0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n011.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 12:33:57 EDT 2019
0.19/0.33	% CPUTime    : 
13.14/13.34	% SZS status Unsatisfiable
13.14/13.34	
13.14/13.34	% SZS output start Proof
13.14/13.34	Take the following subset of the input axioms:
13.57/13.75	  fof(additive_associativity, axiom, ![A, B, C]: addition(addition(A, B), C)=addition(A, addition(B, C))).
13.57/13.75	  fof(additive_commutativity, axiom, ![A, B]: addition(B, A)=addition(A, B)).
13.57/13.75	  fof(distributivity1, axiom, ![A, B, C]: multiplication(A, addition(B, C))=addition(multiplication(A, B), multiplication(A, C))).
13.57/13.75	  fof(distributivity2, axiom, ![A, B, C]: multiplication(addition(A, B), C)=addition(multiplication(A, C), multiplication(B, C))).
13.57/13.75	  fof(goals, negated_conjecture, star(strong_iteration(sK1_goals_X0))!=strong_iteration(sK1_goals_X0)).
13.57/13.75	  fof(idempotence, axiom, ![A]: A=addition(A, A)).
13.57/13.75	  fof(ifeq_axiom, axiom, ![A, B, C]: ifeq3(A, A, B, C)=B).
13.57/13.75	  fof(ifeq_axiom_001, axiom, ![A, B, C]: B=ifeq2(A, A, B, C)).
13.57/13.75	  fof(ifeq_axiom_002, axiom, ![A, B, C]: ifeq(A, A, B, C)=B).
13.57/13.75	  fof(infty_unfold1, axiom, ![A]: strong_iteration(A)=addition(multiplication(A, strong_iteration(A)), one)).
13.57/13.76	  fof(isolation, axiom, ![A]: addition(star(A), multiplication(strong_iteration(A), zero))=strong_iteration(A)).
13.57/13.76	  fof(left_annihilation, axiom, ![A]: multiplication(zero, A)=zero).
13.57/13.76	  fof(multiplicative_associativity, axiom, ![A, B, C]: multiplication(multiplication(A, B), C)=multiplication(A, multiplication(B, C))).
13.57/13.76	  fof(multiplicative_left_identity, axiom, ![A]: A=multiplication(one, A)).
13.57/13.76	  fof(multiplicative_right_identity, axiom, ![A]: A=multiplication(A, one)).
13.57/13.76	  fof(order, axiom, ![A, B]: ifeq3(addition(A, B), B, leq(A, B), true)=true).
13.57/13.76	  fof(order_1, axiom, ![A, B]: B=ifeq2(leq(A, B), true, addition(A, B), B)).
13.57/13.76	  fof(star_induction1, axiom, ![A, B, C]: ifeq(leq(addition(multiplication(A, C), B), C), true, leq(multiplication(star(A), B), C), true)=true).
13.57/13.76	  fof(star_unfold1, axiom, ![A]: star(A)=addition(one, multiplication(A, star(A)))).
13.57/13.76	  fof(star_unfold2, axiom, ![A]: addition(one, multiplication(star(A), A))=star(A)).
13.57/13.76	
13.57/13.76	Now clausify the problem and encode Horn clauses using encoding 3 of
13.57/13.76	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
13.57/13.76	We repeatedly replace C & s=t => u=v by the two clauses:
13.57/13.76	  fresh(y, y, x1...xn) = u
13.57/13.76	  C => fresh(s, t, x1...xn) = v
13.57/13.76	where fresh is a fresh function symbol and x1..xn are the free
13.57/13.76	variables of u and v.
13.57/13.76	A predicate p(X) is encoded as p(X)=true (this is sound, because the
13.57/13.76	input problem has no model of domain size 1).
13.57/13.76	
13.57/13.76	The encoding turns the above axioms into the following unit equations and goals:
13.57/13.76	
13.57/13.76	Axiom 1 (idempotence): X = addition(X, X).
13.57/13.76	Axiom 2 (left_annihilation): multiplication(zero, X) = zero.
