0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.34	% Computer   : n002.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   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Tue Jul 13 16:19:18 EDT 2021
0.13/0.34	% CPUTime    : 
0.20/0.54	% SZS status Theorem
0.20/0.54	
0.20/0.59	% SZS output start Proof
0.20/0.59	Take the following subset of the input axioms:
0.20/0.59	  fof(goals_15, conjecture, ![X17]: '==>'('==>'('==>'(X17, '1'), X17), X17)='0').
0.20/0.59	  fof(sos_01, axiom, ![A, B, C]: '+'(A, '+'(B, C))='+'('+'(A, B), C)).
0.20/0.59	  fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)).
0.20/0.59	  fof(sos_03, axiom, ![A]: '+'(A, '0')=A).
0.20/0.59	  fof(sos_04, axiom, ![A]: '>='(A, A)).
0.20/0.59	  fof(sos_06, axiom, ![X3, X4]: (X4=X3 <= ('>='(X4, X3) & '>='(X3, X4)))).
0.20/0.59	  fof(sos_07, axiom, ![X5, X6, X7]: ('>='(X6, '==>'(X5, X7)) <=> '>='('+'(X5, X6), X7))).
0.20/0.59	  fof(sos_08, axiom, ![A]: '>='(A, '0')).
0.20/0.59	  fof(sos_09, axiom, ![X8, X9, X10]: ('>='(X8, X9) => '>='('+'(X8, X10), '+'(X9, X10)))).
0.20/0.59	  fof(sos_10, axiom, ![X11, X12, X13]: ('>='('==>'(X12, X13), '==>'(X11, X13)) <= '>='(X11, X12))).
0.20/0.59	  fof(sos_11, axiom, ![X14, X15, X16]: ('>='('==>'(X16, X14), '==>'(X16, X15)) <= '>='(X14, X15))).
0.20/0.59	  fof(sos_12, axiom, ![A]: '+'(A, '1')='1').
0.20/0.59	  fof(sos_13, axiom, ![A, B]: '==>'('==>'(B, A), A)='==>'('==>'(A, B), B)).
0.20/0.59	  fof(sos_14, axiom, ![A]: A='+'(A, A)).
0.20/0.59	
0.20/0.59	Now clausify the problem and encode Horn clauses using encoding 3 of
0.20/0.59	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.20/0.59	We repeatedly replace C & s=t => u=v by the two clauses:
0.20/0.59	  fresh(y, y, x1...xn) = u
0.20/0.59	  C => fresh(s, t, x1...xn) = v
0.20/0.59	where fresh is a fresh function symbol and x1..xn are the free
0.20/0.59	variables of u and v.
0.20/0.59	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.20/0.59	input problem has no model of domain size 1).
0.20/0.59	
0.20/0.59	The encoding turns the above axioms into the following unit equations and goals:
0.20/0.59	
0.20/0.59	Axiom 1 (sos_04): X >= X = true.
0.20/0.59	Axiom 2 (sos_08): X >= 0 = true.
0.20/0.59	Axiom 3 (sos_14): X = X + X.
0.20/0.59	Axiom 4 (sos_02): X + Y = Y + X.
0.20/0.59	Axiom 5 (sos_12): X + 1 = 1.
0.20/0.59	Axiom 6 (sos_03): X + 0 = X.
0.20/0.59	Axiom 7 (sos_13): (X ==> Y) ==> Y = (Y ==> X) ==> X.
0.20/0.59	Axiom 8 (sos_01): X + (Y + Z) = (X + Y) + Z.
0.20/0.59	Axiom 9 (sos_06): fresh(X, X, Y, Z) = Y.
0.20/0.59	Axiom 10 (sos_06): fresh2(X, X, Y, Z) = Z.
0.20/0.59	Axiom 11 (sos_07_1): fresh9(X, X, Y, Z, W) = true.
0.20/0.59	Axiom 12 (sos_07): fresh8(X, X, Y, Z, W) = true.
0.20/0.59	Axiom 13 (sos_09): fresh5(X, X, Y, Z, W) = true.
0.20/0.59	Axiom 14 (sos_10): fresh4(X, X, Y, Z, W) = true.
0.20/0.59	Axiom 15 (sos_11): fresh3(X, X, Y, Z, W) = true.
0.20/0.59	Axiom 16 (sos_06): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X).
0.20/0.59	Axiom 17 (sos_09): fresh5(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z).
0.20/0.59	Axiom 18 (sos_10): fresh4(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z).
0.20/0.59	Axiom 19 (sos_11): fresh3(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y).
