TSTP Solution File: BOO076-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO076-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n024.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 18:11:37 EDT 2023
% Result : Unsatisfiable 17.26s 2.60s
% Output : Proof 17.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO076-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 08:10:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 17.26/2.60 Command-line arguments: --ground-connectedness --complete-subsets
% 17.26/2.60
% 17.26/2.60 % SZS status Unsatisfiable
% 17.26/2.60
% 17.26/2.69 % SZS output start Proof
% 17.26/2.69 Axiom 1 (sh_1): nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, X))) = Y.
% 17.26/2.69
% 17.26/2.69 Lemma 2: nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Z, Y), Y)), nand(X, Y)), nand(X, Y))), Z) = nand(Y, nand(nand(Z, Y), Y)).
% 17.26/2.69 Proof:
% 17.26/2.69 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Z, Y), Y)), nand(X, Y)), nand(X, Y))), Z)
% 17.26/2.69 = { by axiom 1 (sh_1) R->L }
% 17.26/2.69 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Z, Y), Y)), nand(X, Y)), nand(X, Y))), nand(nand(Y, nand(nand(Z, Y), Y)), nand(Z, nand(X, Y))))
% 17.26/2.69 = { by axiom 1 (sh_1) }
% 17.26/2.69 nand(Y, nand(nand(Z, Y), Y))
% 17.26/2.69
% 17.26/2.69 Lemma 3: nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, nand(nand(X, Z), Z)))) = Y.
% 17.26/2.69 Proof:
% 17.26/2.69 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, nand(nand(X, Z), Z))))
% 17.26/2.69 = { by lemma 2 R->L }
% 17.26/2.69 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(nand(nand(W, Z), nand(nand(nand(Z, nand(nand(X, Z), Z)), nand(W, Z)), nand(W, Z))), X)))
% 17.26/2.69 = { by axiom 1 (sh_1) }
% 17.26/2.69 Y
% 17.26/2.69
% 17.26/2.69 Lemma 4: nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y) = nand(Y, nand(nand(Y, Y), Y)).
% 17.26/2.69 Proof:
% 17.26/2.69 nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y)
% 17.26/2.69 = { by axiom 1 (sh_1) R->L }
% 17.26/2.69 nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), nand(nand(Y, nand(nand(Y, Y), Y)), nand(Y, nand(nand(X, Y), Y))))
% 17.26/2.69 = { by lemma 3 }
% 17.26/2.69 nand(Y, nand(nand(Y, Y), Y))
% 17.26/2.69
% 17.26/2.69 Lemma 5: nand(X, nand(nand(X, X), X)) = nand(X, X).
% 17.26/2.69 Proof:
% 17.26/2.69 nand(X, nand(nand(X, X), X))
% 17.26/2.69 = { by lemma 4 R->L }
% 17.26/2.69 nand(nand(nand(X, nand(nand(X, X), X)), nand(nand(nand(X, nand(nand(X, X), X)), nand(X, nand(nand(X, X), X))), nand(X, nand(nand(X, X), X)))), X)
% 17.26/2.69 = { by axiom 1 (sh_1) }
% 17.26/2.69 nand(nand(nand(X, nand(nand(X, X), X)), nand(X, nand(X, nand(nand(X, X), X)))), X)
% 17.26/2.69 = { by lemma 3 }
% 17.26/2.69 nand(X, X)
% 17.26/2.69
% 17.26/2.69 Lemma 6: nand(nand(X, nand(nand(nand(Y, Y), X), X)), Y) = nand(Y, Y).
% 17.26/2.69 Proof:
% 17.26/2.69 nand(nand(X, nand(nand(nand(Y, Y), X), X)), Y)
% 17.26/2.69 = { by lemma 5 R->L }
% 17.26/2.69 nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y)
% 17.26/2.69 = { by lemma 4 }
% 17.26/2.69 nand(Y, nand(nand(Y, Y), Y))
% 17.26/2.69 = { by lemma 5 }
% 17.26/2.69 nand(Y, Y)
% 17.26/2.69
% 17.26/2.69 Lemma 7: nand(nand(X, nand(nand(Y, X), X)), nand(Y, Y)) = Y.
