TSTP Solution File: RNG125+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG125+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 : n014.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 13:59:26 EDT 2023
% Result : Theorem 2.58s 0.77s
% Output : Proof 2.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG125+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 : n014.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 01:23:31 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.58/0.77 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 2.58/0.77
% 2.58/0.77 % SZS status Theorem
% 2.58/0.77
% 2.58/0.77 % SZS output start Proof
% 2.58/0.77 Take the following subset of the input axioms:
% 2.58/0.78 fof(mDefDvs, definition, ![W0]: (aElement0(W0) => ![W1]: (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))).
% 2.58/0.78 fof(mDefIdeal, definition, ![W0_2]: (aIdeal0(W0_2) <=> (aSet0(W0_2) & ![W1_2]: (aElementOf0(W1_2, W0_2) => (![W2]: (aElementOf0(W2, W0_2) => aElementOf0(sdtpldt0(W1_2, W2), W0_2)) & ![W2_2]: (aElement0(W2_2) => aElementOf0(sdtasdt0(W2_2, W1_2), W0_2))))))).
% 2.58/0.78 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 2.58/0.78 fof(m__2091, hypothesis, aElement0(xa) & aElement0(xb)).
% 2.58/0.78 fof(m__2174, hypothesis, aIdeal0(xI) & xI=sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))).
% 2.58/0.78 fof(m__2273, hypothesis, aElementOf0(xu, xI) & (xu!=sz00 & ![W0_2]: ((aElementOf0(W0_2, xI) & W0_2!=sz00) => ~iLess0(sbrdtbr0(W0_2), sbrdtbr0(xu))))).
% 2.58/0.78 fof(m__2383, hypothesis, ~(aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb))).
% 2.58/0.78 fof(m__2479, hypothesis, ~~doDivides0(xu, xa)).
% 2.58/0.78 fof(m__2612, hypothesis, ~~doDivides0(xu, xb)).
% 2.58/0.78
% 2.58/0.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.58/0.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.58/0.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.58/0.78 fresh(y, y, x1...xn) = u
% 2.58/0.78 C => fresh(s, t, x1...xn) = v
% 2.58/0.78 where fresh is a fresh function symbol and x1..xn are the free
% 2.58/0.78 variables of u and v.
% 2.58/0.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.58/0.78 input problem has no model of domain size 1).
% 2.58/0.78
% 2.58/0.78 The encoding turns the above axioms into the following unit equations and goals:
% 2.58/0.78
% 2.58/0.78 Axiom 1 (m__2091): aElement0(xa) = true.
% 2.58/0.78 Axiom 2 (m__2091_1): aElement0(xb) = true.
% 2.58/0.78 Axiom 3 (m__2174_1): aIdeal0(xI) = true.
% 2.58/0.78 Axiom 4 (m__2273): aElementOf0(xu, xI) = true.
% 2.58/0.78 Axiom 5 (m__2479): doDivides0(xu, xa) = true.
% 2.58/0.78 Axiom 6 (m__2612): doDivides0(xu, xb) = true.
% 2.58/0.78 Axiom 7 (mDefIdeal_7): fresh46(X, X, Y) = true.
% 2.58/0.78 Axiom 8 (mEOfElem): fresh26(X, X, Y) = true.
% 2.58/0.78 Axiom 9 (mDefDvs): fresh93(X, X, Y, Z) = true.
% 2.58/0.78 Axiom 10 (mDefDvs): fresh56(X, X, Y, Z) = aDivisorOf0(Z, Y).
% 2.58/0.78 Axiom 11 (mDefIdeal_7): fresh46(aIdeal0(X), true, X) = aSet0(X).
% 2.58/0.78 Axiom 12 (mEOfElem): fresh27(X, X, Y, Z) = aElement0(Z).
% 2.58/0.78 Axiom 13 (mDefDvs): fresh92(X, X, Y, Z) = fresh93(aElement0(Y), true, Y, Z).