13.57/13.76	Axiom 3 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
13.57/13.76	Axiom 4 (order_1): X = ifeq2(leq(Y, X), true, addition(Y, X), X).
13.57/13.76	Axiom 5 (ifeq_axiom_002): ifeq(X, X, Y, Z) = Y.
13.57/13.76	Axiom 6 (star_induction1): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
13.57/13.76	Axiom 7 (multiplicative_right_identity): X = multiplication(X, one).
13.57/13.76	Axiom 8 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
13.57/13.76	Axiom 9 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
13.57/13.76	Axiom 10 (ifeq_axiom_001): X = ifeq2(Y, Y, X, Z).
13.57/13.76	Axiom 11 (additive_commutativity): addition(X, Y) = addition(Y, X).
13.57/13.76	Axiom 12 (isolation): addition(star(X), multiplication(strong_iteration(X), zero)) = strong_iteration(X).
13.57/13.76	Axiom 13 (distributivity1): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
13.57/13.76	Axiom 14 (additive_associativity): addition(addition(X, Y), Z) = addition(X, addition(Y, Z)).
13.57/13.76	Axiom 15 (multiplicative_left_identity): X = multiplication(one, X).
13.57/13.76	Axiom 16 (star_unfold1): star(X) = addition(one, multiplication(X, star(X))).
13.57/13.76	Axiom 17 (star_unfold2): addition(one, multiplication(star(X), X)) = star(X).
13.57/13.76	Axiom 18 (multiplicative_associativity): multiplication(multiplication(X, Y), Z) = multiplication(X, multiplication(Y, Z)).
13.57/13.76	Axiom 19 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
13.57/13.76	
13.57/13.76	Lemma 20: addition(X, addition(X, Y)) = addition(X, Y).
13.57/13.76	Proof:
13.57/13.76	  addition(X, addition(X, Y))
13.57/13.76	= { by axiom 14 (additive_associativity) }
13.57/13.76	  addition(addition(X, X), Y)
13.57/13.76	= { by axiom 1 (idempotence) }
13.57/13.76	  addition(X, Y)
13.57/13.76	
13.57/13.76	Lemma 21: addition(one, star(X)) = star(X).
13.57/13.76	Proof:
13.57/13.76	  addition(one, star(X))
13.57/13.76	= { by axiom 16 (star_unfold1) }
13.57/13.76	  addition(one, addition(one, multiplication(X, star(X))))
13.57/13.76	= { by lemma 20 }
13.57/13.76	  addition(one, multiplication(X, star(X)))
13.57/13.76	= { by axiom 16 (star_unfold1) }
13.57/13.76	  star(X)
13.57/13.76	
13.57/13.76	Lemma 22: addition(Y, multiplication(X, Y)) = multiplication(addition(X, one), Y).
13.57/13.76	Proof:
13.57/13.76	  addition(Y, multiplication(X, Y))
13.57/13.76	= { by axiom 15 (multiplicative_left_identity) }
13.57/13.76	  addition(multiplication(one, Y), multiplication(X, Y))
13.57/13.76	= { by axiom 19 (distributivity2) }
13.57/13.76	  multiplication(addition(one, X), Y)
13.57/13.76	= { by axiom 11 (additive_commutativity) }
13.57/13.76	  multiplication(addition(X, one), Y)
13.57/13.76	
13.57/13.76	Lemma 23: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
13.57/13.76	Proof:
13.57/13.76	  addition(X, multiplication(X, Y))
13.57/13.76	= { by axiom 7 (multiplicative_right_identity) }
13.57/13.76	  addition(multiplication(X, one), multiplication(X, Y))
13.57/13.76	= { by axiom 13 (distributivity1) }
13.57/13.76	  multiplication(X, addition(one, Y))
13.57/13.76	= { by axiom 11 (additive_commutativity) }
13.57/13.76	  multiplication(X, addition(Y, one))
13.57/13.76	
13.57/13.76	Lemma 24: leq(X, addition(X, Y)) = true.