% 17.26/2.69 Proof:
% 17.26/2.69 nand(nand(X, nand(nand(Y, X), X)), nand(Y, Y))
% 17.26/2.69 = { by lemma 5 R->L }
% 17.26/2.69 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(nand(Y, Y), Y)))
% 17.26/2.69 = { by axiom 1 (sh_1) R->L }
% 17.26/2.69 nand(nand(X, nand(nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(Y, nand(nand(Y, Y), Y))), X), X)), nand(Y, nand(nand(Y, Y), Y)))
% 17.26/2.69 = { by lemma 6 }
% 17.26/2.69 nand(nand(Y, nand(nand(Y, Y), Y)), nand(Y, nand(nand(Y, Y), Y)))
% 17.26/2.69 = { by axiom 1 (sh_1) }
% 17.26/2.69 Y
% 17.26/2.69
% 17.26/2.69 Lemma 8: nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X)) = nand(Y, X).
% 17.26/2.69 Proof:
% 17.26/2.69 nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X))
% 17.26/2.69 = { by lemma 2 R->L }
% 17.26/2.69 nand(nand(nand(Y, X), nand(nand(nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X)), nand(Y, X)), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))
% 17.26/2.69 = { by lemma 6 }
% 17.26/2.69 nand(nand(nand(Y, X), nand(nand(nand(Y, X), nand(Y, X)), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))
% 17.26/2.69 = { by lemma 7 }
% 17.26/2.69 nand(Y, X)
% 17.26/2.69
% 17.26/2.69 Lemma 9: nand(nand(X, X), nand(Y, X)) = X.
% 17.26/2.69 Proof:
% 17.26/2.69 nand(nand(X, X), nand(Y, X))
% 17.26/2.69 = { by lemma 5 R->L }
% 17.26/2.69 nand(nand(X, nand(nand(X, X), X)), nand(Y, X))
% 17.26/2.69 = { by lemma 8 R->L }
% 17.26/2.69 nand(nand(X, nand(nand(X, X), X)), nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X)))
% 17.26/2.69 = { by axiom 1 (sh_1) }
% 17.26/2.69 X
% 17.26/2.69
% 17.26/2.69 Lemma 10: nand(nand(X, Y), nand(Y, nand(X, Y))) = Y.
% 17.26/2.69 Proof:
% 17.26/2.69 nand(nand(X, Y), nand(Y, nand(X, Y)))
% 17.26/2.69 = { by lemma 9 R->L }
% 17.26/2.69 nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))
% 17.26/2.69 = { by lemma 9 R->L }
% 17.26/2.69 nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Y, Y), nand(X, Y))), nand(X, Y)), nand(X, Y)))
% 17.26/2.69 = { by lemma 9 R->L }
% 17.26/2.69 nand(nand(X, Y), nand(nand(nand(nand(nand(Y, Y), nand(X, Y)), nand(nand(Y, Y), nand(X, Y))), nand(X, Y)), nand(X, Y)))
% 17.26/2.69 = { by lemma 8 }
% 17.26/2.69 nand(nand(Y, Y), nand(X, Y))
% 17.26/2.69 = { by lemma 9 }
% 17.26/2.69 Y
% 17.26/2.69
% 17.26/2.69 Lemma 11: nand(X, nand(nand(Y, X), X)) = nand(Y, X).
% 17.26/2.69 Proof:
% 17.26/2.69 nand(X, nand(nand(Y, X), X))
% 17.26/2.69 = { by lemma 9 R->L }
% 17.26/2.69 nand(X, nand(nand(Y, X), nand(nand(X, X), nand(Y, X))))
% 17.26/2.69 = { by lemma 9 R->L }
% 17.26/2.69 nand(nand(nand(X, X), nand(Y, X)), nand(nand(Y, X), nand(nand(X, X), nand(Y, X))))
% 17.26/2.69 = { by lemma 10 }
% 17.26/2.70 nand(Y, X)
% 17.26/2.70
% 17.26/2.70 Lemma 12: nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, X)) = W.
