Z), W)
% 141.66/18.17 = { by lemma 6 }
% 141.66/18.17 f(f(W, Y, Z), f(X, Y, Z), W)
% 141.66/18.17 = { by axiom 2 (permute2) R->L }
% 141.66/18.17 f(f(W, Y, Z), W, f(X, Y, Z))
% 141.66/18.17 = { by lemma 32 }
% 141.66/18.17 f(W, Y, Z)
% 141.66/18.17
% 141.66/18.17 Lemma 35: f(f(X, Y, Z), f(W, Y, Z), f(f(X, Y, Z), X, V)) = f(X, Y, Z).
% 141.66/18.17 Proof:
% 141.66/18.17 f(f(X, Y, Z), f(W, Y, Z), f(f(X, Y, Z), X, V))
% 141.66/18.17 = { by lemma 12 }
% 141.66/18.17 f(f(X, Y, Z), X, f(f(X, Y, Z), V, f(W, Y, Z)))
% 141.66/18.17 = { by lemma 12 }
% 141.66/18.17 f(f(X, Y, Z), V, f(f(X, Y, Z), f(W, Y, Z), X))
% 141.66/18.17 = { by lemma 33 }
% 141.66/18.17 f(f(X, Y, Z), V, f(X, Y, Z))
% 141.66/18.17 = { by lemma 5 }
% 141.66/18.17 f(X, Y, Z)
% 141.66/18.17
% 141.66/18.17 Lemma 36: f(f(X, Y, Z), f(W, Y, Z), f(f(X, Y, Z), V, W)) = f(V, f(X, Y, Z), f(W, Y, Z)).
% 141.66/18.17 Proof:
% 141.66/18.17 f(f(X, Y, Z), f(W, Y, Z), f(f(X, Y, Z), V, W))
% 141.66/18.17 = { by lemma 10 R->L }
% 141.66/18.17 f(f(X, Y, Z), f(f(X, Y, Z), f(W, Y, Z), W), V)
% 141.66/18.17 = { by lemma 34 }
% 141.66/18.17 f(f(X, Y, Z), f(W, Y, Z), V)
% 141.66/18.17 = { by axiom 2 (permute2) }
% 141.66/18.17 f(f(X, Y, Z), V, f(W, Y, Z))
% 141.66/18.17 = { by lemma 6 R->L }
% 141.66/18.17 f(V, f(X, Y, Z), f(W, Y, Z))
% 141.66/18.17
% 141.66/18.17 Lemma 37: f(f(f(X, Y, Z), f(W, Y, Z), V), f(X, Y, Z), W) = f(f(X, Y, Z), f(W, Y, Z), V).
% 141.66/18.17 Proof:
% 141.66/18.17 f(f(f(X, Y, Z), f(W, Y, Z), V), f(X, Y, Z), W)
% 141.66/18.17 = { by axiom 2 (permute2) R->L }
% 141.66/18.17 f(f(f(X, Y, Z), f(W, Y, Z), V), W, f(X, Y, Z))
% 141.66/18.17 = { by lemma 6 }
% 141.66/18.17 f(W, f(f(X, Y, Z), f(W, Y, Z), V), f(X, Y, Z))
% 141.66/18.17 = { by lemma 31 R->L }
% 141.66/18.17 f(f(f(X, Y, Z), f(W, Y, Z), V), f(X, Y, Z), f(f(X, Y, Z), f(W, Y, Z), W))
% 141.66/18.17 = { by lemma 34 }
% 141.66/18.17 f(f(f(X, Y, Z), f(W, Y, Z), V), f(X, Y, Z), f(W, Y, Z))
% 141.66/18.17 = { by lemma 24 }
% 141.66/18.17 f(f(X, Y, Z), f(W, Y, Z), V)
% 141.66/18.17
% 141.66/18.17 Goal 1 (dist_long): f(f(x, y, z), u, w) = f(f(x, u, w), f(y, u, w), f(z, u, w)).
