TSTP Solution File: ALG212-10 by Twee---2.5.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : ALG212-10 : TPTP v8.2.0. Released v8.1.0.
% 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 : Unsatisfiable 107.01s 13.84s
% Output : Proof 108.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG212-10 : TPTP v8.2.0. Released v8.1.0.
% 0.03/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 16:31:08 EDT 2024
% 0.12/0.33 % CPUTime :
% 107.01/13.84 Command-line arguments: --ground-connectedness --complete-subsets
% 107.01/13.84
% 107.01/13.84 % SZS status Unsatisfiable
% 107.01/13.84
% 107.75/13.91 % SZS output start Proof
% 107.75/13.91 Axiom 1 (majority): f(X, X, Y) = X.
% 107.75/13.91 Axiom 2 (permute2): f(X, Y, Z) = f(X, Z, Y).
% 107.75/13.91 Axiom 3 (permute1): f(X, Y, Z) = f(Z, X, Y).
% 107.75/13.91 Axiom 4 (associativity): f(f(X, Y, Z), Y, W) = f(X, Y, f(Z, Y, W)).
% 107.75/13.91
% 107.75/13.91 Lemma 5: f(X, Y, X) = X.
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, X)
% 107.75/13.91 = { by axiom 2 (permute2) R->L }
% 107.75/13.91 f(X, X, Y)
% 107.75/13.91 = { by axiom 1 (majority) }
% 107.75/13.91 X
% 107.75/13.91
% 107.75/13.91 Lemma 6: f(X, Y, Y) = Y.
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, Y)
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(Y, Y, X)
% 107.75/13.91 = { by axiom 1 (majority) }
% 107.75/13.91 Y
% 107.75/13.91
% 107.75/13.91 Lemma 7: f(Y, X, Z) = f(X, Y, Z).
% 107.75/13.91 Proof:
% 107.75/13.91 f(Y, X, Z)
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(X, Z, Y)
% 107.75/13.91 = { by axiom 2 (permute2) }
% 107.75/13.91 f(X, Y, Z)
% 107.75/13.91
% 107.75/13.91 Lemma 8: f(Z, X, f(W, X, Y)) = f(X, Y, f(Z, X, W)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(Z, X, f(W, X, Y))
% 107.75/13.91 = { by axiom 4 (associativity) R->L }
% 107.75/13.91 f(f(Z, X, W), X, Y)
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(X, Y, f(Z, X, W))
% 107.75/13.91
% 107.75/13.91 Lemma 9: f(X, Y, f(X, Y, Z)) = f(X, Y, Z).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, f(X, Y, Z))
% 107.75/13.91 = { by lemma 8 }
% 107.75/13.91 f(Y, Z, f(X, Y, X))
% 107.75/13.91 = { by lemma 5 }
% 107.75/13.91 f(Y, Z, X)
% 107.75/13.91 = { by axiom 3 (permute1) }
% 107.75/13.91 f(X, Y, Z)
% 107.75/13.91
% 107.75/13.91 Lemma 10: f(X, f(Y, X, Z), W) = f(X, Z, f(W, X, Y)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, f(Y, X, Z), W)
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(f(Y, X, Z), W, X)
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(W, X, f(Y, X, Z))
% 107.75/13.91 = { by lemma 8 }
% 107.75/13.91 f(X, Z, f(W, X, Y))
% 107.75/13.91
% 107.75/13.91 Lemma 11: f(X, f(X, Y, Z), W) = f(X, Y, f(X, W, Z)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, f(X, Y, Z), W)
% 107.75/13.91 = { by axiom 3 (permute1) }
% 107.75/13.91 f(X, f(Z, X, Y), W)
% 107.75/13.91 = { by lemma 10 }
% 107.75/13.91 f(X, Y, f(W, X, Z))
% 107.75/13.91 = { by lemma 7 R->L }
% 107.75/13.91 f(X, Y, f(X, W, Z))
% 107.75/13.91
% 107.75/13.91 Lemma 12: f(X, Y, f(X, Z, W)) = f(X, Z, f(X, Y, W)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, f(X, Z, W))
% 107.75/13.91 = { by axiom 2 (permute2) R->L }
% 107.75/13.91 f(X, f(X, Z, W), Y)
% 107.75/13.91 = { by lemma 11 }
% 107.75/13.91 f(X, Z, f(X, Y, W))
% 107.75/13.91
% 107.75/13.91 Lemma 13: f(X, W, f(X, Y, Z)) = f(X, Y, f(X, Z, W)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, W, f(X, Y, Z))
% 107.75/13.91 = { by axiom 2 (permute2) R->L }
% 107.75/13.91 f(X, W, f(X, Z, Y))
% 107.75/13.91 = { by lemma 11 R->L }
% 107.75/13.91 f(X, f(X, W, Y), Z)