% 17.26/2.70 Proof:
% 17.26/2.70 nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, X))
% 17.26/2.70 = { by axiom 1 (sh_1) R->L }
% 17.26/2.70 nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(Y, Z)))))
% 17.26/2.70 = { by axiom 1 (sh_1) }
% 17.26/2.70 W
% 17.26/2.70
% 17.26/2.70 Lemma 13: nand(nand(nand(X, Y), nand(X, Y)), X) = nand(X, Y).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(nand(nand(X, Y), nand(X, Y)), X)
% 17.26/2.70 = { by lemma 12 R->L }
% 17.26/2.70 nand(nand(nand(X, Y), nand(X, Y)), nand(nand(nand(Y, nand(Z, W)), nand(nand(X, nand(Y, nand(Z, W))), nand(Y, nand(Z, W)))), nand(X, Y)))
% 17.26/2.70 = { by lemma 9 }
% 17.26/2.70 nand(X, Y)
% 17.26/2.70
% 17.26/2.70 Lemma 14: nand(X, nand(nand(X, Y), X)) = nand(X, Y).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(X, nand(nand(X, Y), X))
% 17.26/2.70 = { by lemma 12 R->L }
% 17.26/2.70 nand(X, nand(nand(X, Y), nand(nand(nand(Y, nand(Z, W)), nand(nand(X, nand(Y, nand(Z, W))), nand(Y, nand(Z, W)))), nand(X, Y))))
% 17.26/2.70 = { by lemma 12 R->L }
% 17.26/2.70 nand(nand(nand(nand(Y, nand(Z, W)), nand(nand(X, nand(Y, nand(Z, W))), nand(Y, nand(Z, W)))), nand(X, Y)), nand(nand(X, Y), nand(nand(nand(Y, nand(Z, W)), nand(nand(X, nand(Y, nand(Z, W))), nand(Y, nand(Z, W)))), nand(X, Y))))
% 17.26/2.70 = { by lemma 10 }
% 17.26/2.70 nand(X, Y)
% 17.26/2.70
% 17.26/2.70 Lemma 15: nand(X, Y) = nand(Y, X).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(X, Y)
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(Y, nand(nand(X, Y), Y))
% 17.26/2.70 = { by lemma 2 R->L }
% 17.26/2.70 nand(nand(nand(Y, Y), nand(nand(nand(Y, nand(nand(X, Y), Y)), nand(Y, Y)), nand(Y, Y))), X)
% 17.26/2.70 = { by lemma 10 R->L }
% 17.26/2.70 nand(nand(nand(Y, Y), nand(nand(nand(nand(nand(nand(nand(Y, nand(nand(X, Y), Y)), Y), nand(nand(Y, nand(nand(X, Y), Y)), Y)), nand(Y, nand(nand(X, Y), Y))), nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(nand(Y, nand(nand(X, Y), Y)), Y), nand(nand(Y, nand(nand(X, Y), Y)), Y)), nand(Y, nand(nand(X, Y), Y))))), nand(Y, Y)), nand(Y, Y))), X)
% 17.26/2.70 = { by lemma 13 }
% 17.26/2.70 nand(nand(nand(Y, Y), nand(nand(nand(nand(nand(Y, nand(nand(X, Y), Y)), Y), nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(nand(Y, nand(nand(X, Y), Y)), Y), nand(nand(Y, nand(nand(X, Y), Y)), Y)), nand(Y, nand(nand(X, Y), Y))))), nand(Y, Y)), nand(Y, Y))), X)
% 17.26/2.70 = { by lemma 13 }
% 17.26/2.70 nand(nand(nand(Y, Y), nand(nand(nand(nand(nand(Y, nand(nand(X, Y), Y)), Y), nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(Y, nand(nand(X, Y), Y)), Y))), nand(Y, Y)), nand(Y, Y))), X)
% 17.26/2.70 = { by lemma 14 R->L }
% 17.26/2.70 nand(nand(nand(Y, Y), nand(nand(nand(nand(nand(Y, nand(nand(X, Y), Y)), Y), nand(nand(Y, nand(nand(Y, nand(nand(X, Y), Y)), Y)), nand(nand(Y, nand(nand(X, Y), Y)), Y))), nand(Y, Y)), nand(Y, Y))), X)
% 17.26/2.70 = { by lemma 7 }
% 17.26/2.70 nand(nand(nand(Y, Y), nand(Y, nand(Y, Y))), X)
% 17.26/2.70 = { by lemma 10 }
% 17.26/2.70 nand(Y, X)
% 17.26/2.70
% 17.26/2.70 Lemma 16: nand(nand(X, Y), nand(X, nand(Y, Z))) = X.
