TSTP Solution File: NUM611+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM611+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 : n022.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 33.42s 4.72s
% Output : Proof 33.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM611+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
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Fri Aug 25 13:30:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 33.42/4.72 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 33.42/4.72
% 33.42/4.72 % SZS status Theorem
% 33.42/4.72
% 33.42/4.72 % SZS output start Proof
% 33.42/4.72 Take the following subset of the input axioms:
% 33.42/4.73 fof(mCardDiff, axiom, ![W0]: (aSet0(W0) => ![W1]: ((isFinite0(W0) & aElementOf0(W1, W0)) => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1)))=sbrdtbr0(W0)))).
% 33.42/4.73 fof(mCardNum, axiom, ![W0_2]: (aSet0(W0_2) => (aElementOf0(sbrdtbr0(W0_2), szNzAzT0) <=> isFinite0(W0_2)))).
% 33.42/4.73 fof(mSubFSet, axiom, ![W0_2]: ((aSet0(W0_2) & isFinite0(W0_2)) => ![W1_2]: (aSubsetOf0(W1_2, W0_2) => isFinite0(W1_2)))).
% 33.42/4.73 fof(mSuccEquSucc, axiom, ![W0_2, W1_2]: ((aElementOf0(W0_2, szNzAzT0) & aElementOf0(W1_2, szNzAzT0)) => (szszuzczcdt0(W0_2)=szszuzczcdt0(W1_2) => W0_2=W1_2))).
% 33.42/4.73 fof(m__, conjecture, sbrdtbr0(xP)=xk).
% 33.42/4.73 fof(m__3418, hypothesis, aElementOf0(xK, szNzAzT0)).
% 33.42/4.73 fof(m__3533, hypothesis, aElementOf0(xk, szNzAzT0) & szszuzczcdt0(xk)=xK).
% 33.42/4.73 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)))))).
% 33.42/4.73 fof(m__5147, hypothesis, aElementOf0(xp, xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => sdtlseqdt0(xp, W0_2)) & xp=szmzizndt0(xQ))).
% 33.42/4.73 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))))).
% 33.42/4.73 fof(m__5195, hypothesis, ![W0_2]: (aElementOf0(W0_2, xP) => aElementOf0(W0_2, xQ)) & aSubsetOf0(xP, xQ)).
% 33.42/4.73
% 33.42/4.73 Now clausify the problem and encode Horn clauses using encoding 3 of
% 33.42/4.73 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 33.42/4.73 We repeatedly replace C & s=t => u=v by the two clauses:
% 33.42/4.73 fresh(y, y, x1...xn) = u
% 33.42/4.73 C => fresh(s, t, x1...xn) = v
% 33.42/4.73 where fresh is a fresh function symbol and x1..xn are the free
% 33.42/4.73 variables of u and v.
% 33.42/4.73 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 33.42/4.73 input problem has no model of domain size 1).
% 33.42/4.73
% 33.42/4.73 The encoding turns the above axioms into the following unit equations and goals:
% 33.42/4.73
% 33.42/4.73 Axiom 1 (m__5078_1): aSet0(xQ) = true2.
% 33.42/4.73 Axiom 2 (m__5164_1): aSet0(xP) = true2.
% 33.42/4.73 Axiom 3 (m__5147): xp = szmzizndt0(xQ).
% 33.42/4.73 Axiom 4 (m__5078): sbrdtbr0(xQ) = xK.
% 33.42/4.73 Axiom 5 (m__3533): szszuzczcdt0(xk) = xK.
% 33.42/4.73 Axiom 6 (m__3533_1): aElementOf0(xk, szNzAzT0) = true2.
% 33.42/4.73 Axiom 7 (m__3418): aElementOf0(xK, szNzAzT0) = true2.
% 33.42/4.73 Axiom 8 (m__5147_1): aElementOf0(xp, xQ) = true2.
% 33.42/4.73 Axiom 9 (m__5195): aSubsetOf0(xP, xQ) = true2.