% 107.75/13.91 = { by lemma 7 }
% 107.75/13.91 f(X, f(W, X, Y), Z)
% 107.75/13.91 = { by lemma 10 }
% 107.75/13.91 f(X, Y, f(Z, X, W))
% 107.75/13.91 = { by lemma 7 R->L }
% 107.75/13.91 f(X, Y, f(X, Z, W))
% 107.75/13.91
% 107.75/13.91 Lemma 14: f(X, Y, f(Y, Z, W)) = f(Y, Z, f(Y, W, X)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, f(Y, Z, W))
% 107.75/13.91 = { by lemma 7 }
% 107.75/13.91 f(Y, X, f(Y, Z, W))
% 107.75/13.91 = { by lemma 13 }
% 107.75/13.91 f(Y, Z, f(Y, W, X))
% 107.75/13.91
% 107.75/13.91 Lemma 15: f(Z, Y, f(Y, X, W)) = f(X, Y, f(Z, Y, W)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(Z, Y, f(Y, X, W))
% 107.75/13.91 = { by axiom 3 (permute1) }
% 107.75/13.91 f(Z, Y, f(W, Y, X))
% 107.75/13.91 = { by lemma 8 }
% 107.75/13.91 f(Y, X, f(Z, Y, W))
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(X, f(Z, Y, W), Y)
% 107.75/13.91 = { by axiom 2 (permute2) }
% 107.75/13.91 f(X, Y, f(Z, Y, W))
% 107.75/13.91
% 107.75/13.91 Lemma 16: f(X, Y, f(Y, Z, W)) = f(Z, Y, f(X, W, Y)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, f(Y, Z, W))
% 107.75/13.91 = { by lemma 15 }
% 107.75/13.91 f(Z, Y, f(X, Y, W))
% 107.75/13.91 = { by axiom 2 (permute2) }
% 107.75/13.91 f(Z, Y, f(X, W, Y))
% 107.75/13.91
% 107.75/13.91 Lemma 17: f(X, Y, f(Z, Y, W)) = f(Y, W, f(X, Z, Y)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, f(Z, Y, W))
% 107.75/13.91 = { by lemma 8 }
% 107.75/13.91 f(Y, W, f(X, Y, Z))
% 107.75/13.91 = { by axiom 2 (permute2) }
% 107.75/13.91 f(Y, W, f(X, Z, Y))
% 107.75/13.91
% 107.75/13.91 Lemma 18: f(X, W, f(Y, X, Z)) = f(X, Y, f(Z, W, X)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, W, f(Y, X, Z))
% 107.75/13.91 = { by lemma 7 }
% 107.75/13.91 f(W, X, f(Y, X, Z))
% 107.75/13.91 = { by lemma 8 }
% 107.75/13.91 f(X, Z, f(W, X, Y))
% 107.75/13.91 = { by axiom 2 (permute2) }
% 107.75/13.91 f(X, f(W, X, Y), Z)
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(f(W, X, Y), Z, X)
% 107.75/13.91 = { by axiom 3 (permute1) R->L }
% 107.75/13.91 f(Z, X, f(W, X, Y))
% 107.75/13.91 = { by lemma 17 }
% 107.75/13.91 f(X, Y, f(Z, W, X))
% 107.75/13.91
% 107.75/13.91 Lemma 19: f(X, Y, f(Z, X, W)) = f(X, Z, f(Y, W, X)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, f(Z, X, W))
% 107.75/13.91 = { by lemma 18 }
% 107.75/13.91 f(X, Z, f(W, Y, X))
% 107.75/13.91 = { by lemma 7 R->L }
% 107.75/13.91 f(X, Z, f(Y, W, X))
% 107.75/13.91
% 107.75/13.91 Lemma 20: f(X, Y, f(Z, Y, W)) = f(Y, Z, f(W, Y, X)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(X, Y, f(Z, Y, W))
% 107.75/13.91 = { by lemma 17 }
% 107.75/13.91 f(Y, W, f(X, Z, Y))
% 107.75/13.91 = { by lemma 18 R->L }
% 107.75/13.91 f(Y, Z, f(W, Y, X))
% 107.75/13.91
% 107.75/13.91 Lemma 21: f(Z, X, f(X, Y, W)) = f(X, Y, f(Z, X, W)).
% 107.75/13.91 Proof:
% 107.75/13.91 f(Z, X, f(X, Y, W))
% 107.75/13.91 = { by axiom 3 (permute1) }
% 107.75/13.91 f(Z, X, f(W, X, Y))
% 107.75/13.91 = { by lemma 8 }
% 108.04/13.91 f(X, Y, f(Z, X, W))
% 108.04/13.91
% 108.04/13.91 Lemma 22: f(Z, f(X, Y, W), Y) = f(X, Y, f(Z, Y, W)).
% 108.04/13.91 Proof:
% 108.04/13.91 f(Z, f(X, Y, W), Y)
% 108.04/13.91 = { by axiom 3 (permute1) R->L }
% 108.04/13.91 f(f(X, Y, W), Y, Z)
% 108.04/13.91 = { by axiom 3 (permute1) R->L }
% 108.04/13.91 f(Y, Z, f(X, Y, W))
% 108.04/13.91 = { by lemma 8 R->L }
% 108.04/13.91 f(X, Y, f(W, Y, Z))
% 108.04/13.91 = { by lemma 7 R->L }
% 108.04/13.91 f(X, Y, f(Y, W, Z))
% 108.04/13.91 = { by axiom 3 (permute1) }
% 108.04/13.91 f(X, Y, f(Z, Y, W))
% 108.04/13.91
% 108.04/13.91 Lemma 23: f(W, f(X, Y, Z), Y) = f(X, Y, f(Y, Z, W)).