% 17.26/2.70 Proof:
% 17.26/2.70 nand(nand(X, Y), nand(X, nand(Y, Z)))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(nand(X, Y), nand(X, nand(Z, Y)))
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(nand(Y, nand(nand(X, Y), Y)), nand(X, nand(Z, Y)))
% 17.26/2.70 = { by axiom 1 (sh_1) }
% 17.26/2.70 X
% 17.26/2.70
% 17.26/2.70 Lemma 17: nand(X, nand(Y, nand(X, nand(Y, Z)))) = nand(X, nand(Y, Z)).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(X, nand(Y, nand(X, nand(Y, Z))))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(nand(X, nand(Y, Z)), Y))
% 17.26/2.70 = { by lemma 16 R->L }
% 17.26/2.70 nand(X, nand(nand(X, nand(Y, Z)), nand(nand(Y, Z), nand(Y, nand(Z, W)))))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(nand(nand(Y, Z), X), nand(nand(Y, Z), nand(Y, nand(Z, W)))))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(nand(nand(Y, Z), X), nand(nand(Y, nand(Z, W)), nand(Y, Z))))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(nand(X, nand(Y, Z)), nand(nand(Y, nand(Z, W)), nand(Y, Z))))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(nand(nand(X, nand(Y, Z)), nand(nand(Y, nand(Z, W)), nand(Y, Z))), X)
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(nand(Y, nand(Z, W)), nand(Y, Z))), X)
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(nand(nand(nand(Y, nand(Z, W)), nand(Y, Z)), nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(nand(Y, nand(Z, W)), nand(Y, Z))), nand(nand(Y, nand(Z, W)), nand(Y, Z)))), X)
% 17.26/2.70 = { by axiom 1 (sh_1) R->L }
% 17.26/2.70 nand(nand(nand(nand(Y, nand(Z, W)), nand(Y, Z)), nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(nand(Y, nand(Z, W)), nand(Y, Z))), nand(nand(Y, nand(Z, W)), nand(Y, Z)))), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, nand(nand(Y, nand(Z, W)), nand(Y, Z)))))
% 17.26/2.70 = { by axiom 1 (sh_1) }
% 17.26/2.70 nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z)))
% 17.26/2.70 = { by lemma 11 }
% 17.26/2.70 nand(X, nand(Y, Z))
% 17.26/2.70
% 17.26/2.70 Lemma 18: nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, X)) = Z.
% 17.26/2.70 Proof:
% 17.26/2.70 nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, X))
% 17.26/2.70 = { by lemma 12 R->L }
% 17.26/2.70 nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, nand(nand(nand(Y, nand(W, V)), nand(nand(X, nand(Y, nand(W, V))), nand(Y, nand(W, V)))), nand(X, Y))))
% 17.26/2.70 = { by axiom 1 (sh_1) }
% 17.26/2.70 Z
% 17.26/2.70
% 17.26/2.70 Lemma 19: nand(nand(X, Y), nand(X, nand(Z, Y))) = X.
