TSTP Solution File: NUM612+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM612+3 : 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 : n019.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 11:57:16 EDT 2023
% Result : Theorem 13.09s 2.13s
% Output : Proof 13.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM612+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % 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 : n019.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
% 0.13/0.34 % DateTime : Fri Aug 25 10:36:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 13.09/2.13 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 13.09/2.13
% 13.09/2.13 % SZS status Theorem
% 13.09/2.13
% 13.09/2.13 % SZS output start Proof
% 13.09/2.13 Take the following subset of the input axioms:
% 13.09/2.14 fof(mCardDiff, axiom, ![W0]: (aSet0(W0) => ![W1]: ((isFinite0(W0) & aElementOf0(W1, W0)) => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1)))=sbrdtbr0(W0)))).
% 13.09/2.14 fof(mCardNum, axiom, ![W0_2]: (aSet0(W0_2) => (aElementOf0(sbrdtbr0(W0_2), szNzAzT0) <=> isFinite0(W0_2)))).
% 13.09/2.14 fof(mSubFSet, axiom, ![W0_2]: ((aSet0(W0_2) & isFinite0(W0_2)) => ![W1_2]: (aSubsetOf0(W1_2, W0_2) => isFinite0(W1_2)))).
% 13.09/2.14 fof(m__, conjecture, szszuzczcdt0(sbrdtbr0(xP))=sbrdtbr0(xQ) & aElementOf0(sbrdtbr0(xP), szNzAzT0)).
% 13.09/2.14 fof(m__3418, hypothesis, aElementOf0(xK, szNzAzT0)).
% 13.09/2.14 fof(m__5078, hypothesis, aSet0(xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => aElementOf0(W0_2, xO)) & (aSubsetOf0(xQ, xO) & (sbrdtbr0(xQ)=xK & aElementOf0(xQ, slbdtsldtrb0(xO, xK)))))).
% 13.09/2.14 fof(m__5147, hypothesis, aElementOf0(xp, xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => sdtlseqdt0(xp, W0_2)) & xp=szmzizndt0(xQ))).
% 13.09/2.14 fof(m__5164, hypothesis, aSet0(xP) & (![W0_2]: (aElementOf0(W0_2, xQ) => sdtlseqdt0(szmzizndt0(xQ), W0_2)) & (![W0_2]: (aElementOf0(W0_2, xP) <=> (aElement0(W0_2) & (aElementOf0(W0_2, xQ) & W0_2!=szmzizndt0(xQ)))) & xP=sdtmndt0(xQ, szmzizndt0(xQ))))).
% 13.09/2.14 fof(m__5195, hypothesis, ![W0_2]: (aElementOf0(W0_2, xP) => aElementOf0(W0_2, xQ)) & aSubsetOf0(xP, xQ)).
% 13.09/2.14
% 13.09/2.14 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.09/2.14 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.09/2.14 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.09/2.14 fresh(y, y, x1...xn) = u
% 13.09/2.14 C => fresh(s, t, x1...xn) = v
% 13.09/2.14 where fresh is a fresh function symbol and x1..xn are the free
% 13.09/2.14 variables of u and v.
% 13.09/2.14 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.09/2.14 input problem has no model of domain size 1).
% 13.09/2.14
% 13.09/2.14 The encoding turns the above axioms into the following unit equations and goals:
% 13.09/2.14
% 13.09/2.14 Axiom 1 (m__5078_1): aSet0(xQ) = true2.
% 13.09/2.14 Axiom 2 (m__5164_1): aSet0(xP) = true2.
% 13.09/2.14 Axiom 3 (m__5147): xp = szmzizndt0(xQ).
% 13.09/2.14 Axiom 4 (m__5078): sbrdtbr0(xQ) = xK.
% 13.09/2.14 Axiom 5 (m__3418): aElementOf0(xK, szNzAzT0) = true2.
% 13.09/2.14 Axiom 6 (m__5147_1): aElementOf0(xp, xQ) = true2.
% 13.09/2.14 Axiom 7 (m__5195): aSubsetOf0(xP, xQ) = true2.
% 13.09/2.14 Axiom 8 (m__5164): xP = sdtmndt0(xQ, szmzizndt0(xQ)).
% 13.09/2.14 Axiom 9 (mSubFSet): fresh522(X, X, Y) = true2.
% 13.09/2.14 Axiom 10 (mCardNum): fresh265(X, X, Y) = isFinite0(Y).
% 13.09/2.14 Axiom 11 (mCardNum): fresh264(X, X, Y) = true2.
% 13.09/2.14 Axiom 12 (mCardNum_1): fresh263(X, X, Y) = aElementOf0(sbrdtbr0(Y), szNzAzT0).
% 13.09/2.14 Axiom 13 (mCardNum_1): fresh262(X, X, Y) = true2.
% 13.09/2.14 Axiom 14 (mSubFSet): fresh521(X, X, Y, Z) = fresh522(aSet0(Y), true2, Z).
% 13.09/2.14 Axiom 15 (mCardDiff): fresh458(X, X, Y, Z) = sbrdtbr0(Y).
% 13.09/2.14 Axiom 16 (mCardDiff): fresh269(X, X, Y, Z) = szszuzczcdt0(sbrdtbr0(sdtmndt0(Y, Z))).
% 13.09/2.14 Axiom 17 (mCardNum_1): fresh263(isFinite0(X), true2, X) = fresh262(aSet0(X), true2, X).
% 13.09/2.14 Axiom 18 (mSubFSet): fresh189(X, X, Y, Z) = isFinite0(Z).
% 13.09/2.14 Axiom 19 (mCardDiff): fresh457(X, X, Y, Z) = fresh458(aSet0(Y), true2, Y, Z).
