TSTP Solution File: RNG089+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG089+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n027.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 13:59:13 EDT 2023
% Result : Theorem 0.19s 0.66s
% Output : Proof 0.19s
% 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 : RNG089+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 02:23:20 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.66 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.66
% 0.19/0.66 % SZS status Theorem
% 0.19/0.66
% 0.19/0.67 % SZS output start Proof
% 0.19/0.67 Take the following subset of the input axioms:
% 0.19/0.67 fof(mDefIdeal, definition, ![W0]: (aIdeal0(W0) <=> (aSet0(W0) & ![W1]: (aElementOf0(W1, W0) => (![W2]: (aElementOf0(W2, W0) => aElementOf0(sdtpldt0(W1, W2), W0)) & ![W2_2]: (aElement0(W2_2) => aElementOf0(sdtasdt0(W2_2, W1), W0))))))).
% 0.19/0.67 fof(m__, conjecture, aElementOf0(sdtasdt0(xz, xk), xI) & aElementOf0(sdtasdt0(xz, xl), xJ)).
% 0.19/0.67 fof(m__870, hypothesis, aSet0(xI) & (![W0_2]: (aElementOf0(W0_2, xI) => (![W1_2]: (aElementOf0(W1_2, xI) => aElementOf0(sdtpldt0(W0_2, W1_2), xI)) & ![W1_2]: (aElement0(W1_2) => aElementOf0(sdtasdt0(W1_2, W0_2), xI)))) & (aIdeal0(xI) & (aSet0(xJ) & (![W0_2]: (aElementOf0(W0_2, xJ) => (![W1_2]: (aElementOf0(W1_2, xJ) => aElementOf0(sdtpldt0(W0_2, W1_2), xJ)) & ![W1_2]: (aElement0(W1_2) => aElementOf0(sdtasdt0(W1_2, W0_2), xJ)))) & aIdeal0(xJ)))))).
% 0.19/0.67 fof(m__901, hypothesis, ?[W0_2, W1_2]: (aElementOf0(W0_2, xI) & (aElementOf0(W1_2, xJ) & sdtpldt0(W0_2, W1_2)=xx)) & (aElementOf0(xx, sdtpldt1(xI, xJ)) & (?[W0_2, W1_2]: (aElementOf0(W0_2, xI) & (aElementOf0(W1_2, xJ) & sdtpldt0(W0_2, W1_2)=xy)) & (aElementOf0(xy, sdtpldt1(xI, xJ)) & aElement0(xz))))).
% 0.19/0.67 fof(m__934, hypothesis, aElementOf0(xk, xI) & (aElementOf0(xl, xJ) & xx=sdtpldt0(xk, xl))).
% 0.19/0.67
% 0.19/0.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.67 fresh(y, y, x1...xn) = u
% 0.19/0.67 C => fresh(s, t, x1...xn) = v
% 0.19/0.67 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.67 variables of u and v.
% 0.19/0.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.67 input problem has no model of domain size 1).
% 0.19/0.67
% 0.19/0.67 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.67
% 0.19/0.67 Axiom 1 (m__934_1): aElementOf0(xk, xI) = true.
% 0.19/0.67 Axiom 2 (m__934_2): aElementOf0(xl, xJ) = true.
% 0.19/0.67 Axiom 3 (m__901_2): aElement0(xz) = true.
% 0.19/0.67 Axiom 4 (m__870_2): aIdeal0(xI) = true.
% 0.19/0.67 Axiom 5 (m__870_3): aIdeal0(xJ) = true.
% 0.19/0.67 Axiom 6 (mDefIdeal): fresh49(X, X, Y, Z, W) = true.
% 0.19/0.67 Axiom 7 (mDefIdeal): fresh40(X, X, Y, Z, W) = aElementOf0(sdtasdt0(W, Z), Y).
% 0.19/0.67 Axiom 8 (mDefIdeal): fresh48(X, X, Y, Z, W) = fresh49(aElement0(W), true, Y, Z, W).
% 0.19/0.67 Axiom 9 (mDefIdeal): fresh48(aIdeal0(X), true, X, Y, Z) = fresh40(aElementOf0(Y, X), true, X, Y, Z).
% 0.19/0.67
% 0.19/0.67 Lemma 10: fresh48(X, X, Y, Z, xz) = true.
% 0.19/0.67 Proof:
% 0.19/0.67 fresh48(X, X, Y, Z, xz)
% 0.19/0.67 = { by axiom 8 (mDefIdeal) }
% 0.19/0.67 fresh49(aElement0(xz), true, Y, Z, xz)
% 0.19/0.67 = { by axiom 3 (m__901_2) }
% 0.19/0.67 fresh49(true, true, Y, Z, xz)
% 0.19/0.67 = { by axiom 6 (mDefIdeal) }
% 0.19/0.67 true
% 0.19/0.67
% 0.19/0.67 Goal 1 (m__): tuple(aElementOf0(sdtasdt0(xz, xk), xI), aElementOf0(sdtasdt0(xz, xl), xJ)) = tuple(true, true).
% 0.19/0.67 Proof:
% 0.19/0.67 tuple(aElementOf0(sdtasdt0(xz, xk), xI), aElementOf0(sdtasdt0(xz, xl), xJ))
% 0.19/0.67 = { by axiom 7 (mDefIdeal) R->L }
% 0.19/0.67 tuple(aElementOf0(sdtasdt0(xz, xk), xI), fresh40(true, true, xJ, xl, xz))
% 0.19/0.67 = { by axiom 2 (m__934_2) R->L }
% 0.19/0.67 tuple(aElementOf0(sdtasdt0(xz, xk), xI), fresh40(aElementOf0(xl, xJ), true, xJ, xl, xz))
% 0.19/0.67 = { by axiom 9 (mDefIdeal) R->L }
% 0.19/0.67 tuple(aElementOf0(sdtasdt0(xz, xk), xI), fresh48(aIdeal0(xJ), true, xJ, xl, xz))
% 0.19/0.67 = { by axiom 5 (m__870_3) }
% 0.19/0.67 tuple(aElementOf0(sdtasdt0(xz, xk), xI), fresh48(true, true, xJ, xl, xz))
% 0.19/0.67 = { by lemma 10 }
% 0.19/0.67 tuple(aElementOf0(sdtasdt0(xz, xk), xI), true)
% 0.19/0.67 = { by axiom 7 (mDefIdeal) R->L }
% 0.19/0.67 tuple(fresh40(true, true, xI, xk, xz), true)
% 0.19/0.67 = { by axiom 1 (m__934_1) R->L }
% 0.19/0.67 tuple(fresh40(aElementOf0(xk, xI), true, xI, xk, xz), true)
% 0.19/0.67 = { by axiom 9 (mDefIdeal) R->L }
% 0.19/0.67 tuple(fresh48(aIdeal0(xI), true, xI, xk, xz), true)
% 0.19/0.67 = { by axiom 4 (m__870_2) }
% 0.19/0.67 tuple(fresh48(true, true, xI, xk, xz), true)
% 0.19/0.67 = { by lemma 10 }
% 0.19/0.67 tuple(true, true)
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67
% 0.19/0.67 RESULT: Theorem (the conjecture is true).
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