% 17.26/2.70 Proof:
% 17.26/2.70 nand(nand(X, Y), nand(X, nand(Z, Y)))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(nand(X, nand(Z, Y)), nand(X, Y))
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(nand(nand(Z, Y), nand(nand(X, nand(Z, Y)), nand(Z, Y))), nand(X, Y))
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(nand(nand(Z, Y), nand(nand(X, nand(Y, nand(nand(Z, Y), Y))), nand(Z, Y))), nand(X, Y))
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(nand(nand(Z, Y), nand(nand(X, nand(Y, nand(nand(Z, Y), Y))), nand(Y, nand(nand(Z, Y), Y)))), nand(X, Y))
% 17.26/2.70 = { by lemma 11 R->L }
% 17.26/2.70 nand(nand(nand(Y, nand(nand(Z, Y), Y)), nand(nand(X, nand(Y, nand(nand(Z, Y), Y))), nand(Y, nand(nand(Z, Y), Y)))), nand(X, Y))
% 17.26/2.70 = { by lemma 18 }
% 17.26/2.70 X
% 17.26/2.70
% 17.26/2.70 Lemma 20: nand(X, nand(Y, nand(X, Y))) = nand(X, X).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(X, nand(Y, nand(X, Y)))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(nand(X, Y), Y))
% 17.26/2.70 = { by lemma 17 R->L }
% 17.26/2.70 nand(X, nand(nand(X, Y), nand(X, nand(nand(X, Y), Y))))
% 17.26/2.70 = { by lemma 19 }
% 17.26/2.70 nand(X, X)
% 17.26/2.70
% 17.26/2.70 Lemma 21: nand(X, nand(Y, Y)) = nand(X, nand(X, Y)).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(X, nand(Y, Y))
% 17.26/2.70 = { by lemma 20 R->L }
% 17.26/2.70 nand(X, nand(Y, nand(X, nand(Y, X))))
% 17.26/2.70 = { by lemma 17 }
% 17.26/2.70 nand(X, nand(Y, X))
% 17.26/2.70 = { by lemma 15 }
% 17.26/2.70 nand(X, nand(X, Y))
% 17.26/2.70
% 17.26/2.70 Lemma 22: nand(X, nand(Y, Y)) = nand(X, nand(Y, X)).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(X, nand(Y, Y))
% 17.26/2.70 = { by lemma 21 }
% 17.26/2.70 nand(X, nand(X, Y))
% 17.26/2.70 = { by lemma 15 }
% 17.26/2.70 nand(X, nand(Y, X))
% 17.26/2.70
% 17.26/2.70 Lemma 23: nand(X, nand(X, nand(X, Y))) = nand(X, Y).
% 17.26/2.70 Proof:
% 17.26/2.70 nand(X, nand(X, nand(X, Y)))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(X, nand(Y, X)))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(nand(Y, X), X))
% 17.26/2.70 = { by lemma 15 R->L }
% 17.26/2.70 nand(X, nand(nand(X, Y), X))
% 17.26/2.70 = { by lemma 14 }
% 17.26/2.70 nand(X, Y)
% 17.26/2.70
% 17.26/2.70 Lemma 24: nand(nand(X, nand(Y, Z)), nand(X, Z)) = X.
% 17.26/2.70 Proof:
% 17.26/2.70 nand(nand(X, nand(Y, Z)), nand(X, Z))
% 17.26/2.70 = { by lemma 11 R->L }
% 17.97/2.70 nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Z))
% 17.97/2.70 = { by lemma 9 R->L }
% 17.97/2.70 nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, nand(nand(Z, Z), nand(Y, Z))))
% 17.97/2.70 = { by axiom 1 (sh_1) }
% 17.97/2.70 X
% 17.97/2.70
% 17.97/2.70 Lemma 25: nand(X, nand(Y, nand(X, nand(Z, Y)))) = nand(X, nand(Z, Y)).
% 17.97/2.70 Proof:
% 17.97/2.70 nand(X, nand(Y, nand(X, nand(Z, Y))))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(X, nand(nand(X, nand(Z, Y)), Y))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(nand(nand(X, nand(Z, Y)), Y), X)
% 17.97/2.70 = { by lemma 11 R->L }
% 17.97/2.70 nand(nand(Y, nand(nand(nand(X, nand(Z, Y)), Y), Y)), X)
% 17.97/2.70 = { by lemma 24 R->L }
% 17.97/2.70 nand(nand(Y, nand(nand(nand(X, nand(Z, Y)), Y), Y)), nand(nand(X, nand(Z, Y)), nand(X, Y)))
% 17.97/2.70 = { by axiom 1 (sh_1) }
% 17.97/2.70 nand(X, nand(Z, Y))
% 17.97/2.70
% 17.97/2.70 Lemma 26: nand(X, nand(nand(Y, Z), nand(Z, X))) = nand(X, Z).