% 2.58/0.78 Axiom 14 (mDefDvs): fresh92(doDivides0(X, Y), true, Y, X) = fresh56(aElement0(X), true, Y, X).
% 2.58/0.78 Axiom 15 (mEOfElem): fresh27(aElementOf0(X, Y), true, Y, X) = fresh26(aSet0(Y), true, X).
% 2.58/0.78
% 2.58/0.78 Lemma 16: aElement0(xu) = true.
% 2.58/0.78 Proof:
% 2.58/0.78 aElement0(xu)
% 2.58/0.78 = { by axiom 12 (mEOfElem) R->L }
% 2.58/0.78 fresh27(true, true, xI, xu)
% 2.58/0.78 = { by axiom 4 (m__2273) R->L }
% 2.58/0.78 fresh27(aElementOf0(xu, xI), true, xI, xu)
% 2.58/0.78 = { by axiom 15 (mEOfElem) }
% 2.58/0.78 fresh26(aSet0(xI), true, xu)
% 2.58/0.78 = { by axiom 11 (mDefIdeal_7) R->L }
% 2.58/0.78 fresh26(fresh46(aIdeal0(xI), true, xI), true, xu)
% 2.58/0.78 = { by axiom 3 (m__2174_1) }
% 2.58/0.78 fresh26(fresh46(true, true, xI), true, xu)
% 2.58/0.78 = { by axiom 7 (mDefIdeal_7) }
% 2.58/0.78 fresh26(true, true, xu)
% 2.58/0.78 = { by axiom 8 (mEOfElem) }
% 2.58/0.78 true
% 2.58/0.78
% 2.58/0.78 Goal 1 (m__2383): tuple(aDivisorOf0(xu, xa), aDivisorOf0(xu, xb)) = tuple(true, true).
% 2.58/0.78 Proof:
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), aDivisorOf0(xu, xb))
% 2.58/0.78 = { by axiom 10 (mDefDvs) R->L }
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), fresh56(true, true, xb, xu))
% 2.58/0.78 = { by lemma 16 R->L }
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), fresh56(aElement0(xu), true, xb, xu))
% 2.58/0.78 = { by axiom 14 (mDefDvs) R->L }
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), fresh92(doDivides0(xu, xb), true, xb, xu))
% 2.58/0.78 = { by axiom 6 (m__2612) }
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), fresh92(true, true, xb, xu))
% 2.58/0.78 = { by axiom 13 (mDefDvs) }
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), fresh93(aElement0(xb), true, xb, xu))
% 2.58/0.78 = { by axiom 2 (m__2091_1) }
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), fresh93(true, true, xb, xu))
% 2.58/0.78 = { by axiom 9 (mDefDvs) }
% 2.58/0.78 tuple(aDivisorOf0(xu, xa), true)
% 2.58/0.78 = { by axiom 10 (mDefDvs) R->L }
% 2.58/0.78 tuple(fresh56(true, true, xa, xu), true)
% 2.58/0.78 = { by lemma 16 R->L }
% 2.58/0.78 tuple(fresh56(aElement0(xu), true, xa, xu), true)
% 2.58/0.78 = { by axiom 14 (mDefDvs) R->L }
% 2.58/0.78 tuple(fresh92(doDivides0(xu, xa), true, xa, xu), true)
% 2.58/0.78 = { by axiom 5 (m__2479) }
% 2.58/0.78 tuple(fresh92(true, true, xa, xu), true)
% 2.58/0.78 = { by axiom 13 (mDefDvs) }
% 2.58/0.78 tuple(fresh93(aElement0(xa), true, xa, xu), true)
% 2.58/0.78 = { by axiom 1 (m__2091) }
% 2.58/0.78 tuple(fresh93(true, true, xa, xu), true)
% 2.58/0.78 = { by axiom 9 (mDefDvs) }
% 2.58/0.78 tuple(true, true)
% 2.58/0.78 % SZS output end Proof
% 2.58/0.78
% 2.58/0.78 RESULT: Theorem (the conjecture is true).
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