0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.02/0.23	% Computer   : n002.star.cs.uiowa.edu
0.02/0.23	% Model      : x86_64 x86_64
0.02/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.23	% Memory     : 32218.625MB
0.02/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.23	% CPULimit   : 300
0.02/0.23	% DateTime   : Sat Jul 14 04:57:54 CDT 2018
0.02/0.23	% CPUTime    : 
0.07/0.35	% SZS status Theorem
0.07/0.35	
0.07/0.35	% SZS output start Proof
0.07/0.35	Take the following subset of the input axioms:
0.07/0.39	  fof(goals_14, conjecture, ![X17]: X17='==>'('==>'(X17, '1'), '1')).
0.07/0.39	  fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)).
0.07/0.39	  fof(sos_03, axiom, ![A]: A='+'(A, '0')).
0.07/0.39	  fof(sos_04, axiom, ![A]: '>='(A, A)).
0.07/0.39	  fof(sos_06, axiom,
0.07/0.39	      ![X3, X4]: (X3=X4 <= ('>='(X4, X3) & '>='(X3, X4)))).
0.07/0.39	  fof(sos_07, axiom,
0.07/0.39	      ![X5, X6, X7]:
0.07/0.39	        ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))).
0.07/0.39	  fof(sos_08, axiom, ![A]: '>='(A, '0')).
0.07/0.39	  fof(sos_09, axiom,
0.07/0.39	      ![X8, X9, X10]:
0.07/0.39	        ('>='('+'(X8, X10), '+'(X9, X10)) <= '>='(X8, X9))).
0.07/0.39	  fof(sos_10, axiom,
0.07/0.39	      ![X11, X12, X13]:
0.07/0.39	        ('>='(X11, X12) => '>='('==>'(X12, X13), '==>'(X11, X13)))).
0.07/0.39	  fof(sos_11, axiom,
0.07/0.39	      ![X14, X15, X16]:
0.07/0.39	        ('>='('==>'(X16, X14), '==>'(X16, X15)) <= '>='(X14, X15))).
0.07/0.39	  fof(sos_12, axiom, ![A]: '+'(A, '1')='1').
0.07/0.39	  fof(sos_13, axiom, ![A]: '==>'('==>'('==>'(A, '1'), A), A)='0').
0.07/0.39	
0.07/0.39	Now clausify the problem and encode Horn clauses using encoding 3 of
0.07/0.39	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.07/0.39	We repeatedly replace C & s=t => u=v by the two clauses:
0.07/0.39	  $$fresh(y, y, x1...xn) = u
0.07/0.39	  C => $$fresh(s, t, x1...xn) = v
0.07/0.39	where $$fresh is a fresh function symbol and x1..xn are the free
0.07/0.39	variables of u and v.
0.07/0.39	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
0.07/0.39	input problem has no model of domain size 1).
0.07/0.39	
0.07/0.39	The encoding turns the above axioms into the following unit equations and goals:
0.07/0.39	
0.07/0.39	Axiom 3 (sos_06): $$fresh8(X, X, Y, Z) = Y.
0.07/0.39	Axiom 4 (sos_06): $$fresh9(X, X, Y, Z) = Z.
0.07/0.39	Axiom 5 (sos_07): $$fresh5(X, X, Y, Z, W) = $$true.
0.07/0.39	Axiom 6 (sos_07_1): $$fresh4(X, X, Y, Z, W) = $$true.
0.07/0.39	Axiom 7 (sos_09): $$fresh3(X, X, Y, Z, W) = $$true.
0.07/0.39	Axiom 8 (sos_10): $$fresh2(X, X, Y, Z, W) = $$true.
0.07/0.39	Axiom 9 (sos_11): $$fresh(X, X, Y, Z, W) = $$true.
0.07/0.39	Axiom 10 (sos_13): ((X ==> 1) ==> X) ==> X = 0.
