TSTP Solution File: NUM601+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM601+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 : n017.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 11:57:12 EDT 2023
% Result : Theorem 87.22s 11.58s
% Output : Proof 87.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM601+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % 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 : n017.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 07:33:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 87.22/11.58 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 87.22/11.58
% 87.22/11.58 % SZS status Theorem
% 87.22/11.58
% 87.22/11.58 % SZS output start Proof
% 87.22/11.58 Take the following subset of the input axioms:
% 87.22/11.58 fof(mZeroLess, axiom, ![W0]: (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0))).
% 87.22/11.58 fof(mZeroNum, axiom, aElementOf0(sz00, szNzAzT0)).
% 87.22/11.58 fof(m__, conjecture, ![W0_2]: (aElementOf0(W0_2, xO) => aElementOf0(W0_2, xS)) | aSubsetOf0(xO, xS)).
% 87.22/11.58 fof(m__3623, hypothesis, aFunction0(xN) & (szDzozmdt0(xN)=szNzAzT0 & (sdtlpdtrp0(xN, sz00)=xS & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0_2)) & ![W1]: (aElementOf0(W1, sdtlpdtrp0(xN, W0_2)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0_2), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0_2))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W1_2)) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & (![W1_2]: (aElementOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W1_2) & (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) & W1_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2))) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, szszuzczcdt0(W0_2))) => aElementOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2)), sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2))))))))))))))).
% 87.22/11.58 fof(m__3754, hypothesis, ![W1_2, W0_2]: ((aElementOf0(W0_2, szNzAzT0) & aElementOf0(W1_2, szNzAzT0)) => (sdtlseqdt0(W1_2, W0_2) => (![W2]: (aElementOf0(W2, sdtlpdtrp0(xN, W0_2)) => aElementOf0(W2, sdtlpdtrp0(xN, W1_2))) & aSubsetOf0(sdtlpdtrp0(xN, W0_2), sdtlpdtrp0(xN, W1_2)))))).
% 87.22/11.58 fof(m__4660, hypothesis, aFunction0(xe) & (szDzozmdt0(xe)=szNzAzT0 & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aElementOf0(sdtlpdtrp0(xe, W0_2), sdtlpdtrp0(xN, W0_2)) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(sdtlpdtrp0(xe, W0_2), W1_2)) & sdtlpdtrp0(xe, W0_2)=szmzizndt0(sdtlpdtrp0(xN, W0_2))))))).
% 87.22/11.58 fof(m__4982, hypothesis, ![W0_2]: ((?[W1_2]: (aElementOf0(W1_2, sdtlbdtrb0(xd, szDzizrdt0(xd))) & sdtlpdtrp0(xe, W1_2)=W0_2) | aElementOf0(W0_2, xO)) => ?[W1_2]: (aElementOf0(W1_2, szNzAzT0) & (sdtlpdtrp0(xd, W1_2)=szDzizrdt0(xd) & (aElementOf0(W1_2, sdtlbdtrb0(xd, szDzizrdt0(xd))) & sdtlpdtrp0(xe, W1_2)=W0_2))))).
% 87.22/11.58
% 87.22/11.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 87.22/11.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 87.22/11.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 87.22/11.58 fresh(y, y, x1...xn) = u
% 87.22/11.58 C => fresh(s, t, x1...xn) = v
% 87.22/11.58 where fresh is a fresh function symbol and x1..xn are the free
% 87.22/11.58 variables of u and v.
% 87.22/11.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 87.22/11.58 input problem has no model of domain size 1).
% 87.22/11.58
% 87.22/11.58 The encoding turns the above axioms into the following unit equations and goals:
% 87.22/11.58
% 87.22/11.58 Axiom 1 (mZeroNum): aElementOf0(sz00, szNzAzT0) = true2.
% 87.22/11.58 Axiom 2 (m__): aElementOf0(w0, xO) = true2.
% 87.22/11.58 Axiom 3 (m__3623_1): sdtlpdtrp0(xN, sz00) = xS.
% 87.22/11.58 Axiom 4 (mZeroLess): fresh172(X, X, Y) = true2.
% 87.22/11.58 Axiom 5 (m__4660_3): fresh42(X, X, Y) = true2.
% 87.22/11.58 Axiom 6 (m__4982_6): fresh17(X, X, Y) = true2.
% 87.22/11.58 Axiom 7 (m__4982_4): fresh2(X, X, Y) = Y.
% 87.22/11.58 Axiom 8 (m__3754): fresh320(X, X, Y, Z) = true2.
% 87.22/11.58 Axiom 9 (m__3754): fresh318(X, X, Y, Z, W) = aElementOf0(W, sdtlpdtrp0(xN, Z)).
