TSTP Solution File: NUM594+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM594+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 : n001.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 11:57:10 EDT 2023
% Result : Theorem 143.96s 18.99s
% Output : Proof 144.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM594+1 : 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 : n001.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 16:17:14 EDT 2023
% 0.13/0.34 % CPUTime :
% 143.96/18.99 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 143.96/18.99
% 143.96/18.99 % SZS status Theorem
% 143.96/18.99
% 143.96/19.00 % SZS output start Proof
% 143.96/19.00 Take the following subset of the input axioms:
% 143.96/19.00 fof(mCountNFin, axiom, ![W0]: ((aSet0(W0) & isCountable0(W0)) => ~isFinite0(W0))).
% 143.96/19.00 fof(mCountNFin_01, axiom, ![W0_2]: ((aSet0(W0_2) & isCountable0(W0_2)) => W0_2!=slcrc0)).
% 143.96/19.00 fof(mDefDiff, definition, ![W1, W0_2]: ((aSet0(W0_2) & aElement0(W1)) => ![W2]: (W2=sdtmndt0(W0_2, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0_2) & W3!=W1))))))).
% 143.96/19.00 fof(mDefEmp, definition, ![W0_2]: (W0_2=slcrc0 <=> (aSet0(W0_2) & ~?[W1_2]: aElementOf0(W1_2, W0_2)))).
% 143.96/19.00 fof(mDefSImg, definition, ![W0_2]: (aFunction0(W0_2) => ![W1_2]: (aSubsetOf0(W1_2, szDzozmdt0(W0_2)) => ![W2_2]: (W2_2=sdtlcdtrc0(W0_2, W1_2) <=> (aSet0(W2_2) & ![W3_2]: (aElementOf0(W3_2, W2_2) <=> ?[W4]: (aElementOf0(W4, W1_2) & sdtlpdtrp0(W0_2, W4)=W3_2))))))).
% 143.96/19.00 fof(mNATSet, axiom, aSet0(szNzAzT0) & isCountable0(szNzAzT0)).
% 143.96/19.00 fof(mNatNSucc, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => W0_2!=szszuzczcdt0(W0_2))).
% 143.96/19.00 fof(mNoScLessZr, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ~sdtlseqdt0(szszuzczcdt0(W0_2), sz00))).
% 143.96/19.01 fof(mSubRefl, axiom, ![W0_2]: (aSet0(W0_2) => aSubsetOf0(W0_2, W0_2))).
% 143.96/19.01 fof(mSuccNum, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0_2), szNzAzT0) & szszuzczcdt0(W0_2)!=sz00))).
% 143.96/19.01 fof(m__, conjecture, ?[W0_2]: (aElementOf0(W0_2, szNzAzT0) & sdtlpdtrp0(xd, W0_2)=xx)).
% 143.96/19.01 fof(m__4730, hypothesis, aFunction0(xd) & (szDzozmdt0(xd)=szNzAzT0 & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ![W1_2]: ((aSet0(W1_2) & aElementOf0(W1_2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2)), xk))) => sdtlpdtrp0(xd, W0_2)=sdtlpdtrp0(sdtlpdtrp0(xC, W0_2), W1_2))))).
% 143.96/19.01 fof(m__4781, hypothesis, aElementOf0(xx, sdtlcdtrc0(xd, szDzozmdt0(xd)))).
% 143.96/19.01
% 143.96/19.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 143.96/19.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 143.96/19.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 143.96/19.01 fresh(y, y, x1...xn) = u
% 143.96/19.01 C => fresh(s, t, x1...xn) = v
% 143.96/19.01 where fresh is a fresh function symbol and x1..xn are the free
% 143.96/19.01 variables of u and v.
% 143.96/19.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 143.96/19.01 input problem has no model of domain size 1).
% 143.96/19.01
% 143.96/19.01 The encoding turns the above axioms into the following unit equations and goals:
% 143.96/19.01
% 143.96/19.01 Axiom 1 (m__4730_1): aFunction0(xd) = true2.
% 143.96/19.01 Axiom 2 (m__4730): szDzozmdt0(xd) = szNzAzT0.
% 143.96/19.01 Axiom 3 (mNATSet): aSet0(szNzAzT0) = true2.
% 143.96/19.01 Axiom 4 (mSubRefl): fresh28(X, X, Y) = true2.
% 143.96/19.01 Axiom 5 (mSubRefl): fresh28(aSet0(X), true2, X) = aSubsetOf0(X, X).
% 144.82/19.01 Axiom 6 (mDefSImg): fresh190(X, X, Y, Z, W) = true2.
% 144.82/19.01 Axiom 7 (mDefSImg_7): fresh75(X, X, Y, Z, W) = true2.
% 144.82/19.01 Axiom 8 (mDefSImg_6): fresh2(X, X, Y, Z, W) = W.
% 144.82/19.01 Axiom 9 (m__4781): aElementOf0(xx, sdtlcdtrc0(xd, szDzozmdt0(xd))) = true2.
% 144.82/19.01 Axiom 10 (mDefSImg): fresh188(X, X, Y, Z, W, V) = equiv(Y, Z, V).