% 141.66/18.17 Proof:
% 141.66/18.17 f(f(x, y, z), u, w)
% 141.66/18.17 = { by lemma 5 R->L }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(x, y, z), u, w))
% 141.66/18.17 = { by lemma 35 R->L }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, y, z), u, w), x, y))))
% 141.66/18.17 = { by lemma 11 R->L }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), x, f(f(f(x, y, z), u, w), f(x, y, z), y))))
% 141.66/18.17 = { by axiom 2 (permute2) R->L }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), x, f(f(f(x, y, z), u, w), y, f(x, y, z)))))
% 141.66/18.17 = { by lemma 26 }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), x, y)))
% 141.66/18.17 = { by axiom 2 (permute2) }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), y, x)))
% 141.66/18.17 = { by lemma 36 }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(y, f(f(x, y, z), u, w), f(x, u, w)))
% 141.66/18.17 = { by lemma 6 R->L }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), y, f(x, u, w)))
% 141.66/18.17 = { by axiom 2 (permute2) }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(x, u, w), y))
% 141.66/18.17 = { by lemma 36 }
% 141.66/18.17 f(f(x, u, w), f(f(x, y, z), u, w), f(y, u, w))
% 141.66/18.17 = { by axiom 2 (permute2) R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(x, y, z), u, w))
% 141.66/18.17 = { by lemma 5 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(x, y, z), u, w)))
% 141.66/18.17 = { by lemma 35 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, y, z), u, w), x, z)))))
% 141.66/18.17 = { by lemma 6 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), f(x, y, z), f(x, f(f(x, y, z), u, w), z)))))
% 141.66/18.17 = { by axiom 2 (permute2) R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), f(x, y, z), f(x, z, f(f(x, y, z), u, w))))))
% 141.66/18.17 = { by lemma 6 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(x, y, z), f(f(x, y, z), u, w), f(x, z, f(f(x, y, z), u, w))))))
% 141.66/18.17 = { by lemma 6 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(x, y, z), f(f(x, y, z), u, w), f(z, x, f(f(x, y, z), u, w))))))
% 141.66/18.17 = { by lemma 15 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(z, f(f(x, y, z), u, w), f(f(f(x, y, z), u, w), f(x, y, z), x)))))
% 141.66/18.17 = { by lemma 20 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(z, f(f(x, y, z), u, w), f(x, y, f(f(f(x, y, z), u, w), x, z))))))
% 141.66/18.17 = { by lemma 9 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(z, f(f(x, y, z), u, w), f(x, f(z, x, y), f(f(x, y, z), u, w))))))
% 141.66/18.17 = { by lemma 6 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(z, f(f(x, y, z), u, w), f(f(z, x, y), x, f(f(x, y, z), u, w))))))
% 141.66/18.17 = { by lemma 15 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(z, x, y), f(f(x, y, z), u, w), f(f(f(x, y, z), u, w), z, x)))))
% 141.66/18.17 = { by lemma 13 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), z, f(f(f(x, y, z), u, w), x, f(z, x, y))))))
% 141.66/18.17 = { by lemma 26 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(f(f(x, y, z), u, w), z, x))))
% 141.66/18.17 = { by lemma 36 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(z, f(f(x, y, z), u, w), f(x, u, w))))
% 141.66/18.17 = { by lemma 6 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), z, f(x, u, w))))
% 141.66/18.17 = { by axiom 2 (permute2) }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(f(x, y, z), u, w), f(x, u, w), z)))
% 141.66/18.17 = { by lemma 36 }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(x, u, w), f(f(x, y, z), u, w), f(z, u, w)))
% 141.66/18.17 = { by lemma 6 R->L }
% 141.66/18.17 f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(z, u, w)))
% 141.66/18.17 = { by lemma 20 }
% 141.66/18.17 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w))
% 141.66/18.17 = { by lemma 6 R->L }
% 141.66/18.17 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w), f(x, u, w))
% 141.66/18.17 = { by lemma 32 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), u, w)), f(x, u, w))
% 141.66/18.18 = { by lemma 30 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), u, w))), f(x, u, w))
% 141.66/18.18 = { by lemma 30 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(y, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), u, w)))), f(x, u, w))
% 141.66/18.18 = { by lemma 12 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(y, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), u, w), f(x, u, w)))), f(x, u, w))
% 141.66/18.18 = { by lemma 12 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(y, u, w)))), f(x, u, w))
% 141.66/18.18 = { by lemma 24 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)))), f(x, u, w))
% 141.66/18.18 = { by lemma 5 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w))), f(x, u, w))
% 141.66/18.18 = { by axiom 2 (permute2) }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, y, z)), f(x, u, w))
% 141.66/18.18 = { by lemma 6 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w), f(x, y, z)), f(x, u, w))
% 141.66/18.18 = { by lemma 10 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(x, y, z)))
% 141.66/18.18 = { by lemma 6 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w), f(f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, y, z)))
% 141.66/18.18 = { by axiom 2 (permute2) R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w), f(f(x, u, w), f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w))))
% 141.66/18.18 = { by lemma 6 }
% 141.66/18.18 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w))))
% 141.66/18.18 = { by lemma 6 }
% 141.66/18.18 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w))))
% 141.66/18.18 = { by lemma 15 R->L }
% 141.66/18.18 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w), f(x, u, w)))
% 141.66/18.18 = { by axiom 2 (permute2) R->L }
% 141.66/18.18 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), u, w)))
% 141.66/18.18 = { by lemma 33 R->L }
% 141.66/18.18 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(f(x, y, z), u, w), f(x, u, w), f(x, y, z))))
% 141.66/18.18 = { by lemma 14 R->L }
% 141.66/18.18 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, y, z), u, w), f(x, u, w), f(f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, y, z))))
