TSTP Solution File: NUM617+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM617+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 : n016.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 11:57:18 EDT 2023
% Result : Theorem 22.82s 3.42s
% Output : Proof 22.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM617+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % 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 : n016.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
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Aug 25 09:08:26 EDT 2023
% 0.14/0.37 % CPUTime :
% 22.82/3.42 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 22.82/3.42
% 22.82/3.42 % SZS status Theorem
% 22.82/3.42
% 22.82/3.42 % SZS output start Proof
% 22.82/3.42 Take the following subset of the input axioms:
% 22.82/3.42 fof(mDefSub, definition, ![W0]: (aSet0(W0) => ![W1]: (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2]: (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))).
% 22.82/3.42 fof(mNATSet, axiom, aSet0(szNzAzT0) & isCountable0(szNzAzT0)).
% 22.82/3.42 fof(m__, conjecture, aElementOf0(xx, szNzAzT0)).
% 22.82/3.42 fof(m__5106, hypothesis, aSubsetOf0(xQ, szNzAzT0)).
% 22.82/3.42 fof(m__5195, hypothesis, aSubsetOf0(xP, xQ)).
% 22.82/3.42 fof(m__5348, hypothesis, aElementOf0(xx, xP)).
% 22.82/3.42
% 22.82/3.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 22.82/3.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 22.82/3.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 22.82/3.42 fresh(y, y, x1...xn) = u
% 22.82/3.42 C => fresh(s, t, x1...xn) = v
% 22.82/3.42 where fresh is a fresh function symbol and x1..xn are the free
% 22.82/3.42 variables of u and v.
% 22.82/3.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 22.82/3.42 input problem has no model of domain size 1).
% 22.82/3.42
% 22.82/3.42 The encoding turns the above axioms into the following unit equations and goals:
% 22.82/3.42
% 22.82/3.42 Axiom 1 (m__5348): aElementOf0(xx, xP) = true2.
% 22.82/3.42 Axiom 2 (mNATSet): aSet0(szNzAzT0) = true2.
% 22.82/3.42 Axiom 3 (m__5106): aSubsetOf0(xQ, szNzAzT0) = true2.
% 22.82/3.42 Axiom 4 (m__5195): aSubsetOf0(xP, xQ) = true2.
% 22.82/3.42 Axiom 5 (mDefSub_3): fresh62(X, X, Y) = true2.
% 22.82/3.42 Axiom 6 (mDefSub_2): fresh338(X, X, Y, Z) = true2.
% 22.82/3.42 Axiom 7 (mDefSub_2): fresh64(X, X, Y, Z) = aElementOf0(Z, Y).
% 22.82/3.42 Axiom 8 (mDefSub_3): fresh63(X, X, Y, Z) = aSet0(Z).
% 22.82/3.42 Axiom 9 (mDefSub_2): fresh337(X, X, Y, Z, W) = fresh338(aSet0(Y), true2, Y, W).
% 22.82/3.42 Axiom 10 (mDefSub_3): fresh63(aSubsetOf0(X, Y), true2, Y, X) = fresh62(aSet0(Y), true2, X).
% 22.82/3.42 Axiom 11 (mDefSub_2): fresh337(aSubsetOf0(X, Y), true2, Y, X, Z) = fresh64(aElementOf0(Z, X), true2, Y, Z).
% 22.82/3.42
% 22.82/3.42 Goal 1 (m__): aElementOf0(xx, szNzAzT0) = true2.
% 22.82/3.42 Proof:
% 22.82/3.42 aElementOf0(xx, szNzAzT0)
% 22.82/3.42 = { by axiom 7 (mDefSub_2) R->L }
% 22.82/3.42 fresh64(true2, true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 6 (mDefSub_2) R->L }
% 22.82/3.42 fresh64(fresh338(true2, true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 5 (mDefSub_3) R->L }
% 22.82/3.42 fresh64(fresh338(fresh62(true2, true2, xQ), true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 2 (mNATSet) R->L }
% 22.82/3.42 fresh64(fresh338(fresh62(aSet0(szNzAzT0), true2, xQ), true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 10 (mDefSub_3) R->L }
% 22.82/3.42 fresh64(fresh338(fresh63(aSubsetOf0(xQ, szNzAzT0), true2, szNzAzT0, xQ), true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 3 (m__5106) }
% 22.82/3.42 fresh64(fresh338(fresh63(true2, true2, szNzAzT0, xQ), true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 8 (mDefSub_3) }
% 22.82/3.42 fresh64(fresh338(aSet0(xQ), true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 9 (mDefSub_2) R->L }
% 22.82/3.42 fresh64(fresh337(true2, true2, xQ, xP, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 4 (m__5195) R->L }
% 22.82/3.42 fresh64(fresh337(aSubsetOf0(xP, xQ), true2, xQ, xP, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 11 (mDefSub_2) }
% 22.82/3.42 fresh64(fresh64(aElementOf0(xx, xP), true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 1 (m__5348) }
% 22.82/3.42 fresh64(fresh64(true2, true2, xQ, xx), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 7 (mDefSub_2) }
% 22.82/3.42 fresh64(aElementOf0(xx, xQ), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 11 (mDefSub_2) R->L }
% 22.82/3.42 fresh337(aSubsetOf0(xQ, szNzAzT0), true2, szNzAzT0, xQ, xx)
% 22.82/3.42 = { by axiom 3 (m__5106) }
% 22.82/3.42 fresh337(true2, true2, szNzAzT0, xQ, xx)
% 22.82/3.42 = { by axiom 9 (mDefSub_2) }
% 22.82/3.42 fresh338(aSet0(szNzAzT0), true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 2 (mNATSet) }
% 22.82/3.42 fresh338(true2, true2, szNzAzT0, xx)
% 22.82/3.42 = { by axiom 6 (mDefSub_2) }
% 22.82/3.42 true2
% 22.82/3.42 % SZS output end Proof
% 22.82/3.42
% 22.82/3.42 RESULT: Theorem (the conjecture is true).
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