TSTP Solution File: RNG120+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG120+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 : n007.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 13:59:24 EDT 2023
% Result : Theorem 6.79s 1.43s
% Output : Proof 8.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG120+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % 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 : n007.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 02:07:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.79/1.43 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 6.79/1.43
% 6.79/1.43 % SZS status Theorem
% 6.79/1.43
% 8.13/1.43 % SZS output start Proof
% 8.13/1.43 Take the following subset of the input axioms:
% 8.13/1.44 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))))))).
% 8.13/1.44 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 8.13/1.44 fof(mMulMnOne, axiom, ![W0_2]: (aElement0(W0_2) => (sdtasdt0(smndt0(sz10), W0_2)=smndt0(W0_2) & smndt0(W0_2)=sdtasdt0(W0_2, smndt0(sz10))))).
% 8.13/1.44 fof(mSortsC_01, axiom, aElement0(sz10)).
% 8.13/1.44 fof(mSortsU, axiom, ![W0_2]: (aElement0(W0_2) => aElement0(smndt0(W0_2)))).
% 8.13/1.44 fof(m__, conjecture, aElementOf0(smndt0(sdtasdt0(xq, xu)), xI)).
% 8.13/1.44 fof(m__2174, hypothesis, aIdeal0(xI) & xI=sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))).
% 8.13/1.44 fof(m__2273, hypothesis, aElementOf0(xu, xI) & (xu!=sz00 & ![W0_2]: ((aElementOf0(W0_2, xI) & W0_2!=sz00) => ~iLess0(sbrdtbr0(W0_2), sbrdtbr0(xu))))).
% 8.13/1.44 fof(m__2666, hypothesis, aElement0(xq) & (aElement0(xr) & (xb=sdtpldt0(sdtasdt0(xq, xu), xr) & (xr=sz00 | iLess0(sbrdtbr0(xr), sbrdtbr0(xu)))))).
% 8.13/1.44
% 8.13/1.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 8.13/1.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 8.13/1.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 8.13/1.44 fresh(y, y, x1...xn) = u
% 8.13/1.44 C => fresh(s, t, x1...xn) = v
% 8.13/1.44 where fresh is a fresh function symbol and x1..xn are the free
% 8.13/1.44 variables of u and v.
% 8.13/1.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 8.13/1.44 input problem has no model of domain size 1).
% 8.13/1.44
% 8.13/1.44 The encoding turns the above axioms into the following unit equations and goals:
% 8.13/1.44
% 8.13/1.44 Axiom 1 (mSortsC_01): aElement0(sz10) = true.
% 8.13/1.44 Axiom 2 (m__2666_2): aElement0(xq) = true.
% 8.13/1.44 Axiom 3 (m__2273): aElementOf0(xu, xI) = true.
% 8.13/1.44 Axiom 4 (m__2174_1): aIdeal0(xI) = true.
% 8.13/1.44 Axiom 5 (mDefIdeal_7): fresh46(X, X, Y) = true.
% 8.13/1.44 Axiom 6 (mEOfElem): fresh26(X, X, Y) = true.
% 8.13/1.44 Axiom 7 (mMulMnOne_1): fresh17(X, X, Y) = smndt0(Y).
% 8.13/1.44 Axiom 8 (mSortsU): fresh9(X, X, Y) = true.
% 8.13/1.44 Axiom 9 (mDefIdeal_7): fresh46(aIdeal0(X), true, X) = aSet0(X).
% 8.13/1.44 Axiom 10 (mEOfElem): fresh27(X, X, Y, Z) = aElement0(Z).
% 8.13/1.44 Axiom 11 (mMulMnOne_1): fresh17(aElement0(X), true, X) = sdtasdt0(smndt0(sz10), X).
% 8.13/1.44 Axiom 12 (mSortsU): fresh9(aElement0(X), true, X) = aElement0(smndt0(X)).
% 8.13/1.44 Axiom 13 (mDefIdeal): fresh126(X, X, Y, Z, W) = true.
% 8.13/1.44 Axiom 14 (mDefIdeal): fresh49(X, X, Y, Z, W) = aElementOf0(sdtasdt0(W, Z), Y).
% 8.13/1.44 Axiom 15 (mEOfElem): fresh27(aElementOf0(X, Y), true, Y, X) = fresh26(aSet0(Y), true, X).
% 8.13/1.44 Axiom 16 (mDefIdeal): fresh125(X, X, Y, Z, W) = fresh126(aElement0(W), true, Y, Z, W).
