TSTP Solution File: NUM558+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM558+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 : n014.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 11:56:58 EDT 2023
% Result : Timeout 286.59s 37.65s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM558+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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 : n014.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 09:02:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 286.59/37.65 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 286.59/37.65
% 286.59/37.65 % SZS status Theorem
% 286.59/37.65
% 286.59/37.66 % SZS output start Proof
% 286.59/37.66 Take the following subset of the input axioms:
% 286.59/37.67 fof(mDefCons, definition, ![W0, W1]: ((aSet0(W0) & aElement0(W1)) => ![W2]: (W2=sdtpldt0(W0, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | W3=W1))))))).
% 286.59/37.67 fof(mDefDiff, definition, ![W1_2, W0_2]: ((aSet0(W0_2) & aElement0(W1_2)) => ![W2_2]: (W2_2=sdtmndt0(W0_2, W1_2) <=> (aSet0(W2_2) & ![W3_2]: (aElementOf0(W3_2, W2_2) <=> (aElement0(W3_2) & (aElementOf0(W3_2, W0_2) & W3_2!=W1_2))))))).
% 286.59/37.67 fof(mDefSel, definition, ![W1_2, W0_2]: ((aSet0(W0_2) & aElementOf0(W1_2, szNzAzT0)) => ![W2_2]: (W2_2=slbdtsldtrb0(W0_2, W1_2) <=> (aSet0(W2_2) & ![W3_2]: (aElementOf0(W3_2, W2_2) <=> (aSubsetOf0(W3_2, W0_2) & sbrdtbr0(W3_2)=W1_2)))))).
% 286.59/37.67 fof(mDefSub, definition, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aSubsetOf0(W1_2, W0_2) <=> (aSet0(W1_2) & ![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, W0_2)))))).
% 286.59/37.67 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 286.59/37.67 fof(m__, conjecture, aElementOf0(xx, xT)).
% 286.59/37.67 fof(m__2202, hypothesis, aElementOf0(xk, szNzAzT0)).
% 286.59/37.67 fof(m__2202_02, hypothesis, aSet0(xS) & (aSet0(xT) & xk!=sz00)).
% 286.59/37.67 fof(m__2227, hypothesis, aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)) & slbdtsldtrb0(xS, xk)!=slcrc0).
% 286.59/37.67 fof(m__2256, hypothesis, aElementOf0(xx, xS)).
% 286.59/37.67 fof(m__2291, hypothesis, aSet0(xQ) & (isFinite0(xQ) & sbrdtbr0(xQ)=xk)).
% 286.59/37.67 fof(m__2304, hypothesis, aElement0(xy) & aElementOf0(xy, xQ)).
% 286.59/37.67 fof(m__2357, hypothesis, xP=sdtpldt0(sdtmndt0(xQ, xy), xx)).
% 286.59/37.67 fof(m__2378, hypothesis, aElementOf0(xP, slbdtsldtrb0(xS, xk))).
% 286.59/37.67
% 286.59/37.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 286.59/37.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 286.59/37.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 286.59/37.67 fresh(y, y, x1...xn) = u
% 286.59/37.67 C => fresh(s, t, x1...xn) = v
% 286.59/37.67 where fresh is a fresh function symbol and x1..xn are the free
% 286.59/37.67 variables of u and v.
% 286.59/37.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 286.59/37.67 input problem has no model of domain size 1).
% 286.59/37.67
% 286.59/37.67 The encoding turns the above axioms into the following unit equations and goals:
% 286.59/37.67
% 286.59/37.67 Axiom 1 (m__2202): aElementOf0(xk, szNzAzT0) = true2.
% 286.59/37.67 Axiom 2 (m__2256): aElementOf0(xx, xS) = true2.
% 286.59/37.67 Axiom 3 (m__2291_1): aSet0(xQ) = true2.
% 286.59/37.67 Axiom 4 (m__2202_02): aSet0(xS) = true2.
% 286.59/37.67 Axiom 5 (m__2202_02_1): aSet0(xT) = true2.
% 286.59/37.67 Axiom 6 (m__2304): aElement0(xy) = true2.
