TSTP Solution File: RNG047+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG047+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 : n011.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 13:59:02 EDT 2023
% Result : Theorem 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG047+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sun Aug 27 02:51:09 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.54 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.54
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 Take the following subset of the input axioms:
% 0.19/0.54 fof(mDimNat, axiom, ![W0]: (aVector0(W0) => aNaturalNumber0(aDimensionOf0(W0)))).
% 0.19/0.54 fof(mSuccEqu, axiom, ![W1, W0_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1)) => (szszuzczcdt0(W0_2)=szszuzczcdt0(W1) => W0_2=W1))).
% 0.19/0.54 fof(m__, conjecture, (aVector0(sziznziztdt0(xs)) & (szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))=aDimensionOf0(xs) & ![W0_2]: (aNaturalNumber0(W0_2) => sdtlbdtrb0(sziznziztdt0(xs), W0_2)=sdtlbdtrb0(xs, W0_2)))) => ((aVector0(sziznziztdt0(xt)) & (szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt)))=aDimensionOf0(xt) & ![W0_2]: (aNaturalNumber0(W0_2) => sdtlbdtrb0(sziznziztdt0(xt), W0_2)=sdtlbdtrb0(xt, W0_2)))) => aDimensionOf0(sziznziztdt0(xs))=aDimensionOf0(sziznziztdt0(xt)))).
% 0.19/0.54 fof(m__1329_01, hypothesis, aDimensionOf0(xs)=aDimensionOf0(xt) & aDimensionOf0(xt)!=sz00).
% 0.19/0.54
% 0.19/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.54 fresh(y, y, x1...xn) = u
% 0.19/0.54 C => fresh(s, t, x1...xn) = v
% 0.19/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.54 variables of u and v.
% 0.19/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.54 input problem has no model of domain size 1).
% 0.19/0.54
% 0.19/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.54
% 0.19/0.54 Axiom 1 (m__1329_01): aDimensionOf0(xs) = aDimensionOf0(xt).
% 0.19/0.54 Axiom 2 (m___3): aVector0(sziznziztdt0(xt)) = true2.
% 0.19/0.54 Axiom 3 (m___2): aVector0(sziznziztdt0(xs)) = true2.
% 0.19/0.54 Axiom 4 (m___1): szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt).
% 0.19/0.54 Axiom 5 (m__): szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs).
% 0.19/0.54 Axiom 6 (mDimNat): fresh32(X, X, Y) = true2.
% 0.19/0.54 Axiom 7 (mSuccEqu): fresh88(X, X, Y, Z) = Y.
% 0.19/0.54 Axiom 8 (mDimNat): fresh32(aVector0(X), true2, X) = aNaturalNumber0(aDimensionOf0(X)).
% 0.19/0.54 Axiom 9 (mSuccEqu): fresh5(X, X, Y, Z) = Z.
% 0.19/0.54 Axiom 10 (mSuccEqu): fresh87(X, X, Y, Z) = fresh88(aNaturalNumber0(Y), true2, Y, Z).
% 0.19/0.54 Axiom 11 (mSuccEqu): fresh87(aNaturalNumber0(X), true2, Y, X) = fresh5(szszuzczcdt0(Y), szszuzczcdt0(X), Y, X).
% 0.19/0.54
% 0.19/0.54 Goal 1 (m___4): aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)).
% 0.19/0.54 Proof:
% 0.19/0.54 aDimensionOf0(sziznziztdt0(xs))
% 0.19/0.54 = { by axiom 9 (mSuccEqu) R->L }
% 0.19/0.54 fresh5(aDimensionOf0(xt), aDimensionOf0(xt), aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 1 (m__1329_01) R->L }
% 0.19/0.54 fresh5(aDimensionOf0(xt), aDimensionOf0(xs), aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 5 (m__) R->L }
% 0.19/0.54 fresh5(aDimensionOf0(xt), szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))), aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 4 (m___1) R->L }
% 0.19/0.54 fresh5(szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))), szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))), aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 11 (mSuccEqu) R->L }
% 0.19/0.54 fresh87(aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))), true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 8 (mDimNat) R->L }
% 0.19/0.54 fresh87(fresh32(aVector0(sziznziztdt0(xs)), true2, sziznziztdt0(xs)), true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 3 (m___2) }
% 0.19/0.54 fresh87(fresh32(true2, true2, sziznziztdt0(xs)), true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 6 (mDimNat) }
% 0.19/0.54 fresh87(true2, true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 10 (mSuccEqu) }
% 0.19/0.54 fresh88(aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))), true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 8 (mDimNat) R->L }
% 0.19/0.54 fresh88(fresh32(aVector0(sziznziztdt0(xt)), true2, sziznziztdt0(xt)), true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 2 (m___3) }
% 0.19/0.54 fresh88(fresh32(true2, true2, sziznziztdt0(xt)), true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 6 (mDimNat) }
% 0.19/0.54 fresh88(true2, true2, aDimensionOf0(sziznziztdt0(xt)), aDimensionOf0(sziznziztdt0(xs)))
% 0.19/0.54 = { by axiom 7 (mSuccEqu) }
% 0.19/0.54 aDimensionOf0(sziznziztdt0(xt))
% 0.19/0.54 % SZS output end Proof
% 0.19/0.54
% 0.19/0.54 RESULT: Theorem (the conjecture is true).
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