0.07/0.39	Axiom 11 (sos_06): $$fresh8(X >= Y, $$true, Y, X) = $$fresh9(Y >= X, $$true, Y, X).
0.07/0.39	Axiom 12 (sos_04): X >= X = $$true.
0.07/0.39	Axiom 13 (sos_02): X + Y = Y + X.
0.07/0.39	Axiom 14 (sos_07_1): $$fresh4((X + Y) >= Z, $$true, X, Y, Z) = Y >= (X ==> Z).
0.07/0.39	Axiom 15 (sos_07): $$fresh5(X >= (Y ==> Z), $$true, Y, X, Z) = (Y + X) >= Z.
0.07/0.39	Axiom 16 (sos_11): $$fresh(X >= Y, $$true, X, Y, Z) = (Z ==> X) >= (Z ==> Y).
0.07/0.39	Axiom 18 (sos_12): X + 1 = 1.
0.07/0.39	Axiom 19 (sos_08): X >= 0 = $$true.
0.07/0.39	Axiom 21 (sos_10): $$fresh2(X >= Y, $$true, X, Y, Z) = (Y ==> Z) >= (X ==> Z).
0.07/0.39	Axiom 22 (sos_09): $$fresh3(X >= Y, $$true, X, Y, Z) = (X + Z) >= (Y + Z).
0.07/0.39	Axiom 23 (sos_03): X = X + 0.
0.07/0.39	
0.07/0.39	Lemma 24: 0 + X = X.
0.07/0.39	Proof:
0.07/0.39	  0 + X
0.07/0.39	= { by axiom 13 (sos_02) }
0.07/0.39	  X + 0
0.07/0.39	= { by axiom 23 (sos_03) }
0.07/0.39	  X
0.07/0.39	
0.07/0.39	Lemma 25: (X + Y) >= X = $$true.
0.07/0.39	Proof:
0.07/0.39	  (X + Y) >= X
0.07/0.39	= { by axiom 13 (sos_02) }
0.07/0.39	  (Y + X) >= X
0.07/0.39	= { by lemma 24 }
0.07/0.39	  (Y + X) >= (0 + X)
0.07/0.39	= { by axiom 22 (sos_09) }
0.07/0.39	  $$fresh3(Y >= 0, $$true, Y, 0, X)
0.07/0.39	= { by axiom 19 (sos_08) }
0.07/0.39	  $$fresh3($$true, $$true, Y, 0, X)
0.07/0.39	= { by axiom 7 (sos_09) }
0.07/0.39	  $$true
0.07/0.39	
0.07/0.39	Lemma 26: 1 >= X = $$true.
0.07/0.39	Proof:
0.07/0.39	  1 >= X
0.07/0.39	= { by axiom 18 (sos_12) }
0.07/0.39	  (X + 1) >= X
0.07/0.39	= { by lemma 25 }
0.07/0.39	  $$true
0.07/0.39	
0.07/0.39	Lemma 27: (X + (X ==> Y)) >= Y = $$true.
0.07/0.39	Proof:
0.07/0.39	  (X + (X ==> Y)) >= Y
0.07/0.39	= { by axiom 15 (sos_07) }
0.07/0.39	  $$fresh5((X ==> Y) >= (X ==> Y), $$true, X, X ==> Y, Y)
0.07/0.39	= { by axiom 12 (sos_04) }
0.07/0.39	  $$fresh5($$true, $$true, X, X ==> Y, Y)
0.07/0.39	= { by axiom 5 (sos_07) }
0.07/0.44	  $$true
0.07/0.44	
0.07/0.44	Goal 1 (goals_14): sK1_goals_14_X17 = (sK1_goals_14_X17 ==> 1) ==> 1.
