0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.35	% Computer   : n020.cluster.edu
0.12/0.35	% Model      : x86_64 x86_64
0.12/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.35	% Memory     : 8042.1875MB
0.12/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.35	% CPULimit   : 180
0.12/0.35	% DateTime   : Thu Aug 29 10:21:55 EDT 2019
0.12/0.35	% CPUTime    : 
4.19/4.46	% SZS status Theorem
4.19/4.46	
4.34/4.55	% SZS output start Proof
4.34/4.55	Take the following subset of the input axioms:
4.34/4.60	  fof(axiom_1, axiom, ?[Y24]: ![X19]: ((Y24=X19 & r1(X19)) | (~r1(X19) & X19!=Y24))).
4.34/4.60	  fof(axiom_1a, axiom, ![X1, X8]: ?[Y4]: (?[Y7]: (r2(Y7, Y4) & r3(X1, X8, Y7)) & ?[Y5]: (?[Y15]: (r2(X8, Y15) & r3(X1, Y15, Y5)) & Y4=Y5))).
4.34/4.60	  fof(axiom_2, axiom, ![X11]: ?[Y21]: ![X12]: ((~r2(X11, X12) & Y21!=X12) | (X12=Y21 & r2(X11, X12)))).
4.34/4.60	  fof(axiom_2a, axiom, ![X2, X9]: ?[Y2]: (?[Y6]: (r4(X2, X9, Y6) & r3(Y6, X2, Y2)) & ?[Y3]: (Y2=Y3 & ?[Y14]: (r2(X9, Y14) & r4(X2, Y14, Y3))))).
4.34/4.60	  fof(axiom_3, axiom, ![X13, X14]: ?[Y22]: ![X15]: ((r3(X13, X14, X15) & Y22=X15) | (~r3(X13, X14, X15) & X15!=Y22))).
4.34/4.60	  fof(axiom_4, axiom, ![X16, X17]: ?[Y23]: ![X18]: ((Y23=X18 & r4(X16, X17, X18)) | (~r4(X16, X17, X18) & Y23!=X18))).
4.34/4.60	  fof(axiom_4a, axiom, ![X4]: ?[Y9]: (Y9=X4 & ?[Y16]: (r3(X4, Y16, Y9) & r1(Y16)))).
4.34/4.60	  fof(axiom_5a, axiom, ![X5]: ?[Y8]: (?[Y17]: (r4(X5, Y17, Y8) & r1(Y17)) & ?[Y18]: (r1(Y18) & Y8=Y18))).
4.34/4.60	  fof(axiom_7a, axiom, ![X7, Y10]: (~r2(X7, Y10) | ![Y20]: (Y10!=Y20 | ~r1(Y20)))).
4.34/4.60	  fof(xtimesyeqtwo, conjecture, ?[Y1, Y2, Y3]: (?[Y4]: (?[Y5]: (r2(Y5, Y4) & ?[Y6]: (r2(Y6, Y5) & r1(Y6))) & Y3=Y4) & r4(Y1, Y2, Y3))).
4.34/4.60	
4.34/4.60	Now clausify the problem and encode Horn clauses using encoding 3 of
4.34/4.60	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
4.34/4.60	We repeatedly replace C & s=t => u=v by the two clauses:
4.34/4.60	  fresh(y, y, x1...xn) = u
4.34/4.60	  C => fresh(s, t, x1...xn) = v
4.34/4.60	where fresh is a fresh function symbol and x1..xn are the free
4.34/4.60	variables of u and v.
4.34/4.60	A predicate p(X) is encoded as p(X)=true (this is sound, because the
4.34/4.60	input problem has no model of domain size 1).
4.34/4.60	
4.34/4.60	The encoding turns the above axioms into the following unit equations and goals:
4.34/4.60	
4.34/4.60	Axiom 1 (axiom_1): fresh9(X, X, Y) = true2.
4.34/4.60	Axiom 2 (axiom_1_1): fresh(X, X, Y) = Y.
4.34/4.60	Axiom 3 (axiom_2): fresh10(X, X, Y, Z) = true2.
4.34/4.60	Axiom 4 (axiom_2_1): fresh5(X, X, Y, Z) = Z.
4.34/4.60	Axiom 5 (axiom_3_1): fresh4(X, X, Y, Z, W) = W.
4.34/4.60	Axiom 6 (axiom_4_1): fresh6(X, X, Y, Z, W) = W.
4.34/4.60	Axiom 7 (axiom_1a_4): r3(X, sK14_axiom_1a_Y15(X, Y), sK15_axiom_1a_Y5(X, Y)) = true2.
4.34/4.60	Axiom 8 (axiom_1a_3): r3(X, Y, sK16_axiom_1a_Y7(X, Y)) = true2.
