TSTP Solution File: NUM629+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM629+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 : n007.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 11:57:23 EDT 2023
% Result : Theorem 22.70s 3.40s
% Output : Proof 23.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM629+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % 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 : n007.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 09:09:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 22.70/3.40 Command-line arguments: --no-flatten-goal
% 22.70/3.40
% 22.70/3.40 % SZS status Theorem
% 22.70/3.40
% 22.70/3.40 % SZS output start Proof
% 22.70/3.40 Take the following subset of the input axioms:
% 23.27/3.41 fof(m__, conjecture, ![W0]: (aElementOf0(W0, xP) => aElementOf0(W0, xD)) | (aSubsetOf0(xP, xD) | aElementOf0(xP, slbdtsldtrb0(xD, xk)))).
% 23.27/3.41 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))))))))))))))).
% 23.27/3.41 fof(m__3671, hypothesis, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aSet0(sdtlpdtrp0(xN, W0_2)) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => aElementOf0(W1_2, szNzAzT0)) & (aSubsetOf0(sdtlpdtrp0(xN, W0_2), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0_2))))))).
% 23.27/3.41 fof(m__5309, hypothesis, aElementOf0(xn, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, xn)=szDzizrdt0(xd) & (aElementOf0(xn, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (aElementOf0(xn, szNzAzT0) & sdtlpdtrp0(xe, xn)=xp)))).
% 23.27/3.41 fof(m__5334, hypothesis, ![W0_2]: (aElementOf0(W0_2, xP) => aElementOf0(W0_2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) & aSubsetOf0(xP, sdtlpdtrp0(xN, szszuzczcdt0(xn)))).
% 23.27/3.41 fof(m__5585, hypothesis, ![W0_2]: (aElementOf0(W0_2, sdtlpdtrp0(xN, xn)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0_2)) & (aSet0(xD) & (![W0_2]: (aElementOf0(W0_2, xD) <=> (aElement0(W0_2) & (aElementOf0(W0_2, sdtlpdtrp0(xN, xn)) & W0_2!=szmzizndt0(sdtlpdtrp0(xN, xn))))) & xD=sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))).
% 23.27/3.41
% 23.27/3.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 23.27/3.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 23.27/3.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 23.27/3.41 fresh(y, y, x1...xn) = u
% 23.27/3.41 C => fresh(s, t, x1...xn) = v
% 23.27/3.41 where fresh is a fresh function symbol and x1..xn are the free
% 23.27/3.41 variables of u and v.
% 23.27/3.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 23.27/3.41 input problem has no model of domain size 1).
% 23.27/3.41
% 23.27/3.41 The encoding turns the above axioms into the following unit equations and goals:
% 23.27/3.41
% 23.27/3.41 Axiom 1 (m__): aElementOf0(w0, xP) = true2.
% 23.27/3.41 Axiom 2 (m__5309_2): aElementOf0(xn, szNzAzT0) = true2.
% 23.27/3.41 Axiom 3 (m__3623_7): fresh344(X, X, Y) = true2.
% 23.27/3.41 Axiom 4 (m__3623_7): fresh146(X, X, Y) = or5(Y).
% 23.27/3.41 Axiom 5 (m__3671_1): fresh140(X, X, Y) = true2.
% 23.27/3.41 Axiom 6 (m__3671_2): fresh139(X, X, Y) = true2.
% 23.27/3.41 Axiom 7 (m__5334_1): fresh19(X, X, Y) = true2.
% 23.27/3.41 Axiom 8 (m__3623_11): fresh152(X, X, Y, Z) = true2.
% 23.27/3.41 Axiom 9 (m__3623_7): fresh343(X, X, Y) = fresh344(aElementOf0(Y, szNzAzT0), true2, Y).
% 23.27/3.41 Axiom 10 (m__3671_1): fresh140(aElementOf0(X, szNzAzT0), true2, X) = isCountable0(sdtlpdtrp0(xN, X)).
% 23.27/3.41 Axiom 11 (m__3671_2): fresh139(aElementOf0(X, szNzAzT0), true2, X) = aSubsetOf0(sdtlpdtrp0(xN, X), szNzAzT0).