13.57/13.76	Proof:
13.57/13.76	  leq(X, addition(X, Y))
13.57/13.76	= { by axiom 8 (ifeq_axiom) }
13.57/13.76	  ifeq3(addition(X, Y), addition(X, Y), leq(X, addition(X, Y)), true)
13.57/13.76	= { by lemma 20 }
13.57/13.76	  ifeq3(addition(X, addition(X, Y)), addition(X, Y), leq(X, addition(X, Y)), true)
13.57/13.76	= { by axiom 9 (order) }
13.57/13.76	  true
13.57/13.76	
13.57/13.76	Lemma 25: addition(Z, multiplication(X, multiplication(Y, Z))) = multiplication(addition(one, multiplication(X, Y)), Z).
13.57/13.76	Proof:
13.57/13.76	  addition(Z, multiplication(X, multiplication(Y, Z)))
13.57/13.76	= { by axiom 18 (multiplicative_associativity) }
13.57/13.76	  addition(Z, multiplication(multiplication(X, Y), Z))
13.57/13.76	= { by lemma 22 }
13.57/13.76	  multiplication(addition(multiplication(X, Y), one), Z)
13.57/13.76	= { by axiom 11 (additive_commutativity) }
13.57/13.76	  multiplication(addition(one, multiplication(X, Y)), Z)
13.57/13.76	
13.57/13.76	Lemma 26: ifeq2(leq(Y, X), true, addition(X, Y), X) = X.
13.57/13.76	Proof:
13.57/13.76	  ifeq2(leq(Y, X), true, addition(X, Y), X)
13.57/13.76	= { by axiom 11 (additive_commutativity) }
13.57/13.76	  ifeq2(leq(Y, X), true, addition(Y, X), X)
13.57/13.76	= { by axiom 4 (order_1) }
13.57/13.76	  X
13.57/13.76	
13.57/13.76	Lemma 27: addition(one, multiplication(star(X), addition(X, Y))) = multiplication(star(X), addition(Y, one)).
13.57/13.76	Proof:
13.57/13.76	  addition(one, multiplication(star(X), addition(X, Y)))
13.57/13.76	= { by axiom 13 (distributivity1) }
13.57/13.76	  addition(one, addition(multiplication(star(X), X), multiplication(star(X), Y)))
13.57/13.76	= { by axiom 14 (additive_associativity) }
13.57/13.76	  addition(addition(one, multiplication(star(X), X)), multiplication(star(X), Y))
13.57/13.76	= { by axiom 17 (star_unfold2) }
13.57/13.76	  addition(star(X), multiplication(star(X), Y))
13.57/13.76	= { by lemma 23 }
13.57/13.76	  multiplication(star(X), addition(Y, one))
13.57/13.76	
13.57/13.76	Lemma 28: addition(one, multiplication(X, strong_iteration(X))) = strong_iteration(X).
13.57/13.76	Proof:
13.57/13.76	  addition(one, multiplication(X, strong_iteration(X)))
13.57/13.76	= { by axiom 11 (additive_commutativity) }
13.57/13.76	  addition(multiplication(X, strong_iteration(X)), one)
13.57/13.76	= { by axiom 3 (infty_unfold1) }
13.57/13.76	  strong_iteration(X)
13.57/13.76	
13.57/13.76	Lemma 29: addition(X, addition(Y, Z)) = addition(Z, addition(X, Y)).
13.57/13.76	Proof:
13.57/13.76	  addition(X, addition(Y, Z))
13.57/13.76	= { by axiom 14 (additive_associativity) }
13.57/13.76	  addition(addition(X, Y), Z)
13.57/13.76	= { by axiom 11 (additive_commutativity) }
13.97/14.16	  addition(Z, addition(X, Y))
13.97/14.16	
13.97/14.16	Goal 1 (goals): star(strong_iteration(sK1_goals_X0)) = strong_iteration(sK1_goals_X0).
