TSTP Solution File: RNG126+4 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG126+4 : 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 : n019.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 126.46s 16.68s
% Output : Proof 126.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG126+4 : 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
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Aug 27 01:54:58 EDT 2023
% 0.11/0.33 % CPUTime :
% 126.46/16.68 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 126.46/16.68
% 126.46/16.68 % SZS status Theorem
% 126.46/16.68
% 126.46/16.69 % SZS output start Proof
% 126.46/16.69 Take the following subset of the input axioms:
% 126.46/16.69 fof(mDefDvs, definition, ![W0]: (aElement0(W0) => ![W1]: (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))).
% 126.46/16.69 fof(mMulComm, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => sdtasdt0(W0_2, W1_2)=sdtasdt0(W1_2, W0_2))).
% 126.46/16.69 fof(m__, conjecture, ![W0_2]: (aElementOf0(W0_2, slsdtgt0(xa)) <=> ?[W1_2]: (aElement0(W1_2) & sdtasdt0(xa, W1_2)=W0_2)) => (![W0_2]: (aElementOf0(W0_2, slsdtgt0(xb)) <=> ?[W1_2]: (aElement0(W1_2) & sdtasdt0(xb, W1_2)=W0_2)) => (?[W0_2, W1_2]: (aElementOf0(W0_2, slsdtgt0(xa)) & (aElementOf0(W1_2, slsdtgt0(xb)) & sdtpldt0(W0_2, W1_2)=xc)) | aElementOf0(xc, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))).
% 126.46/16.69 fof(m__2091, hypothesis, aElement0(xa) & aElement0(xb)).
% 126.46/16.69 fof(m__2174, 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) & (![W0_2]: (aElementOf0(W0_2, slsdtgt0(xa)) <=> ?[W1_2]: (aElement0(W1_2) & sdtasdt0(xa, W1_2)=W0_2)) & (![W0_2]: (aElementOf0(W0_2, slsdtgt0(xb)) <=> ?[W1_2]: (aElement0(W1_2) & sdtasdt0(xb, W1_2)=W0_2)) & (![W0_2]: (aElementOf0(W0_2, xI) <=> ?[W2, W1_2]: (aElementOf0(W1_2, slsdtgt0(xa)) & (aElementOf0(W2, slsdtgt0(xb)) & sdtpldt0(W1_2, W2)=W0_2))) & xI=sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))).
% 126.46/16.69 fof(m__2273, hypothesis, ?[W0_2, W1_2]: (aElementOf0(W0_2, slsdtgt0(xa)) & (aElementOf0(W1_2, slsdtgt0(xb)) & sdtpldt0(W0_2, W1_2)=xu)) & (aElementOf0(xu, xI) & (xu!=sz00 & ![W0_2]: (((?[W1_2, W2_2]: (aElementOf0(W1_2, slsdtgt0(xa)) & (aElementOf0(W2_2, slsdtgt0(xb)) & sdtpldt0(W1_2, W2_2)=W0_2)) | aElementOf0(W0_2, xI)) & W0_2!=sz00) => ~iLess0(sbrdtbr0(W0_2), sbrdtbr0(xu)))))).
% 126.46/16.69 fof(m__2373, hypothesis, ?[W0_2]: (aElement0(W0_2) & sdtasdt0(xu, W0_2)=xa) & (doDivides0(xu, xa) & (aDivisorOf0(xu, xa) & (?[W0_2]: (aElement0(W0_2) & sdtasdt0(xu, W0_2)=xb) & (doDivides0(xu, xb) & aDivisorOf0(xu, xb)))))).
% 126.46/16.69 fof(m__2744, hypothesis, ?[W0_2]: (aElement0(W0_2) & sdtasdt0(xu, W0_2)=xc)).
% 126.46/16.69
% 126.46/16.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 126.46/16.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 126.46/16.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 126.46/16.69 fresh(y, y, x1...xn) = u
% 126.46/16.69 C => fresh(s, t, x1...xn) = v
% 126.46/16.69 where fresh is a fresh function symbol and x1..xn are the free
% 126.46/16.69 variables of u and v.
% 126.46/16.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 126.46/16.69 input problem has no model of domain size 1).
% 126.46/16.69
% 126.46/16.69 The encoding turns the above axioms into the following unit equations and goals:
% 126.46/16.69
% 126.46/16.69 Axiom 1 (m__2091): aElement0(xa) = true2.
% 126.46/16.69 Axiom 2 (m__2744_1): aElement0(w0) = true2.
