TSTP Solution File: NUM458+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM458+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 : 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 11:56:23 EDT 2023
% Result : Theorem 0.22s 0.56s
% 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 : NUM458+1 : 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
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 08:53:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.56 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.22/0.56
% 0.22/0.56 % SZS status Theorem
% 0.22/0.56
% 0.22/0.57 % SZS output start Proof
% 0.22/0.57 Take the following subset of the input axioms:
% 0.22/0.57 fof(mDefLE, definition, ![W0, W1]: ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) <=> ?[W2]: (aNaturalNumber0(W2) & sdtpldt0(W0, W2)=W1)))).
% 0.22/0.57 fof(mSortsC, axiom, aNaturalNumber0(sz00)).
% 0.22/0.57 fof(m_AddZero, axiom, ![W0_2]: (aNaturalNumber0(W0_2) => (sdtpldt0(W0_2, sz00)=W0_2 & W0_2=sdtpldt0(sz00, W0_2)))).
% 0.22/0.57 fof(m__, conjecture, sdtlseqdt0(xm, xm)).
% 0.22/0.57 fof(m__718, hypothesis, aNaturalNumber0(xm)).
% 0.22/0.57
% 0.22/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.57 fresh(y, y, x1...xn) = u
% 0.22/0.57 C => fresh(s, t, x1...xn) = v
% 0.22/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.57 variables of u and v.
% 0.22/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.57 input problem has no model of domain size 1).
% 0.22/0.57
% 0.22/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.57
% 0.22/0.57 Axiom 1 (mSortsC): aNaturalNumber0(sz00) = true.
% 0.22/0.57 Axiom 2 (m__718): aNaturalNumber0(xm) = true.
% 0.22/0.57 Axiom 3 (m_AddZero): fresh9(X, X, Y) = Y.
% 0.22/0.57 Axiom 4 (mDefLE): fresh41(X, X, Y, Z) = true.
% 0.22/0.57 Axiom 5 (m_AddZero): fresh9(aNaturalNumber0(X), true, X) = sdtpldt0(X, sz00).
% 0.22/0.57 Axiom 6 (mDefLE): fresh39(X, X, Y, Z, W) = sdtlseqdt0(Y, Z).
% 0.22/0.57 Axiom 7 (mDefLE): fresh40(X, X, Y, Z, W) = fresh41(sdtpldt0(Y, W), Z, Y, Z).
% 0.22/0.57 Axiom 8 (mDefLE): fresh38(X, X, Y, Z, W) = fresh39(aNaturalNumber0(Y), true, Y, Z, W).
% 0.22/0.57 Axiom 9 (mDefLE): fresh38(aNaturalNumber0(X), true, Y, Z, X) = fresh40(aNaturalNumber0(Z), true, Y, Z, X).
% 0.22/0.57
% 0.22/0.57 Goal 1 (m__): sdtlseqdt0(xm, xm) = true.
% 0.22/0.57 Proof:
% 0.22/0.57 sdtlseqdt0(xm, xm)
% 0.22/0.57 = { by axiom 6 (mDefLE) R->L }
% 0.22/0.57 fresh39(true, true, xm, xm, sz00)
% 0.22/0.57 = { by axiom 2 (m__718) R->L }
% 0.22/0.57 fresh39(aNaturalNumber0(xm), true, xm, xm, sz00)
% 0.22/0.57 = { by axiom 8 (mDefLE) R->L }
% 0.22/0.57 fresh38(true, true, xm, xm, sz00)
% 0.22/0.57 = { by axiom 1 (mSortsC) R->L }
% 0.22/0.57 fresh38(aNaturalNumber0(sz00), true, xm, xm, sz00)
% 0.22/0.57 = { by axiom 9 (mDefLE) }
% 0.22/0.57 fresh40(aNaturalNumber0(xm), true, xm, xm, sz00)
% 0.22/0.57 = { by axiom 2 (m__718) }
% 0.22/0.57 fresh40(true, true, xm, xm, sz00)
% 0.22/0.57 = { by axiom 3 (m_AddZero) R->L }
% 0.22/0.57 fresh40(true, true, xm, fresh9(true, true, xm), sz00)
% 0.22/0.57 = { by axiom 2 (m__718) R->L }
% 0.22/0.57 fresh40(true, true, xm, fresh9(aNaturalNumber0(xm), true, xm), sz00)
% 0.22/0.57 = { by axiom 5 (m_AddZero) }
% 0.22/0.57 fresh40(true, true, xm, sdtpldt0(xm, sz00), sz00)
% 0.22/0.57 = { by axiom 7 (mDefLE) }
% 0.22/0.57 fresh41(sdtpldt0(xm, sz00), sdtpldt0(xm, sz00), xm, sdtpldt0(xm, sz00))
% 0.22/0.57 = { by axiom 4 (mDefLE) }
% 0.22/0.57 true
% 0.22/0.57 % SZS output end Proof
% 0.22/0.57
% 0.22/0.57 RESULT: Theorem (the conjecture is true).
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