TSTP Solution File: NUN062+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 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 : n018.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 12:51:47 EDT 2023
% Result : Theorem 0.21s 0.56s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 09:22:46 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.56 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.56
% 0.21/0.56 % SZS status Theorem
% 0.21/0.56
% 0.21/0.57 % SZS output start Proof
% 0.21/0.57 Take the following subset of the input axioms:
% 0.21/0.57 fof(axiom_1a, axiom, ![X1, X8]: ?[Y4]: (?[Y5]: (id(Y5, Y4) & ?[Y15]: (r2(X8, Y15) & r3(X1, Y15, Y5))) & ?[Y7]: (r2(Y7, Y4) & r3(X1, X8, Y7)))).
% 0.21/0.57 fof(axiom_2, axiom, ![X11]: ?[Y21]: ![X12]: ((id(X12, Y21) & r2(X11, X12)) | (~r2(X11, X12) & ~id(X12, Y21)))).
% 0.21/0.57 fof(axiom_5, axiom, ![X20]: id(X20, X20)).
% 0.21/0.57 fof(axiom_7a, axiom, ![X7, Y10]: (![Y20]: (~id(Y20, Y10) | ~r1(Y20)) | ~r2(X7, Y10))).
% 0.21/0.57 fof(axiom_8, axiom, ![X26, X27]: (~id(X26, X27) | ((~r1(X26) & ~r1(X27)) | (r1(X26) & r1(X27))))).
% 0.21/0.57 fof(infiniteNumbersid, conjecture, ![X1_2]: ?[Y2, Y1]: (![Y4_2]: (~id(Y1, Y4_2) | ~r1(Y4_2)) & ?[Y3]: (id(Y3, Y2) & r3(X1_2, Y1, Y3)))).
% 0.21/0.57
% 0.21/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.57 fresh(y, y, x1...xn) = u
% 0.21/0.57 C => fresh(s, t, x1...xn) = v
% 0.21/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.57 variables of u and v.
% 0.21/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.57 input problem has no model of domain size 1).
% 0.21/0.57
% 0.21/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.57
% 0.21/0.57 Axiom 1 (axiom_5): id(X, X) = true2.
% 0.21/0.57 Axiom 2 (infiniteNumbersid_1): fresh(X, X, Y) = true2.
% 0.21/0.57 Axiom 3 (axiom_8_1): fresh7(X, X, Y) = true2.
% 0.21/0.57 Axiom 4 (infiniteNumbersid): fresh3(X, X, Y) = true2.
% 0.21/0.57 Axiom 5 (axiom_2): fresh20(X, X, Y, Z) = true2.
% 0.21/0.57 Axiom 6 (axiom_8_1): fresh8(X, X, Y, Z) = r1(Y).
% 0.21/0.57 Axiom 7 (axiom_1a_3): r3(X, Y, y7(X, Y)) = true2.
% 0.21/0.57 Axiom 8 (axiom_8_1): fresh8(r1(X), true2, Y, X) = fresh7(id(Y, X), true2, Y).
% 0.21/0.57 Axiom 9 (infiniteNumbersid): fresh4(X, X, Y, Z, W) = id(Z, y4(Z)).
% 0.21/0.57 Axiom 10 (infiniteNumbersid_1): fresh2(X, X, Y, Z, W) = r1(y4(Z)).
% 0.21/0.57 Axiom 11 (axiom_2): fresh20(id(X, y21(Y)), true2, Y, X) = r2(Y, X).
% 0.21/0.57 Axiom 12 (infiniteNumbersid): fresh4(r3(x1, X, Y), true2, Z, X, Y) = fresh3(id(Y, Z), true2, X).
% 0.21/0.57 Axiom 13 (infiniteNumbersid_1): fresh2(r3(x1, X, Y), true2, Z, X, Y) = fresh(id(Y, Z), true2, X).
% 0.21/0.57
% 0.21/0.57 Goal 1 (axiom_7a): tuple(id(X, Y), r1(X), r2(Z, Y)) = tuple(true2, true2, true2).
