TSTP Solution File: NUN087+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUN087+1 : 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 : n002.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 12:51:56 EDT 2023
% Result : Theorem 149.89s 19.57s
% Output : Proof 149.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUN087+1 : TPTP v8.1.2. Released v7.3.0.
% 0.13/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun Aug 27 10:13:18 EDT 2023
% 0.16/0.36 % CPUTime :
% 149.89/19.57 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 149.89/19.57
% 149.89/19.57 % SZS status Theorem
% 149.89/19.57
% 149.89/19.57 % SZS output start Proof
% 149.89/19.57 Take the following subset of the input axioms:
% 149.89/19.58 fof(axiom_1, axiom, ?[Y24]: ![X19]: ((id(X19, Y24) & r1(X19)) | (~r1(X19) & ~id(X19, Y24)))).
% 149.89/19.58 fof(axiom_11, axiom, ![X38, X39, X40, X41, X42, X43]: (~id(X38, X41) | (~id(X39, X42) | (~id(X40, X43) | ((~r4(X38, X39, X40) & ~r4(X41, X42, X43)) | (r4(X38, X39, X40) & r4(X41, X42, X43))))))).
% 149.89/19.58 fof(axiom_2a, axiom, ![X2, X9]: ?[Y2]: (?[Y3]: (id(Y3, Y2) & ?[Y14]: (r2(X9, Y14) & r4(X2, Y14, Y3))) & ?[Y6]: (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))).
% 149.89/19.58 fof(axiom_4, axiom, ![X16, X17]: ?[Y23]: ![X18]: ((id(X18, Y23) & r4(X16, X17, X18)) | (~r4(X16, X17, X18) & ~id(X18, Y23)))).
% 149.89/19.58 fof(axiom_5, axiom, ![X20]: id(X20, X20)).
% 149.89/19.58 fof(axiom_5a, axiom, ![X5]: ?[Y8]: (?[Y17]: (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18]: (id(Y8, Y18) & r1(Y18)))).
% 149.89/19.58 fof(axiom_7a, axiom, ![X7, Y10]: (![Y20]: (~id(Y20, Y10) | ~r1(Y20)) | ~r2(X7, Y10))).
% 149.89/19.58 fof(axiom_8, axiom, ![X26, X27]: (~id(X26, X27) | ((~r1(X26) & ~r1(X27)) | (r1(X26) & r1(X27))))).
% 149.89/19.58 fof(zerotimeszeroeqzero, conjecture, ?[Y1]: (?[Y2_2]: (r1(Y2_2) & r4(Y2_2, Y2_2, Y1)) & ?[Y3_2]: (id(Y1, Y3_2) & r1(Y3_2)))).
% 149.89/19.58
% 149.89/19.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 149.89/19.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 149.89/19.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 149.89/19.58 fresh(y, y, x1...xn) = u
% 149.89/19.58 C => fresh(s, t, x1...xn) = v
% 149.89/19.58 where fresh is a fresh function symbol and x1..xn are the free
% 149.89/19.58 variables of u and v.
% 149.89/19.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 149.89/19.58 input problem has no model of domain size 1).
% 149.89/19.58
% 149.89/19.58 The encoding turns the above axioms into the following unit equations and goals:
% 149.89/19.58
% 149.89/19.58 Axiom 1 (axiom_5): id(X, X) = true2.
% 149.89/19.58 Axiom 2 (axiom_5a_1): r1(y17(X)) = true2.
% 149.89/19.58 Axiom 3 (axiom_5a_2): r1(y18(X)) = true2.
% 149.89/19.58 Axiom 4 (axiom_1_1): fresh17(X, X, Y) = true2.
% 149.89/19.58 Axiom 5 (axiom_8): fresh5(X, X, Y) = true2.
% 149.89/19.58 Axiom 6 (axiom_8_1): fresh3(X, X, Y) = true2.
% 149.89/19.58 Axiom 7 (axiom_5a): id(y8(X), y18(X)) = true2.
% 149.89/19.58 Axiom 8 (axiom_1_1): fresh17(r1(X), true2, X) = id(X, y24).
% 149.89/19.58 Axiom 9 (axiom_8): fresh6(X, X, Y, Z) = r1(Z).
% 149.89/19.58 Axiom 10 (axiom_8_1): fresh4(X, X, Y, Z) = r1(Y).
% 149.89/19.58 Axiom 11 (axiom_2a_3): r4(X, Y, y6(X, Y)) = true2.
% 149.89/19.58 Axiom 12 (axiom_5a_3): r4(X, y17(X), y8(X)) = true2.
% 149.89/19.58 Axiom 13 (axiom_11_1): fresh28(X, X, Y, Z, W) = true2.
% 149.89/19.58 Axiom 14 (axiom_4_1): fresh10(X, X, Y, Z, W) = true2.
% 149.89/19.58 Axiom 15 (axiom_8): fresh6(r1(X), true2, X, Y) = fresh5(id(X, Y), true2, Y).
% 149.89/19.58 Axiom 16 (axiom_8_1): fresh4(r1(X), true2, Y, X) = fresh3(id(Y, X), true2, Y).