% 286.59/37.67 Axiom 7 (m__2378): aElementOf0(xP, slbdtsldtrb0(xS, xk)) = true2.
% 286.59/37.67 Axiom 8 (m__2357): xP = sdtpldt0(sdtmndt0(xQ, xy), xx).
% 286.59/37.67 Axiom 9 (mDefDiff): fresh137(X, X, Y) = true2.
% 286.59/37.67 Axiom 10 (mDefSel_1): fresh75(X, X, Y) = true2.
% 286.59/37.67 Axiom 11 (mEOfElem): fresh28(X, X, Y) = true2.
% 286.59/37.67 Axiom 12 (m__2227): aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)) = true2.
% 286.59/37.67 Axiom 13 (mDefSub_2): fresh180(X, X, Y, Z) = true2.
% 286.59/37.67 Axiom 14 (mDefCons_2): fresh160(X, X, Y, Z) = true2.
% 286.59/37.67 Axiom 15 (mDefCons_5): fresh53(X, X, Y, Z) = true2.
% 286.59/37.67 Axiom 16 (mDefSel_7): fresh34(X, X, Y, Z) = true2.
% 286.59/37.67 Axiom 17 (mDefSub_2): fresh32(X, X, Y, Z) = aElementOf0(Z, Y).
% 286.59/37.67 Axiom 18 (mEOfElem): fresh29(X, X, Y, Z) = aElement0(Z).
% 286.59/37.67 Axiom 19 (mDefSub_2): fresh179(X, X, Y, Z, W) = fresh180(aSet0(Y), true2, Y, W).
% 286.59/37.67 Axiom 20 (mDefDiff): fresh136(X, X, Y, Z, W) = fresh137(W, sdtmndt0(Y, Z), W).
% 286.59/37.67 Axiom 21 (mDefSel_2): fresh79(X, X, Y, Z, W) = true2.
% 286.59/37.67 Axiom 22 (mDefSel_1): fresh74(X, X, Y, Z, W) = fresh75(W, slbdtsldtrb0(Y, Z), W).
% 286.59/37.67 Axiom 23 (mDefCons_5): fresh53(aElement0(X), true2, Y, X) = equiv4(Y, X, X).
% 286.59/37.67 Axiom 24 (mDefDiff): fresh49(X, X, Y, Z, W) = aSet0(W).
% 286.59/37.67 Axiom 25 (mDefSel_1): fresh35(X, X, Y, Z, W) = aSet0(W).
% 286.59/37.67 Axiom 26 (mEOfElem): fresh29(aElementOf0(X, Y), true2, Y, X) = fresh28(aSet0(Y), true2, X).
% 286.59/37.67 Axiom 27 (mDefSub_2): fresh179(aSubsetOf0(X, Y), true2, Y, X, Z) = fresh32(aElementOf0(Z, X), true2, Y, Z).
% 286.59/37.67 Axiom 28 (mDefCons_2): fresh159(X, X, Y, Z, W, V) = fresh160(W, sdtpldt0(Y, Z), W, V).
% 286.59/37.67 Axiom 29 (mDefCons_2): fresh158(X, X, Y, Z, W, V) = aElementOf0(V, W).
% 286.59/37.67 Axiom 30 (mDefSel_2): fresh78(X, X, Y, Z, W, V) = fresh79(W, slbdtsldtrb0(Y, Z), Y, Z, V).
% 286.59/37.67 Axiom 31 (mDefSel_2): fresh77(X, X, Y, Z, W, V) = equiv(Y, Z, V).
% 286.59/37.67 Axiom 32 (mDefDiff): fresh136(aElement0(X), true2, Y, X, Z) = fresh49(aSet0(Y), true2, Y, X, Z).
% 286.59/37.67 Axiom 33 (mDefSel_1): fresh74(aElementOf0(X, szNzAzT0), true2, Y, X, Z) = fresh35(aSet0(Y), true2, Y, X, Z).
% 286.59/37.67 Axiom 34 (mDefSel_7): fresh34(equiv(X, Y, Z), true2, X, Z) = aSubsetOf0(Z, X).