13.97/14.16	Proof:
13.97/14.16	  star(strong_iteration(sK1_goals_X0))
13.97/14.16	= { by axiom 4 (order_1) }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by axiom 16 (star_unfold1) }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), addition(one, multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by axiom 1 (idempotence) }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), addition(one, addition(multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0)))))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by axiom 14 (additive_associativity) }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), addition(addition(one, multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0)))), multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by axiom 16 (star_unfold1) }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), addition(star(strong_iteration(sK1_goals_X0)), multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by lemma 22 }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), multiplication(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0)))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by axiom 16 (star_unfold1) }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), multiplication(addition(strong_iteration(sK1_goals_X0), one), addition(one, multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0)))))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by axiom 11 (additive_commutativity) }
13.97/14.16	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), multiplication(addition(strong_iteration(sK1_goals_X0), one), addition(multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), one))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.16	= { by lemma 23 }
13.97/14.17	  ifeq2(leq(addition(strong_iteration(sK1_goals_X0), one), addition(addition(strong_iteration(sK1_goals_X0), one), multiplication(addition(strong_iteration(sK1_goals_X0), one), multiplication(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0)))))), true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.17	= { by lemma 24 }
13.97/14.17	  ifeq2(true, true, addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0))), star(strong_iteration(sK1_goals_X0)))
13.97/14.17	= { by axiom 10 (ifeq_axiom_001) }
13.97/14.17	  addition(addition(strong_iteration(sK1_goals_X0), one), star(strong_iteration(sK1_goals_X0)))
13.97/14.17	= { by axiom 14 (additive_associativity) }
13.97/14.17	  addition(strong_iteration(sK1_goals_X0), addition(one, star(strong_iteration(sK1_goals_X0))))
13.97/14.17	= { by lemma 21 }
13.97/14.17	  addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0)))
13.97/14.17	= { by axiom 10 (ifeq_axiom_001) }
13.97/14.17	  ifeq2(true, true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 6 (star_induction1) }
13.97/14.17	  ifeq2(ifeq(leq(addition(multiplication(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 11 (additive_commutativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 12 (isolation) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(star(sK1_goals_X0), multiplication(strong_iteration(sK1_goals_X0), zero)), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 11 (additive_commutativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(multiplication(strong_iteration(sK1_goals_X0), zero), star(sK1_goals_X0)), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 28 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(multiplication(strong_iteration(sK1_goals_X0), zero), star(sK1_goals_X0)), addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 20 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(multiplication(strong_iteration(sK1_goals_X0), zero), star(sK1_goals_X0)), addition(one, addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 28 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(multiplication(strong_iteration(sK1_goals_X0), zero), star(sK1_goals_X0)), addition(one, strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 11 (additive_commutativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(multiplication(strong_iteration(sK1_goals_X0), zero), star(sK1_goals_X0)), addition(strong_iteration(sK1_goals_X0), one))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 19 (distributivity2) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(multiplication(multiplication(strong_iteration(sK1_goals_X0), zero), addition(strong_iteration(sK1_goals_X0), one)), multiplication(star(sK1_goals_X0), addition(strong_iteration(sK1_goals_X0), one)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 18 (multiplicative_associativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(multiplication(strong_iteration(sK1_goals_X0), multiplication(zero, addition(strong_iteration(sK1_goals_X0), one))), multiplication(star(sK1_goals_X0), addition(strong_iteration(sK1_goals_X0), one)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 2 (left_annihilation) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(multiplication(strong_iteration(sK1_goals_X0), zero), multiplication(star(sK1_goals_X0), addition(strong_iteration(sK1_goals_X0), one)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 23 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(multiplication(strong_iteration(sK1_goals_X0), zero), addition(star(sK1_goals_X0), multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0))))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 29 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)), addition(multiplication(strong_iteration(sK1_goals_X0), zero), star(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 29 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(star(sK1_goals_X0), addition(multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)), multiplication(strong_iteration(sK1_goals_X0), zero)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 14 (additive_associativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(addition(star(sK1_goals_X0), multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0))), multiplication(strong_iteration(sK1_goals_X0), zero))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 