0.20/0.59	Axiom 20 (sos_07_1): fresh9((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z).
0.20/0.59	Axiom 21 (sos_07): fresh8(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z.
0.20/0.59	
0.20/0.59	Lemma 22: 0 + X = X.
0.20/0.59	Proof:
0.20/0.59	  0 + X
0.20/0.59	= { by axiom 4 (sos_02) R->L }
0.20/0.59	  X + 0
0.20/0.59	= { by axiom 6 (sos_03) }
0.20/0.59	  X
0.20/0.59	
0.20/0.59	Lemma 23: (X + (X ==> Y)) >= Y = true.
0.20/0.59	Proof:
0.20/0.59	  (X + (X ==> Y)) >= Y
0.20/0.59	= { by axiom 21 (sos_07) R->L }
0.20/0.59	  fresh8((X ==> Y) >= (X ==> Y), true, X, X ==> Y, Y)
0.20/0.59	= { by axiom 1 (sos_04) }
0.20/0.59	  fresh8(true, true, X, X ==> Y, Y)
0.20/0.59	= { by axiom 12 (sos_07) }
0.20/0.59	  true
0.20/0.59	
0.20/0.59	Lemma 24: X >= (Y ==> X) = true.
0.20/0.59	Proof:
0.20/0.59	  X >= (Y ==> X)
0.20/0.59	= { by axiom 20 (sos_07_1) R->L }
0.20/0.59	  fresh9((Y + X) >= X, true, Y, X, X)
0.20/0.59	= { by lemma 22 R->L }
0.20/0.59	  fresh9((Y + X) >= (0 + X), true, Y, X, X)
0.20/0.59	= { by axiom 17 (sos_09) R->L }
0.20/0.59	  fresh9(fresh5(Y >= 0, true, Y, 0, X), true, Y, X, X)
0.20/0.59	= { by axiom 2 (sos_08) }
0.20/0.59	  fresh9(fresh5(true, true, Y, 0, X), true, Y, X, X)
0.20/0.59	= { by axiom 13 (sos_09) }
0.20/0.59	  fresh9(true, true, Y, X, X)
0.20/0.59	= { by axiom 11 (sos_07_1) }
0.20/0.59	  true
0.20/0.59	
0.20/0.59	Lemma 25: 0 ==> X = X.
0.20/0.59	Proof:
0.20/0.59	  0 ==> X
0.20/0.59	= { by axiom 10 (sos_06) R->L }
0.20/0.59	  fresh2(true, true, X, 0 ==> X)
0.20/0.59	= { by lemma 23 R->L }
0.20/0.59	  fresh2((0 + (0 ==> X)) >= X, true, X, 0 ==> X)
0.20/0.59	= { by lemma 22 }
0.20/0.59	  fresh2((0 ==> X) >= X, true, X, 0 ==> X)
0.20/0.59	= { by axiom 16 (sos_06) }
0.20/0.59	  fresh(X >= (0 ==> X), true, X, 0 ==> X)
0.20/0.59	= { by lemma 24 }
0.20/0.59	  fresh(true, true, X, 0 ==> X)
0.20/0.59	= { by axiom 9 (sos_06) }
0.20/0.59	  X
0.20/0.59	
0.20/0.59	Lemma 26: (X ==> 1) >= (X ==> Y) = true.
0.20/0.59	Proof:
0.20/0.59	  (X ==> 1) >= (X ==> Y)
0.20/0.59	= { by axiom 19 (sos_11) R->L }
0.20/0.59	  fresh3(1 >= Y, true, 1, Y, X)
0.20/0.59	= { by axiom 5 (sos_12) R->L }
0.20/0.59	  fresh3(((1 ==> Y) + 1) >= Y, true, 1, Y, X)
0.20/0.59	= { by axiom 4 (sos_02) }
0.20/0.59	  fresh3((1 + (1 ==> Y)) >= Y, true, 1, Y, X)
0.20/0.59	= { by lemma 23 }
0.20/0.59	  fresh3(true, true, 1, Y, X)
0.20/0.59	= { by axiom 15 (sos_11) }
0.20/0.59	  true
0.20/0.59	
0.20/0.59	Lemma 27: fresh9(X >= Y, true, X, 0, Y) = 0 >= (X ==> Y).
0.20/0.59	Proof:
0.20/0.59	  fresh9(X >= Y, true, X, 0, Y)
0.20/0.59	= { by axiom 6 (sos_03) R->L }
0.20/0.59	  fresh9((X + 0) >= Y, true, X, 0, Y)
0.20/0.59	= { by axiom 20 (sos_07_1) }
0.20/0.59	  0 >= (X ==> Y)
0.20/0.59	
0.20/0.59	Goal 1 (goals_15): ((x17 ==> 1) ==> x17) ==> x17 = 0.
