TSTP Solution File: NUM489+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM489+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 : n013.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 11:56:34 EDT 2023
% Result : Theorem 0.21s 0.78s
% Output : Proof 0.21s
% 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 : NUM489+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
% 0.17/0.35 % Computer : n013.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Fri Aug 25 16:20:47 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.78 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.78
% 0.21/0.78 % SZS status Theorem
% 0.21/0.78
% 0.21/0.78 % SZS output start Proof
% 0.21/0.78 Take the following subset of the input axioms:
% 0.21/0.78 fof(mDefDiff, definition, ![W0, W1]: ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2]: (W2=sdtmndt0(W1, W0) <=> (aNaturalNumber0(W2) & sdtpldt0(W0, W2)=W1))))).
% 0.21/0.78 fof(m__, conjecture, xn=sdtpldt0(xp, xr)).
% 0.21/0.78 fof(m__1837, hypothesis, aNaturalNumber0(xn) & (aNaturalNumber0(xm) & aNaturalNumber0(xp))).
% 0.21/0.78 fof(m__1870, hypothesis, sdtlseqdt0(xp, xn)).
% 0.21/0.78 fof(m__1883, hypothesis, xr=sdtmndt0(xn, xp)).
% 0.21/0.78
% 0.21/0.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.78 fresh(y, y, x1...xn) = u
% 0.21/0.78 C => fresh(s, t, x1...xn) = v
% 0.21/0.78 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.78 variables of u and v.
% 0.21/0.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.78 input problem has no model of domain size 1).
% 0.21/0.78
% 0.21/0.78 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.78
% 0.21/0.78 Axiom 1 (m__1837): aNaturalNumber0(xn) = true2.
% 0.21/0.78 Axiom 2 (m__1837_2): aNaturalNumber0(xp) = true2.
% 0.21/0.78 Axiom 3 (m__1870): sdtlseqdt0(xp, xn) = true2.
% 0.21/0.78 Axiom 4 (m__1883): xr = sdtmndt0(xn, xp).
% 0.21/0.78 Axiom 5 (mDefDiff_1): fresh79(X, X, Y, Z, W) = sdtpldt0(Y, W).
% 0.21/0.78 Axiom 6 (mDefDiff_1): fresh4(X, X, Y, Z, W) = Z.
% 0.21/0.78 Axiom 7 (mDefDiff_1): fresh78(X, X, Y, Z, W) = fresh79(aNaturalNumber0(Y), true2, Y, Z, W).
% 0.21/0.78 Axiom 8 (mDefDiff_1): fresh77(X, X, Y, Z, W) = fresh78(aNaturalNumber0(Z), true2, Y, Z, W).
% 0.21/0.79 Axiom 9 (mDefDiff_1): fresh77(sdtlseqdt0(X, Y), true2, X, Y, Z) = fresh4(Z, sdtmndt0(Y, X), X, Y, Z).
% 0.21/0.79
% 0.21/0.79 Goal 1 (m__): xn = sdtpldt0(xp, xr).
% 0.21/0.79 Proof:
% 0.21/0.79 xn
% 0.21/0.79 = { by axiom 6 (mDefDiff_1) R->L }
% 0.21/0.79 fresh4(sdtmndt0(xn, xp), sdtmndt0(xn, xp), xp, xn, sdtmndt0(xn, xp))
% 0.21/0.79 = { by axiom 9 (mDefDiff_1) R->L }
% 0.21/0.79 fresh77(sdtlseqdt0(xp, xn), true2, xp, xn, sdtmndt0(xn, xp))
% 0.21/0.79 = { by axiom 3 (m__1870) }
% 0.21/0.79 fresh77(true2, true2, xp, xn, sdtmndt0(xn, xp))
% 0.21/0.79 = { by axiom 4 (m__1883) R->L }
% 0.21/0.79 fresh77(true2, true2, xp, xn, xr)
% 0.21/0.79 = { by axiom 8 (mDefDiff_1) }
% 0.21/0.79 fresh78(aNaturalNumber0(xn), true2, xp, xn, xr)
% 0.21/0.79 = { by axiom 1 (m__1837) }
% 0.21/0.79 fresh78(true2, true2, xp, xn, xr)
% 0.21/0.79 = { by axiom 7 (mDefDiff_1) }
% 0.21/0.79 fresh79(aNaturalNumber0(xp), true2, xp, xn, xr)
% 0.21/0.79 = { by axiom 2 (m__1837_2) }
% 0.21/0.79 fresh79(true2, true2, xp, xn, xr)
% 0.21/0.79 = { by axiom 5 (mDefDiff_1) }
% 0.21/0.79 sdtpldt0(xp, xr)
% 0.21/0.79 % SZS output end Proof
% 0.21/0.79
% 0.21/0.79 RESULT: Theorem (the conjecture is true).
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