% 33.42/4.73 Axiom 10 (m__5164): xP = sdtmndt0(xQ, szmzizndt0(xQ)).
% 33.42/4.73 Axiom 11 (mSubFSet): fresh522(X, X, Y) = true2.
% 33.42/4.73 Axiom 12 (mCardNum): fresh265(X, X, Y) = isFinite0(Y).
% 33.42/4.73 Axiom 13 (mCardNum): fresh264(X, X, Y) = true2.
% 33.42/4.73 Axiom 14 (mCardNum_1): fresh263(X, X, Y) = aElementOf0(sbrdtbr0(Y), szNzAzT0).
% 33.42/4.73 Axiom 15 (mCardNum_1): fresh262(X, X, Y) = true2.
% 33.42/4.73 Axiom 16 (mSubFSet): fresh521(X, X, Y, Z) = fresh522(aSet0(Y), true2, Z).
% 33.42/4.73 Axiom 17 (mSuccEquSucc): fresh473(X, X, Y, Z) = Z.
% 33.42/4.73 Axiom 18 (mCardDiff): fresh458(X, X, Y, Z) = sbrdtbr0(Y).
% 33.42/4.73 Axiom 19 (mCardDiff): fresh269(X, X, Y, Z) = szszuzczcdt0(sbrdtbr0(sdtmndt0(Y, Z))).
% 33.42/4.73 Axiom 20 (mCardNum_1): fresh263(isFinite0(X), true2, X) = fresh262(aSet0(X), true2, X).
% 33.42/4.73 Axiom 21 (mSubFSet): fresh189(X, X, Y, Z) = isFinite0(Z).
% 33.42/4.73 Axiom 22 (mSuccEquSucc): fresh14(X, X, Y, Z) = Y.
% 33.42/4.73 Axiom 23 (mCardDiff): fresh457(X, X, Y, Z) = fresh458(aSet0(Y), true2, Y, Z).
% 33.42/4.73 Axiom 24 (mSubFSet): fresh521(aSubsetOf0(X, Y), true2, Y, X) = fresh189(isFinite0(Y), true2, Y, X).
% 33.42/4.73 Axiom 25 (mSuccEquSucc): fresh472(X, X, Y, Z) = fresh473(szszuzczcdt0(Y), szszuzczcdt0(Z), Y, Z).
% 33.42/4.73 Axiom 26 (mCardDiff): fresh457(isFinite0(X), true2, X, Y) = fresh269(aElementOf0(Y, X), true2, X, Y).
% 33.42/4.73 Axiom 27 (mCardNum): fresh265(aElementOf0(sbrdtbr0(X), szNzAzT0), true2, X) = fresh264(aSet0(X), true2, X).
% 33.42/4.73 Axiom 28 (mSuccEquSucc): fresh472(aElementOf0(X, szNzAzT0), true2, Y, X) = fresh14(aElementOf0(Y, szNzAzT0), true2, Y, X).
% 33.42/4.73
% 33.42/4.73 Lemma 29: isFinite0(xQ) = true2.
% 33.42/4.73 Proof:
% 33.42/4.73 isFinite0(xQ)
% 33.42/4.73 = { by axiom 12 (mCardNum) R->L }
% 33.42/4.73 fresh265(true2, true2, xQ)
% 33.42/4.73 = { by axiom 7 (m__3418) R->L }
% 33.42/4.73 fresh265(aElementOf0(xK, szNzAzT0), true2, xQ)
% 33.42/4.73 = { by axiom 4 (m__5078) R->L }
% 33.42/4.73 fresh265(aElementOf0(sbrdtbr0(xQ), szNzAzT0), true2, xQ)
% 33.42/4.73 = { by axiom 27 (mCardNum) }
% 33.42/4.73 fresh264(aSet0(xQ), true2, xQ)
% 33.42/4.73 = { by axiom 1 (m__5078_1) }
% 33.42/4.73 fresh264(true2, true2, xQ)
% 33.42/4.73 = { by axiom 13 (mCardNum) }
% 33.42/4.73 true2
% 33.42/4.73
% 33.42/4.73 Goal 1 (m__): sbrdtbr0(xP) = xk.
