0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n009.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   : 180
0.13/0.34	% DateTime   : Thu Aug 29 15:22:57 EDT 2019
0.13/0.34	% CPUTime    : 
57.67/57.85	% SZS status Theorem
57.67/57.85	
57.67/57.85	% SZS output start Proof
57.67/57.85	Take the following subset of the input axioms:
57.83/58.00	  fof(goals_13, conjecture, ![X17, X18, X19]: ('>='(X17, X19) <= ('>='(X17, '==>'(X17, X18)) & '==>'(X19, X18)=X19))).
57.83/58.00	  fof(sos_01, axiom, ![A, B, C]: '+'('+'(A, B), C)='+'(A, '+'(B, C))).
57.83/58.00	  fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)).
57.83/58.00	  fof(sos_03, axiom, ![A]: '+'(A, '0')=A).
57.83/58.00	  fof(sos_04, axiom, ![A]: '>='(A, A)).
57.83/58.00	  fof(sos_06, axiom, ![X3, X4]: (('>='(X3, X4) & '>='(X4, X3)) => X4=X3)).
57.83/58.00	  fof(sos_07, axiom, ![X5, X6, X7]: ('>='(X6, '==>'(X5, X7)) <=> '>='('+'(X5, X6), X7))).
57.83/58.00	  fof(sos_08, axiom, ![A]: '>='(A, '0')).
57.83/58.00	  fof(sos_09, axiom, ![X8, X9, X10]: ('>='('+'(X8, X10), '+'(X9, X10)) <= '>='(X8, X9))).
57.83/58.00	  fof(sos_10, axiom, ![X11, X12, X13]: ('>='('==>'(X12, X13), '==>'(X11, X13)) <= '>='(X11, X12))).
57.83/58.00	  fof(sos_11, axiom, ![X14, X15, X16]: ('>='('==>'(X16, X14), '==>'(X16, X15)) <= '>='(X14, X15))).
57.83/58.00	  fof(sos_12, axiom, ![A, B]: '+'(A, '==>'(A, B))='+'(B, '==>'(B, A))).
57.83/58.00	
57.83/58.00	Now clausify the problem and encode Horn clauses using encoding 3 of
57.83/58.00	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
57.83/58.00	We repeatedly replace C & s=t => u=v by the two clauses:
57.83/58.00	  fresh(y, y, x1...xn) = u
57.83/58.00	  C => fresh(s, t, x1...xn) = v
57.83/58.00	where fresh is a fresh function symbol and x1..xn are the free
57.83/58.00	variables of u and v.
57.83/58.00	A predicate p(X) is encoded as p(X)=true (this is sound, because the
57.83/58.00	input problem has no model of domain size 1).
57.83/58.00	
57.83/58.00	The encoding turns the above axioms into the following unit equations and goals:
57.83/58.00	
57.83/58.00	Axiom 1 (sos_06): fresh(X, X, Y, Z) = Y.
57.83/58.00	Axiom 2 (sos_06): fresh2(X, X, Y, Z) = Z.
57.83/58.00	Axiom 3 (sos_07): fresh6(X, X, Y, Z, W) = true.
57.83/58.00	Axiom 4 (sos_07_1): fresh5(X, X, Y, Z, W) = true.
57.83/58.00	Axiom 5 (sos_09): fresh4(X, X, Y, Z, W) = true.
57.83/58.00	Axiom 6 (sos_10): fresh9(X, X, Y, Z, W) = true.
57.83/58.00	Axiom 7 (sos_11): fresh3(X, X, Y, Z, W) = true.
57.83/58.00	Axiom 8 (sos_10): fresh9(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z).
57.83/58.00	Axiom 9 (sos_02): X + Y = Y + X.
57.83/58.00	Axiom 10 (sos_07_1): fresh5((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z).
57.83/58.00	Axiom 11 (sos_07): fresh6(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z.
57.83/58.00	Axiom 12 (sos_09): fresh4(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z).