% 149.89/19.58 Axiom 17 (axiom_11_1): fresh26(X, X, Y, Z, W, V) = r4(Y, Z, W).
% 149.89/19.58 Axiom 18 (axiom_11_1): fresh27(X, X, Y, Z, W, V, U) = fresh28(id(Y, V), true2, Y, Z, W).
% 149.89/19.58 Axiom 19 (axiom_11_1): fresh25(X, X, Y, Z, W, V, U, T) = fresh26(id(Z, U), true2, Y, Z, W, V).
% 149.89/19.58 Axiom 20 (axiom_4_1): fresh10(r4(X, Y, Z), true2, X, Y, Z) = id(Z, y23(X, Y)).
% 149.89/19.58 Axiom 21 (axiom_11_1): fresh25(r4(X, Y, Z), true2, W, V, U, X, Y, Z) = fresh27(id(U, Z), true2, W, V, U, X, Y).
% 149.89/19.58
% 149.89/19.58 Goal 1 (zerotimeszeroeqzero): tuple(id(X, Y), r1(Z), r1(Y), r4(Z, Z, X)) = tuple(true2, true2, true2, true2).
% 149.89/19.58 The goal is true when:
% 149.89/19.58 X = y6(y24, y17(y24))
% 149.89/19.58 Y = y23(y24, y17(y24))
% 149.89/19.58 Z = y17(y24)
% 149.89/19.58
% 149.89/19.58 Proof:
% 149.89/19.58 tuple(id(y6(y24, y17(y24)), y23(y24, y17(y24))), r1(y17(y24)), r1(y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 20 (axiom_4_1) R->L }
% 149.89/19.58 tuple(fresh10(r4(y24, y17(y24), y6(y24, y17(y24))), true2, y24, y17(y24), y6(y24, y17(y24))), r1(y17(y24)), r1(y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 11 (axiom_2a_3) }
% 149.89/19.58 tuple(fresh10(true2, true2, y24, y17(y24), y6(y24, y17(y24))), r1(y17(y24)), r1(y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 14 (axiom_4_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), r1(y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 9 (axiom_8) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh6(true2, true2, y8(y24), y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 6 (axiom_8_1) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh6(fresh3(true2, true2, y8(y24)), true2, y8(y24), y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 7 (axiom_5a) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh6(fresh3(id(y8(y24), y18(y24)), true2, y8(y24)), true2, y8(y24), y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 16 (axiom_8_1) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh6(fresh4(r1(y18(y24)), true2, y8(y24), y18(y24)), true2, y8(y24), y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 3 (axiom_5a_2) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh6(fresh4(true2, true2, y8(y24), y18(y24)), true2, y8(y24), y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 10 (axiom_8_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh6(r1(y8(y24)), true2, y8(y24), y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 15 (axiom_8) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh5(id(y8(y24), y23(y24, y17(y24))), true2, y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 20 (axiom_4_1) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh5(fresh10(r4(y24, y17(y24), y8(y24)), true2, y24, y17(y24), y8(y24)), true2, y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 12 (axiom_5a_3) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh5(fresh10(true2, true2, y24, y17(y24), y8(y24)), true2, y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 14 (axiom_4_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), fresh5(true2, true2, y23(y24, y17(y24))), r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 5 (axiom_8) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, r4(y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 17 (axiom_11_1) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh26(true2, true2, y17(y24), y17(y24), y6(y24, y17(y24)), y24))
% 149.89/19.58 = { by axiom 1 (axiom_5) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh26(id(y17(y24), y17(y24)), true2, y17(y24), y17(y24), y6(y24, y17(y24)), y24))
% 149.89/19.58 = { by axiom 19 (axiom_11_1) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh25(true2, true2, y17(y24), y17(y24), y6(y24, y17(y24)), y24, y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 11 (axiom_2a_3) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh25(r4(y24, y17(y24), y6(y24, y17(y24))), true2, y17(y24), y17(y24), y6(y24, y17(y24)), y24, y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 21 (axiom_11_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh27(id(y6(y24, y17(y24)), y6(y24, y17(y24))), true2, y17(y24), y17(y24), y6(y24, y17(y24)), y24, y17(y24)))
% 149.89/19.58 = { by axiom 1 (axiom_5) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh27(true2, true2, y17(y24), y17(y24), y6(y24, y17(y24)), y24, y17(y24)))
% 149.89/19.58 = { by axiom 18 (axiom_11_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh28(id(y17(y24), y24), true2, y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 8 (axiom_1_1) R->L }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh28(fresh17(r1(y17(y24)), true2, y17(y24)), true2, y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 2 (axiom_5a_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh28(fresh17(true2, true2, y17(y24)), true2, y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 4 (axiom_1_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, fresh28(true2, true2, y17(y24), y17(y24), y6(y24, y17(y24))))
% 149.89/19.58 = { by axiom 13 (axiom_11_1) }
% 149.89/19.58 tuple(true2, r1(y17(y24)), true2, true2)
% 149.89/19.58 = { by axiom 2 (axiom_5a_1) }
% 149.89/19.58 tuple(true2, true2, true2, true2)
% 149.89/19.58 % SZS output end Proof
% 149.89/19.58
% 149.89/19.58 RESULT: Theorem (the conjecture is true).
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