TSTP Solution File: PUZ128+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ128+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 : n031.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 13:24:20 EDT 2023
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PUZ128+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % 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 : n031.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 22:53:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.38 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.38
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 Take the following subset of the input axioms:
% 0.20/0.39 fof(iokaste_oedipus, axiom, parent_of(iokaste, oedipus)).
% 0.20/0.39 fof(iokaste_parent_particide_parent_not_patricide, conjecture, ?[P, NP]: (parent_of(iokaste, P) & (patricide(P) & (parent_of(P, NP) & ~patricide(NP))))).
% 0.20/0.39 fof(iokaste_polyneikes, axiom, parent_of(iokaste, polyneikes)).
% 0.20/0.39 fof(oedipus_patricidal, axiom, patricide(oedipus)).
% 0.20/0.39 fof(oedipus_polyneikes, axiom, parent_of(oedipus, polyneikes)).
% 0.20/0.39 fof(polyneikes_thersandros, axiom, parent_of(polyneikes, thersandros)).
% 0.20/0.39 fof(thersandros_not_patricidal, axiom, ~patricide(thersandros)).
% 0.20/0.39
% 0.20/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.39 fresh(y, y, x1...xn) = u
% 0.20/0.39 C => fresh(s, t, x1...xn) = v
% 0.20/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.39 variables of u and v.
% 0.20/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39 input problem has no model of domain size 1).
% 0.20/0.39
% 0.20/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39
% 0.20/0.39 Axiom 1 (oedipus_patricidal): patricide(oedipus) = true.
% 0.20/0.39 Axiom 2 (iokaste_oedipus): parent_of(iokaste, oedipus) = true.
% 0.20/0.39 Axiom 3 (iokaste_polyneikes): parent_of(iokaste, polyneikes) = true.
% 0.20/0.39 Axiom 4 (oedipus_polyneikes): parent_of(oedipus, polyneikes) = true.
% 0.20/0.39 Axiom 5 (polyneikes_thersandros): parent_of(polyneikes, thersandros) = true.
% 0.20/0.39 Axiom 6 (iokaste_parent_particide_parent_not_patricide): fresh3(X, X, Y) = true.
% 0.20/0.39 Axiom 7 (iokaste_parent_particide_parent_not_patricide): fresh(X, X, Y, Z) = patricide(Z).
% 0.20/0.39 Axiom 8 (iokaste_parent_particide_parent_not_patricide): fresh2(X, X, Y, Z) = fresh3(parent_of(Y, Z), true, Z).
% 0.20/0.39 Axiom 9 (iokaste_parent_particide_parent_not_patricide): fresh2(patricide(X), true, X, Y) = fresh(parent_of(iokaste, X), true, X, Y).
% 0.20/0.39
% 0.20/0.39 Goal 1 (thersandros_not_patricidal): patricide(thersandros) = true.
% 0.20/0.39 Proof:
% 0.20/0.39 patricide(thersandros)
% 0.20/0.39 = { by axiom 7 (iokaste_parent_particide_parent_not_patricide) R->L }
% 0.20/0.39 fresh(true, true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 3 (iokaste_polyneikes) R->L }
% 0.20/0.39 fresh(parent_of(iokaste, polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 9 (iokaste_parent_particide_parent_not_patricide) R->L }
% 0.20/0.39 fresh2(patricide(polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 7 (iokaste_parent_particide_parent_not_patricide) R->L }
% 0.20/0.39 fresh2(fresh(true, true, oedipus, polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 2 (iokaste_oedipus) R->L }
% 0.20/0.39 fresh2(fresh(parent_of(iokaste, oedipus), true, oedipus, polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 9 (iokaste_parent_particide_parent_not_patricide) R->L }
% 0.20/0.39 fresh2(fresh2(patricide(oedipus), true, oedipus, polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 1 (oedipus_patricidal) }
% 0.20/0.39 fresh2(fresh2(true, true, oedipus, polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 8 (iokaste_parent_particide_parent_not_patricide) }
% 0.20/0.39 fresh2(fresh3(parent_of(oedipus, polyneikes), true, polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 4 (oedipus_polyneikes) }
% 0.20/0.39 fresh2(fresh3(true, true, polyneikes), true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 6 (iokaste_parent_particide_parent_not_patricide) }
% 0.20/0.39 fresh2(true, true, polyneikes, thersandros)
% 0.20/0.39 = { by axiom 8 (iokaste_parent_particide_parent_not_patricide) }
% 0.20/0.39 fresh3(parent_of(polyneikes, thersandros), true, thersandros)
% 0.20/0.39 = { by axiom 5 (polyneikes_thersandros) }
% 0.20/0.39 fresh3(true, true, thersandros)
% 0.20/0.39 = { by axiom 6 (iokaste_parent_particide_parent_not_patricide) }
% 0.20/0.39 true
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39
% 0.20/0.39 RESULT: Theorem (the conjecture is true).
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