% 33.42/4.73 Proof:
% 33.42/4.73 sbrdtbr0(xP)
% 33.42/4.73 = { by axiom 17 (mSuccEquSucc) R->L }
% 33.42/4.73 fresh473(xK, xK, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 4 (m__5078) R->L }
% 33.42/4.73 fresh473(xK, sbrdtbr0(xQ), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 18 (mCardDiff) R->L }
% 33.42/4.73 fresh473(xK, fresh458(true2, true2, xQ, xp), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 1 (m__5078_1) R->L }
% 33.42/4.73 fresh473(xK, fresh458(aSet0(xQ), true2, xQ, xp), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 23 (mCardDiff) R->L }
% 33.42/4.73 fresh473(xK, fresh457(true2, true2, xQ, xp), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by lemma 29 R->L }
% 33.42/4.73 fresh473(xK, fresh457(isFinite0(xQ), true2, xQ, xp), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 26 (mCardDiff) }
% 33.42/4.73 fresh473(xK, fresh269(aElementOf0(xp, xQ), true2, xQ, xp), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 8 (m__5147_1) }
% 33.42/4.73 fresh473(xK, fresh269(true2, true2, xQ, xp), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 19 (mCardDiff) }
% 33.42/4.73 fresh473(xK, szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xp))), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 3 (m__5147) }
% 33.42/4.73 fresh473(xK, szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, szmzizndt0(xQ)))), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 10 (m__5164) R->L }
% 33.42/4.73 fresh473(xK, szszuzczcdt0(sbrdtbr0(xP)), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 5 (m__3533) R->L }
% 33.42/4.73 fresh473(szszuzczcdt0(xk), szszuzczcdt0(sbrdtbr0(xP)), xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 25 (mSuccEquSucc) R->L }
% 33.42/4.73 fresh472(true2, true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 15 (mCardNum_1) R->L }
% 33.42/4.73 fresh472(fresh262(true2, true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 2 (m__5164_1) R->L }
% 33.42/4.73 fresh472(fresh262(aSet0(xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 20 (mCardNum_1) R->L }
% 33.42/4.73 fresh472(fresh263(isFinite0(xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 21 (mSubFSet) R->L }
% 33.42/4.73 fresh472(fresh263(fresh189(true2, true2, xQ, xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by lemma 29 R->L }
% 33.42/4.73 fresh472(fresh263(fresh189(isFinite0(xQ), true2, xQ, xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 24 (mSubFSet) R->L }
% 33.42/4.73 fresh472(fresh263(fresh521(aSubsetOf0(xP, xQ), true2, xQ, xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 9 (m__5195) }
% 33.42/4.73 fresh472(fresh263(fresh521(true2, true2, xQ, xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 16 (mSubFSet) }
% 33.42/4.73 fresh472(fresh263(fresh522(aSet0(xQ), true2, xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 1 (m__5078_1) }
% 33.42/4.73 fresh472(fresh263(fresh522(true2, true2, xP), true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 11 (mSubFSet) }
% 33.42/4.73 fresh472(fresh263(true2, true2, xP), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 14 (mCardNum_1) }
% 33.42/4.73 fresh472(aElementOf0(sbrdtbr0(xP), szNzAzT0), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 28 (mSuccEquSucc) }
% 33.42/4.73 fresh14(aElementOf0(xk, szNzAzT0), true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 6 (m__3533_1) }
% 33.42/4.73 fresh14(true2, true2, xk, sbrdtbr0(xP))
% 33.42/4.73 = { by axiom 22 (mSuccEquSucc) }
% 33.42/4.73 xk
% 33.42/4.73 % SZS output end Proof
% 33.42/4.73
% 33.42/4.73 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------