% 87.22/11.58 Axiom 10 (mZeroLess): fresh172(aElementOf0(X, szNzAzT0), true2, X) = sdtlseqdt0(sz00, X).
% 87.22/11.58 Axiom 11 (m__4982_6): fresh17(aElementOf0(X, xO), true2, X) = aElementOf0(w1(X), szNzAzT0).
% 87.22/11.58 Axiom 12 (m__4982_4): fresh2(aElementOf0(X, xO), true2, X) = sdtlpdtrp0(xe, w1(X)).
% 87.22/11.58 Axiom 13 (m__4660_3): fresh42(aElementOf0(X, szNzAzT0), true2, X) = aElementOf0(sdtlpdtrp0(xe, X), sdtlpdtrp0(xN, X)).
% 87.22/11.58 Axiom 14 (m__3754): fresh319(X, X, Y, Z, W) = fresh320(aElementOf0(Y, szNzAzT0), true2, Z, W).
% 87.22/11.58 Axiom 15 (m__3754): fresh317(X, X, Y, Z, W) = fresh318(aElementOf0(Z, szNzAzT0), true2, Y, Z, W).
% 87.22/11.58 Axiom 16 (m__3754): fresh317(sdtlseqdt0(X, Y), true2, Y, X, Z) = fresh319(aElementOf0(Z, sdtlpdtrp0(xN, Y)), true2, Y, X, Z).
% 87.22/11.58
% 87.22/11.58 Lemma 17: aElementOf0(w1(w0), szNzAzT0) = true2.
% 87.22/11.58 Proof:
% 87.22/11.58 aElementOf0(w1(w0), szNzAzT0)
% 87.22/11.58 = { by axiom 11 (m__4982_6) R->L }
% 87.22/11.58 fresh17(aElementOf0(w0, xO), true2, w0)
% 87.22/11.58 = { by axiom 2 (m__) }
% 87.22/11.58 fresh17(true2, true2, w0)
% 87.22/11.58 = { by axiom 6 (m__4982_6) }
% 87.22/11.58 true2
% 87.22/11.58
% 87.22/11.58 Goal 1 (m___1): aElementOf0(w0, xS) = true2.
% 87.22/11.58 Proof:
% 87.22/11.58 aElementOf0(w0, xS)
% 87.22/11.58 = { by axiom 7 (m__4982_4) R->L }
% 87.22/11.58 aElementOf0(fresh2(true2, true2, w0), xS)
% 87.22/11.58 = { by axiom 2 (m__) R->L }
% 87.22/11.58 aElementOf0(fresh2(aElementOf0(w0, xO), true2, w0), xS)
% 87.22/11.58 = { by axiom 12 (m__4982_4) }
% 87.22/11.58 aElementOf0(sdtlpdtrp0(xe, w1(w0)), xS)
% 87.22/11.58 = { by axiom 3 (m__3623_1) R->L }
% 87.22/11.58 aElementOf0(sdtlpdtrp0(xe, w1(w0)), sdtlpdtrp0(xN, sz00))
% 87.22/11.58 = { by axiom 9 (m__3754) R->L }
% 87.22/11.58 fresh318(true2, true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 1 (mZeroNum) R->L }
% 87.22/11.58 fresh318(aElementOf0(sz00, szNzAzT0), true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 15 (m__3754) R->L }
% 87.22/11.58 fresh317(true2, true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 4 (mZeroLess) R->L }
% 87.22/11.58 fresh317(fresh172(true2, true2, w1(w0)), true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by lemma 17 R->L }
% 87.22/11.58 fresh317(fresh172(aElementOf0(w1(w0), szNzAzT0), true2, w1(w0)), true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 10 (mZeroLess) }
% 87.22/11.58 fresh317(sdtlseqdt0(sz00, w1(w0)), true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 16 (m__3754) }
% 87.22/11.58 fresh319(aElementOf0(sdtlpdtrp0(xe, w1(w0)), sdtlpdtrp0(xN, w1(w0))), true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 13 (m__4660_3) R->L }
% 87.22/11.58 fresh319(fresh42(aElementOf0(w1(w0), szNzAzT0), true2, w1(w0)), true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by lemma 17 }
% 87.22/11.58 fresh319(fresh42(true2, true2, w1(w0)), true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 5 (m__4660_3) }
% 87.22/11.58 fresh319(true2, true2, w1(w0), sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 14 (m__3754) }
% 87.22/11.58 fresh320(aElementOf0(w1(w0), szNzAzT0), true2, sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by lemma 17 }
% 87.22/11.58 fresh320(true2, true2, sz00, sdtlpdtrp0(xe, w1(w0)))
% 87.22/11.58 = { by axiom 8 (m__3754) }
% 87.22/11.58 true2
% 87.22/11.58 % SZS output end Proof
% 87.22/11.58
% 87.22/11.58 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------