% 108.04/13.91 Proof:
% 108.04/13.91 f(W, f(X, Y, Z), Y)
% 108.04/13.91 = { by lemma 22 }
% 108.04/13.91 f(X, Y, f(W, Y, Z))
% 108.04/13.91 = { by axiom 3 (permute1) R->L }
% 108.04/13.91 f(Y, f(W, Y, Z), X)
% 108.04/13.91 = { by lemma 10 }
% 108.04/13.91 f(Y, Z, f(X, Y, W))
% 108.04/13.91 = { by lemma 21 R->L }
% 108.04/13.91 f(X, Y, f(Y, Z, W))
% 108.04/13.91
% 108.04/13.91 Lemma 24: f(f(X, Y, Z), X, Y) = f(X, Y, Z).
% 108.04/13.91 Proof:
% 108.04/13.91 f(f(X, Y, Z), X, Y)
% 108.04/13.91 = { by axiom 3 (permute1) R->L }
% 108.04/13.91 f(X, Y, f(X, Y, Z))
% 108.04/13.91 = { by lemma 9 }
% 108.04/13.91 f(X, Y, Z)
% 108.04/13.91
% 108.04/13.91 Lemma 25: f(X, Y, f(X, Z, f(Y, Z, W))) = f(X, Y, Z).
% 108.04/13.91 Proof:
% 108.04/13.91 f(X, Y, f(X, Z, f(Y, Z, W)))
% 108.04/13.91 = { by lemma 7 }
% 108.04/13.91 f(X, Y, f(X, Z, f(Z, Y, W)))
% 108.04/13.91 = { by lemma 9 R->L }
% 108.04/13.91 f(X, Y, f(X, Y, f(X, Z, f(Z, Y, W))))
% 108.04/13.91 = { by lemma 12 R->L }
% 108.04/13.91 f(X, Y, f(X, Z, f(X, Y, f(Z, Y, W))))
% 108.04/13.91 = { by lemma 20 }
% 108.04/13.91 f(X, Y, f(X, Z, f(Y, Z, f(W, Y, X))))
% 108.04/13.91 = { by axiom 2 (permute2) R->L }
% 108.04/13.91 f(X, Y, f(X, f(Y, Z, f(W, Y, X)), Z))
% 108.04/13.91 = { by lemma 10 R->L }
% 108.04/13.91 f(X, Y, f(X, f(Y, f(X, Y, Z), W), Z))
% 108.04/13.91 = { by lemma 11 R->L }
% 108.04/13.91 f(X, f(X, Y, Z), f(Y, f(X, Y, Z), W))
% 108.04/13.91 = { by lemma 17 }
% 108.04/13.91 f(f(X, Y, Z), W, f(X, Y, f(X, Y, Z)))
% 108.04/13.91 = { by lemma 9 }
% 108.04/13.91 f(f(X, Y, Z), W, f(X, Y, Z))
% 108.04/13.91 = { by lemma 5 }
% 108.04/13.91 f(X, Y, Z)
% 108.04/13.91
% 108.04/13.91 Lemma 26: f(X, Y, f(f(Z, X, W), Y, V)) = f(Y, V, f(Z, X, f(W, X, Y))).
% 108.04/13.91 Proof:
% 108.04/13.91 f(X, Y, f(f(Z, X, W), Y, V))
% 108.04/13.91 = { by lemma 8 }
% 108.04/13.91 f(Y, V, f(X, Y, f(Z, X, W)))
% 108.04/13.91 = { by lemma 8 R->L }
% 108.04/13.91 f(Y, V, f(Z, X, f(W, X, Y)))
% 108.04/13.91
% 108.04/13.91 Lemma 27: f(X, Y, f(f(Z, X, W), Y, V)) = f(Y, V, f(Z, X, f(X, W, Y))).
% 108.04/13.91 Proof:
% 108.04/13.91 f(X, Y, f(f(Z, X, W), Y, V))
% 108.04/13.91 = { by lemma 26 }
% 108.04/13.91 f(Y, V, f(Z, X, f(W, X, Y)))
% 108.04/13.91 = { by lemma 7 R->L }
% 108.04/13.91 f(Y, V, f(Z, X, f(X, W, Y)))
% 108.04/13.91
% 108.04/13.91 Lemma 28: f(X, Y, f(Z, W, f(Y, Z, X))) = f(X, Z, Y).
% 108.04/13.91 Proof:
% 108.04/13.91 f(X, Y, f(Z, W, f(Y, Z, X)))
% 108.04/13.91 = { by lemma 10 R->L }
% 108.04/13.91 f(X, Y, f(Z, f(X, Z, W), Y))
% 108.04/13.91 = { by lemma 7 }
% 108.04/13.91 f(X, Y, f(f(X, Z, W), Z, Y))
% 108.04/13.91 = { by lemma 16 R->L }
% 108.04/13.91 f(f(X, Z, W), Y, f(Y, X, Z))
% 108.04/13.91 = { by lemma 14 }
% 108.04/13.91 f(Y, X, f(Y, Z, f(X, Z, W)))
% 108.04/13.91 = { by lemma 25 }
% 108.04/13.91 f(Y, X, Z)
% 108.04/13.91 = { by lemma 7 R->L }
% 108.04/13.91 f(X, Y, Z)
% 108.04/13.91 = { by axiom 2 (permute2) }
% 108.04/13.91 f(X, Z, Y)
% 108.04/13.91
% 108.04/13.91 Lemma 29: f(X, Y, f(f(Z, X, W), Y, Z)) = f(X, Z, Y).
