TSTP Solution File: RNG088+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG088+1 : 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 : n028.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 0.20s 0.56s
% 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
% 0.00/0.13 % Problem : RNG088+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 03:24:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.56
% 0.20/0.56 % SZS status Theorem
% 0.20/0.56
% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Take the following subset of the input axioms:
% 0.20/0.56 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))))))).
% 0.20/0.56 fof(m__, conjecture, aElementOf0(sdtpldt0(xk, xm), xI) & aElementOf0(sdtpldt0(xl, xn), xJ)).
% 0.20/0.56 fof(m__870, hypothesis, aIdeal0(xI) & aIdeal0(xJ)).
% 0.20/0.56 fof(m__934, hypothesis, aElementOf0(xk, xI) & (aElementOf0(xl, xJ) & xx=sdtpldt0(xk, xl))).
% 0.20/0.56 fof(m__967, hypothesis, aElementOf0(xm, xI) & (aElementOf0(xn, xJ) & xy=sdtpldt0(xm, xn))).
% 0.20/0.56
% 0.20/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.56 fresh(y, y, x1...xn) = u
% 0.20/0.56 C => fresh(s, t, x1...xn) = v
% 0.20/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.56 variables of u and v.
% 0.20/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.56 input problem has no model of domain size 1).
% 0.20/0.56
% 0.20/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.56
% 0.20/0.56 Axiom 1 (m__870): aIdeal0(xI) = true.
% 0.20/0.56 Axiom 2 (m__870_1): aIdeal0(xJ) = true.
% 0.20/0.56 Axiom 3 (m__934_1): aElementOf0(xk, xI) = true.
% 0.20/0.56 Axiom 4 (m__934_2): aElementOf0(xl, xJ) = true.
% 0.20/0.56 Axiom 5 (m__967_1): aElementOf0(xm, xI) = true.
% 0.20/0.56 Axiom 6 (m__967_2): aElementOf0(xn, xJ) = true.
% 0.20/0.56 Axiom 7 (mDefIdeal_6): fresh45(X, X, Y, Z, W) = true.
% 0.20/0.56 Axiom 8 (mDefIdeal_6): fresh30(X, X, Y, Z, W) = aElementOf0(sdtpldt0(Z, W), Y).
% 0.20/0.56 Axiom 9 (mDefIdeal_6): fresh44(X, X, Y, Z, W) = fresh45(aElementOf0(Z, Y), true, Y, Z, W).
% 0.20/0.56 Axiom 10 (mDefIdeal_6): fresh44(aIdeal0(X), true, X, Y, Z) = fresh30(aElementOf0(Z, X), true, X, Y, Z).
% 0.20/0.56
% 0.20/0.56 Goal 1 (m__): tuple(aElementOf0(sdtpldt0(xk, xm), xI), aElementOf0(sdtpldt0(xl, xn), xJ)) = tuple(true, true).
% 0.20/0.56 Proof:
% 0.20/0.56 tuple(aElementOf0(sdtpldt0(xk, xm), xI), aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.56 = { by axiom 8 (mDefIdeal_6) R->L }
% 0.20/0.56 tuple(fresh30(true, true, xI, xk, xm), aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.56 = { by axiom 5 (m__967_1) R->L }
% 0.20/0.56 tuple(fresh30(aElementOf0(xm, xI), true, xI, xk, xm), aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.56 = { by axiom 10 (mDefIdeal_6) R->L }
% 0.20/0.56 tuple(fresh44(aIdeal0(xI), true, xI, xk, xm), aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.56 = { by axiom 1 (m__870) }
% 0.20/0.56 tuple(fresh44(true, true, xI, xk, xm), aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.56 = { by axiom 9 (mDefIdeal_6) }
% 0.20/0.56 tuple(fresh45(aElementOf0(xk, xI), true, xI, xk, xm), aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.56 = { by axiom 3 (m__934_1) }
% 0.20/0.56 tuple(fresh45(true, true, xI, xk, xm), aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.57 = { by axiom 7 (mDefIdeal_6) }
% 0.20/0.57 tuple(true, aElementOf0(sdtpldt0(xl, xn), xJ))
% 0.20/0.57 = { by axiom 8 (mDefIdeal_6) R->L }
% 0.20/0.57 tuple(true, fresh30(true, true, xJ, xl, xn))
% 0.20/0.57 = { by axiom 6 (m__967_2) R->L }
% 0.20/0.57 tuple(true, fresh30(aElementOf0(xn, xJ), true, xJ, xl, xn))
% 0.20/0.57 = { by axiom 10 (mDefIdeal_6) R->L }
% 0.20/0.57 tuple(true, fresh44(aIdeal0(xJ), true, xJ, xl, xn))
% 0.20/0.57 = { by axiom 2 (m__870_1) }
% 0.20/0.57 tuple(true, fresh44(true, true, xJ, xl, xn))
% 0.20/0.57 = { by axiom 9 (mDefIdeal_6) }
% 0.20/0.57 tuple(true, fresh45(aElementOf0(xl, xJ), true, xJ, xl, xn))
% 0.20/0.57 = { by axiom 4 (m__934_2) }
% 0.20/0.57 tuple(true, fresh45(true, true, xJ, xl, xn))
% 0.20/0.57 = { by axiom 7 (mDefIdeal_6) }
% 0.20/0.57 tuple(true, true)
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Theorem (the conjecture is true).
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