% 13.09/2.14 Axiom 20 (mSubFSet): fresh521(aSubsetOf0(X, Y), true2, Y, X) = fresh189(isFinite0(Y), true2, Y, X).
% 13.09/2.14 Axiom 21 (mCardDiff): fresh457(isFinite0(X), true2, X, Y) = fresh269(aElementOf0(Y, X), true2, X, Y).
% 13.09/2.14 Axiom 22 (mCardNum): fresh265(aElementOf0(sbrdtbr0(X), szNzAzT0), true2, X) = fresh264(aSet0(X), true2, X).
% 13.09/2.14
% 13.09/2.14 Lemma 23: isFinite0(xQ) = true2.
% 13.09/2.14 Proof:
% 13.09/2.14 isFinite0(xQ)
% 13.09/2.14 = { by axiom 10 (mCardNum) R->L }
% 13.09/2.14 fresh265(true2, true2, xQ)
% 13.09/2.14 = { by axiom 5 (m__3418) R->L }
% 13.09/2.14 fresh265(aElementOf0(xK, szNzAzT0), true2, xQ)
% 13.09/2.14 = { by axiom 4 (m__5078) R->L }
% 13.09/2.14 fresh265(aElementOf0(sbrdtbr0(xQ), szNzAzT0), true2, xQ)
% 13.09/2.14 = { by axiom 22 (mCardNum) }
% 13.09/2.14 fresh264(aSet0(xQ), true2, xQ)
% 13.09/2.14 = { by axiom 1 (m__5078_1) }
% 13.09/2.14 fresh264(true2, true2, xQ)
% 13.09/2.14 = { by axiom 11 (mCardNum) }
% 13.09/2.14 true2
% 13.09/2.14
% 13.09/2.14 Goal 1 (m__): tuple4(szszuzczcdt0(sbrdtbr0(xP)), aElementOf0(sbrdtbr0(xP), szNzAzT0)) = tuple4(sbrdtbr0(xQ), true2).
% 13.09/2.14 Proof:
% 13.09/2.14 tuple4(szszuzczcdt0(sbrdtbr0(xP)), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 8 (m__5164) }
% 13.09/2.14 tuple4(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, szmzizndt0(xQ)))), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 3 (m__5147) R->L }
% 13.09/2.14 tuple4(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xp))), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 16 (mCardDiff) R->L }
% 13.09/2.14 tuple4(fresh269(true2, true2, xQ, xp), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 6 (m__5147_1) R->L }
% 13.09/2.14 tuple4(fresh269(aElementOf0(xp, xQ), true2, xQ, xp), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 21 (mCardDiff) R->L }
% 13.09/2.14 tuple4(fresh457(isFinite0(xQ), true2, xQ, xp), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by lemma 23 }
% 13.09/2.14 tuple4(fresh457(true2, true2, xQ, xp), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 19 (mCardDiff) }
% 13.09/2.14 tuple4(fresh458(aSet0(xQ), true2, xQ, xp), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 1 (m__5078_1) }
% 13.09/2.14 tuple4(fresh458(true2, true2, xQ, xp), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 15 (mCardDiff) }
% 13.09/2.14 tuple4(sbrdtbr0(xQ), aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 4 (m__5078) }
% 13.09/2.14 tuple4(xK, aElementOf0(sbrdtbr0(xP), szNzAzT0))
% 13.09/2.14 = { by axiom 12 (mCardNum_1) R->L }
% 13.09/2.14 tuple4(xK, fresh263(true2, true2, xP))
% 13.09/2.14 = { by axiom 9 (mSubFSet) R->L }
% 13.09/2.14 tuple4(xK, fresh263(fresh522(true2, true2, xP), true2, xP))
% 13.09/2.14 = { by axiom 1 (m__5078_1) R->L }
% 13.09/2.14 tuple4(xK, fresh263(fresh522(aSet0(xQ), true2, xP), true2, xP))
% 13.09/2.14 = { by axiom 14 (mSubFSet) R->L }
% 13.09/2.14 tuple4(xK, fresh263(fresh521(true2, true2, xQ, xP), true2, xP))
% 13.09/2.14 = { by axiom 7 (m__5195) R->L }
% 13.09/2.14 tuple4(xK, fresh263(fresh521(aSubsetOf0(xP, xQ), true2, xQ, xP), true2, xP))
% 13.09/2.14 = { by axiom 20 (mSubFSet) }
% 13.09/2.14 tuple4(xK, fresh263(fresh189(isFinite0(xQ), true2, xQ, xP), true2, xP))
% 13.09/2.14 = { by lemma 23 }
% 13.09/2.14 tuple4(xK, fresh263(fresh189(true2, true2, xQ, xP), true2, xP))
% 13.09/2.14 = { by axiom 18 (mSubFSet) }
% 13.09/2.14 tuple4(xK, fresh263(isFinite0(xP), true2, xP))
% 13.09/2.14 = { by axiom 17 (mCardNum_1) }
% 13.09/2.14 tuple4(xK, fresh262(aSet0(xP), true2, xP))
% 13.09/2.14 = { by axiom 2 (m__5164_1) }
% 13.09/2.14 tuple4(xK, fresh262(true2, true2, xP))
% 13.09/2.14 = { by axiom 13 (mCardNum_1) }
% 13.09/2.14 tuple4(xK, true2)
% 13.09/2.14 = { by axiom 4 (m__5078) R->L }
% 13.09/2.14 tuple4(sbrdtbr0(xQ), true2)
% 13.09/2.14 % SZS output end Proof
% 13.09/2.14
% 13.09/2.14 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------