% 108.04/13.91 Proof:
% 108.04/13.91 f(X, Y, f(f(Z, X, W), Y, Z))
% 108.04/13.91 = { by lemma 27 }
% 108.04/13.91 f(Y, Z, f(Z, X, f(X, W, Y)))
% 108.04/13.91 = { by lemma 16 }
% 108.04/13.91 f(X, Z, f(Y, f(X, W, Y), Z))
% 108.04/13.91 = { by axiom 2 (permute2) R->L }
% 108.04/13.91 f(X, Z, f(Y, Z, f(X, W, Y)))
% 108.04/13.91 = { by lemma 18 R->L }
% 108.04/13.91 f(X, Z, f(Y, W, f(Z, Y, X)))
% 108.04/13.91 = { by lemma 28 }
% 108.04/13.91 f(X, Y, Z)
% 108.04/13.91 = { by axiom 2 (permute2) }
% 108.04/13.91 f(X, Z, Y)
% 108.04/13.91
% 108.04/13.91 Lemma 30: f(X, Y, f(X, Z, f(W, Y, Z))) = f(X, Y, Z).
% 108.04/13.91 Proof:
% 108.04/13.91 f(X, Y, f(X, Z, f(W, Y, Z)))
% 108.04/13.91 = { by axiom 2 (permute2) R->L }
% 108.04/13.91 f(X, Y, f(X, f(W, Y, Z), Z))
% 108.04/13.91 = { by lemma 14 R->L }
% 108.04/13.91 f(Z, X, f(X, Y, f(W, Y, Z)))
% 108.04/13.91 = { by lemma 26 R->L }
% 108.04/13.91 f(Y, Z, f(f(X, Y, W), Z, X))
% 108.04/13.91 = { by lemma 29 }
% 108.04/13.91 f(Y, X, Z)
% 108.04/13.91 = { by lemma 7 R->L }
% 108.04/13.91 f(X, Y, Z)
% 108.04/13.91
% 108.04/13.91 Lemma 31: f(X, f(Y, Z, W), f(X, Z, W)) = f(X, Z, W).
% 108.04/13.91 Proof:
% 108.04/13.91 f(X, f(Y, Z, W), f(X, Z, W))
% 108.04/13.91 = { by axiom 2 (permute2) R->L }
% 108.04/13.91 f(X, f(Y, Z, W), f(X, W, Z))
% 108.04/13.91 = { by lemma 12 R->L }
% 108.04/13.91 f(X, W, f(X, f(Y, Z, W), Z))
% 108.04/13.91 = { by lemma 7 }
% 108.04/13.91 f(W, X, f(X, f(Y, Z, W), Z))
% 108.04/13.91 = { by axiom 2 (permute2) R->L }
% 108.04/13.91 f(W, X, f(X, Z, f(Y, Z, W)))
% 108.04/13.91 = { by lemma 26 R->L }
% 108.04/13.92 f(Z, W, f(f(X, Z, Y), W, X))
% 108.04/13.92 = { by lemma 7 R->L }
% 108.04/13.92 f(Z, W, f(W, f(X, Z, Y), X))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(Z, W, f(W, f(X, Y, Z), X))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(Z, W, f(W, X, f(X, Y, Z)))
% 108.04/13.92 = { by lemma 27 R->L }
% 108.04/13.92 f(X, Z, f(f(W, X, Y), Z, W))
% 108.04/13.92 = { by lemma 29 }
% 108.04/13.92 f(X, W, Z)
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(X, Z, W)
% 108.04/13.92
% 108.04/13.92 Lemma 32: f(f(X, Y, Z), X, f(X, Y, W)) = f(W, f(X, Y, Z), X).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(X, Y, Z), X, f(X, Y, W))
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(X, Y, Z), X, f(Y, X, W))
% 108.04/13.92 = { by lemma 20 }
% 108.04/13.92 f(X, Y, f(W, X, f(X, Y, Z)))
% 108.04/13.92 = { by lemma 8 R->L }
% 108.04/13.92 f(W, X, f(f(X, Y, Z), X, Y))
% 108.04/13.92 = { by lemma 24 }
% 108.04/13.92 f(W, X, f(X, Y, Z))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(W, f(X, Y, Z), X)
% 108.04/13.92
% 108.04/13.92 Lemma 33: f(f(X, Y, Z), X, f(X, Z, W)) = f(W, f(X, Y, Z), X).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(X, Y, Z), X, f(X, Z, W))
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(X, Y, Z), X, f(Z, X, W))
% 108.04/13.92 = { by lemma 20 }
% 108.04/13.92 f(X, Z, f(W, X, f(X, Y, Z)))
% 108.04/13.92 = { by lemma 8 R->L }
% 108.04/13.92 f(W, X, f(f(X, Y, Z), X, Z))
% 108.04/13.92 = { by axiom 3 (permute1) R->L }
% 108.04/13.92 f(W, X, f(X, Z, f(X, Y, Z)))
% 108.04/13.92 = { by axiom 2 (permute2) R->L }
% 108.04/13.92 f(W, X, f(X, Z, f(X, Z, Y)))
% 108.04/13.92 = { by lemma 8 }
% 108.04/13.92 f(W, X, f(Z, Y, f(X, Z, X)))
% 108.04/13.92 = { by lemma 5 }
% 108.04/13.92 f(W, X, f(Z, Y, X))