11 (additive_commutativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(addition(multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)), star(sK1_goals_X0)), multiplication(strong_iteration(sK1_goals_X0), zero))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 14 (additive_associativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)), addition(star(sK1_goals_X0), multiplication(strong_iteration(sK1_goals_X0), zero)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 12 (isolation) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 11 (additive_commutativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(strong_iteration(sK1_goals_X0), multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 22 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(star(sK1_goals_X0), one), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 11 (additive_commutativity) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(addition(one, star(sK1_goals_X0)), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 21 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 3 (infty_unfold1) }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(star(sK1_goals_X0), addition(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), one))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 27 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, addition(one, multiplication(star(sK1_goals_X0), addition(sK1_goals_X0, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 20 }
13.97/14.17	  ifeq2(ifeq(leq(addition(one, multiplication(star(sK1_goals_X0), addition(sK1_goals_X0, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 27 }
13.97/14.17	  ifeq2(ifeq(leq(multiplication(star(sK1_goals_X0), addition(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), one)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 16 (star_unfold1) }
13.97/14.17	  ifeq2(ifeq(leq(multiplication(addition(one, multiplication(sK1_goals_X0, star(sK1_goals_X0))), addition(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), one)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 3 (infty_unfold1) }
13.97/14.17	  ifeq2(ifeq(leq(multiplication(addition(one, multiplication(sK1_goals_X0, star(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 25 }
13.97/14.17	  ifeq2(ifeq(leq(addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 10 (ifeq_axiom_001) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(true, true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 6 (star_induction1) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(leq(addition(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(sK1_goals_X0), multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 1 (idempotence) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(leq(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(sK1_goals_X0), multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 3 (infty_unfold1) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(leq(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), addition(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), one)), true, leq(multiplication(star(sK1_goals_X0), multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 24 }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(star(sK1_goals_X0), multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 18 (multiplicative_associativity) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(multiplication(star(sK1_goals_X0), sK1_goals_X0), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 16 (star_unfold1) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(multiplication(addition(one, multiplication(sK1_goals_X0, star(sK1_goals_X0))), sK1_goals_X0), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 25 }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(addition(sK1_goals_X0, multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), sK1_goals_X0))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 23 }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(multiplication(sK1_goals_X0, addition(multiplication(star(sK1_goals_X0), sK1_goals_X0), one)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 11 (additive_commutativity) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(multiplication(sK1_goals_X0, addition(one, multiplication(star(sK1_goals_X0), sK1_goals_X0))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 17 (star_unfold2) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(multiplication(sK1_goals_X0, star(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 18 (multiplicative_associativity) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(ifeq(true, true, leq(multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 5 (ifeq_axiom_002) }
13.97/14.17	  ifeq2(ifeq(leq(ifeq2(leq(multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, addition(strong_iteration(sK1_goals_X0), multiplication(sK1_goals_X0, multiplication(star(sK1_goals_X0), strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 26 }
13.97/14.17	  ifeq2(ifeq(leq(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 8 (ifeq_axiom) }
13.97/14.17	  ifeq2(ifeq(ifeq3(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0), leq(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), true), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 1 (idempotence) }
13.97/14.17	  ifeq2(ifeq(ifeq3(addition(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0), leq(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), true), true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 9 (order) }
13.97/14.17	  ifeq2(ifeq(true, true, leq(multiplication(star(strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 7 (multiplicative_right_identity) }
13.97/14.17	  ifeq2(ifeq(true, true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by axiom 5 (ifeq_axiom_002) }
13.97/14.17	  ifeq2(leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0))
13.97/14.17	= { by lemma 26 }
13.97/14.17	  strong_iteration(sK1_goals_X0)
13.97/14.17	% SZS output end Proof
13.97/14.17	
13.97/14.17	RESULT: Unsatisfiable (the axioms are contradictory).
13.97/14.18	EOF