% 23.27/3.41 Axiom 12 (m__5334_1): fresh19(aElementOf0(X, xP), true2, X) = aElementOf0(X, sdtlpdtrp0(xN, szszuzczcdt0(xn))).
% 23.27/3.41 Axiom 13 (m__3623_7): fresh343(aSubsetOf0(sdtlpdtrp0(xN, X), szNzAzT0), true2, X) = fresh146(isCountable0(sdtlpdtrp0(xN, X)), true2, X).
% 23.27/3.41 Axiom 14 (m__5585): xD = sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))).
% 23.27/3.41 Axiom 15 (m__3623_11): fresh153(or5(X), true2, X, Y) = fresh152(aElementOf0(Y, sdtlpdtrp0(xN, szszuzczcdt0(X))), true2, X, Y).
% 23.27/3.41 Axiom 16 (m__3623_11): fresh153(X, X, Y, Z) = aElementOf0(Z, sdtmndt0(sdtlpdtrp0(xN, Y), szmzizndt0(sdtlpdtrp0(xN, Y)))).
% 23.27/3.41
% 23.27/3.41 Goal 1 (m___2): aElementOf0(w0, xD) = true2.
% 23.27/3.41 Proof:
% 23.27/3.41 aElementOf0(w0, xD)
% 23.27/3.41 = { by axiom 14 (m__5585) }
% 23.27/3.41 aElementOf0(w0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))
% 23.27/3.41 = { by axiom 16 (m__3623_11) R->L }
% 23.27/3.41 fresh153(true2, true2, xn, w0)
% 23.27/3.41 = { by axiom 3 (m__3623_7) R->L }
% 23.27/3.41 fresh153(fresh344(true2, true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 2 (m__5309_2) R->L }
% 23.27/3.41 fresh153(fresh344(aElementOf0(xn, szNzAzT0), true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 9 (m__3623_7) R->L }
% 23.27/3.41 fresh153(fresh343(true2, true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 6 (m__3671_2) R->L }
% 23.27/3.41 fresh153(fresh343(fresh139(true2, true2, xn), true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 2 (m__5309_2) R->L }
% 23.27/3.41 fresh153(fresh343(fresh139(aElementOf0(xn, szNzAzT0), true2, xn), true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 11 (m__3671_2) }
% 23.27/3.41 fresh153(fresh343(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0), true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 13 (m__3623_7) }
% 23.27/3.41 fresh153(fresh146(isCountable0(sdtlpdtrp0(xN, xn)), true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 10 (m__3671_1) R->L }
% 23.27/3.41 fresh153(fresh146(fresh140(aElementOf0(xn, szNzAzT0), true2, xn), true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 2 (m__5309_2) }
% 23.27/3.41 fresh153(fresh146(fresh140(true2, true2, xn), true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 5 (m__3671_1) }
% 23.27/3.41 fresh153(fresh146(true2, true2, xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 4 (m__3623_7) }
% 23.27/3.41 fresh153(or5(xn), true2, xn, w0)
% 23.27/3.41 = { by axiom 15 (m__3623_11) }
% 23.27/3.41 fresh152(aElementOf0(w0, sdtlpdtrp0(xN, szszuzczcdt0(xn))), true2, xn, w0)
% 23.27/3.41 = { by axiom 12 (m__5334_1) R->L }
% 23.27/3.41 fresh152(fresh19(aElementOf0(w0, xP), true2, w0), true2, xn, w0)
% 23.27/3.41 = { by axiom 1 (m__) }
% 23.27/3.41 fresh152(fresh19(true2, true2, w0), true2, xn, w0)
% 23.27/3.41 = { by axiom 7 (m__5334_1) }
% 23.27/3.41 fresh152(true2, true2, xn, w0)
% 23.27/3.41 = { by axiom 8 (m__3623_11) }
% 23.27/3.41 true2
% 23.27/3.41 % SZS output end Proof
% 23.27/3.41
% 23.27/3.41 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------