% 108.04/13.92 = { by axiom 3 (permute1) }
% 108.04/13.92 f(W, X, f(X, Z, Y))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(W, X, f(X, Y, Z))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(W, f(X, Y, Z), X)
% 108.04/13.92
% 108.04/13.92 Lemma 34: f(f(X, Y, Z), X, f(W, Y, Z)) = f(X, Y, Z).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(X, Y, Z), X, f(W, Y, Z))
% 108.04/13.92 = { by axiom 2 (permute2) R->L }
% 108.04/13.92 f(f(X, Y, Z), f(W, Y, Z), X)
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(W, Y, Z), f(X, Y, Z), X)
% 108.04/13.92 = { by lemma 32 R->L }
% 108.04/13.92 f(f(X, Y, Z), X, f(X, Y, f(W, Y, Z)))
% 108.04/13.92 = { by lemma 22 R->L }
% 108.04/13.92 f(f(X, Y, Z), X, f(W, f(X, Y, Z), Y))
% 108.04/13.92 = { by lemma 21 R->L }
% 108.04/13.92 f(W, f(X, Y, Z), f(f(X, Y, Z), X, Y))
% 108.04/13.92 = { by lemma 24 }
% 108.04/13.92 f(W, f(X, Y, Z), f(X, Y, Z))
% 108.04/13.92 = { by lemma 6 }
% 108.04/13.92 f(X, Y, Z)
% 108.04/13.92
% 108.04/13.92 Lemma 35: f(X, Y, f(X, f(Z, W, V), f(Y, W, V))) = f(X, Y, f(Z, W, V)).
% 108.04/13.92 Proof:
% 108.04/13.92 f(X, Y, f(X, f(Z, W, V), f(Y, W, V)))
% 108.04/13.92 = { by lemma 31 R->L }
% 108.04/13.92 f(X, Y, f(X, f(Z, W, V), f(Y, f(Z, W, V), f(Y, W, V))))
% 108.04/13.92 = { by lemma 25 }
% 108.04/13.92 f(X, Y, f(Z, W, V))
% 108.04/13.92
% 108.04/13.92 Lemma 36: f(f(X, Y, Z), f(Y, W, V), X) = f(f(X, Y, Z), f(Z, W, V), X).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(X, Y, Z), f(Y, W, V), X)
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(Y, W, V), f(X, Y, Z), X)
% 108.04/13.92 = { by lemma 33 R->L }
% 108.04/13.92 f(f(X, Y, Z), X, f(X, Z, f(Y, W, V)))
% 108.04/13.92 = { by lemma 35 R->L }
% 108.04/13.92 f(f(X, Y, Z), X, f(X, Z, f(X, f(Y, W, V), f(Z, W, V))))
% 108.04/13.92 = { by lemma 33 }
% 108.04/13.92 f(f(X, f(Y, W, V), f(Z, W, V)), f(X, Y, Z), X)
% 108.04/13.92 = { by lemma 7 R->L }
% 108.04/13.92 f(f(X, Y, Z), f(X, f(Y, W, V), f(Z, W, V)), X)
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(f(X, Y, Z), X, f(X, f(Y, W, V), f(Z, W, V)))
% 108.04/13.92 = { by lemma 7 R->L }
% 108.04/13.92 f(f(X, Y, Z), X, f(f(Y, W, V), X, f(Z, W, V)))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(f(X, Y, Z), X, f(f(Y, W, V), f(Z, W, V), X))
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(X, Y, Z), X, f(f(Z, W, V), f(Y, W, V), X))
% 108.04/13.92 = { by axiom 2 (permute2) R->L }
% 108.04/13.92 f(f(X, Y, Z), X, f(f(Z, W, V), X, f(Y, W, V)))
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(X, Y, Z), X, f(X, f(Z, W, V), f(Y, W, V)))
% 108.04/13.92 = { by axiom 2 (permute2) R->L }
% 108.04/13.92 f(f(X, Y, Z), f(X, f(Z, W, V), f(Y, W, V)), X)
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(X, f(Z, W, V), f(Y, W, V)), f(X, Y, Z), X)
% 108.04/13.92 = { by lemma 32 R->L }
% 108.04/13.92 f(f(X, Y, Z), X, f(X, Y, f(X, f(Z, W, V), f(Y, W, V))))
% 108.04/13.92 = { by lemma 35 }
% 108.04/13.92 f(f(X, Y, Z), X, f(X, Y, f(Z, W, V)))
% 108.04/13.92 = { by lemma 32 }
% 108.04/13.92 f(f(Z, W, V), f(X, Y, Z), X)
% 108.04/13.92 = { by lemma 7 R->L }
% 108.04/13.92 f(f(X, Y, Z), f(Z, W, V), X)
% 108.04/13.92
% 108.04/13.92 Lemma 37: f(f(X, Y, Z), f(V, Y, Z), f(W, Y, Z)) = f(f(X, Y, Z), f(W, Y, Z), V).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(X, Y, Z), f(V, Y, Z), f(W, Y, Z))
% 108.04/13.92 = { by lemma 34 R->L }
