TSTP Solution File: NUN085+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% 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 : n008.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 : Thu Aug 31 12:51:55 EDT 2023
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 09:36:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.42 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.42
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Take the following subset of the input axioms:
% 0.20/0.45 fof(axiom_1, axiom, ?[Y24]: ![X19]: ((~r1(X19) & X19!=Y24) | (r1(X19) & X19=Y24))).
% 0.20/0.45 fof(axiom_1a, axiom, ![X1, X8]: ?[Y4]: (?[Y5]: (?[Y15]: (r2(X8, Y15) & r3(X1, Y15, Y5)) & Y5=Y4) & ?[Y7]: (r2(Y7, Y4) & r3(X1, X8, Y7)))).
% 0.20/0.45 fof(axiom_2, axiom, ![X11]: ?[Y21]: ![X12]: ((~r2(X11, X12) & X12!=Y21) | (r2(X11, X12) & X12=Y21))).
% 0.20/0.45 fof(axiom_3, axiom, ![X13, X14]: ?[Y22]: ![X15]: ((~r3(X13, X14, X15) & X15!=Y22) | (r3(X13, X14, X15) & X15=Y22))).
% 0.20/0.45 fof(axiom_4a, axiom, ![X4]: ?[Y9]: (?[Y16]: (r1(Y16) & r3(X4, Y16, Y9)) & Y9=X4)).
% 0.20/0.45 fof(axiom_7a, axiom, ![X7, Y10]: (![Y20]: (~r1(Y20) | Y20!=Y10) | ~r2(X7, Y10))).
% 0.20/0.45 fof(zeroplusoneidzero, conjecture, ![Y1]: (![Y2]: (![Y3]: (~r1(Y3) | ~r3(Y3, Y2, Y1)) | ![Y4_2]: (~r1(Y4_2) | ~r2(Y4_2, Y2))) | ![Y5_2]: (Y1!=Y5_2 | ~r1(Y5_2)))).
% 0.20/0.45
% 0.20/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.45 fresh(y, y, x1...xn) = u
% 0.20/0.45 C => fresh(s, t, x1...xn) = v
% 0.20/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.45 variables of u and v.
% 0.20/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.45 input problem has no model of domain size 1).
% 0.20/0.45
% 0.20/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.45
% 0.20/0.45 Axiom 1 (zeroplusoneidzero): y1 = y5.
% 0.20/0.45 Axiom 2 (axiom_4a): y9(X) = X.
% 0.20/0.45 Axiom 3 (zeroplusoneidzero_1): r1(y3) = true2.
% 0.20/0.45 Axiom 4 (zeroplusoneidzero_2): r1(y4) = true2.
% 0.20/0.45 Axiom 5 (zeroplusoneidzero_3): r1(y5) = true2.
% 0.20/0.45 Axiom 6 (axiom_1a): y5_2(X, Y) = y4_2(X, Y).
% 0.20/0.45 Axiom 7 (axiom_4a_1): r1(y16(X)) = true2.
% 0.20/0.45 Axiom 8 (zeroplusoneidzero_4): r2(y4, y2) = true2.
% 0.20/0.45 Axiom 9 (axiom_1_1): fresh10(X, X, Y) = y24.
% 0.20/0.45 Axiom 10 (axiom_1): fresh9(X, X, Y) = true2.
% 0.20/0.45 Axiom 11 (axiom_1): fresh9(X, y24, X) = r1(X).
% 0.20/0.45 Axiom 12 (zeroplusoneidzero_5): r3(y3, y2, y1) = true2.
% 0.20/0.45 Axiom 13 (axiom_1_1): fresh10(r1(X), true2, X) = X.
% 0.20/0.45 Axiom 14 (axiom_2): fresh8(X, X, Y, Z) = true2.
% 0.20/0.45 Axiom 15 (axiom_2_1): fresh5(X, X, Y, Z) = Z.
% 0.20/0.45 Axiom 16 (axiom_1a_1): r2(X, y15(Y, X)) = true2.
% 0.20/0.45 Axiom 17 (axiom_2): fresh8(X, y21(Y), Y, X) = r2(Y, X).
% 0.20/0.45 Axiom 18 (axiom_3_1): fresh4(X, X, Y, Z, W) = W.
% 0.20/0.45 Axiom 19 (axiom_1a_3): r3(X, Y, y7(X, Y)) = true2.
% 0.20/0.45 Axiom 20 (axiom_4a_2): r3(X, y16(X), y9(X)) = true2.
% 0.20/0.45 Axiom 21 (axiom_2_1): fresh5(r2(X, Y), true2, X, Y) = y21(X).
% 0.20/0.45 Axiom 22 (axiom_1a_2): r2(y7(X, Y), y4_2(X, Y)) = true2.
% 0.20/0.45 Axiom 23 (axiom_1a_4): r3(X, y15(X, Y), y5_2(X, Y)) = true2.
% 0.20/0.45 Axiom 24 (axiom_3_1): fresh4(r3(X, Y, Z), true2, X, Y, Z) = y22(X, Y).
% 0.20/0.45
% 0.20/0.45 Goal 1 (axiom_7a): tuple(r1(X), r2(Y, X)) = tuple(true2, true2).