57.83/58.00	Axiom 13 (sos_03): X + 0 = X.
57.83/58.00	Axiom 14 (sos_08): X >= 0 = true.
57.83/58.00	Axiom 15 (sos_11): fresh3(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y).
57.83/58.00	Axiom 16 (sos_04): X >= X = true.
57.83/58.00	Axiom 17 (sos_06): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X).
57.83/58.00	Axiom 18 (sos_01): (X + Y) + Z = X + (Y + Z).
57.83/58.00	Axiom 19 (sos_12): X + (X ==> Y) = Y + (Y ==> X).
57.83/58.00	Axiom 20 (goals_13): sK2_goals_13_X19 ==> sK3_goals_13_X18 = sK2_goals_13_X19.
57.83/58.00	Axiom 21 (goals_13_1): sK1_goals_13_X17 >= (sK1_goals_13_X17 ==> sK3_goals_13_X18) = true.
57.83/58.00	
57.83/58.00	Lemma 22: 0 + X = X.
57.83/58.00	Proof:
57.83/58.00	  0 + X
57.83/58.00	= { by axiom 9 (sos_02) }
57.83/58.00	  X + 0
57.83/58.00	= { by axiom 13 (sos_03) }
57.95/58.15	  X
57.95/58.15	
57.95/58.15	Goal 1 (goals_13_2): sK1_goals_13_X17 >= sK2_goals_13_X19 = true.
57.95/58.15	Proof:
57.95/58.15	  sK1_goals_13_X17 >= sK2_goals_13_X19
57.95/58.15	= { by axiom 13 (sos_03) }
57.95/58.15	  (sK1_goals_13_X17 + 0) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 2 (sos_06) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(true, true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 4 (sos_07_1) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(true, true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 4 (sos_07_1) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(true, true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 4 (sos_07_1) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(true, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 3 (sos_07) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(fresh6(true, true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 3 (sos_07) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(fresh6(fresh6(true, true, sK2_goals_13_X19, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 7 (sos_11) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(fresh6(fresh6(fresh3(true, true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK3_goals_13_X18, sK2_goals_13_X19), true, sK2_goals_13_X19, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 21 (goals_13_1) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(fresh6(fresh6(fresh3(sK1_goals_13_X17 >= (sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK3_goals_13_X18, sK2_goals_13_X19), true, sK2_goals_13_X19, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 15 (sos_11) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(fresh6(fresh6((sK2_goals_13_X19 ==> sK1_goals_13_X17) >= (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK2_goals_13_X19, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 11 (sos_07) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(fresh6((sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) >= (sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 11 (sos_07) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5((sK1_goals_13_X17 + (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 18 (sos_01) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(((sK1_goals_13_X17 + sK2_goals_13_X19) + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 9 (sos_02) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5(((sK2_goals_13_X19 + sK1_goals_13_X17) + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 18 (sos_01) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(fresh5((sK2_goals_13_X19 + (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 10 (sos_07_1) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5((sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 9 (sos_02) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(((sK2_goals_13_X19 ==> sK1_goals_13_X17) + sK1_goals_13_X17) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 20 (goals_13) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(fresh5(((sK2_goals_13_X19 ==> sK1_goals_13_X17) + sK1_goals_13_X17) >= sK2_goals_13_X19, true, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK1_goals_13_X17, sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 10 (sos_07_1) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5(sK1_goals_13_X17 >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 13 (sos_03) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(fresh5((sK1_goals_13_X17 + 0) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 10 (sos_07_1) }
57.95/58.15	  (sK1_goals_13_X17 + fresh2(0 >= (sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19)), true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.15	= { by axiom 17 (sos_06) }
57.95/58.16	  (sK1_goals_13_X17 + fresh((sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19)) >= 0, true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.16	= { by axiom 14 (sos_08) }