% 286.59/37.67 Axiom 35 (mDefCons_2): fresh157(X, X, Y, Z, W, V) = fresh158(aSet0(Y), true2, Y, Z, W, V).
% 286.59/37.67 Axiom 36 (mDefSel_2): fresh76(X, X, Y, Z, W, V) = fresh77(aSet0(Y), true2, Y, Z, W, V).
% 286.59/37.67 Axiom 37 (mDefSel_2): fresh76(aElementOf0(X, Y), true2, Z, W, Y, X) = fresh78(aElementOf0(W, szNzAzT0), true2, Z, W, Y, X).
% 286.59/37.67 Axiom 38 (mDefCons_2): fresh157(equiv4(X, Y, Z), true2, X, Y, W, Z) = fresh159(aElement0(Y), true2, X, Y, W, Z).
% 286.59/37.67
% 286.59/37.67 Lemma 39: aElement0(xx) = true2.
% 286.59/37.67 Proof:
% 286.59/37.67 aElement0(xx)
% 286.59/37.67 = { by axiom 18 (mEOfElem) R->L }
% 286.59/37.67 fresh29(true2, true2, xS, xx)
% 286.59/37.67 = { by axiom 2 (m__2256) R->L }
% 286.59/37.67 fresh29(aElementOf0(xx, xS), true2, xS, xx)
% 286.59/37.67 = { by axiom 26 (mEOfElem) }
% 286.59/37.67 fresh28(aSet0(xS), true2, xx)
% 286.59/37.67 = { by axiom 4 (m__2202_02) }
% 286.59/37.67 fresh28(true2, true2, xx)
% 286.59/37.67 = { by axiom 11 (mEOfElem) }
% 286.59/37.67 true2
% 286.59/37.67
% 286.59/37.67 Goal 1 (m__): aElementOf0(xx, xT) = true2.
% 286.59/37.67 Proof:
% 286.59/37.67 aElementOf0(xx, xT)
% 286.59/37.67 = { by axiom 17 (mDefSub_2) R->L }
% 286.59/37.67 fresh32(true2, true2, xT, xx)
% 286.59/37.67 = { by axiom 14 (mDefCons_2) R->L }
% 286.59/37.67 fresh32(fresh160(sdtpldt0(sdtmndt0(xQ, xy), xx), sdtpldt0(sdtmndt0(xQ, xy), xx), sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 28 (mDefCons_2) R->L }
% 286.59/37.67 fresh32(fresh159(true2, true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by lemma 39 R->L }
% 286.59/37.67 fresh32(fresh159(aElement0(xx), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 38 (mDefCons_2) R->L }
% 286.59/37.67 fresh32(fresh157(equiv4(sdtmndt0(xQ, xy), xx, xx), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 23 (mDefCons_5) R->L }
% 286.59/37.67 fresh32(fresh157(fresh53(aElement0(xx), true2, sdtmndt0(xQ, xy), xx), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by lemma 39 }
% 286.59/37.67 fresh32(fresh157(fresh53(true2, true2, sdtmndt0(xQ, xy), xx), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 15 (mDefCons_5) }
% 286.59/37.67 fresh32(fresh157(true2, true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 35 (mDefCons_2) }
% 286.59/37.67 fresh32(fresh158(aSet0(sdtmndt0(xQ, xy)), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 24 (mDefDiff) R->L }
% 286.59/37.67 fresh32(fresh158(fresh49(true2, true2, xQ, xy, sdtmndt0(xQ, xy)), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 3 (m__2291_1) R->L }
% 286.59/37.67 fresh32(fresh158(fresh49(aSet0(xQ), true2, xQ, xy, sdtmndt0(xQ, xy)), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 32 (mDefDiff) R->L }
% 286.59/37.67 fresh32(fresh158(fresh136(aElement0(xy), true2, xQ, xy, sdtmndt0(xQ, xy)), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 6 (m__2304) }
% 286.59/37.67 fresh32(fresh158(fresh136(true2, true2, xQ, xy, sdtmndt0(xQ, xy)), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 20 (mDefDiff) }
% 286.59/37.67 fresh32(fresh158(fresh137(sdtmndt0(xQ, xy), sdtmndt0(xQ, xy), sdtmndt0(xQ, xy)), true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 9 (mDefDiff) }
% 286.59/37.67 fresh32(fresh158(true2, true2, sdtmndt0(xQ, xy), xx, sdtpldt0(sdtmndt0(xQ, xy), xx), xx), true2, xT, xx)
% 286.59/37.67 = { by axiom 29 (mDefCons_2) }
% 286.59/37.67 fresh32(aElementOf0(xx, sdtpldt0(sdtmndt0(xQ, xy), xx)), true2, xT, xx)
% 286.59/37.67 = { by axiom 8 (m__2357) R->L }
% 286.59/37.67 fresh32(aElementOf0(xx, xP), true2, xT, xx)
% 286.59/37.67 = { by axiom 27 (mDefSub_2) R->L }