4.34/4.60	Axiom 9 (axiom_1a_2): r2(sK16_axiom_1a_Y7(X, Y), sK17_axiom_1a_Y4(X, Y)) = true2.
4.34/4.60	Axiom 10 (axiom_1a_1): r2(X, sK14_axiom_1a_Y15(Y, X)) = true2.
4.34/4.60	Axiom 11 (axiom_1a): sK17_axiom_1a_Y4(X, Y) = sK15_axiom_1a_Y5(X, Y).
4.34/4.60	Axiom 12 (axiom_4_1): fresh6(r4(X, Y, Z), true2, X, Y, Z) = sK13_axiom_4_Y23(X, Y).
4.34/4.60	Axiom 13 (axiom_2a_4): r4(X, sK9_axiom_2a_Y14(X, Y), sK10_axiom_2a_Y3(X, Y)) = true2.
4.34/4.60	Axiom 14 (axiom_2a_3): r4(X, Y, sK11_axiom_2a_Y6(X, Y)) = true2.
4.34/4.60	Axiom 15 (axiom_2a_2): r3(sK11_axiom_2a_Y6(X, Y), X, sK12_axiom_2a_Y2(X, Y)) = true2.
4.34/4.60	Axiom 16 (axiom_2a_1): r2(X, sK9_axiom_2a_Y14(Y, X)) = true2.
4.34/4.60	Axiom 17 (axiom_2a): sK12_axiom_2a_Y2(X, Y) = sK10_axiom_2a_Y3(X, Y).
4.34/4.60	Axiom 18 (axiom_2_1): fresh5(r2(X, Y), true2, X, Y) = sK8_axiom_2_Y21(X).
4.34/4.60	Axiom 19 (axiom_2): fresh10(sK8_axiom_2_Y21(X), Y, X, Y) = r2(X, Y).
4.34/4.60	Axiom 20 (axiom_3_1): fresh4(r3(X, Y, Z), true2, X, Y, Z) = sK7_axiom_3_Y22(X, Y).
4.34/4.60	Axiom 21 (axiom_1_1): fresh(r1(X), true2, X) = sK6_axiom_1_Y24.
4.34/4.60	Axiom 22 (axiom_1): fresh9(X, sK6_axiom_1_Y24, X) = r1(X).
4.34/4.60	Axiom 23 (axiom_5a_3): r1(sK3_axiom_5a_Y18(X)) = true2.
4.34/4.60	Axiom 24 (axiom_5a_2): r1(sK4_axiom_5a_Y17(X)) = true2.
4.34/4.60	Axiom 25 (axiom_5a_1): r4(X, sK4_axiom_5a_Y17(X), sK5_axiom_5a_Y8(X)) = true2.
4.34/4.60	Axiom 26 (axiom_5a): sK5_axiom_5a_Y8(X) = sK3_axiom_5a_Y18(X).
4.34/4.60	Axiom 27 (axiom_4a_2): r1(sK1_axiom_4a_Y16(X)) = true2.
4.34/4.60	Axiom 28 (axiom_4a_1): r3(X, sK1_axiom_4a_Y16(X), sK2_axiom_4a_Y9(X)) = true2.
4.34/4.60	Axiom 29 (axiom_4a): sK2_axiom_4a_Y9(X) = X.
4.34/4.60	
4.34/4.60	Lemma 30: r2(X, sK8_axiom_2_Y21(X)) = true2.
4.34/4.60	Proof:
4.34/4.60	  r2(X, sK8_axiom_2_Y21(X))
4.34/4.60	= { by axiom 19 (axiom_2) }
4.34/4.60	  fresh10(sK8_axiom_2_Y21(X), sK8_axiom_2_Y21(X), X, sK8_axiom_2_Y21(X))
4.34/4.60	= { by axiom 3 (axiom_2) }
4.34/4.60	  true2
4.34/4.60	
4.34/4.60	Lemma 31: sK7_axiom_3_Y22(X, Y) = sK16_axiom_1a_Y7(X, Y).
4.34/4.60	Proof:
4.34/4.60	  sK7_axiom_3_Y22(X, Y)
4.34/4.60	= { by axiom 20 (axiom_3_1) }
4.34/4.60	  fresh4(r3(X, Y, sK16_axiom_1a_Y7(X, Y)), true2, X, Y, sK16_axiom_1a_Y7(X, Y))
4.34/4.60	= { by axiom 8 (axiom_1a_3) }
4.34/4.60	  fresh4(true2, true2, X, Y, sK16_axiom_1a_Y7(X, Y))
4.34/4.60	= { by axiom 5 (axiom_3_1) }
4.34/4.60	  sK16_axiom_1a_Y7(X, Y)
4.34/4.60	
4.34/4.60	Lemma 32: sK16_axiom_1a_Y7(X, sK8_axiom_2_Y21(Y)) = sK17_axiom_1a_Y4(X, Y).