% 17.97/2.70 Proof:
% 17.97/2.70 nand(X, nand(nand(Y, Z), nand(Z, X)))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(X, nand(nand(Y, Z), nand(X, Z)))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(X, nand(nand(X, Z), nand(Y, Z)))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(nand(nand(X, Z), nand(Y, Z)), X)
% 17.97/2.70 = { by lemma 11 R->L }
% 17.97/2.70 nand(nand(nand(Z, nand(nand(X, Z), Z)), nand(Y, Z)), X)
% 17.97/2.70 = { by lemma 11 R->L }
% 17.97/2.70 nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(X, Z), Z)), nand(Y, Z)), nand(Y, Z))), X)
% 17.97/2.70 = { by lemma 2 }
% 17.97/2.70 nand(Z, nand(nand(X, Z), Z))
% 17.97/2.70 = { by lemma 11 }
% 17.97/2.70 nand(X, Z)
% 17.97/2.70
% 17.97/2.70 Lemma 27: nand(nand(X, Y), nand(Y, nand(Z, X))) = Y.
% 17.97/2.70 Proof:
% 17.97/2.70 nand(nand(X, Y), nand(Y, nand(Z, X)))
% 17.97/2.70 = { by lemma 14 R->L }
% 17.97/2.70 nand(nand(X, nand(nand(X, Y), X)), nand(Y, nand(Z, X)))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, X)))
% 17.97/2.70 = { by axiom 1 (sh_1) }
% 17.97/2.70 Y
% 17.97/2.70
% 17.97/2.70 Lemma 28: nand(nand(X, nand(Y, Z)), nand(X, Y)) = X.
% 17.97/2.70 Proof:
% 17.97/2.70 nand(nand(X, nand(Y, Z)), nand(X, Y))
% 17.97/2.70 = { by lemma 11 R->L }
% 17.97/2.70 nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y))
% 17.97/2.70 = { by lemma 18 }
% 17.97/2.70 X
% 17.97/2.70
% 17.97/2.70 Lemma 29: nand(nand(nand(X, Y), Z), nand(X, Z)) = Z.
% 17.97/2.70 Proof:
% 17.97/2.70 nand(nand(nand(X, Y), Z), nand(X, Z))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(nand(nand(X, Y), Z), nand(Z, X))
% 17.97/2.70 = { by lemma 14 R->L }
% 17.97/2.70 nand(nand(nand(X, Y), nand(nand(nand(X, Y), Z), nand(X, Y))), nand(Z, X))
% 17.97/2.70 = { by lemma 15 R->L }
% 17.97/2.70 nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, X))
% 17.97/2.70 = { by lemma 18 }
% 17.97/2.71 Z
% 17.97/2.71
% 17.97/2.71 Goal 1 (prove_meredith_2_basis_2): nand(a, nand(b, nand(a, c))) = nand(nand(nand(c, b), b), a).