% 126.46/16.69 Axiom 3 (m__2273_1): aElementOf0(xu, xI) = true2.
% 126.46/16.69 Axiom 4 (m__2744): sdtasdt0(xu, w0) = xc.
% 126.46/16.69 Axiom 5 (m__2373_6): aDivisorOf0(xu, xa) = true2.
% 126.46/16.69 Axiom 6 (mDefDvs_1): fresh91(X, X, Y) = true2.
% 126.46/16.69 Axiom 7 (m__2174): xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)).
% 126.46/16.69 Axiom 8 (mDefDvs_1): fresh92(X, X, Y, Z) = aElement0(Z).
% 126.46/16.69 Axiom 9 (mMulComm): fresh57(X, X, Y, Z) = sdtasdt0(Y, Z).
% 126.46/16.69 Axiom 10 (mMulComm): fresh56(X, X, Y, Z) = sdtasdt0(Z, Y).
% 126.46/16.69 Axiom 11 (m__2174_6): fresh30(X, X, Y, Z) = aElementOf0(sdtasdt0(Z, Y), xI).
% 126.46/16.69 Axiom 12 (m__2174_6): fresh29(X, X, Y, Z) = true2.
% 126.46/16.69 Axiom 13 (mMulComm): fresh57(aElement0(X), true2, Y, X) = fresh56(aElement0(Y), true2, Y, X).
% 126.46/16.69 Axiom 14 (mDefDvs_1): fresh92(aDivisorOf0(X, Y), true2, Y, X) = fresh91(aElement0(Y), true2, X).
% 126.46/16.69 Axiom 15 (m__2174_6): fresh30(aElementOf0(X, xI), true2, X, Y) = fresh29(aElement0(Y), true2, X, Y).
% 126.46/16.69
% 126.46/16.69 Goal 1 (m___7): aElementOf0(xc, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) = true2.
% 126.46/16.69 Proof:
% 126.46/16.69 aElementOf0(xc, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))
% 126.46/16.69 = { by axiom 7 (m__2174) R->L }
% 126.46/16.69 aElementOf0(xc, xI)
% 126.46/16.70 = { by axiom 4 (m__2744) R->L }
% 126.46/16.70 aElementOf0(sdtasdt0(xu, w0), xI)
% 126.46/16.70 = { by axiom 10 (mMulComm) R->L }
% 126.46/16.70 aElementOf0(fresh56(true2, true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 2 (m__2744_1) R->L }
% 126.46/16.70 aElementOf0(fresh56(aElement0(w0), true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 13 (mMulComm) R->L }
% 126.46/16.70 aElementOf0(fresh57(aElement0(xu), true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 8 (mDefDvs_1) R->L }
% 126.46/16.70 aElementOf0(fresh57(fresh92(true2, true2, xa, xu), true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 5 (m__2373_6) R->L }
% 126.46/16.70 aElementOf0(fresh57(fresh92(aDivisorOf0(xu, xa), true2, xa, xu), true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 14 (mDefDvs_1) }
% 126.46/16.70 aElementOf0(fresh57(fresh91(aElement0(xa), true2, xu), true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 1 (m__2091) }
% 126.46/16.70 aElementOf0(fresh57(fresh91(true2, true2, xu), true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 6 (mDefDvs_1) }
% 126.46/16.70 aElementOf0(fresh57(true2, true2, w0, xu), xI)
% 126.46/16.70 = { by axiom 9 (mMulComm) }
% 126.46/16.70 aElementOf0(sdtasdt0(w0, xu), xI)
% 126.46/16.70 = { by axiom 11 (m__2174_6) R->L }
% 126.46/16.70 fresh30(true2, true2, xu, w0)
% 126.46/16.70 = { by axiom 3 (m__2273_1) R->L }
% 126.46/16.70 fresh30(aElementOf0(xu, xI), true2, xu, w0)
% 126.46/16.70 = { by axiom 15 (m__2174_6) }
% 126.46/16.70 fresh29(aElement0(w0), true2, xu, w0)
% 126.46/16.70 = { by axiom 2 (m__2744_1) }
% 126.46/16.70 fresh29(true2, true2, xu, w0)
% 126.46/16.70 = { by axiom 12 (m__2174_6) }
% 126.46/16.70 true2
% 126.46/16.70 % SZS output end Proof
% 126.46/16.70
% 126.46/16.70 RESULT: Theorem (the conjecture is true).
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