4.34/4.60	Proof:
4.34/4.60	  sK16_axiom_1a_Y7(X, sK8_axiom_2_Y21(Y))
4.34/4.60	= { by axiom 18 (axiom_2_1) }
4.34/4.60	  sK16_axiom_1a_Y7(X, fresh5(r2(Y, sK14_axiom_1a_Y15(X, Y)), true2, Y, sK14_axiom_1a_Y15(X, Y)))
4.34/4.60	= { by axiom 10 (axiom_1a_1) }
4.34/4.60	  sK16_axiom_1a_Y7(X, fresh5(true2, true2, Y, sK14_axiom_1a_Y15(X, Y)))
4.34/4.60	= { by axiom 4 (axiom_2_1) }
4.34/4.60	  sK16_axiom_1a_Y7(X, sK14_axiom_1a_Y15(X, Y))
4.34/4.60	= { by lemma 31 }
4.34/4.60	  sK7_axiom_3_Y22(X, sK14_axiom_1a_Y15(X, Y))
4.34/4.60	= { by axiom 20 (axiom_3_1) }
4.34/4.60	  fresh4(r3(X, sK14_axiom_1a_Y15(X, Y), sK15_axiom_1a_Y5(X, Y)), true2, X, sK14_axiom_1a_Y15(X, Y), sK15_axiom_1a_Y5(X, Y))
4.34/4.60	= { by axiom 7 (axiom_1a_4) }
4.34/4.60	  fresh4(true2, true2, X, sK14_axiom_1a_Y15(X, Y), sK15_axiom_1a_Y5(X, Y))
4.34/4.60	= { by axiom 5 (axiom_3_1) }
4.34/4.60	  sK15_axiom_1a_Y5(X, Y)
4.34/4.60	= { by axiom 11 (axiom_1a) }
4.34/4.60	  sK17_axiom_1a_Y4(X, Y)
4.34/4.60	
4.34/4.60	Lemma 33: sK8_axiom_2_Y21(sK16_axiom_1a_Y7(X, Y)) = sK17_axiom_1a_Y4(X, Y).
4.34/4.60	Proof:
4.34/4.60	  sK8_axiom_2_Y21(sK16_axiom_1a_Y7(X, Y))
4.34/4.60	= { by axiom 18 (axiom_2_1) }
4.34/4.60	  fresh5(r2(sK16_axiom_1a_Y7(X, Y), sK17_axiom_1a_Y4(X, Y)), true2, sK16_axiom_1a_Y7(X, Y), sK17_axiom_1a_Y4(X, Y))
4.34/4.60	= { by axiom 9 (axiom_1a_2) }
4.34/4.60	  fresh5(true2, true2, sK16_axiom_1a_Y7(X, Y), sK17_axiom_1a_Y4(X, Y))
4.34/4.60	= { by axiom 4 (axiom_2_1) }
4.43/4.64	  sK17_axiom_1a_Y4(X, Y)
4.43/4.64	
4.43/4.64	Goal 1 (xtimesyeqtwo): tuple(r2(X, Y), r2(Z, X), r4(W, V, Y), r1(Z)) = tuple(true2, true2, true2, true2).