% 8.13/1.44 Axiom 17 (mDefIdeal): fresh125(aIdeal0(X), true, X, Y, Z) = fresh49(aElementOf0(Y, X), true, X, Y, Z).
% 8.13/1.44
% 8.13/1.44 Lemma 18: aElementOf0(sdtasdt0(xq, xu), xI) = true.
% 8.13/1.44 Proof:
% 8.13/1.44 aElementOf0(sdtasdt0(xq, xu), xI)
% 8.13/1.44 = { by axiom 14 (mDefIdeal) R->L }
% 8.13/1.44 fresh49(true, true, xI, xu, xq)
% 8.13/1.44 = { by axiom 3 (m__2273) R->L }
% 8.13/1.44 fresh49(aElementOf0(xu, xI), true, xI, xu, xq)
% 8.13/1.44 = { by axiom 17 (mDefIdeal) R->L }
% 8.13/1.44 fresh125(aIdeal0(xI), true, xI, xu, xq)
% 8.13/1.44 = { by axiom 4 (m__2174_1) }
% 8.13/1.44 fresh125(true, true, xI, xu, xq)
% 8.13/1.44 = { by axiom 16 (mDefIdeal) }
% 8.13/1.44 fresh126(aElement0(xq), true, xI, xu, xq)
% 8.13/1.44 = { by axiom 2 (m__2666_2) }
% 8.13/1.44 fresh126(true, true, xI, xu, xq)
% 8.13/1.44 = { by axiom 13 (mDefIdeal) }
% 8.13/1.44 true
% 8.13/1.44
% 8.13/1.44 Goal 1 (m__): aElementOf0(smndt0(sdtasdt0(xq, xu)), xI) = true.
% 8.13/1.44 Proof:
% 8.13/1.44 aElementOf0(smndt0(sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 7 (mMulMnOne_1) R->L }
% 8.13/1.44 aElementOf0(fresh17(true, true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 6 (mEOfElem) R->L }
% 8.13/1.44 aElementOf0(fresh17(fresh26(true, true, sdtasdt0(xq, xu)), true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 5 (mDefIdeal_7) R->L }
% 8.13/1.44 aElementOf0(fresh17(fresh26(fresh46(true, true, xI), true, sdtasdt0(xq, xu)), true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 4 (m__2174_1) R->L }
% 8.13/1.44 aElementOf0(fresh17(fresh26(fresh46(aIdeal0(xI), true, xI), true, sdtasdt0(xq, xu)), true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 9 (mDefIdeal_7) }
% 8.13/1.44 aElementOf0(fresh17(fresh26(aSet0(xI), true, sdtasdt0(xq, xu)), true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 15 (mEOfElem) R->L }
% 8.13/1.44 aElementOf0(fresh17(fresh27(aElementOf0(sdtasdt0(xq, xu), xI), true, xI, sdtasdt0(xq, xu)), true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by lemma 18 }
% 8.13/1.44 aElementOf0(fresh17(fresh27(true, true, xI, sdtasdt0(xq, xu)), true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 10 (mEOfElem) }
% 8.13/1.44 aElementOf0(fresh17(aElement0(sdtasdt0(xq, xu)), true, sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 11 (mMulMnOne_1) }
% 8.13/1.44 aElementOf0(sdtasdt0(smndt0(sz10), sdtasdt0(xq, xu)), xI)
% 8.13/1.44 = { by axiom 14 (mDefIdeal) R->L }
% 8.13/1.44 fresh49(true, true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by lemma 18 R->L }
% 8.13/1.44 fresh49(aElementOf0(sdtasdt0(xq, xu), xI), true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by axiom 17 (mDefIdeal) R->L }
% 8.13/1.44 fresh125(aIdeal0(xI), true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by axiom 4 (m__2174_1) }
% 8.13/1.44 fresh125(true, true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by axiom 16 (mDefIdeal) }
% 8.13/1.44 fresh126(aElement0(smndt0(sz10)), true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by axiom 12 (mSortsU) R->L }
% 8.13/1.44 fresh126(fresh9(aElement0(sz10), true, sz10), true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by axiom 1 (mSortsC_01) }
% 8.13/1.44 fresh126(fresh9(true, true, sz10), true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by axiom 8 (mSortsU) }
% 8.13/1.44 fresh126(true, true, xI, sdtasdt0(xq, xu), smndt0(sz10))
% 8.13/1.44 = { by axiom 13 (mDefIdeal) }
% 8.13/1.44 true
% 8.13/1.44 % SZS output end Proof
% 8.13/1.44
% 8.13/1.44 RESULT: Theorem (the conjecture is true).
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