% 144.82/19.01 Axiom 11 (mDefSImg): fresh189(X, X, Y, Z, W, V) = fresh190(W, sdtlcdtrc0(Y, Z), Y, Z, V).
% 144.82/19.01 Axiom 12 (mDefSImg): fresh187(X, X, Y, Z, W, V) = fresh188(aElementOf0(V, W), true2, Y, Z, W, V).
% 144.82/19.01 Axiom 13 (mDefSImg_7): fresh75(equiv(X, Y, Z), true2, X, Y, Z) = aElementOf0(w4_2(X, Y, Z), Y).
% 144.82/19.01 Axiom 14 (mDefSImg_6): fresh2(equiv(X, Y, Z), true2, X, Y, Z) = sdtlpdtrp0(X, w4_2(X, Y, Z)).
% 144.82/19.01 Axiom 15 (mDefSImg): fresh187(aFunction0(X), true2, X, Y, Z, W) = fresh189(aSubsetOf0(Y, szDzozmdt0(X)), true2, X, Y, Z, W).
% 144.82/19.01
% 144.82/19.01 Lemma 16: equiv(xd, szNzAzT0, xx) = true2.
% 144.82/19.01 Proof:
% 144.82/19.01 equiv(xd, szNzAzT0, xx)
% 144.82/19.01 = { by axiom 10 (mDefSImg) R->L }
% 144.82/19.01 fresh188(true2, true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 9 (m__4781) R->L }
% 144.82/19.01 fresh188(aElementOf0(xx, sdtlcdtrc0(xd, szDzozmdt0(xd))), true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 2 (m__4730) }
% 144.82/19.01 fresh188(aElementOf0(xx, sdtlcdtrc0(xd, szNzAzT0)), true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 12 (mDefSImg) R->L }
% 144.82/19.01 fresh187(true2, true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 1 (m__4730_1) R->L }
% 144.82/19.01 fresh187(aFunction0(xd), true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 15 (mDefSImg) }
% 144.82/19.01 fresh189(aSubsetOf0(szNzAzT0, szDzozmdt0(xd)), true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 2 (m__4730) }
% 144.82/19.01 fresh189(aSubsetOf0(szNzAzT0, szNzAzT0), true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 5 (mSubRefl) R->L }
% 144.82/19.01 fresh189(fresh28(aSet0(szNzAzT0), true2, szNzAzT0), true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 3 (mNATSet) }
% 144.82/19.01 fresh189(fresh28(true2, true2, szNzAzT0), true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 4 (mSubRefl) }
% 144.82/19.01 fresh189(true2, true2, xd, szNzAzT0, sdtlcdtrc0(xd, szNzAzT0), xx)
% 144.82/19.01 = { by axiom 11 (mDefSImg) }
% 144.82/19.01 fresh190(sdtlcdtrc0(xd, szNzAzT0), sdtlcdtrc0(xd, szNzAzT0), xd, szNzAzT0, xx)
% 144.82/19.01 = { by axiom 6 (mDefSImg) }
% 144.82/19.01 true2
% 144.82/19.01
% 144.82/19.01 Goal 1 (m__): tuple4(sdtlpdtrp0(xd, X), aElementOf0(X, szNzAzT0)) = tuple4(xx, true2).
% 144.82/19.01 The goal is true when:
% 144.82/19.01 X = w4_2(xd, szNzAzT0, xx)
% 144.82/19.01
% 144.82/19.01 Proof:
% 144.82/19.01 tuple4(sdtlpdtrp0(xd, w4_2(xd, szNzAzT0, xx)), aElementOf0(w4_2(xd, szNzAzT0, xx), szNzAzT0))
% 144.82/19.01 = { by axiom 14 (mDefSImg_6) R->L }
% 144.82/19.01 tuple4(fresh2(equiv(xd, szNzAzT0, xx), true2, xd, szNzAzT0, xx), aElementOf0(w4_2(xd, szNzAzT0, xx), szNzAzT0))
% 144.82/19.01 = { by lemma 16 }
% 144.82/19.01 tuple4(fresh2(true2, true2, xd, szNzAzT0, xx), aElementOf0(w4_2(xd, szNzAzT0, xx), szNzAzT0))
% 144.82/19.01 = { by axiom 8 (mDefSImg_6) }
% 144.82/19.01 tuple4(xx, aElementOf0(w4_2(xd, szNzAzT0, xx), szNzAzT0))
% 144.82/19.01 = { by axiom 13 (mDefSImg_7) R->L }
% 144.82/19.01 tuple4(xx, fresh75(equiv(xd, szNzAzT0, xx), true2, xd, szNzAzT0, xx))
% 144.82/19.01 = { by lemma 16 }
% 144.82/19.01 tuple4(xx, fresh75(true2, true2, xd, szNzAzT0, xx))
% 144.82/19.01 = { by axiom 7 (mDefSImg_7) }
% 144.82/19.01 tuple4(xx, true2)
% 144.82/19.01 % SZS output end Proof
% 144.82/19.01
% 144.82/19.01 RESULT: Theorem (the conjecture is true).
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