0.07/0.44	Proof:
0.07/0.44	  sK1_goals_14_X17
0.07/0.44	= { by axiom 3 (sos_06) }
0.07/0.44	  $$fresh8($$true, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.44	= { by axiom 9 (sos_11) }
0.07/0.45	  $$fresh8($$fresh($$true, $$true, sK1_goals_14_X17 + 1, sK1_goals_14_X17, sK1_goals_14_X17 ==> 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by lemma 25 }
0.07/0.45	  $$fresh8($$fresh((sK1_goals_14_X17 + 1) >= sK1_goals_14_X17, $$true, sK1_goals_14_X17 + 1, sK1_goals_14_X17, sK1_goals_14_X17 ==> 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 16 (sos_11) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 4 (sos_06) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$true, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 8 (sos_10) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh2($$true, $$true, sK1_goals_14_X17 ==> 1, 0, sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 19 (sos_08) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh2((sK1_goals_14_X17 ==> 1) >= 0, $$true, sK1_goals_14_X17 ==> 1, 0, sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 21 (sos_10) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9((0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 4 (sos_06) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh9($$true, $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 6 (sos_07_1) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh9($$fresh4($$true, $$true, 0, sK1_goals_14_X17, 0 + sK1_goals_14_X17), $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 12 (sos_04) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh9($$fresh4((0 + sK1_goals_14_X17) >= (0 + sK1_goals_14_X17), $$true, 0, sK1_goals_14_X17, 0 + sK1_goals_14_X17), $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 14 (sos_07_1) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh9(sK1_goals_14_X17 >= (0 ==> (0 + sK1_goals_14_X17)), $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 13 (sos_02) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh9(sK1_goals_14_X17 >= (0 ==> (sK1_goals_14_X17 + 0)), $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 23 (sos_03) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh9(sK1_goals_14_X17 >= (0 ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 11 (sos_06) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh8((0 ==> sK1_goals_14_X17) >= sK1_goals_14_X17, $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by lemma 24 }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh8((0 + (0 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by lemma 27 }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9($$fresh8($$true, $$true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 3 (sos_06) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh9(sK1_goals_14_X17 >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 11 (sos_06) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh8(((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) >= sK1_goals_14_X17, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 23 (sos_03) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh8((((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) + 0) >= sK1_goals_14_X17, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 10 (sos_13) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh8((((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) + (((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by lemma 27 }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= $$fresh8($$true, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 3 (sos_06) }
0.07/0.45	  $$fresh8(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= sK1_goals_14_X17, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 11 (sos_06) }
0.07/0.45	  $$fresh9(sK1_goals_14_X17 >= ((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 14 (sos_07_1) }
0.07/0.45	  $$fresh9($$fresh4(((sK1_goals_14_X17 ==> 1) + sK1_goals_14_X17) >= (sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 13 (sos_02) }
0.07/0.45	  $$fresh9($$fresh4((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1)) >= (sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 3 (sos_06) }
0.07/0.45	  $$fresh9($$fresh4($$fresh8($$true, $$true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by lemma 26 }
0.07/0.45	  $$fresh9($$fresh4($$fresh8(1 >= (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1)), $$true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 11 (sos_06) }
0.07/0.45	  $$fresh9($$fresh4($$fresh9((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1)) >= 1, $$true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by lemma 27 }
0.07/0.45	  $$fresh9($$fresh4($$fresh9($$true, $$true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 4 (sos_06) }
0.07/0.45	  $$fresh9($$fresh4(1 >= (sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by lemma 26 }
0.07/0.45	  $$fresh9($$fresh4($$true, $$true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 6 (sos_07_1) }
0.07/0.45	  $$fresh9($$true, $$true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1))
0.07/0.45	= { by axiom 4 (sos_06) }
0.07/0.45	  (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)
0.07/0.45	= { by axiom 18 (sos_12) }
0.07/0.45	  (sK1_goals_14_X17 ==> 1) ==> 1
0.07/0.45	% SZS output end Proof
0.07/0.45	
0.07/0.45	RESULT: Theorem (the conjecture is true).
0.07/0.46	EOF