% 108.04/13.92 f(f(X, Y, Z), f(f(V, Y, Z), V, f(X, Y, Z)), f(W, Y, Z))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(f(X, Y, Z), f(f(V, Y, Z), f(X, Y, Z), V), f(W, Y, Z))
% 108.04/13.92 = { by lemma 7 R->L }
% 108.04/13.92 f(f(X, Y, Z), f(f(X, Y, Z), f(V, Y, Z), V), f(W, Y, Z))
% 108.04/13.92 = { by lemma 11 }
% 108.04/13.92 f(f(X, Y, Z), f(V, Y, Z), f(f(X, Y, Z), f(W, Y, Z), V))
% 108.04/13.92 = { by lemma 12 R->L }
% 108.04/13.92 f(f(X, Y, Z), f(W, Y, Z), f(f(X, Y, Z), f(V, Y, Z), V))
% 108.04/13.92 = { by axiom 2 (permute2) R->L }
% 108.04/13.92 f(f(X, Y, Z), f(W, Y, Z), f(f(X, Y, Z), V, f(V, Y, Z)))
% 108.04/13.92 = { by lemma 12 R->L }
% 108.04/13.92 f(f(X, Y, Z), V, f(f(X, Y, Z), f(W, Y, Z), f(V, Y, Z)))
% 108.04/13.92 = { by lemma 35 }
% 108.04/13.92 f(f(X, Y, Z), V, f(W, Y, Z))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(f(X, Y, Z), f(W, Y, Z), V)
% 108.04/13.92
% 108.04/13.92 Lemma 38: f(f(X, Y, Z), X, f(f(X, Y, Z), f(W, Y, Z), V)) = f(X, Y, Z).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(X, Y, Z), X, f(f(X, Y, Z), f(W, Y, Z), V))
% 108.04/13.92 = { by lemma 13 }
% 108.04/13.92 f(f(X, Y, Z), f(W, Y, Z), f(f(X, Y, Z), V, X))
% 108.04/13.92 = { by lemma 13 }
% 108.04/13.92 f(f(X, Y, Z), V, f(f(X, Y, Z), X, f(W, Y, Z)))
% 108.04/13.92 = { by lemma 34 }
% 108.04/13.92 f(f(X, Y, Z), V, f(X, Y, Z))
% 108.04/13.92 = { by lemma 5 }
% 108.04/13.92 f(X, Y, Z)
% 108.04/13.92
% 108.04/13.92 Lemma 39: f(f(V, U, X), f(X, Y, Z), f(W, f(X, Y, Z), V)) = f(f(X, Y, Z), W, f(f(V, U, X), f(U, Y, Z), V)).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(V, U, X), f(X, Y, Z), f(W, f(X, Y, Z), V))
% 108.04/13.92 = { by axiom 2 (permute2) R->L }
% 108.04/13.92 f(f(V, U, X), f(X, Y, Z), f(W, V, f(X, Y, Z)))
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(X, Y, Z), f(V, U, X), f(W, V, f(X, Y, Z)))
% 108.04/13.92 = { by lemma 19 R->L }
% 108.04/13.92 f(f(X, Y, Z), W, f(f(V, U, X), f(X, Y, Z), V))
% 108.04/13.92 = { by lemma 36 R->L }
% 108.04/13.92 f(f(X, Y, Z), W, f(f(V, U, X), f(U, Y, Z), V))
% 108.04/13.92
% 108.04/13.92 Lemma 40: f(f(X, Y, Z), f(Z, W, V), f(f(Y, W, V), f(Z, W, V), X)) = f(f(Y, W, V), f(Z, W, V), X).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(X, Y, Z), f(Z, W, V), f(f(Y, W, V), f(Z, W, V), X))
% 108.04/13.92 = { by lemma 39 }
% 108.04/13.92 f(f(Z, W, V), f(Y, W, V), f(f(X, Y, Z), f(Y, W, V), X))
% 108.04/13.92 = { by lemma 7 R->L }
% 108.04/13.92 f(f(Y, W, V), f(Z, W, V), f(f(X, Y, Z), f(Y, W, V), X))
% 108.04/13.92 = { by lemma 36 }
% 108.04/13.92 f(f(Y, W, V), f(Z, W, V), f(f(X, Y, Z), f(Z, W, V), X))
% 108.04/13.92 = { by lemma 6 R->L }
% 108.04/13.92 f(f(Y, W, V), f(Z, W, V), f(f(X, Y, Z), f(Z, W, V), f(f(Z, W, V), X, X)))
% 108.04/13.92 = { by lemma 15 }
% 108.04/13.92 f(f(Y, W, V), f(Z, W, V), f(X, f(Z, W, V), f(f(X, Y, Z), f(Z, W, V), X)))
% 108.04/13.92 = { by lemma 36 R->L }
% 108.04/13.92 f(f(Y, W, V), f(Z, W, V), f(X, f(Z, W, V), f(f(X, Y, Z), f(Y, W, V), X)))
% 108.04/13.92 = { by lemma 19 R->L }
% 108.04/13.92 f(f(Y, W, V), f(Z, W, V), f(X, f(X, Y, Z), f(f(Z, W, V), X, f(Y, W, V))))
% 108.04/13.92 = { by lemma 28 }
% 108.04/13.92 f(f(Y, W, V), X, f(Z, W, V))
% 108.04/13.92 = { by axiom 2 (permute2) }
% 108.04/13.92 f(f(Y, W, V), f(Z, W, V), X)
% 108.04/13.92
% 108.04/13.92 Goal 1 (dist_long): f(f(x, y, z), u, w) = f(f(x, u, w), f(y, u, w), f(z, u, w)).
