TSTP Solution File: NUM482+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM482+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 : n024.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 11:56:32 EDT 2023
% Result : Theorem 3.30s 0.78s
% Output : Proof 3.30s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM482+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 15:02:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 3.30/0.78 Command-line arguments: --no-flatten-goal
% 3.30/0.78
% 3.30/0.78 % SZS status Theorem
% 3.30/0.78
% 3.30/0.78 % SZS output start Proof
% 3.30/0.78 Take the following subset of the input axioms:
% 3.30/0.79 fof(mDefDiv, definition, ![W0, W1]: ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2]: (aNaturalNumber0(W2) & W1=sdtasdt0(W0, W2))))).
% 3.30/0.79 fof(mDefPrime, definition, ![W0_2]: (aNaturalNumber0(W0_2) => (isPrime0(W0_2) <=> (W0_2!=sz00 & (W0_2!=sz10 & ![W1_2]: ((aNaturalNumber0(W1_2) & doDivides0(W1_2, W0_2)) => (W1_2=sz10 | W1_2=W0_2))))))).
% 3.30/0.79 fof(mSortsC_01, axiom, aNaturalNumber0(sz10) & sz10!=sz00).
% 3.30/0.79 fof(m_MulUnit, axiom, ![W0_2]: (aNaturalNumber0(W0_2) => (sdtasdt0(W0_2, sz10)=W0_2 & W0_2=sdtasdt0(sz10, W0_2)))).
% 3.30/0.79 fof(m__, conjecture, isPrime0(xk) => ?[W0_2]: (aNaturalNumber0(W0_2) & (doDivides0(W0_2, xk) & isPrime0(W0_2)))).
% 3.30/0.79 fof(m__1716, hypothesis, aNaturalNumber0(xk)).
% 3.30/0.79
% 3.30/0.79 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.30/0.79 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.30/0.79 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.30/0.79 fresh(y, y, x1...xn) = u
% 3.30/0.79 C => fresh(s, t, x1...xn) = v
% 3.30/0.79 where fresh is a fresh function symbol and x1..xn are the free
% 3.30/0.79 variables of u and v.
% 3.30/0.79 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.30/0.79 input problem has no model of domain size 1).
% 3.30/0.79
% 3.30/0.79 The encoding turns the above axioms into the following unit equations and goals:
% 3.30/0.79
% 3.30/0.79 Axiom 1 (m__): isPrime0(xk) = true2.
% 3.30/0.79 Axiom 2 (m__1716): aNaturalNumber0(xk) = true2.
% 3.30/0.79 Axiom 3 (mSortsC_01): aNaturalNumber0(sz10) = true2.
% 3.30/0.79 Axiom 4 (m_MulUnit): fresh9(X, X, Y) = Y.
% 3.30/0.79 Axiom 5 (mDefDiv): fresh51(X, X, Y, Z) = true2.
% 3.30/0.79 Axiom 6 (m_MulUnit): fresh9(aNaturalNumber0(X), true2, X) = sdtasdt0(X, sz10).
% 3.30/0.79 Axiom 7 (mDefDiv): fresh49(X, X, Y, Z, W) = doDivides0(Y, Z).
% 3.30/0.79 Axiom 8 (mDefDiv): fresh50(X, X, Y, Z, W) = fresh51(Z, sdtasdt0(Y, W), Y, Z).
% 3.30/0.79 Axiom 9 (mDefDiv): fresh48(X, X, Y, Z, W) = fresh49(aNaturalNumber0(Y), true2, Y, Z, W).
% 3.30/0.79 Axiom 10 (mDefDiv): fresh48(aNaturalNumber0(X), true2, Y, Z, X) = fresh50(aNaturalNumber0(Z), true2, Y, Z, X).
% 3.30/0.79
% 3.30/0.79 Goal 1 (m___1): tuple(aNaturalNumber0(X), doDivides0(X, xk), isPrime0(X)) = tuple(true2, true2, true2).
% 3.30/0.79 The goal is true when:
% 3.30/0.79 X = xk
% 3.30/0.79
% 3.30/0.79 Proof:
% 3.30/0.79 tuple(aNaturalNumber0(xk), doDivides0(xk, xk), isPrime0(xk))
% 3.30/0.79 = { by axiom 7 (mDefDiv) R->L }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh49(true2, true2, xk, xk, sz10), isPrime0(xk))
% 3.30/0.79 = { by axiom 2 (m__1716) R->L }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh49(aNaturalNumber0(xk), true2, xk, xk, sz10), isPrime0(xk))
% 3.30/0.79 = { by axiom 9 (mDefDiv) R->L }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh48(true2, true2, xk, xk, sz10), isPrime0(xk))
% 3.30/0.79 = { by axiom 3 (mSortsC_01) R->L }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh48(aNaturalNumber0(sz10), true2, xk, xk, sz10), isPrime0(xk))
% 3.30/0.79 = { by axiom 10 (mDefDiv) }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh50(aNaturalNumber0(xk), true2, xk, xk, sz10), isPrime0(xk))
% 3.30/0.79 = { by axiom 2 (m__1716) }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh50(true2, true2, xk, xk, sz10), isPrime0(xk))
% 3.30/0.79 = { by axiom 8 (mDefDiv) }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh51(xk, sdtasdt0(xk, sz10), xk, xk), isPrime0(xk))
% 3.30/0.79 = { by axiom 6 (m_MulUnit) R->L }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh51(xk, fresh9(aNaturalNumber0(xk), true2, xk), xk, xk), isPrime0(xk))
% 3.30/0.79 = { by axiom 2 (m__1716) }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh51(xk, fresh9(true2, true2, xk), xk, xk), isPrime0(xk))
% 3.30/0.79 = { by axiom 4 (m_MulUnit) }
% 3.30/0.79 tuple(aNaturalNumber0(xk), fresh51(xk, xk, xk, xk), isPrime0(xk))
% 3.30/0.79 = { by axiom 5 (mDefDiv) }
% 3.30/0.79 tuple(aNaturalNumber0(xk), true2, isPrime0(xk))
% 3.30/0.79 = { by axiom 2 (m__1716) }
% 3.30/0.79 tuple(true2, true2, isPrime0(xk))
% 3.30/0.79 = { by axiom 1 (m__) }
% 3.30/0.79 tuple(true2, true2, true2)
% 3.30/0.79 % SZS output end Proof
% 3.30/0.79
% 3.30/0.79 RESULT: Theorem (the conjecture is true).
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