0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n003.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 14:11:32 EDT 2019
0.13/0.34	% CPUTime    : 
44.52/44.72	% SZS status Unsatisfiable
44.52/44.72	
44.52/44.72	% SZS output start Proof
44.52/44.72	Take the following subset of the input axioms:
45.02/45.25	  fof(goals_14, negated_conjecture, '==>'(sK2_goals_14_X19, sK3_goals_14_X18)=sK2_goals_14_X19).
45.02/45.25	  fof(goals_14_1, negated_conjecture, '>='('==>'(sK1_goals_14_X17, sK3_goals_14_X18), sK1_goals_14_X17)=true).
45.02/45.25	  fof(goals_14_2, negated_conjecture, '>='(sK2_goals_14_X19, sK1_goals_14_X17)!=true).
45.02/45.25	  fof(ifeq_axiom, axiom, ![A, B, C]: B=ifeq2(A, A, B, C)).
45.02/45.25	  fof(ifeq_axiom_001, axiom, ![A, B, C]: ifeq(A, A, B, C)=B).
45.02/45.25	  fof(sos_01, axiom, ![A, B, C]: '+'('+'(A, B), C)='+'(A, '+'(B, C))).
45.02/45.25	  fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)).
45.02/45.25	  fof(sos_03, axiom, ![A]: A='+'(A, '0')).
45.02/45.25	  fof(sos_07, axiom, ![X4, X3]: ifeq2('>='(X4, X3), true, ifeq2('>='(X3, X4), true, X3, X4), X4)=X4).
45.02/45.25	  fof(sos_08, axiom, ![X6, X5, X7]: ifeq('>='(X6, '==>'(X5, X7)), true, '>='('+'(X5, X6), X7), true)=true).
45.02/45.25	  fof(sos_08_1, axiom, ![X6, X5, X7]: ifeq('>='('+'(X5, X6), X7), true, '>='(X6, '==>'(X5, X7)), true)=true).
45.02/45.25	  fof(sos_09, axiom, ![A]: true='>='(A, '0')).
45.02/45.25	  fof(sos_10, axiom, ![X8, X9, X10]: true=ifeq('>='(X8, X9), true, '>='('+'(X8, X10), '+'(X9, X10)), true)).
45.02/45.25	  fof(sos_11, axiom, ![X11, X12, X13]: ifeq('>='(X11, X12), true, '>='('==>'(X12, X13), '==>'(X11, X13)), true)=true).
45.02/45.25	  fof(sos_12, axiom, ![X14, X15, X16]: true=ifeq('>='(X14, X15), true, '>='('==>'(X16, X14), '==>'(X16, X15)), true)).
45.02/45.25	  fof(sos_13, axiom, ![A, B]: '+'(A, '==>'(A, B))='+'(B, '==>'(B, A))).
45.02/45.25	
45.02/45.25	Now clausify the problem and encode Horn clauses using encoding 3 of
45.02/45.25	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
45.02/45.25	We repeatedly replace C & s=t => u=v by the two clauses:
45.02/45.25	  fresh(y, y, x1...xn) = u
45.02/45.25	  C => fresh(s, t, x1...xn) = v
45.02/45.25	where fresh is a fresh function symbol and x1..xn are the free
45.02/45.25	variables of u and v.
45.02/45.25	A predicate p(X) is encoded as p(X)=true (this is sound, because the
45.02/45.25	input problem has no model of domain size 1).
45.02/45.25	
45.02/45.25	The encoding turns the above axioms into the following unit equations and goals:
45.02/45.25	
45.02/45.25	Axiom 1 (goals_14): sK2_goals_14_X19 ==> sK3_goals_14_X18 = sK2_goals_14_X19.
45.02/45.25	Axiom 2 (sos_08_1): ifeq((X + Y) >= Z, true, Y >= (X ==> Z), true) = true.
45.02/45.25	Axiom 3 (sos_01): (X + Y) + Z = X + (Y + Z).
45.02/45.25	Axiom 4 (goals_14_1): (sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17 = true.
45.02/45.25	Axiom 5 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
45.02/45.25	Axiom 6 (sos_09): true = X >= 0.
45.02/45.25	Axiom 7 (sos_13): X + (X ==> Y) = Y + (Y ==> X).
45.02/45.25	Axiom 8 (sos_12): true = ifeq(X >= Y, true, (Z ==> X) >= (Z ==> Y), true).
45.02/45.25	Axiom 9 (sos_02): X + Y = Y + X.
45.02/45.25	Axiom 10 (sos_11): ifeq(X >= Y, true, (Y ==> Z) >= (X ==> Z), true) = true.
45.02/45.25	Axiom 11 (ifeq_axiom): X = ifeq2(Y, Y, X, Z).
45.02/45.25	Axiom 12 (sos_08): ifeq(X >= (Y ==> Z), true, (Y + X) >= Z, true) = true.
45.02/45.25	Axiom 13 (sos_07): ifeq2(X >= Y, true, ifeq2(Y >= X, true, Y, X), X) = X.
45.02/45.25	Axiom 14 (sos_10): true = ifeq(X >= Y, true, (X + Z) >= (Y + Z), true).
45.02/45.25	Axiom 15 (sos_03): X = X + 0.
45.02/45.25	
45.02/45.25	Lemma 16: 0 + X = X.
45.02/45.25	Proof:
45.02/45.25	  0 + X
45.02/45.25	= { by axiom 9 (sos_02) }
45.02/45.25	  X + 0
45.02/45.25	= { by axiom 15 (sos_03) }
45.02/45.25	  X
45.02/45.25	
45.02/45.25	Lemma 17: (X + Y) >= X = true.