57.95/58.16	  (sK1_goals_13_X17 + fresh(true, true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19
57.95/58.16	= { by axiom 1 (sos_06) }
57.95/58.16	  (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19))) >= sK2_goals_13_X19
57.95/58.16	= { by axiom 19 (sos_12) }
57.95/58.16	  (((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17)) >= sK2_goals_13_X19
57.95/58.16	= { by axiom 9 (sos_02) }
57.95/58.16	  ((((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) + ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19)) >= sK2_goals_13_X19
57.95/58.16	= { by axiom 11 (sos_07) }
57.95/58.16	  fresh6(((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) >= ((((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 8 (sos_10) }
57.95/58.16	  fresh6(fresh9((((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) >= (sK2_goals_13_X19 ==> sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 8 (sos_10) }
57.95/58.16	  fresh6(fresh9(fresh9(sK2_goals_13_X19 >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 2 (sos_06) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh2(true, true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 4 (sos_07_1) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh2(fresh5(true, true, 0, sK2_goals_13_X19, 0 + sK2_goals_13_X19), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 16 (sos_04) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh2(fresh5((0 + sK2_goals_13_X19) >= (0 + sK2_goals_13_X19), true, 0, sK2_goals_13_X19, 0 + sK2_goals_13_X19), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 10 (sos_07_1) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh2(sK2_goals_13_X19 >= (0 ==> (0 + sK2_goals_13_X19)), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 9 (sos_02) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh2(sK2_goals_13_X19 >= (0 ==> (sK2_goals_13_X19 + 0)), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 13 (sos_03) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh2(sK2_goals_13_X19 >= (0 ==> sK2_goals_13_X19), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 17 (sos_06) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh((0 ==> sK2_goals_13_X19) >= sK2_goals_13_X19, true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by lemma 22 }
57.95/58.16	  fresh6(fresh9(fresh9(fresh((0 + (0 ==> sK2_goals_13_X19)) >= sK2_goals_13_X19, true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 19 (sos_12) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh((sK2_goals_13_X19 + (sK2_goals_13_X19 ==> 0)) >= sK2_goals_13_X19, true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 9 (sos_02) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh(((sK2_goals_13_X19 ==> 0) + sK2_goals_13_X19) >= sK2_goals_13_X19, true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by lemma 22 }
57.95/58.16	  fresh6(fresh9(fresh9(fresh(((sK2_goals_13_X19 ==> 0) + sK2_goals_13_X19) >= (0 + sK2_goals_13_X19), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 12 (sos_09) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh(fresh4((sK2_goals_13_X19 ==> 0) >= 0, true, sK2_goals_13_X19 ==> 0, 0, sK2_goals_13_X19), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 14 (sos_08) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh(fresh4(true, true, sK2_goals_13_X19 ==> 0, 0, sK2_goals_13_X19), true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 5 (sos_09) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh(true, true, 0 ==> sK2_goals_13_X19, sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 1 (sos_06) }
57.95/58.16	  fresh6(fresh9(fresh9((0 ==> sK2_goals_13_X19) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 8 (sos_10) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh9((sK2_goals_13_X19 ==> sK1_goals_13_X17) >= 0, true, sK2_goals_13_X19 ==> sK1_goals_13_X17, 0, sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 14 (sos_08) }
57.95/58.16	  fresh6(fresh9(fresh9(fresh9(true, true, sK2_goals_13_X19 ==> sK1_goals_13_X17, 0, sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 6 (sos_10) }
57.95/58.16	  fresh6(fresh9(fresh9(true, true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 6 (sos_10) }
57.95/58.16	  fresh6(fresh9(true, true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19 ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 6 (sos_10) }
57.95/58.16	  fresh6(true, true, ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, (sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK2_goals_13_X19)
57.95/58.16	= { by axiom 3 (sos_07) }
57.95/58.16	  true
57.95/58.16	% SZS output end Proof
57.95/58.16	
57.95/58.16	RESULT: Theorem (the conjecture is true).
57.95/58.17	EOF