0.20/0.59	Proof:
0.20/0.59	  ((x17 ==> 1) ==> x17) ==> x17
0.20/0.59	= { by lemma 25 R->L }
0.20/0.59	  0 ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.59	= { by axiom 10 (sos_06) R->L }
0.20/0.59	  fresh2(true, true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 11 (sos_07_1) R->L }
0.20/0.60	  fresh2(fresh9(true, true, 0 ==> (x17 ==> 1), 0, (x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 14 (sos_10) R->L }
0.20/0.60	  fresh2(fresh9(fresh4(true, true, x17 ==> (x17 ==> 1), 0, x17 ==> 1), true, 0 ==> (x17 ==> 1), 0, (x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 2 (sos_08) R->L }
0.20/0.60	  fresh2(fresh9(fresh4((x17 ==> (x17 ==> 1)) >= 0, true, x17 ==> (x17 ==> 1), 0, x17 ==> 1), true, 0 ==> (x17 ==> 1), 0, (x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 18 (sos_10) }
0.20/0.60	  fresh2(fresh9((0 ==> (x17 ==> 1)) >= ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), true, 0 ==> (x17 ==> 1), 0, (x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by lemma 27 }
0.20/0.60	  fresh2(0 >= ((0 ==> (x17 ==> 1)) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1))), true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by lemma 25 }
0.20/0.60	  fresh2(0 >= ((x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1))), true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 16 (sos_06) }
0.20/0.60	  fresh(((x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1))) >= 0, true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 2 (sos_08) }
0.20/0.60	  fresh(true, true, (x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)), 0) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 9 (sos_06) }
0.20/0.60	  ((x17 ==> 1) ==> ((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1))) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 7 (sos_13) R->L }
0.20/0.60	  ((x17 ==> 1) ==> (((x17 ==> 1) ==> x17) ==> x17)) ==> (((x17 ==> 1) ==> x17) ==> x17)
0.20/0.60	= { by axiom 7 (sos_13) R->L }
0.20/0.60	  ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 10 (sos_06) R->L }
0.20/0.60	  fresh2(true, true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by lemma 23 R->L }
0.20/0.60	  fresh2((((x17 ==> 1) ==> (x17 ==> (x17 ==> 1))) + (((x17 ==> 1) ==> (x17 ==> (x17 ==> 1))) ==> (x17 ==> (x17 ==> 1)))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 7 (sos_13) }
0.20/0.60	  fresh2((((x17 ==> 1) ==> (x17 ==> (x17 ==> 1))) + (((x17 ==> (x17 ==> 1)) ==> (x17 ==> 1)) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 7 (sos_13) R->L }
0.20/0.60	  fresh2((((x17 ==> 1) ==> (x17 ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 9 (sos_06) R->L }
0.20/0.60	  fresh2((fresh(true, true, (x17 ==> 1) ==> (x17 ==> (x17 ==> 1)), 0) + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 2 (sos_08) R->L }
0.20/0.60	  fresh2((fresh(((x17 ==> 1) ==> (x17 ==> (x17 ==> 1))) >= 0, true, (x17 ==> 1) ==> (x17 ==> (x17 ==> 1)), 0) + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 16 (sos_06) R->L }
0.20/0.60	  fresh2((fresh2(0 >= ((x17 ==> 1) ==> (x17 ==> (x17 ==> 1))), true, (x17 ==> 1) ==> (x17 ==> (x17 ==> 1)), 0) + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by lemma 27 R->L }
0.20/0.60	  fresh2((fresh2(fresh9((x17 ==> 1) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, 0, x17 ==> (x17 ==> 1)), true, (x17 ==> 1) ==> (x17 ==> (x17 ==> 1)), 0) + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by lemma 26 }
0.20/0.60	  fresh2((fresh2(fresh9(true, true, x17 ==> 1, 0, x17 ==> (x17 ==> 1)), true, (x17 ==> 1) ==> (x17 ==> (x17 ==> 1)), 0) + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 11 (sos_07_1) }
0.20/0.60	  fresh2((fresh2(true, true, (x17 ==> 1) ==> (x17 ==> (x17 ==> 1)), 0) + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 10 (sos_06) }
0.20/0.60	  fresh2((0 + ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1))) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by lemma 22 }
