TSTP Solution File: NUM610+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM610+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 : n008.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 11:57:15 EDT 2023
% Result : Theorem 16.47s 2.49s
% Output : Proof 16.47s
% 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 : NUM610+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
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 13:14:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 16.47/2.49 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 16.47/2.49
% 16.47/2.49 % SZS status Theorem
% 16.47/2.49
% 16.47/2.49 % SZS output start Proof
% 16.47/2.49 Take the following subset of the input axioms:
% 16.47/2.50 fof(mDefSub, definition, ![W0]: (aSet0(W0) => ![W1]: (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2]: (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))).
% 16.47/2.50 fof(mNATSet, axiom, aSet0(szNzAzT0) & isCountable0(szNzAzT0)).
% 16.47/2.50 fof(mSubTrans, axiom, ![W0_2, W1_2, W2_2]: ((aSet0(W0_2) & (aSet0(W1_2) & aSet0(W2_2))) => ((aSubsetOf0(W0_2, W1_2) & aSubsetOf0(W1_2, W2_2)) => aSubsetOf0(W0_2, W2_2)))).
% 16.47/2.50 fof(m__, conjecture, aSubsetOf0(xP, xO)).
% 16.47/2.50 fof(m__4891, hypothesis, aSet0(xO) & xO=sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))).
% 16.47/2.50 fof(m__5093, hypothesis, aSubsetOf0(xQ, xO) & xQ!=slcrc0).
% 16.47/2.50 fof(m__5106, hypothesis, aSubsetOf0(xQ, szNzAzT0)).
% 16.47/2.50 fof(m__5164, hypothesis, aSet0(xP) & xP=sdtmndt0(xQ, szmzizndt0(xQ))).
% 16.47/2.50 fof(m__5195, hypothesis, aSubsetOf0(xP, xQ)).
% 16.47/2.50
% 16.47/2.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.47/2.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.47/2.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.47/2.50 fresh(y, y, x1...xn) = u
% 16.47/2.50 C => fresh(s, t, x1...xn) = v
% 16.47/2.50 where fresh is a fresh function symbol and x1..xn are the free
% 16.47/2.50 variables of u and v.
% 16.47/2.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.47/2.50 input problem has no model of domain size 1).
% 16.47/2.50
% 16.47/2.50 The encoding turns the above axioms into the following unit equations and goals:
% 16.47/2.50
% 16.47/2.50 Axiom 1 (mNATSet): aSet0(szNzAzT0) = true2.
% 16.47/2.50 Axiom 2 (m__4891_1): aSet0(xO) = true2.
% 16.47/2.50 Axiom 3 (m__5164_1): aSet0(xP) = true2.
% 16.47/2.50 Axiom 4 (m__5106): aSubsetOf0(xQ, szNzAzT0) = true2.
% 16.47/2.50 Axiom 5 (m__5093): aSubsetOf0(xQ, xO) = true2.
% 16.47/2.50 Axiom 6 (m__5195): aSubsetOf0(xP, xQ) = true2.
% 16.47/2.50 Axiom 7 (mDefSub_3): fresh62(X, X, Y) = true2.
% 16.47/2.50 Axiom 8 (mSubTrans): fresh328(X, X, Y, Z) = true2.
% 16.47/2.50 Axiom 9 (mSubTrans): fresh326(X, X, Y, Z) = aSubsetOf0(Y, Z).
% 16.47/2.50 Axiom 10 (mDefSub_3): fresh63(X, X, Y, Z) = aSet0(Z).
% 16.47/2.50 Axiom 11 (mSubTrans): fresh327(X, X, Y, Z, W) = fresh328(aSet0(Y), true2, Y, W).
% 16.47/2.50 Axiom 12 (mSubTrans): fresh325(X, X, Y, Z, W) = fresh326(aSet0(Z), true2, Y, W).
% 16.47/2.50 Axiom 13 (mSubTrans): fresh324(X, X, Y, Z, W) = fresh327(aSet0(W), true2, Y, Z, W).
% 16.47/2.50 Axiom 14 (mDefSub_3): fresh63(aSubsetOf0(X, Y), true2, Y, X) = fresh62(aSet0(Y), true2, X).
% 16.47/2.50 Axiom 15 (mSubTrans): fresh324(aSubsetOf0(X, Y), true2, Z, X, Y) = fresh325(aSubsetOf0(Z, X), true2, Z, X, Y).
% 16.47/2.50
% 16.47/2.50 Goal 1 (m__): aSubsetOf0(xP, xO) = true2.
% 16.47/2.50 Proof:
% 16.47/2.50 aSubsetOf0(xP, xO)
% 16.47/2.50 = { by axiom 9 (mSubTrans) R->L }
% 16.47/2.50 fresh326(true2, true2, xP, xO)
% 16.47/2.50 = { by axiom 7 (mDefSub_3) R->L }
% 16.47/2.50 fresh326(fresh62(true2, true2, xQ), true2, xP, xO)
% 16.47/2.50 = { by axiom 1 (mNATSet) R->L }
% 16.47/2.50 fresh326(fresh62(aSet0(szNzAzT0), true2, xQ), true2, xP, xO)
% 16.47/2.50 = { by axiom 14 (mDefSub_3) R->L }
% 16.47/2.50 fresh326(fresh63(aSubsetOf0(xQ, szNzAzT0), true2, szNzAzT0, xQ), true2, xP, xO)
% 16.47/2.50 = { by axiom 4 (m__5106) }
% 16.47/2.50 fresh326(fresh63(true2, true2, szNzAzT0, xQ), true2, xP, xO)
% 16.47/2.50 = { by axiom 10 (mDefSub_3) }
% 16.47/2.50 fresh326(aSet0(xQ), true2, xP, xO)
% 16.47/2.50 = { by axiom 12 (mSubTrans) R->L }
% 16.47/2.50 fresh325(true2, true2, xP, xQ, xO)
% 16.47/2.50 = { by axiom 6 (m__5195) R->L }
% 16.47/2.50 fresh325(aSubsetOf0(xP, xQ), true2, xP, xQ, xO)
% 16.47/2.50 = { by axiom 15 (mSubTrans) R->L }
% 16.47/2.50 fresh324(aSubsetOf0(xQ, xO), true2, xP, xQ, xO)
% 16.47/2.50 = { by axiom 5 (m__5093) }
% 16.47/2.50 fresh324(true2, true2, xP, xQ, xO)
% 16.47/2.50 = { by axiom 13 (mSubTrans) }
% 16.47/2.50 fresh327(aSet0(xO), true2, xP, xQ, xO)
% 16.47/2.50 = { by axiom 2 (m__4891_1) }
% 16.47/2.50 fresh327(true2, true2, xP, xQ, xO)
% 16.47/2.50 = { by axiom 11 (mSubTrans) }
% 16.47/2.50 fresh328(aSet0(xP), true2, xP, xO)
% 16.47/2.50 = { by axiom 3 (m__5164_1) }
% 16.47/2.50 fresh328(true2, true2, xP, xO)
% 16.47/2.50 = { by axiom 8 (mSubTrans) }
% 16.47/2.50 true2
% 16.47/2.50 % SZS output end Proof
% 16.47/2.50
% 16.47/2.50 RESULT: Theorem (the conjecture is true).
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