TSTP Solution File: BOO075-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO075-1 : 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 : n031.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 0.17s 0.42s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO075-1 : TPTP v8.1.2. Released v2.6.0.
% 0.10/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n031.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 : Sun Aug 27 08:43:38 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.42 Command-line arguments: --no-flatten-goal
% 0.17/0.42
% 0.17/0.42 % SZS status Unsatisfiable
% 0.17/0.42
% 0.17/0.43 % SZS output start Proof
% 0.17/0.43 Axiom 1 (sh_1): nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, X))) = Y.
% 0.17/0.43
% 0.17/0.43 Lemma 2: nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, X)) = W.
% 0.17/0.43 Proof:
% 0.17/0.43 nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, X))
% 0.17/0.43 = { by axiom 1 (sh_1) R->L }
% 0.17/0.43 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)))))
% 0.17/0.43 = { by axiom 1 (sh_1) }
% 0.17/0.44 W
% 0.17/0.44
% 0.17/0.44 Lemma 3: nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, nand(nand(X, Z), Z)))) = Y.
% 0.17/0.44 Proof:
% 0.17/0.44 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, nand(nand(X, Z), Z))))
% 0.17/0.44 = { by axiom 1 (sh_1) R->L }
% 0.17/0.44 nand(nand(X, nand(nand(Y, nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(W, Z)))), X)), nand(Y, nand(Z, nand(nand(X, Z), Z))))
% 0.17/0.44 = { by axiom 1 (sh_1) R->L }
% 0.17/0.44 nand(nand(X, nand(nand(Y, nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(W, Z)))), nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(W, Z))))), nand(Y, nand(Z, nand(nand(X, Z), Z))))
% 0.17/0.44 = { by axiom 1 (sh_1) R->L }
% 0.17/0.44 nand(nand(nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(W, Z))), nand(nand(Y, nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(W, Z)))), nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(W, Z))))), nand(Y, nand(Z, nand(nand(X, Z), Z))))
% 0.17/0.44 = { by lemma 2 }
% 0.17/0.44 Y
% 0.17/0.44
% 0.17/0.44 Lemma 4: nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y) = nand(Y, nand(nand(Y, Y), Y)).
% 0.17/0.44 Proof:
% 0.17/0.44 nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y)
% 0.17/0.44 = { by axiom 1 (sh_1) R->L }
% 0.17/0.44 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))))
% 0.17/0.44 = { by lemma 3 }
% 0.17/0.44 nand(Y, nand(nand(Y, Y), Y))
% 0.17/0.44
% 0.17/0.44 Lemma 5: nand(X, nand(nand(X, X), X)) = nand(X, X).
% 0.17/0.44 Proof:
% 0.17/0.44 nand(X, nand(nand(X, X), X))
% 0.17/0.44 = { by lemma 4 R->L }
% 0.17/0.44 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)
% 0.17/0.44 = { by axiom 1 (sh_1) }
% 0.17/0.44 nand(nand(nand(X, nand(nand(X, X), X)), nand(X, nand(X, nand(nand(X, X), X)))), X)
% 0.17/0.44 = { by lemma 3 }
% 0.17/0.44 nand(X, X)
% 0.17/0.44
% 0.17/0.44 Lemma 6: nand(nand(X, X), nand(X, X)) = X.
% 0.17/0.44 Proof:
% 0.17/0.44 nand(nand(X, X), nand(X, X))
% 0.17/0.44 = { by lemma 5 R->L }
% 0.17/0.44 nand(nand(X, nand(nand(X, X), X)), nand(X, X))
% 0.17/0.44 = { by lemma 5 R->L }
% 0.17/0.44 nand(nand(X, nand(nand(X, X), X)), nand(X, nand(nand(X, X), X)))
% 0.17/0.44 = { by axiom 1 (sh_1) }
% 0.17/0.44 X
% 0.17/0.44
% 0.17/0.44 Goal 1 (prove_meredith_2_basis_1): nand(nand(a, a), nand(b, a)) = a.
% 0.17/0.44 Proof:
% 0.17/0.44 nand(nand(a, a), nand(b, a))
% 0.17/0.44 = { by lemma 5 R->L }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(b, a))
% 0.17/0.44 = { by axiom 1 (sh_1) R->L }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.44 = { by lemma 2 R->L }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(nand(X, nand(nand(nand(b, a), X), X)), nand(nand(b, a), nand(Y, X)))), nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(nand(b, a), nand(nand(X, nand(nand(nand(b, a), X), X)), nand(nand(b, a), nand(Y, X))))), nand(nand(b, a), nand(nand(X, nand(nand(nand(b, a), X), X)), nand(nand(b, a), nand(Y, X)))))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.44 = { by axiom 1 (sh_1) }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(nand(b, a), nand(nand(X, nand(nand(nand(b, a), X), X)), nand(nand(b, a), nand(Y, X))))), nand(nand(b, a), nand(nand(X, nand(nand(nand(b, a), X), X)), nand(nand(b, a), nand(Y, X)))))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.44 = { by axiom 1 (sh_1) }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(nand(b, a), nand(nand(X, nand(nand(nand(b, a), X), X)), nand(nand(b, a), nand(Y, X))))), nand(nand(b, a), nand(b, a)))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.44 = { by axiom 1 (sh_1) }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(nand(b, a), nand(b, a))), nand(nand(b, a), nand(b, a)))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.44 = { by lemma 5 R->L }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))), nand(nand(b, a), nand(b, a)))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.44 = { by axiom 1 (sh_1) }
% 0.17/0.44 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(b, a), nand(nand(b, a), nand(b, a)))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.44 = { by lemma 6 R->L }
% 0.17/0.45 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(b, a), nand(b, a))), nand(nand(b, a), nand(b, a)))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.45 = { by lemma 5 }
% 0.17/0.45 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(nand(nand(b, a), nand(b, a)), nand(nand(b, a), nand(b, a))), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.45 = { by lemma 6 }
% 0.17/0.45 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.45 = { by lemma 4 R->L }
% 0.17/0.45 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(b, a), nand(nand(nand(a, nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), a), a)), nand(b, a)), nand(b, a))), nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a)))))
% 0.17/0.45 = { by axiom 1 (sh_1) R->L }
% 0.17/0.45 nand(nand(a, nand(nand(a, a), a)), nand(nand(nand(b, a), nand(nand(nand(a, nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), a), a)), nand(b, a)), nand(b, a))), nand(nand(a, nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), a), a)), nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), nand(b, a)))))
% 0.17/0.45 = { by axiom 1 (sh_1) }
% 0.17/0.45 nand(nand(a, nand(nand(a, a), a)), nand(a, nand(nand(nand(nand(b, a), nand(nand(nand(b, a), nand(b, a)), nand(b, a))), a), a)))
% 0.17/0.45 = { by lemma 5 }
% 0.17/0.45 nand(nand(a, nand(nand(a, a), a)), nand(a, nand(nand(nand(nand(b, a), nand(b, a)), a), a)))
% 0.17/0.45 = { by axiom 1 (sh_1) }
% 0.17/0.45 a
% 0.17/0.45 % SZS output end Proof
% 0.17/0.45
% 0.17/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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