% 17.97/2.71 Proof:
% 17.97/2.71 nand(a, nand(b, nand(a, c)))
% 17.97/2.71 = { by lemma 11 R->L }
% 17.97/2.71 nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c))))
% 17.97/2.71 = { by lemma 7 R->L }
% 17.97/2.71 nand(nand(nand(a, a), nand(nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(a, a)), nand(a, a))), nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c))))))
% 17.97/2.71 = { by lemma 7 }
% 17.97/2.71 nand(nand(nand(a, a), nand(a, nand(a, a))), nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c))))))
% 17.97/2.71 = { by lemma 10 }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c))))))
% 17.97/2.71 = { by lemma 11 }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(a, nand(b, nand(a, c)))))
% 17.97/2.71 = { by lemma 11 }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(a, nand(b, nand(a, c)))))
% 17.97/2.71 = { by lemma 20 R->L }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), nand(nand(a, nand(b, nand(a, c))), nand(nand(c, b), a)))))
% 17.97/2.71 = { by lemma 15 R->L }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), nand(nand(a, nand(b, nand(a, c))), nand(a, nand(c, b))))))
% 17.97/2.71 = { by lemma 19 R->L }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), nand(nand(nand(nand(a, c), nand(a, nand(a, c))), nand(b, nand(a, c))), nand(a, nand(c, b))))))
% 17.97/2.71 = { by lemma 11 R->L }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(a, c), nand(a, nand(a, c))), nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(a, nand(c, b))))))
% 17.97/2.71 = { by lemma 28 R->L }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(a, c), nand(nand(nand(a, nand(c, b)), nand(a, c)), nand(a, c))), nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(a, nand(c, b))))))
% 17.97/2.71 = { by lemma 2 }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), nand(nand(a, c), nand(nand(nand(a, nand(c, b)), nand(a, c)), nand(a, c))))))
% 17.97/2.71 = { by lemma 11 }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), nand(nand(a, nand(c, b)), nand(a, c)))))
% 17.97/2.71 = { by lemma 28 }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), a), a)))
% 17.97/2.71 = { by lemma 15 }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(a, nand(nand(c, b), a))))
% 17.97/2.71 = { by lemma 22 R->L }
% 17.97/2.71 nand(a, nand(nand(a, nand(b, nand(a, c))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 15 R->L }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), a), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 11 R->L }
% 17.97/2.71 nand(a, nand(nand(a, nand(nand(nand(b, nand(a, c)), a), a)), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 2 R->L }
% 17.97/2.71 nand(a, nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(a, nand(nand(nand(b, nand(a, c)), a), a)), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(b, nand(a, c))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 15 }
% 17.97/2.71 nand(a, nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(a, nand(nand(a, nand(b, nand(a, c))), a)), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(b, nand(a, c))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 11 }
% 17.97/2.71 nand(a, nand(nand(nand(nand(a, nand(nand(a, nand(b, nand(a, c))), a)), nand(nand(nand(c, b), b), a)), nand(b, nand(a, c))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 14 }
% 17.97/2.71 nand(a, nand(nand(nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), b), a)), nand(b, nand(a, c))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 15 }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), b), a))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 15 }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 23 R->L }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 23 R->L }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 21 R->L }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 17 R->L }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.71 = { by lemma 26 }
% 17.97/2.71 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), a))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 12 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(nand(c, b), b), nand(b, nand(a, c))), nand(nand(a, nand(nand(nand(c, b), b), nand(b, nand(a, c)))), nand(nand(nand(c, b), b), nand(b, nand(a, c))))), nand(a, nand(nand(c, b), b)))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 15 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(nand(c, b), b), nand(b, nand(a, c))), nand(nand(a, nand(nand(nand(c, b), b), nand(b, nand(a, c)))), nand(nand(nand(c, b), b), nand(b, nand(a, c))))), nand(nand(nand(c, b), b), a))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 11 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(a, nand(nand(nand(c, b), b), nand(b, nand(a, c)))), nand(nand(nand(c, b), b), a))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 15 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(nand(c, b), b), nand(b, nand(a, c)))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 15 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(nand(c, b), b))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 25 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(b, nand(nand(b, nand(a, c)), nand(nand(c, b), b))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 11 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(b, nand(nand(b, nand(a, c)), nand(b, nand(nand(nand(c, b), b), b)))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 10 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(nand(nand(c, b), nand(b, nand(c, b))), nand(nand(b, nand(a, c)), nand(b, nand(nand(nand(c, b), b), b)))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 24 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(nand(nand(c, b), nand(nand(nand(b, nand(a, c)), nand(b, c)), nand(c, b))), nand(nand(b, nand(a, c)), nand(b, nand(nand(nand(c, b), b), b)))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 