% 141.66/18.18 = { by lemma 29 }
% 141.66/18.18 f(f(x, u, w), f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)))
% 141.66/18.18 = { by axiom 2 (permute2) }
% 141.66/18.18 f(f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, y, z))
% 141.66/18.18 = { by lemma 6 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(x, y, z))
% 141.66/18.18 = { by axiom 2 (permute2) R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, y, z), f(x, u, w))
% 141.66/18.18 = { by lemma 6 }
% 141.66/18.18 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w))
% 141.66/18.18 = { by axiom 2 (permute2) R->L }
% 141.66/18.18 f(f(x, y, z), f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)))
% 141.66/18.18 = { by lemma 37 R->L }
% 141.66/18.18 f(f(x, y, z), f(x, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), y))
% 141.66/18.18 = { by lemma 14 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), f(x, y, z), y))
% 141.66/18.18 = { by lemma 23 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(x, y, f(y, z, f(x, u, w))))
% 141.66/18.18 = { by lemma 28 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(x, y, f(z, f(x, u, w), f(y, f(x, u, w), f(y, z, f(f(x, u, w), f(y, u, w), f(z, u, w)))))))
% 141.66/18.18 = { by lemma 27 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(x, y, f(y, f(x, u, w), f(y, z, f(z, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)))))))
% 141.66/18.18 = { by lemma 14 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), y, f(x, y, f(y, z, f(z, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)))))))
% 141.66/18.18 = { by lemma 23 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), y, f(f(z, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w))), f(x, y, z), y)))
% 141.66/18.18 = { by lemma 6 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), y, f(f(x, y, z), f(z, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w))), y)))
% 141.66/18.18 = { by axiom 2 (permute2) }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), y, f(f(x, y, z), y, f(z, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w))))))
% 141.66/18.18 = { by lemma 6 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), y, f(f(x, y, z), y, f(f(x, u, w), z, f(f(x, u, w), f(y, u, w), f(z, u, w))))))
% 141.66/18.18 = { by axiom 2 (permute2) }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), y, f(f(x, y, z), y, f(f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), z))))
% 141.66/18.18 = { by lemma 14 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(y, f(x, u, w), f(f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), z))))
% 141.66/18.18 = { by lemma 14 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(y, f(x, u, w), z))))
% 141.66/18.18 = { by axiom 2 (permute2) R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(y, z, f(x, u, w)))))
% 141.66/18.18 = { by lemma 6 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(y, z, f(x, u, w)))))
% 141.66/18.18 = { by lemma 18 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), z))))
% 141.66/18.18 = { by axiom 2 (permute2) R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(f(f(x, u, w), f(y, u, w), f(z, u, w)), z, f(x, u, w)))))
% 141.66/18.18 = { by lemma 6 }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(z, f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w)))))
% 141.66/18.18 = { by axiom 2 (permute2) R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(z, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w))))))
% 141.66/18.18 = { by lemma 25 R->L }
% 141.66/18.18 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(z, f(x, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(z, u, w))))))
% 141.66/18.19 = { by lemma 7 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(f(x, u, w), f(z, u, w), f(z, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)))))))
% 141.66/18.19 = { by lemma 21 R->L }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(z, u, w), f(x, u, w), z)))))
% 141.66/18.19 = { by lemma 6 R->L }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, u, w), f(z, u, w), z)))))
% 141.66/18.19 = { by lemma 34 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(z, u, w)))))
% 141.66/18.19 = { by lemma 25 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), y, f(f(x, u, w), f(y, u, w), f(z, u, w)))))
% 141.66/18.19 = { by lemma 6 R->L }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(y, f(x, u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)))))
% 141.66/18.19 = { by axiom 2 (permute2) }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(y, f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w))))
% 141.66/18.19 = { by lemma 15 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), y, f(f(x, y, z), f(x, u, w), y)))
% 141.66/18.19 = { by axiom 2 (permute2) R->L }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), y, f(f(x, y, z), y, f(x, u, w))))
% 141.66/18.19 = { by lemma 6 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(y, f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), y, f(x, u, w))))
% 141.66/18.19 = { by lemma 18 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(y, f(x, y, z), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), y)))
% 141.66/18.19 = { by lemma 37 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(y, f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w))))
% 141.66/18.19 = { by lemma 6 R->L }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), y, f(f(x, u, w), f(y, u, w), f(z, u, w))))
% 141.66/18.19 = { by axiom 2 (permute2) }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), y))
% 141.66/18.19 = { by lemma 6 R->L }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, y, z), y))
% 141.66/18.19 = { by lemma 10 R->L }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, u, w), y), f(x, y, z))
% 141.66/18.19 = { by lemma 37 }
% 141.66/18.19 f(f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(x, y, z))
% 141.66/18.19 = { by axiom 1 (majority) }
% 141.66/18.19 f(f(x, u, w), f(y, u, w), f(z, u, w))
% 141.66/18.19 % SZS output end Proof
% 141.66/18.19
% 141.66/18.19 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------