4.43/4.64	The goal is true when:
4.43/4.64	  X = sK8_axiom_2_Y21(sK6_axiom_1_Y24)
4.43/4.64	  Y = sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))
4.43/4.64	  Z = sK6_axiom_1_Y24
4.43/4.64	  W = sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))
4.43/4.64	  V = sK8_axiom_2_Y21(sK6_axiom_1_Y24)
4.43/4.64	
4.43/4.64	Proof:
4.43/4.64	  tuple(r2(sK8_axiom_2_Y21(sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r2(sK6_axiom_1_Y24, sK8_axiom_2_Y21(sK6_axiom_1_Y24)), r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK8_axiom_2_Y21(sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 30 }
4.43/4.64	  tuple(true2, r2(sK6_axiom_1_Y24, sK8_axiom_2_Y21(sK6_axiom_1_Y24)), r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK8_axiom_2_Y21(sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 30 }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK8_axiom_2_Y21(sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 18 (axiom_2_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), fresh5(r2(sK6_axiom_1_Y24, sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), true2, sK6_axiom_1_Y24, sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 16 (axiom_2a_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), fresh5(true2, true2, sK6_axiom_1_Y24, sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 4 (axiom_2_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 29 (axiom_4a) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK2_axiom_4a_Y9(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 5 (axiom_3_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(fresh4(true2, true2, sK6_axiom_1_Y24, sK1_axiom_4a_Y16(sK6_axiom_1_Y24), sK2_axiom_4a_Y9(sK6_axiom_1_Y24))))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 28 (axiom_4a_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(fresh4(r3(sK6_axiom_1_Y24, sK1_axiom_4a_Y16(sK6_axiom_1_Y24), sK2_axiom_4a_Y9(sK6_axiom_1_Y24)), true2, sK6_axiom_1_Y24, sK1_axiom_4a_Y16(sK6_axiom_1_Y24), sK2_axiom_4a_Y9(sK6_axiom_1_Y24))))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 20 (axiom_3_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK7_axiom_3_Y22(sK6_axiom_1_Y24, sK1_axiom_4a_Y16(sK6_axiom_1_Y24))))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 31 }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK16_axiom_1a_Y7(sK6_axiom_1_Y24, sK1_axiom_4a_Y16(sK6_axiom_1_Y24))))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 2 (axiom_1_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK16_axiom_1a_Y7(sK6_axiom_1_Y24, fresh(true2, true2, sK1_axiom_4a_Y16(sK6_axiom_1_Y24)))))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 27 (axiom_4a_2) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK16_axiom_1a_Y7(sK6_axiom_1_Y24, fresh(r1(sK1_axiom_4a_Y16(sK6_axiom_1_Y24)), true2, sK1_axiom_4a_Y16(sK6_axiom_1_Y24)))))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 21 (axiom_1_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK16_axiom_1a_Y7(sK6_axiom_1_Y24, sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 33 }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK17_axiom_1a_Y4(sK6_axiom_1_Y24, sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 32 }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK16_axiom_1a_Y7(sK6_axiom_1_Y24, sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 33 }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK17_axiom_1a_Y4(sK6_axiom_1_Y24, sK8_axiom_2_Y21(sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 32 }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK6_axiom_1_Y24, sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 21 (axiom_1_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(fresh(r1(sK3_axiom_5a_Y18(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), true2, sK3_axiom_5a_Y18(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 23 (axiom_5a_3) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(fresh(true2, true2, sK3_axiom_5a_Y18(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 2 (axiom_1_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK3_axiom_5a_Y18(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 26 (axiom_5a) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK5_axiom_5a_Y8(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 6 (axiom_4_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(fresh6(true2, true2, sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK4_axiom_5a_Y17(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), sK5_axiom_5a_Y8(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 25 (axiom_5a_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(fresh6(r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK4_axiom_5a_Y17(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), sK5_axiom_5a_Y8(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), true2, sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK4_axiom_5a_Y17(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))), sK5_axiom_5a_Y8(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 12 (axiom_4_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK13_axiom_4_Y23(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK4_axiom_5a_Y17(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 2 (axiom_1_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK13_axiom_4_Y23(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), fresh(true2, true2, sK4_axiom_5a_Y17(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 24 (axiom_5a_2) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK13_axiom_4_Y23(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), fresh(r1(sK4_axiom_5a_Y17(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), true2, sK4_axiom_5a_Y17(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24))))), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 21 (axiom_1_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK13_axiom_4_Y23(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 12 (axiom_4_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(fresh6(r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24, sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), true2, sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24, sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 14 (axiom_2a_3) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(fresh6(true2, true2, sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24, sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 6 (axiom_4_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK16_axiom_1a_Y7(sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by lemma 31 }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK7_axiom_3_Y22(sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 20 (axiom_3_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), fresh4(r3(sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK12_axiom_2a_Y2(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), true2, sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK12_axiom_2a_Y2(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 15 (axiom_2a_2) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), fresh4(true2, true2, sK11_axiom_2a_Y6(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK12_axiom_2a_Y2(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24))), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 5 (axiom_3_1) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK12_axiom_2a_Y2(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 17 (axiom_2a) }
4.43/4.64	  tuple(true2, true2, r4(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK9_axiom_2a_Y14(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24), sK10_axiom_2a_Y3(sK8_axiom_2_Y21(sK8_axiom_2_Y21(sK6_axiom_1_Y24)), sK6_axiom_1_Y24)), r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 13 (axiom_2a_4) }
4.43/4.64	  tuple(true2, true2, true2, r1(sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 22 (axiom_1) }
4.43/4.64	  tuple(true2, true2, true2, fresh9(sK6_axiom_1_Y24, sK6_axiom_1_Y24, sK6_axiom_1_Y24))
4.43/4.64	= { by axiom 1 (axiom_1) }
4.43/4.64	  tuple(true2, true2, true2, true2)
4.43/4.64	% SZS output end Proof
4.43/4.64	
4.43/4.64	RESULT: Theorem (the conjecture is true).
4.43/4.65	EOF