% 0.20/0.45 The goal is true when:
% 0.20/0.45 X = y24
% 0.20/0.45 Y = y24
% 0.20/0.45
% 0.20/0.45 Proof:
% 0.20/0.45 tuple(r1(y24), r2(y24, y24))
% 0.20/0.45 = { by axiom 9 (axiom_1_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh10(true2, true2, y1)))
% 0.20/0.45 = { by axiom 5 (zeroplusoneidzero_3) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh10(r1(y5), true2, y1)))
% 0.20/0.45 = { by axiom 1 (zeroplusoneidzero) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh10(r1(y1), true2, y1)))
% 0.20/0.45 = { by axiom 13 (axiom_1_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y1))
% 0.20/0.45 = { by axiom 18 (axiom_3_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh4(true2, true2, y3, y2, y1)))
% 0.20/0.45 = { by axiom 12 (zeroplusoneidzero_5) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh4(r3(y3, y2, y1), true2, y3, y2, y1)))
% 0.20/0.45 = { by axiom 24 (axiom_3_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y3, y2)))
% 0.20/0.45 = { by axiom 13 (axiom_1_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(fresh10(r1(y3), true2, y3), y2)))
% 0.20/0.45 = { by axiom 3 (zeroplusoneidzero_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(fresh10(true2, true2, y3), y2)))
% 0.20/0.45 = { by axiom 9 (axiom_1_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, y2)))
% 0.20/0.45 = { by axiom 15 (axiom_2_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, fresh5(true2, true2, y4, y2))))
% 0.20/0.45 = { by axiom 8 (zeroplusoneidzero_4) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, fresh5(r2(y4, y2), true2, y4, y2))))
% 0.20/0.45 = { by axiom 21 (axiom_2_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, y21(y4))))
% 0.20/0.45 = { by axiom 13 (axiom_1_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, y21(fresh10(r1(y4), true2, y4)))))
% 0.20/0.45 = { by axiom 4 (zeroplusoneidzero_2) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, y21(fresh10(true2, true2, y4)))))
% 0.20/0.45 = { by axiom 9 (axiom_1_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, y21(y24))))
% 0.20/0.45 = { by axiom 21 (axiom_2_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, fresh5(r2(y24, y15(y24, y24)), true2, y24, y15(y24, y24)))))
% 0.20/0.45 = { by axiom 16 (axiom_1a_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, fresh5(true2, true2, y24, y15(y24, y24)))))
% 0.20/0.45 = { by axiom 15 (axiom_2_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y22(y24, y15(y24, y24))))
% 0.20/0.45 = { by axiom 24 (axiom_3_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh4(r3(y24, y15(y24, y24), y4_2(y24, y24)), true2, y24, y15(y24, y24), y4_2(y24, y24))))
% 0.20/0.45 = { by axiom 6 (axiom_1a) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh4(r3(y24, y15(y24, y24), y5_2(y24, y24)), true2, y24, y15(y24, y24), y4_2(y24, y24))))
% 0.20/0.45 = { by axiom 23 (axiom_1a_4) }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh4(true2, true2, y24, y15(y24, y24), y4_2(y24, y24))))
% 0.20/0.45 = { by axiom 18 (axiom_3_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y4_2(y24, y24)))
% 0.20/0.45 = { by axiom 15 (axiom_2_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh5(true2, true2, y7(y24, y24), y4_2(y24, y24))))
% 0.20/0.45 = { by axiom 22 (axiom_1a_2) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, fresh5(r2(y7(y24, y24), y4_2(y24, y24)), true2, y7(y24, y24), y4_2(y24, y24))))
% 0.20/0.45 = { by axiom 21 (axiom_2_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(y7(y24, y24))))
% 0.20/0.45 = { by axiom 18 (axiom_3_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(fresh4(true2, true2, y24, y24, y7(y24, y24)))))
% 0.20/0.45 = { by axiom 19 (axiom_1a_3) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(fresh4(r3(y24, y24, y7(y24, y24)), true2, y24, y24, y7(y24, y24)))))
% 0.20/0.45 = { by axiom 24 (axiom_3_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(y22(y24, y24))))
% 0.20/0.45 = { by axiom 9 (axiom_1_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(y22(y24, fresh10(true2, true2, y16(y24))))))
% 0.20/0.45 = { by axiom 7 (axiom_4a_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(y22(y24, fresh10(r1(y16(y24)), true2, y16(y24))))))
% 0.20/0.45 = { by axiom 13 (axiom_1_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(y22(y24, y16(y24)))))
% 0.20/0.45 = { by axiom 24 (axiom_3_1) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(fresh4(r3(y24, y16(y24), y24), true2, y24, y16(y24), y24))))
% 0.20/0.45 = { by axiom 2 (axiom_4a) R->L }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(fresh4(r3(y24, y16(y24), y9(y24)), true2, y24, y16(y24), y24))))
% 0.20/0.45 = { by axiom 20 (axiom_4a_2) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(fresh4(true2, true2, y24, y16(y24), y24))))
% 0.20/0.45 = { by axiom 18 (axiom_3_1) }
% 0.20/0.45 tuple(r1(y24), r2(y24, y21(y24)))
% 0.20/0.45 = { by axiom 17 (axiom_2) R->L }
% 0.20/0.45 tuple(r1(y24), fresh8(y21(y24), y21(y24), y24, y21(y24)))
% 0.20/0.45 = { by axiom 14 (axiom_2) }
% 0.20/0.45 tuple(r1(y24), true2)
% 0.20/0.45 = { by axiom 11 (axiom_1) R->L }
% 0.20/0.45 tuple(fresh9(y24, y24, y24), true2)
% 0.20/0.45 = { by axiom 10 (axiom_1) }
% 0.20/0.45 tuple(true2, true2)
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45
% 0.20/0.45 RESULT: Theorem (the conjecture is true).
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