% 108.04/13.92 Proof:
% 108.04/13.92 f(f(x, y, z), u, w)
% 108.04/13.92 = { by lemma 34 R->L }
% 108.04/13.92 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))
% 108.04/13.92 = { by lemma 31 R->L }
% 108.04/13.92 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)))
% 108.04/13.92 = { by lemma 31 R->L }
% 108.04/13.92 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))))
% 108.04/13.92 = { by lemma 13 }
% 108.04/13.92 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))))
% 108.04/13.92 = { by lemma 13 }
% 108.04/13.92 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))))
% 108.04/13.92 = { by lemma 24 }
% 108.04/13.92 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))))
% 108.04/13.92 = { by lemma 5 }
% 108.04/13.92 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)))
% 108.04/13.92 = { by lemma 7 }
% 108.04/13.92 f(f(x, y, z), f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)))
% 108.04/13.92 = { by axiom 2 (permute2) R->L }
% 108.04/13.92 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, y, z), u, w))
% 108.04/13.92 = { by lemma 38 R->L }
% 108.04/13.92 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, y, z), f(f(f(x, y, z), u, w), f(y, u, w), x)))
% 108.04/13.92 = { by lemma 12 R->L }
% 108.04/13.92 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(y, u, w), f(f(f(x, y, z), u, w), f(x, y, z), x)))
% 108.04/13.92 = { by lemma 32 R->L }
% 108.04/13.92 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(y, u, w), f(f(x, y, z), x, f(x, y, f(f(x, y, z), u, w)))))
% 108.04/13.92 = { by lemma 35 R->L }
% 108.04/13.93 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(y, u, w), f(f(x, y, z), x, f(x, y, f(x, f(f(x, y, z), u, w), f(y, u, w))))))
% 108.04/13.93 = { by lemma 32 }
% 108.04/13.93 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(y, u, w), f(f(x, f(f(x, y, z), u, w), f(y, u, w)), f(x, y, z), x)))
% 108.04/13.93 = { by lemma 7 R->L }
% 108.04/13.93 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(y, u, w), f(f(x, y, z), f(x, f(f(x, y, z), u, w), f(y, u, w)), x)))
% 108.04/13.93 = { by axiom 2 (permute2) }
% 108.04/13.93 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(y, u, w), f(f(x, y, z), x, f(x, f(f(x, y, z), u, w), f(y, u, w)))))
% 108.04/13.93 = { by lemma 21 }
% 108.04/13.93 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(y, u, w), f(x, f(f(x, y, z), u, w), f(f(x, y, z), x, f(y, u, w)))))
% 108.04/13.93 = { by axiom 2 (permute2) R->L }
% 108.04/13.93 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(y, u, w), f(x, f(f(x, y, z), u, w), f(f(x, y, z), f(y, u, w), x))))
% 108.04/13.93 = { by lemma 19 R->L }
% 108.04/13.93 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(y, u, w), f(x, f(x, y, z), f(f(f(x, y, z), u, w), x, f(y, u, w)))))
% 108.04/13.93 = { by lemma 7 R->L }
% 108.04/13.93 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(y, u, w), f(f(x, y, z), x, f(f(f(x, y, z), u, w), x, f(y, u, w)))))
% 108.04/13.93 = { by axiom 2 (permute2) }
% 108.04/13.93 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(y, u, w), f(f(x, y, z), x, f(f(f(x, y, z), u, w), f(y, u, w), x))))
% 108.04/13.93 = { by lemma 16 R->L }
% 108.04/13.93 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(y, u, w), f(f(f(x, y, z), u, w), x, f(x, f(x, y, z), f(y, u, w)))))
% 108.04/13.93 = { by lemma 7 R->L }
% 108.04/13.93 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(y, u, w), f(f(f(x, y, z), u, w), x, f(f(x, y, z), x, f(y, u, w)))))
% 108.04/13.93 = { by axiom 2 (permute2) }
% 108.04/13.93 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(y, u, w), f(f(f(x, y, z), u, w), x, f(f(x, y, z), f(y, u, w), x))))
% 108.04/13.93 = { by lemma 30 }
% 108.04/13.93 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(y, u, w), x))
% 108.04/13.93 = { by lemma 37 R->L }
% 108.04/13.93 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(y, u, w)))
% 108.04/13.93 = { by lemma 7 }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(f(x, y, z), u, w), f(y, u, w)))
% 108.04/13.93 = { by axiom 2 (permute2) R->L }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), f(f(x, y, z), u, w)))
% 108.04/13.93 = { by lemma 38 R->L }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), 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))))
% 108.04/13.93 = { by lemma 12 R->L }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), 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, y, z), y))))