% 0.21/0.57 The goal is true when:
% 0.21/0.57 X = y21(X)
% 0.21/0.57 Y = y21(X)
% 0.21/0.57 Z = X
% 0.21/0.57
% 0.21/0.57 Proof:
% 0.21/0.57 tuple(id(y21(X), y21(X)), r1(y21(X)), r2(X, y21(X)))
% 0.21/0.57 = { by axiom 1 (axiom_5) }
% 0.21/0.57 tuple(true2, r1(y21(X)), r2(X, y21(X)))
% 0.21/0.57 = { by axiom 11 (axiom_2) R->L }
% 0.21/0.57 tuple(true2, r1(y21(X)), fresh20(id(y21(X), y21(X)), true2, X, y21(X)))
% 0.21/0.57 = { by axiom 1 (axiom_5) }
% 0.21/0.57 tuple(true2, r1(y21(X)), fresh20(true2, true2, X, y21(X)))
% 0.21/0.57 = { by axiom 5 (axiom_2) }
% 0.21/0.57 tuple(true2, r1(y21(X)), true2)
% 0.21/0.57 = { by axiom 6 (axiom_8_1) R->L }
% 0.21/0.57 tuple(true2, fresh8(true2, true2, y21(X), y4(y21(X))), true2)
% 0.21/0.57 = { by axiom 2 (infiniteNumbersid_1) R->L }
% 0.21/0.57 tuple(true2, fresh8(fresh(true2, true2, y21(X)), true2, y21(X), y4(y21(X))), true2)
% 0.21/0.57 = { by axiom 1 (axiom_5) R->L }
% 0.21/0.57 tuple(true2, fresh8(fresh(id(y7(x1, y21(X)), y7(x1, y21(X))), true2, y21(X)), true2, y21(X), y4(y21(X))), true2)
% 0.21/0.57 = { by axiom 13 (infiniteNumbersid_1) R->L }
% 0.21/0.57 tuple(true2, fresh8(fresh2(r3(x1, y21(X), y7(x1, y21(X))), true2, y7(x1, y21(X)), y21(X), y7(x1, y21(X))), true2, y21(X), y4(y21(X))), true2)
% 0.21/0.57 = { by axiom 7 (axiom_1a_3) }
% 0.21/0.57 tuple(true2, fresh8(fresh2(true2, true2, y7(x1, y21(X)), y21(X), y7(x1, y21(X))), true2, y21(X), y4(y21(X))), true2)
% 0.21/0.57 = { by axiom 10 (infiniteNumbersid_1) }
% 0.21/0.57 tuple(true2, fresh8(r1(y4(y21(X))), true2, y21(X), y4(y21(X))), true2)
% 0.21/0.57 = { by axiom 8 (axiom_8_1) }
% 0.21/0.58 tuple(true2, fresh7(id(y21(X), y4(y21(X))), true2, y21(X)), true2)
% 0.21/0.58 = { by axiom 9 (infiniteNumbersid) R->L }
% 0.21/0.58 tuple(true2, fresh7(fresh4(true2, true2, y7(x1, y21(X)), y21(X), y7(x1, y21(X))), true2, y21(X)), true2)
% 0.21/0.58 = { by axiom 7 (axiom_1a_3) R->L }
% 0.21/0.58 tuple(true2, fresh7(fresh4(r3(x1, y21(X), y7(x1, y21(X))), true2, y7(x1, y21(X)), y21(X), y7(x1, y21(X))), true2, y21(X)), true2)
% 0.21/0.58 = { by axiom 12 (infiniteNumbersid) }
% 0.21/0.58 tuple(true2, fresh7(fresh3(id(y7(x1, y21(X)), y7(x1, y21(X))), true2, y21(X)), true2, y21(X)), true2)
% 0.21/0.58 = { by axiom 1 (axiom_5) }
% 0.21/0.58 tuple(true2, fresh7(fresh3(true2, true2, y21(X)), true2, y21(X)), true2)
% 0.21/0.58 = { by axiom 4 (infiniteNumbersid) }
% 0.21/0.58 tuple(true2, fresh7(true2, true2, y21(X)), true2)
% 0.21/0.58 = { by axiom 3 (axiom_8_1) }
% 0.21/0.58 tuple(true2, true2, true2)
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58
% 0.21/0.58 RESULT: Theorem (the conjecture is true).
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