% 286.59/37.67 fresh179(aSubsetOf0(xP, xT), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 34 (mDefSel_7) R->L }
% 286.59/37.67 fresh179(fresh34(equiv(xT, xk, xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 31 (mDefSel_2) R->L }
% 286.59/37.67 fresh179(fresh34(fresh77(true2, true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 5 (m__2202_02_1) R->L }
% 286.59/37.67 fresh179(fresh34(fresh77(aSet0(xT), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 36 (mDefSel_2) R->L }
% 286.59/37.67 fresh179(fresh34(fresh76(true2, true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 13 (mDefSub_2) R->L }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh180(true2, true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 10 (mDefSel_1) R->L }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh180(fresh75(slbdtsldtrb0(xT, xk), slbdtsldtrb0(xT, xk), slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 22 (mDefSel_1) R->L }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh180(fresh74(true2, true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 1 (m__2202) R->L }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh180(fresh74(aElementOf0(xk, szNzAzT0), true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 33 (mDefSel_1) }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh180(fresh35(aSet0(xT), true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 5 (m__2202_02_1) }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh180(fresh35(true2, true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 25 (mDefSel_1) }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh180(aSet0(slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 19 (mDefSub_2) R->L }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh179(true2, true2, slbdtsldtrb0(xT, xk), slbdtsldtrb0(xS, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 12 (m__2227) R->L }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh179(aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), slbdtsldtrb0(xS, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 27 (mDefSub_2) }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh32(aElementOf0(xP, slbdtsldtrb0(xS, xk)), true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 7 (m__2378) }
% 286.59/37.67 fresh179(fresh34(fresh76(fresh32(true2, true2, slbdtsldtrb0(xT, xk), xP), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 17 (mDefSub_2) }
% 286.59/37.67 fresh179(fresh34(fresh76(aElementOf0(xP, slbdtsldtrb0(xT, xk)), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 37 (mDefSel_2) }
% 286.59/37.67 fresh179(fresh34(fresh78(aElementOf0(xk, szNzAzT0), true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 1 (m__2202) }
% 286.59/37.67 fresh179(fresh34(fresh78(true2, true2, xT, xk, slbdtsldtrb0(xT, xk), xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 30 (mDefSel_2) }
% 286.59/37.67 fresh179(fresh34(fresh79(slbdtsldtrb0(xT, xk), slbdtsldtrb0(xT, xk), xT, xk, xP), true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 21 (mDefSel_2) }
% 286.59/37.67 fresh179(fresh34(true2, true2, xT, xP), true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 16 (mDefSel_7) }
% 286.59/37.67 fresh179(true2, true2, xT, xP, xx)
% 286.59/37.67 = { by axiom 19 (mDefSub_2) }
% 286.59/37.67 fresh180(aSet0(xT), true2, xT, xx)
% 286.59/37.67 = { by axiom 5 (m__2202_02_1) }
% 286.59/37.67 fresh180(true2, true2, xT, xx)
% 286.59/37.67 = { by axiom 13 (mDefSub_2) }
% 286.59/37.67 true2
% 286.59/37.67 % SZS output end Proof
% 286.59/37.67
% 286.59/37.67 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------