% 108.04/13.93 = { by lemma 23 }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(x, y, f(y, z, f(f(x, y, z), u, w))))))
% 108.04/13.93 = { by lemma 35 R->L }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(x, y, f(y, z, f(y, f(f(x, y, z), u, w), f(z, u, w)))))))
% 108.04/13.93 = { by lemma 23 R->L }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), f(f(y, f(f(x, y, z), u, w), f(z, u, w)), f(x, y, z), y))))
% 108.04/13.93 = { by lemma 7 R->L }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), 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), f(y, f(f(x, y, z), u, w), f(z, u, w)), y))))
% 108.04/13.93 = { by axiom 2 (permute2) }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), 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), y, f(y, f(f(x, y, z), u, w), f(z, u, w))))))
% 108.04/13.93 = { by lemma 16 }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), 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), y, f(f(x, y, z), f(z, u, w), y)))))
% 108.04/13.93 = { by lemma 30 }
% 108.04/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(z, u, w), y)))
% 108.19/13.93 = { by lemma 37 R->L }
% 108.19/13.93 f(f(x, y, z), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(x, u, w), f(y, u, w), f(f(f(x, y, z), u, w), f(y, u, w), f(z, u, w))))
% 108.19/13.93 = { by lemma 22 R->L }
% 108.19/13.93 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(f(x, u, w), f(y, u, w), f(z, u, w)), f(y, u, w)))
% 108.19/13.93 = { by lemma 15 R->L }
% 108.19/13.93 f(f(f(x, y, z), u, w), 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, y, z), f(y, u, w)))
% 108.19/13.93 = { by lemma 7 }
% 108.19/13.93 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(f(x, u, w), f(y, u, w), f(z, u, w)), f(y, u, w)))
% 108.19/13.93 = { by lemma 22 }
% 108.19/13.93 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(y, u, w), f(f(x, y, z), f(y, u, w), f(z, u, w))))
% 108.19/13.93 = { by lemma 25 R->L }
% 108.19/13.93 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(y, u, w), f(f(x, y, z), f(y, u, w), f(f(x, y, z), f(z, u, w), f(f(y, u, w), f(z, u, w), x)))))
% 108.19/13.93 = { by lemma 40 }
% 108.19/13.93 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(y, u, w), f(f(x, y, z), f(y, u, w), f(f(y, u, w), f(z, u, w), x))))
% 108.19/13.93 = { by lemma 15 }
% 108.19/13.93 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(y, u, w), f(f(z, u, w), f(y, u, w), f(f(x, y, z), f(y, u, w), x))))
% 108.19/13.93 = { by lemma 39 R->L }
% 108.19/13.93 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(y, u, w), f(f(x, y, z), f(z, u, w), f(f(y, u, w), f(z, u, w), x))))
% 108.19/13.93 = { by lemma 40 }
% 108.19/13.93 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(y, u, w), f(f(y, u, w), f(z, u, w), x)))
% 108.19/13.93 = { by axiom 2 (permute2) R->L }
% 108.19/13.93 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(y, u, w), f(f(y, u, w), x, f(z, u, w))))
% 108.19/13.93 = { by lemma 7 }
% 108.19/13.93 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(y, u, w), f(x, f(y, u, w), f(z, u, w))))
% 108.19/13.93 = { by lemma 8 }
% 108.19/13.93 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(y, u, w), f(z, u, w), f(f(x, u, w), f(y, u, w), x)))
% 108.19/13.93 = { by axiom 2 (permute2) R->L }
% 108.19/13.93 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(y, u, w), f(z, u, w), f(f(x, u, w), x, f(y, u, w))))
% 108.19/13.93 = { by lemma 34 }
% 108.19/13.93 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(y, u, w), f(z, u, w), f(x, u, w)))
% 108.19/13.93 = { by lemma 7 R->L }
% 108.19/13.93 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(z, u, w), f(y, u, w), f(x, u, w)))
% 108.19/13.93 = { by axiom 2 (permute2) }
% 108.19/13.93 f(f(f(x, y, z), u, w), f(f(x, u, w), f(y, u, w), f(z, u, w)), f(f(z, u, w), f(x, u, w), f(y, u, w)))
% 108.19/13.93 = { by lemma 7 R->L }
% 108.19/13.93 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(z, u, w), f(y, u, w)))
% 108.19/13.93 = { by axiom 2 (permute2) }
% 108.19/13.93 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(y, u, w), f(z, u, w)))
% 108.19/13.93 = { by lemma 6 }
% 108.19/13.93 f(f(x, u, w), f(y, u, w), f(z, u, w))
% 108.19/13.93 % SZS output end Proof
% 108.19/13.93
% 108.19/13.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------