TSTP Solution File: NUM460+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM460+2 : 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 11:56:25 EDT 2023
% Result : Theorem 21.15s 3.16s
% Output : Proof 21.15s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM460+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Aug 25 15:37:26 EDT 2023
% 0.11/0.33 % CPUTime :
% 21.15/3.16 Command-line arguments: --no-flatten-goal
% 21.15/3.16
% 21.15/3.16 % SZS status Theorem
% 21.15/3.16
% 21.15/3.16 % SZS output start Proof
% 21.15/3.16 Take the following subset of the input axioms:
% 21.15/3.16 fof(mAddAsso, axiom, ![W0, W1, W2]: ((aNaturalNumber0(W0) & (aNaturalNumber0(W1) & aNaturalNumber0(W2))) => sdtpldt0(sdtpldt0(W0, W1), W2)=sdtpldt0(W0, sdtpldt0(W1, W2)))).
% 21.15/3.16 fof(mSortsB, axiom, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => aNaturalNumber0(sdtpldt0(W0_2, W1_2)))).
% 21.15/3.16 fof(m__, conjecture, (?[W0_2]: (aNaturalNumber0(W0_2) & sdtpldt0(xm, W0_2)=xn) & (sdtlseqdt0(xm, xn) & (?[W0_2]: (aNaturalNumber0(W0_2) & sdtpldt0(xn, W0_2)=xl) & sdtlseqdt0(xn, xl)))) => (?[W0_2]: (aNaturalNumber0(W0_2) & sdtpldt0(xm, W0_2)=xl) | sdtlseqdt0(xm, xl))).
% 21.15/3.16 fof(m__773, hypothesis, aNaturalNumber0(xm) & (aNaturalNumber0(xn) & aNaturalNumber0(xl))).
% 21.15/3.16
% 21.15/3.16 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.15/3.16 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.15/3.16 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.15/3.16 fresh(y, y, x1...xn) = u
% 21.15/3.16 C => fresh(s, t, x1...xn) = v
% 21.15/3.16 where fresh is a fresh function symbol and x1..xn are the free
% 21.15/3.16 variables of u and v.
% 21.15/3.16 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.15/3.16 input problem has no model of domain size 1).
% 21.15/3.16
% 21.15/3.16 The encoding turns the above axioms into the following unit equations and goals:
% 21.15/3.16
% 21.15/3.16 Axiom 1 (m___2): aNaturalNumber0(w0_2) = true2.
% 21.15/3.16 Axiom 2 (m___3): aNaturalNumber0(w0) = true2.
% 21.15/3.16 Axiom 3 (m__773): aNaturalNumber0(xm) = true2.
% 21.15/3.16 Axiom 4 (m__): sdtpldt0(xm, w0_2) = xn.
% 21.15/3.16 Axiom 5 (m___1): sdtpldt0(xn, w0) = xl.
% 21.15/3.16 Axiom 6 (mSortsB): fresh16(X, X, Y, Z) = aNaturalNumber0(sdtpldt0(Y, Z)).
% 21.15/3.16 Axiom 7 (mSortsB): fresh15(X, X, Y, Z) = true2.
% 21.15/3.16 Axiom 8 (mAddAsso): fresh68(X, X, Y, Z, W) = sdtpldt0(Y, sdtpldt0(Z, W)).
% 21.15/3.16 Axiom 9 (mAddAsso): fresh25(X, X, Y, Z, W) = sdtpldt0(sdtpldt0(Y, Z), W).
% 21.15/3.16 Axiom 10 (mSortsB): fresh16(aNaturalNumber0(X), true2, Y, X) = fresh15(aNaturalNumber0(Y), true2, Y, X).
% 21.15/3.17 Axiom 11 (mAddAsso): fresh67(X, X, Y, Z, W) = fresh68(aNaturalNumber0(Y), true2, Y, Z, W).
% 21.15/3.17 Axiom 12 (mAddAsso): fresh67(aNaturalNumber0(X), true2, Y, Z, X) = fresh25(aNaturalNumber0(Z), true2, Y, Z, X).
% 21.15/3.17
% 21.15/3.17 Goal 1 (m___6): tuple(sdtpldt0(xm, X), aNaturalNumber0(X)) = tuple(xl, true2).
% 21.15/3.17 The goal is true when:
% 21.15/3.17 X = sdtpldt0(w0_2, w0)
% 21.15/3.17
% 21.15/3.17 Proof:
% 21.15/3.17 tuple(sdtpldt0(xm, sdtpldt0(w0_2, w0)), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 8 (mAddAsso) R->L }
% 21.15/3.17 tuple(fresh68(true2, true2, xm, w0_2, w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 3 (m__773) R->L }
% 21.15/3.17 tuple(fresh68(aNaturalNumber0(xm), true2, xm, w0_2, w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 11 (mAddAsso) R->L }
% 21.15/3.17 tuple(fresh67(true2, true2, xm, w0_2, w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 2 (m___3) R->L }
% 21.15/3.17 tuple(fresh67(aNaturalNumber0(w0), true2, xm, w0_2, w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 12 (mAddAsso) }
% 21.15/3.17 tuple(fresh25(aNaturalNumber0(w0_2), true2, xm, w0_2, w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 1 (m___2) }
% 21.15/3.17 tuple(fresh25(true2, true2, xm, w0_2, w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 9 (mAddAsso) }
% 21.15/3.17 tuple(sdtpldt0(sdtpldt0(xm, w0_2), w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 4 (m__) }
% 21.15/3.17 tuple(sdtpldt0(xn, w0), aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 5 (m___1) }
% 21.15/3.17 tuple(xl, aNaturalNumber0(sdtpldt0(w0_2, w0)))
% 21.15/3.17 = { by axiom 6 (mSortsB) R->L }
% 21.15/3.17 tuple(xl, fresh16(true2, true2, w0_2, w0))
% 21.15/3.17 = { by axiom 2 (m___3) R->L }
% 21.15/3.17 tuple(xl, fresh16(aNaturalNumber0(w0), true2, w0_2, w0))
% 21.15/3.17 = { by axiom 10 (mSortsB) }
% 21.15/3.17 tuple(xl, fresh15(aNaturalNumber0(w0_2), true2, w0_2, w0))
% 21.15/3.17 = { by axiom 1 (m___2) }
% 21.15/3.17 tuple(xl, fresh15(true2, true2, w0_2, w0))
% 21.15/3.17 = { by axiom 7 (mSortsB) }
% 21.15/3.17 tuple(xl, true2)
% 21.15/3.17 % SZS output end Proof
% 21.15/3.17
% 21.15/3.17 RESULT: Theorem (the conjecture is true).
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