45.02/45.25	Proof:
45.02/45.25	  (X + Y) >= X
45.02/45.25	= { by axiom 9 (sos_02) }
45.02/45.25	  (Y + X) >= X
45.02/45.25	= { by axiom 5 (ifeq_axiom_001) }
45.02/45.25	  ifeq(true, true, (Y + X) >= X, true)
45.02/45.25	= { by axiom 6 (sos_09) }
45.02/45.25	  ifeq(Y >= 0, true, (Y + X) >= X, true)
45.02/45.25	= { by lemma 16 }
45.02/45.25	  ifeq(Y >= 0, true, (Y + X) >= (0 + X), true)
45.02/45.25	= { by axiom 14 (sos_10) }
45.64/45.82	  true
45.64/45.82	
45.64/45.82	Goal 1 (goals_14_2): sK2_goals_14_X19 >= sK1_goals_14_X17 = true.
45.64/45.82	Proof:
45.64/45.82	  sK2_goals_14_X19 >= sK1_goals_14_X17
45.64/45.82	= { by axiom 15 (sos_03) }
45.64/45.82	  (sK2_goals_14_X19 + 0) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 13 (sos_07) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(true, true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 2 (sos_08_1) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) + sK2_goals_14_X19) >= sK1_goals_14_X17, true, sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 9 (sos_02) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(ifeq((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true, sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(ifeq(true, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true), true, sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 8 (sos_12) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(ifeq(ifeq((sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17, true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true), true, sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 4 (goals_14_1) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true), true, sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(ifeq((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true), true, sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 12 (sos_08) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(true, true, sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq(sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 15 (sos_03) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(ifeq((sK2_goals_14_X19 + 0) >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true), true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 2 (sos_08_1) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(true, true, ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 11 (ifeq_axiom) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 6 (sos_09) }
45.64/45.82	  (sK2_goals_14_X19 + ifeq2(true, true, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), 0)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 11 (ifeq_axiom) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 13 (sos_07) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(true, true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 2 (sos_08_1) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK2_goals_14_X19 + (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 9 (sos_02) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK2_goals_14_X19 + ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) + sK1_goals_14_X17)) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 3 (sos_01) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) + sK1_goals_14_X17) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 9 (sos_02) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK1_goals_14_X17 + (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 7 (sos_13) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK1_goals_14_X17 + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 3 (sos_01) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK3_goals_14_X18)) + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 7 (sos_13) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(((sK3_goals_14_X18 + (sK3_goals_14_X18 ==> sK1_goals_14_X17)) + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 3 (sos_01) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK3_goals_14_X18 + ((sK3_goals_14_X18 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 9 (sos_02) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK3_goals_14_X18 + (((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) + (sK3_goals_14_X18 ==> sK1_goals_14_X17))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by lemma 17 }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(true, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 1 (goals_14) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(true, true, (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK2_goals_14_X19, true), true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK2_goals_14_X19, true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 2 (sos_08_1) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(true, true, ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 11 (ifeq_axiom) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(true, true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 2 (sos_08_1) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK1_goals_14_X17 + (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 9 (sos_02) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK1_goals_14_X17 + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) + sK2_goals_14_X19)) >= sK3_goals_14_X18, true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 3 (sos_01) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(ifeq(true, true, ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true), true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by lemma 17 }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(ifeq((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) >= sK2_goals_14_X19, true, ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true), true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 7 (sos_13) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(ifeq((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= sK2_goals_14_X19, true, ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true), true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 1 (goals_14) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(ifeq((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true, ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true), true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 9 (sos_02) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(ifeq((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true, (sK2_goals_14_X19 + (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true), true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 12 (sos_08) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(true, true, (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true), true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 2 (sos_08_1) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(true, true, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 11 (ifeq_axiom) }
45.64/45.82	  (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 7 (sos_13) }
45.64/45.82	  (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) + (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 9 (sos_02) }
45.64/45.82	  ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  ifeq(true, true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 10 (sos_11) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 15 (sos_03) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + 0) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 11 (ifeq_axiom) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(true, true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 2 (sos_08_1) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(ifeq((sK1_goals_14_X17 + 0) >= 0, true, 0 >= (sK1_goals_14_X17 ==> 0), true), true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 6 (sos_09) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(ifeq(true, true, 0 >= (sK1_goals_14_X17 ==> 0), true), true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(0 >= (sK1_goals_14_X17 ==> 0), true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 11 (ifeq_axiom) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(true, true, ifeq2(0 >= (sK1_goals_14_X17 ==> 0), true, 0, sK1_goals_14_X17 ==> 0), sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 6 (sos_09) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2((sK1_goals_14_X17 ==> 0) >= 0, true, ifeq2(0 >= (sK1_goals_14_X17 ==> 0), true, 0, sK1_goals_14_X17 ==> 0), sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 13 (sos_07) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 7 (sos_13) }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 + (0 ==> sK1_goals_14_X17)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by lemma 16 }
45.64/45.82	  ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.82	  ifeq(ifeq(ifeq(true, true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.82	= { by axiom 10 (sos_11) }
45.64/45.83	  ifeq(ifeq(ifeq(ifeq((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= 0, true, (0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.83	= { by axiom 6 (sos_09) }
45.64/45.83	  ifeq(ifeq(ifeq(ifeq(true, true, (0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.83	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.83	  ifeq(ifeq(ifeq((0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.83	= { by axiom 10 (sos_11) }
45.64/45.83	  ifeq(ifeq(true, true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.83	= { by axiom 5 (ifeq_axiom_001) }
45.64/45.83	  ifeq(((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
45.64/45.83	= { by axiom 12 (sos_08) }
45.64/45.83	  true
45.64/45.83	% SZS output end Proof
45.64/45.83	
45.64/45.83	RESULT: Unsatisfiable (the axioms are contradictory).
45.64/45.83	EOF