15 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(nand(nand(c, b), nand(nand(nand(b, nand(a, c)), nand(c, b)), nand(c, b))), nand(nand(b, nand(a, c)), nand(b, nand(nand(nand(c, b), b), b)))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 3 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(b, nand(a, c)))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 27 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), a))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 17 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), a))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 15 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(b, nand(a, c)), nand(a, nand(a, nand(b, nand(a, c)))))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 25 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(a, nand(a, nand(b, nand(a, c)))))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 15 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(nand(nand(c, b), b), a), nand(nand(a, nand(b, nand(a, c))), a))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 16 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 8 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 5 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 5 R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by axiom 1 (sh_1) R->L }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a)))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))))))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 19 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a)))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.72 = { by lemma 5 }
% 17.97/2.72 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(a, nand(nand(c, b), nand(c, b)))))
% 17.97/2.73 = { by lemma 15 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(c, b), nand(c, b)), a)))
% 17.97/2.73 = { by lemma 26 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(c, b), nand(c, b)), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(c, b), nand(c, b)))))))
% 17.97/2.73 = { by lemma 22 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(c, b), nand(c, b)), nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(c, b), a))))))
% 17.97/2.73 = { by lemma 15 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(c, b), nand(c, b)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), a), a)))))
% 17.97/2.73 = { by lemma 29 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(c, b), nand(c, b)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), a), nand(nand(nand(nand(c, b), b), a), nand(nand(c, b), a)))))))
% 17.97/2.73 = { by lemma 20 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(c, b), nand(c, b)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))))
% 17.97/2.73 = { by lemma 15 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(c, b)))))
% 17.97/2.73 = { by lemma 20 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), b)))))))
% 17.97/2.73 = { by lemma 15 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(c, b), nand(b, nand(nand(nand(c, b), b), a))))))))
% 17.97/2.73 = { by lemma 15 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(b, nand(nand(nand(c, b), b), a)), nand(c, b)))))))
% 17.97/2.73 = { by lemma 27 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(nand(nand(c, b), nand(b, nand(X, c))), nand(nand(nand(c, b), b), a)), nand(c, b)))))))
% 17.97/2.73 = { by lemma 11 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(nand(nand(b, nand(X, c)), nand(nand(nand(c, b), nand(b, nand(X, c))), nand(b, nand(X, c)))), nand(nand(nand(c, b), b), a)), nand(c, b)))))))
% 17.97/2.73 = { by lemma 12 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(nand(nand(b, nand(X, c)), nand(nand(nand(c, b), nand(b, nand(X, c))), nand(b, nand(X, c)))), nand(nand(nand(c, b), b), a)), nand(nand(nand(b, nand(X, c)), nand(nand(nand(c, b), nand(b, nand(X, c))), nand(b, nand(X, c)))), nand(nand(c, b), b))))))))
% 17.97/2.73 = { by lemma 28 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(b, nand(X, c)), nand(nand(nand(c, b), nand(b, nand(X, c))), nand(b, nand(X, c)))))))))
% 17.97/2.73 = { by lemma 11 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), nand(nand(c, b), nand(b, nand(X, c))))))))
% 17.97/2.73 = { by lemma 27 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), b), b)))))
% 17.97/2.73 = { by lemma 15 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(b, nand(nand(nand(nand(c, b), b), a), b))))))
% 17.97/2.73 = { by lemma 22 R->L }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(c, b), nand(b, nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))))))
% 17.97/2.73 = { by lemma 26 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), b)))
% 17.97/2.73 = { by lemma 15 }
% 17.97/2.73 nand(a, nand(nand(nand(b, nand(a, c)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(b, nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))))
% 17.97/2.73 = { by lemma 29 }
% 17.97/2.73 nand(a, nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))
% 17.97/2.73 = { by lemma 10 R->L }
% 17.97/2.73 nand(nand(nand(nand(nand(nand(c, b), b), a), a), nand(a, nand(nand(nand(nand(c, b), b), a), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))
% 17.97/2.73 = { by lemma 10 R->L }
% 17.97/2.73 nand(nand(nand(nand(nand(nand(c, b), b), a), a), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(nand(nand(c, b), b), a))), nand(nand(nand(nand(c, b), b), a), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))
% 17.97/2.73 = { by lemma 15 }
% 17.97/2.73 nand(nand(nand(nand(nand(nand(c, b), b), a), a), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), b), a), a)), nand(nand(nand(nand(c, b), b), a), a))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)))
% 17.97/2.73 = { by lemma 18 }
% 17.97/2.73 nand(nand(nand(c, b), b), a)
% 17.97/2.73 % SZS output end Proof
% 17.97/2.73
% 17.97/2.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------