TSTP Solution File: NUN080+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUN080+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 : n022.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 12:51:53 EDT 2023
% Result : Theorem 9.96s 1.64s
% Output : Proof 9.96s
% 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 : NUN080+1 : 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 : n022.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 09:22:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 9.96/1.64 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 9.96/1.64
% 9.96/1.64 % SZS status Theorem
% 9.96/1.64
% 9.96/1.65 % SZS output start Proof
% 9.96/1.65 Take the following subset of the input axioms:
% 9.96/1.65 fof(axiom_1, axiom, ?[Y24]: ![X19]: ((id(X19, Y24) & r1(X19)) | (~r1(X19) & ~id(X19, Y24)))).
% 9.96/1.65 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)))).
% 9.96/1.66 fof(axiom_4a, axiom, ![X4]: ?[Y9]: (id(Y9, X4) & ?[Y16]: (r1(Y16) & r3(X4, Y16, Y9)))).
% 9.96/1.66 fof(axiom_5, axiom, ![X20]: id(X20, X20)).
% 9.96/1.66 fof(axiom_7a, axiom, ![X7, Y10]: (![Y20]: (~id(Y20, Y10) | ~r1(Y20)) | ~r2(X7, Y10))).
% 9.96/1.66 fof(axiom_9, axiom, ![X28, X29, X30, X31]: (~id(X28, X30) | (~id(X29, X31) | ((~r2(X28, X29) & ~r2(X30, X31)) | (r2(X28, X29) & r2(X30, X31)))))).
% 9.96/1.66 fof(xplustwoidy, conjecture, ?[Y2, Y3, Y1]: (id(Y3, Y2) & ?[Y4_2]: (r3(Y1, Y4_2, Y3) & ?[Y5_2]: (r2(Y5_2, Y4_2) & ?[Y6]: (r1(Y6) & r2(Y6, Y5_2)))))).
% 9.96/1.66
% 9.96/1.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.96/1.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.96/1.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.96/1.66 fresh(y, y, x1...xn) = u
% 9.96/1.66 C => fresh(s, t, x1...xn) = v
% 9.96/1.66 where fresh is a fresh function symbol and x1..xn are the free
% 9.96/1.66 variables of u and v.
% 9.96/1.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.96/1.66 input problem has no model of domain size 1).
% 9.96/1.66
% 9.96/1.66 The encoding turns the above axioms into the following unit equations and goals:
% 9.96/1.66
% 9.96/1.66 Axiom 1 (axiom_5): id(X, X) = true2.
% 9.96/1.66 Axiom 2 (axiom_4a_1): r1(y16(X)) = true2.
% 9.96/1.66 Axiom 3 (axiom_1_1): fresh17(X, X, Y) = true2.
% 9.96/1.66 Axiom 4 (axiom_1a_1): r2(X, y15(Y, X)) = true2.
% 9.96/1.66 Axiom 5 (axiom_9_1): fresh40(X, X, Y, Z) = true2.
% 9.96/1.66 Axiom 6 (axiom_1_1): fresh17(r1(X), true2, X) = id(X, y24).
% 9.96/1.66 Axiom 7 (axiom_1a_3): r3(X, Y, y7(X, Y)) = true2.
% 9.96/1.66 Axiom 8 (axiom_9_1): fresh(X, X, Y, Z, W) = r2(Y, Z).
% 9.96/1.66 Axiom 9 (axiom_9_1): fresh39(X, X, Y, Z, W, V) = fresh40(id(Y, W), true2, Y, Z).
% 9.96/1.66 Axiom 10 (axiom_9_1): fresh39(r2(X, Y), true2, Z, W, X, Y) = fresh(id(W, Y), true2, Z, W, X).
% 9.96/1.66
% 9.96/1.66 Goal 1 (xplustwoidy): tuple(id(X, Y), r1(Z), r2(W, V), r2(Z, W), r3(U, V, X)) = tuple(true2, true2, true2, true2, true2).
% 9.96/1.66 The goal is true when:
% 9.96/1.66 X = y7(W, y15(Z, y15(Y, y24)))
% 9.96/1.66 Y = y7(W, y15(Z, y15(Y, y24)))
% 9.96/1.66 Z = y16(X)
% 9.96/1.66 W = y15(Y, y24)
% 9.96/1.66 V = y15(Z, y15(Y, y24))
% 9.96/1.66 U = W
% 9.96/1.66
% 9.96/1.66 Proof:
% 9.96/1.66 tuple(id(y7(W, y15(Z, y15(Y, y24))), y7(W, y15(Z, y15(Y, y24)))), r1(y16(X)), r2(y15(Y, y24), y15(Z, y15(Y, y24))), r2(y16(X), y15(Y, y24)), r3(W, y15(Z, y15(Y, y24)), y7(W, y15(Z, y15(Y, y24)))))
% 9.96/1.66 = { by axiom 1 (axiom_5) }
% 9.96/1.66 tuple(true2, r1(y16(X)), r2(y15(Y, y24), y15(Z, y15(Y, y24))), r2(y16(X), y15(Y, y24)), r3(W, y15(Z, y15(Y, y24)), y7(W, y15(Z, y15(Y, y24)))))
% 9.96/1.66 = { by axiom 7 (axiom_1a_3) }
% 9.96/1.66 tuple(true2, r1(y16(X)), r2(y15(Y, y24), y15(Z, y15(Y, y24))), r2(y16(X), y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 4 (axiom_1a_1) }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, r2(y16(X), y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 8 (axiom_9_1) R->L }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh(true2, true2, y16(X), y15(Y, y24), y24), true2)
% 9.96/1.66 = { by axiom 1 (axiom_5) R->L }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh(id(y15(Y, y24), y15(Y, y24)), true2, y16(X), y15(Y, y24), y24), true2)
% 9.96/1.66 = { by axiom 10 (axiom_9_1) R->L }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh39(r2(y24, y15(Y, y24)), true2, y16(X), y15(Y, y24), y24, y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 4 (axiom_1a_1) }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh39(true2, true2, y16(X), y15(Y, y24), y24, y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 9 (axiom_9_1) }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh40(id(y16(X), y24), true2, y16(X), y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 6 (axiom_1_1) R->L }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh40(fresh17(r1(y16(X)), true2, y16(X)), true2, y16(X), y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 2 (axiom_4a_1) }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh40(fresh17(true2, true2, y16(X)), true2, y16(X), y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 3 (axiom_1_1) }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, fresh40(true2, true2, y16(X), y15(Y, y24)), true2)
% 9.96/1.66 = { by axiom 5 (axiom_9_1) }
% 9.96/1.66 tuple(true2, r1(y16(X)), true2, true2, true2)
% 9.96/1.66 = { by axiom 2 (axiom_4a_1) }
% 9.96/1.66 tuple(true2, true2, true2, true2, true2)
% 9.96/1.66 % SZS output end Proof
% 9.96/1.66
% 9.96/1.66 RESULT: Theorem (the conjecture is true).
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