0.20/0.60	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 10 (sos_06) R->L }
0.20/0.60	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2(true, true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 11 (sos_07_1) R->L }
0.20/0.60	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2(fresh9(true, true, x17, x17 ==> (x17 ==> 1), 1), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 12 (sos_07) R->L }
0.20/0.60	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2(fresh9(fresh8(true, true, x17, x17 + (x17 ==> (x17 ==> 1)), 1), true, x17, x17 ==> (x17 ==> 1), 1), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by lemma 23 R->L }
0.20/0.60	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2(fresh9(fresh8((x17 + (x17 ==> (x17 ==> 1))) >= (x17 ==> 1), true, x17, x17 + (x17 ==> (x17 ==> 1)), 1), true, x17, x17 ==> (x17 ==> 1), 1), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 21 (sos_07) }
0.20/0.60	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2(fresh9((x17 + (x17 + (x17 ==> (x17 ==> 1)))) >= 1, true, x17, x17 ==> (x17 ==> 1), 1), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 8 (sos_01) }
0.20/0.60	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2(fresh9(((x17 + x17) + (x17 ==> (x17 ==> 1))) >= 1, true, x17, x17 ==> (x17 ==> 1), 1), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.60	= { by axiom 3 (sos_14) R->L }
0.20/0.61	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2(fresh9((x17 + (x17 ==> (x17 ==> 1))) >= 1, true, x17, x17 ==> (x17 ==> 1), 1), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.61	= { by axiom 20 (sos_07_1) }
0.20/0.61	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh2((x17 ==> (x17 ==> 1)) >= (x17 ==> 1), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.61	= { by axiom 16 (sos_06) }
0.20/0.61	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh((x17 ==> 1) >= (x17 ==> (x17 ==> 1)), true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.61	= { by lemma 26 }
0.20/0.61	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= fresh(true, true, x17 ==> 1, x17 ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.61	= { by axiom 9 (sos_06) }
0.20/0.61	  fresh2(((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) >= (x17 ==> 1), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.61	= { by axiom 16 (sos_06) }
0.20/0.61	  fresh((x17 ==> 1) >= ((((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)), true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.61	= { by lemma 24 }
0.20/0.61	  fresh(true, true, x17 ==> 1, (((x17 ==> 1) ==> x17) ==> x17) ==> (x17 ==> 1)) ==> (x17 ==> 1)
0.20/0.61	= { by axiom 9 (sos_06) }
0.20/0.61	  (x17 ==> 1) ==> (x17 ==> 1)
0.20/0.61	= { by lemma 22 R->L }
0.20/0.61	  (x17 ==> 1) ==> (0 + (x17 ==> 1))
0.20/0.61	= { by axiom 10 (sos_06) R->L }
0.20/0.61	  fresh2(true, true, 0, (x17 ==> 1) ==> (0 + (x17 ==> 1)))
0.20/0.61	= { by axiom 2 (sos_08) R->L }
0.20/0.61	  fresh2(((x17 ==> 1) ==> (0 + (x17 ==> 1))) >= 0, true, 0, (x17 ==> 1) ==> (0 + (x17 ==> 1)))
0.20/0.61	= { by axiom 16 (sos_06) }
0.20/0.61	  fresh(0 >= ((x17 ==> 1) ==> (0 + (x17 ==> 1))), true, 0, (x17 ==> 1) ==> (0 + (x17 ==> 1)))
0.20/0.61	= { by axiom 4 (sos_02) R->L }
0.20/0.61	  fresh(0 >= ((x17 ==> 1) ==> ((x17 ==> 1) + 0)), true, 0, (x17 ==> 1) ==> (0 + (x17 ==> 1)))
0.20/0.61	= { by axiom 20 (sos_07_1) R->L }
0.20/0.61	  fresh(fresh9(((x17 ==> 1) + 0) >= ((x17 ==> 1) + 0), true, x17 ==> 1, 0, (x17 ==> 1) + 0), true, 0, (x17 ==> 1) ==> (0 + (x17 ==> 1)))
0.20/0.61	= { by axiom 1 (sos_04) }
0.20/0.61	  fresh(fresh9(true, true, x17 ==> 1, 0, (x17 ==> 1) + 0), true, 0, (x17 ==> 1) ==> (0 + (x17 ==> 1)))
0.20/0.61	= { by axiom 11 (sos_07_1) }
0.20/0.61	  fresh(true, true, 0, (x17 ==> 1) ==> (0 + (x17 ==> 1)))
0.20/0.61	= { by axiom 9 (sos_06) }
0.20/0.61	  0
0.20/0.61	% SZS output end Proof
0.20/0.61	
0.20/0.61	RESULT: Theorem (the conjecture is true).
1.87/0.61	EOF