TSTP Solution File: NUM551+3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM551+3 : 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 : n012.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 11:56:55 EDT 2023
% Result : Theorem 0.22s 0.72s
% Output : Proof 0.22s
% 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 : NUM551+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n012.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 25 09:36:11 EDT 2023
% 0.18/0.36 % CPUTime :
% 0.22/0.72 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.72
% 0.22/0.72 % SZS status Theorem
% 0.22/0.73
% 0.22/0.74 % SZS output start Proof
% 0.22/0.74 Take the following subset of the input axioms:
% 0.22/0.74 fof(mCountNFin, axiom, ![W0]: ((aSet0(W0) & isCountable0(W0)) => ~isFinite0(W0))).
% 0.22/0.74 fof(mCountNFin_01, axiom, ![W0_2]: ((aSet0(W0_2) & isCountable0(W0_2)) => W0_2!=slcrc0)).
% 0.22/0.74 fof(mDefDiff, definition, ![W1, W0_2]: ((aSet0(W0_2) & aElement0(W1)) => ![W2]: (W2=sdtmndt0(W0_2, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0_2) & W3!=W1))))))).
% 0.22/0.74 fof(mDefEmp, definition, ![W0_2]: (W0_2=slcrc0 <=> (aSet0(W0_2) & ~?[W1_2]: aElementOf0(W1_2, W0_2)))).
% 0.22/0.74 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 0.22/0.74 fof(mNatNSucc, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => W0_2!=szszuzczcdt0(W0_2))).
% 0.22/0.74 fof(mNoScLessZr, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ~sdtlseqdt0(szszuzczcdt0(W0_2), sz00))).
% 0.22/0.74 fof(mSuccNum, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0_2), szNzAzT0) & szszuzczcdt0(W0_2)!=sz00))).
% 0.22/0.74 fof(m__, conjecture, ?[W0_2]: (aElement0(W0_2) & aElementOf0(W0_2, xQ))).
% 0.22/0.74 fof(m__2270, hypothesis, aSet0(xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => aElementOf0(W0_2, xS)) & (aSubsetOf0(xQ, xS) & (sbrdtbr0(xQ)=xk & aElementOf0(xQ, slbdtsldtrb0(xS, xk)))))).
% 0.22/0.74 fof(m__2313, hypothesis, ~(~?[W0_2]: aElementOf0(W0_2, xQ) | xQ=slcrc0)).
% 0.22/0.74
% 0.22/0.74 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.74 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.74 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.74 fresh(y, y, x1...xn) = u
% 0.22/0.74 C => fresh(s, t, x1...xn) = v
% 0.22/0.74 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.74 variables of u and v.
% 0.22/0.74 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.74 input problem has no model of domain size 1).
% 0.22/0.74
% 0.22/0.74 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.74
% 0.22/0.74 Axiom 1 (m__2270_1): aSet0(xQ) = true2.
% 0.22/0.74 Axiom 2 (m__2313): aElementOf0(w0, xQ) = true2.
% 0.22/0.74 Axiom 3 (mEOfElem): fresh54(X, X, Y) = true2.
% 0.22/0.74 Axiom 4 (mEOfElem): fresh55(X, X, Y, Z) = aElement0(Z).
% 0.22/0.74 Axiom 5 (mEOfElem): fresh55(aElementOf0(X, Y), true2, Y, X) = fresh54(aSet0(Y), true2, X).
% 0.22/0.74
% 0.22/0.74 Goal 1 (m__): tuple2(aElement0(X), aElementOf0(X, xQ)) = tuple2(true2, true2).
% 0.22/0.74 The goal is true when:
% 0.22/0.74 X = w0
% 0.22/0.74
% 0.22/0.74 Proof:
% 0.22/0.74 tuple2(aElement0(w0), aElementOf0(w0, xQ))
% 0.22/0.74 = { by axiom 4 (mEOfElem) R->L }
% 0.22/0.74 tuple2(fresh55(true2, true2, xQ, w0), aElementOf0(w0, xQ))
% 0.22/0.74 = { by axiom 2 (m__2313) R->L }
% 0.22/0.74 tuple2(fresh55(aElementOf0(w0, xQ), true2, xQ, w0), aElementOf0(w0, xQ))
% 0.22/0.74 = { by axiom 5 (mEOfElem) }
% 0.22/0.74 tuple2(fresh54(aSet0(xQ), true2, w0), aElementOf0(w0, xQ))
% 0.22/0.74 = { by axiom 1 (m__2270_1) }
% 0.22/0.74 tuple2(fresh54(true2, true2, w0), aElementOf0(w0, xQ))
% 0.22/0.74 = { by axiom 3 (mEOfElem) }
% 0.22/0.74 tuple2(true2, aElementOf0(w0, xQ))
% 0.22/0.74 = { by axiom 2 (m__2313) }
% 0.22/0.74 tuple2(true2, true2)
% 0.22/0.74 % SZS output end Proof
% 0.22/0.74
% 0.22/0.74 RESULT: Theorem (the conjecture is true).
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