TSTP Solution File: NUM555+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM555+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 : n004.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 11:56:57 EDT 2023
% Result : Theorem 16.95s 2.66s
% Output : Proof 16.95s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 10:57:08 EDT 2023
% 0.15/0.35 % CPUTime :
% 16.95/2.66 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 16.95/2.66
% 16.95/2.66 % SZS status Theorem
% 16.95/2.66
% 16.95/2.66 % SZS output start Proof
% 16.95/2.66 Take the following subset of the input axioms:
% 16.95/2.66 fof(mDefDiff, definition, ![W0, W1]: ((aSet0(W0) & aElement0(W1)) => ![W2]: (W2=sdtmndt0(W0, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) & W3!=W1))))))).
% 16.95/2.66 fof(m__, conjecture, ~aElementOf0(xx, sdtmndt0(xQ, xy))).
% 16.95/2.66 fof(m__2291, hypothesis, aSet0(xQ) & (isFinite0(xQ) & sbrdtbr0(xQ)=xk)).
% 16.95/2.66 fof(m__2304, hypothesis, aElement0(xy) & aElementOf0(xy, xQ)).
% 16.95/2.66 fof(m__2323, hypothesis, ~aElementOf0(xx, xQ)).
% 16.95/2.66 fof(m__2338, hypothesis, ~aElementOf0(xx, xQ)).
% 16.95/2.66
% 16.95/2.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.95/2.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.95/2.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.95/2.66 fresh(y, y, x1...xn) = u
% 16.95/2.66 C => fresh(s, t, x1...xn) = v
% 16.95/2.66 where fresh is a fresh function symbol and x1..xn are the free
% 16.95/2.66 variables of u and v.
% 16.95/2.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.95/2.66 input problem has no model of domain size 1).
% 16.95/2.66
% 16.95/2.66 The encoding turns the above axioms into the following unit equations and goals:
% 16.95/2.66
% 16.95/2.66 Axiom 1 (m__2291_1): aSet0(xQ) = true2.
% 16.95/2.66 Axiom 2 (m__2304): aElement0(xy) = true2.
% 16.95/2.66 Axiom 3 (m__): aElementOf0(xx, sdtmndt0(xQ, xy)) = true2.
% 16.95/2.66 Axiom 4 (mDefDiff_8): fresh47(X, X, Y, Z) = true2.
% 16.95/2.66 Axiom 5 (mDefDiff_1): fresh141(X, X, Y, Z, W) = true2.
% 16.95/2.66 Axiom 6 (mDefDiff_1): fresh139(X, X, Y, Z, W, V) = equiv3(Y, Z, V).
% 16.95/2.66 Axiom 7 (mDefDiff_1): fresh140(X, X, Y, Z, W, V) = fresh141(W, sdtmndt0(Y, Z), Y, Z, V).
% 16.95/2.66 Axiom 8 (mDefDiff_1): fresh138(X, X, Y, Z, W, V) = fresh139(aSet0(Y), true2, Y, Z, W, V).
% 16.95/2.66 Axiom 9 (mDefDiff_8): fresh47(equiv3(X, Y, Z), true2, X, Z) = aElementOf0(Z, X).
% 16.95/2.66 Axiom 10 (mDefDiff_1): fresh138(aElementOf0(X, Y), true2, Z, W, Y, X) = fresh140(aElement0(W), true2, Z, W, Y, X).
% 16.95/2.68
% 16.95/2.68 Lemma 11: aElementOf0(xx, xQ) = true2.
% 16.95/2.68 Proof:
% 16.95/2.68 aElementOf0(xx, xQ)
% 16.95/2.68 = { by axiom 9 (mDefDiff_8) R->L }
% 16.95/2.68 fresh47(equiv3(xQ, xy, xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 6 (mDefDiff_1) R->L }
% 16.95/2.68 fresh47(fresh139(true2, true2, xQ, xy, sdtmndt0(xQ, xy), xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 1 (m__2291_1) R->L }
% 16.95/2.68 fresh47(fresh139(aSet0(xQ), true2, xQ, xy, sdtmndt0(xQ, xy), xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 8 (mDefDiff_1) R->L }
% 16.95/2.68 fresh47(fresh138(true2, true2, xQ, xy, sdtmndt0(xQ, xy), xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 3 (m__) R->L }
% 16.95/2.68 fresh47(fresh138(aElementOf0(xx, sdtmndt0(xQ, xy)), true2, xQ, xy, sdtmndt0(xQ, xy), xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 10 (mDefDiff_1) }
% 16.95/2.68 fresh47(fresh140(aElement0(xy), true2, xQ, xy, sdtmndt0(xQ, xy), xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 2 (m__2304) }
% 16.95/2.68 fresh47(fresh140(true2, true2, xQ, xy, sdtmndt0(xQ, xy), xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 7 (mDefDiff_1) }
% 16.95/2.68 fresh47(fresh141(sdtmndt0(xQ, xy), sdtmndt0(xQ, xy), xQ, xy, xx), true2, xQ, xx)
% 16.95/2.68 = { by axiom 5 (mDefDiff_1) }
% 16.95/2.68 fresh47(true2, true2, xQ, xx)
% 16.95/2.68 = { by axiom 4 (mDefDiff_8) }
% 16.95/2.68 true2
% 16.95/2.68
% 16.95/2.68 Goal 1 (m__2338): aElementOf0(xx, xQ) = true2.
% 16.95/2.68 Proof:
% 16.95/2.68 aElementOf0(xx, xQ)
% 16.95/2.68 = { by lemma 11 }
% 16.95/2.68 true2
% 16.95/2.68
% 16.95/2.68 Goal 2 (m__2323): aElementOf0(xx, xQ) = true2.
% 16.95/2.68 Proof:
% 16.95/2.68 aElementOf0(xx, xQ)
% 16.95/2.68 = { by lemma 11 }
% 16.95/2.68 true2
% 16.95/2.68 % SZS output end Proof
% 16.95/2.68
% 16.95/2.68 RESULT: Theorem (the conjecture is true).
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