0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% 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 11:54:57 EDT 2019
0.12/0.34	% CPUTime    : 
29.63/29.82	% SZS status Unsatisfiable
29.63/29.82	
29.63/29.82	% SZS output start Proof
29.63/29.82	Take the following subset of the input axioms:
29.93/30.09	  fof(additive_associativity, axiom, ![A, B, C]: addition(addition(A, B), C)=addition(A, addition(B, C))).
29.93/30.09	  fof(additive_commutativity, axiom, ![A, B]: addition(B, A)=addition(A, B)).
29.93/30.09	  fof(additive_idempotence, axiom, ![A]: addition(A, A)=A).
29.93/30.09	  fof(goals, negated_conjecture, tuple(leq(star(addition(one, sK2_goals_X0)), star(sK2_goals_X0)), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))!=tuple(true, true)).
29.93/30.09	  fof(ifeq_axiom, axiom, ![A, B, C]: B=ifeq3(A, A, B, C)).
29.93/30.09	  fof(ifeq_axiom_001, axiom, ![A, B, C]: ifeq2(A, A, B, C)=B).
29.93/30.09	  fof(ifeq_axiom_002, axiom, ![A, B, C]: ifeq(A, A, B, C)=B).
29.93/30.09	  fof(left_distributivity, axiom, ![A, B, C]: addition(multiplication(A, C), multiplication(B, C))=multiplication(addition(A, B), C)).
29.93/30.09	  fof(multiplicative_associativity, axiom, ![A, B, C]: multiplication(A, multiplication(B, C))=multiplication(multiplication(A, B), C)).
29.93/30.09	  fof(multiplicative_left_identity, axiom, ![A]: multiplication(one, A)=A).
29.93/30.09	  fof(multiplicative_right_identity, axiom, ![A]: multiplication(A, one)=A).
29.93/30.09	  fof(order, axiom, ![A, B]: true=ifeq3(addition(A, B), B, leq(A, B), true)).
29.93/30.09	  fof(order_1, axiom, ![A, B]: ifeq2(leq(A, B), true, addition(A, B), B)=B).
29.93/30.09	  fof(right_distributivity, axiom, ![A, B, C]: addition(multiplication(A, B), multiplication(A, C))=multiplication(A, addition(B, C))).
29.93/30.09	  fof(star_induction_right, axiom, ![A, B, C]: ifeq(leq(addition(multiplication(A, B), C), A), true, leq(multiplication(C, star(B)), A), true)=true).
29.93/30.09	  fof(star_unfold_left, axiom, ![A]: true=leq(addition(one, multiplication(star(A), A)), star(A))).
29.93/30.09	  fof(star_unfold_right, axiom, ![A]: leq(addition(one, multiplication(A, star(A))), star(A))=true).
29.93/30.09	
29.93/30.09	Now clausify the problem and encode Horn clauses using encoding 3 of
29.93/30.09	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
29.93/30.09	We repeatedly replace C & s=t => u=v by the two clauses:
29.93/30.09	  fresh(y, y, x1...xn) = u
29.93/30.09	  C => fresh(s, t, x1...xn) = v
29.93/30.09	where fresh is a fresh function symbol and x1..xn are the free
29.93/30.09	variables of u and v.
29.93/30.09	A predicate p(X) is encoded as p(X)=true (this is sound, because the
29.93/30.09	input problem has no model of domain size 1).
29.93/30.09	
29.93/30.09	The encoding turns the above axioms into the following unit equations and goals:
29.93/30.09	
29.93/30.09	Axiom 1 (ifeq_axiom_002): ifeq(X, X, Y, Z) = Y.
29.93/30.09	Axiom 2 (left_distributivity): addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(X, Z), Y).
29.93/30.09	Axiom 3 (ifeq_axiom): X = ifeq3(Y, Y, X, Z).
29.93/30.09	Axiom 4 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
29.93/30.09	Axiom 5 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
29.93/30.09	Axiom 6 (order): true = ifeq3(addition(X, Y), Y, leq(X, Y), true).
29.93/30.09	Axiom 7 (additive_associativity): addition(addition(X, Y), Z) = addition(X, addition(Y, Z)).
29.93/30.09	Axiom 8 (star_induction_right): ifeq(leq(addition(multiplication(X, Y), Z), X), true, leq(multiplication(Z, star(Y)), X), true) = true.
29.93/30.09	Axiom 9 (multiplicative_left_identity): multiplication(one, X) = X.
29.93/30.09	Axiom 10 (additive_commutativity): addition(X, Y) = addition(Y, X).
29.93/30.09	Axiom 11 (ifeq_axiom_001): ifeq2(X, X, Y, Z) = Y.
29.93/30.09	Axiom 12 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
29.93/30.09	Axiom 13 (right_distributivity): addition(multiplication(X, Y), multiplication(X, Z)) = multiplication(X, addition(Y, Z)).
29.93/30.09	Axiom 14 (multiplicative_right_identity): multiplication(X, one) = X.
29.93/30.09	Axiom 15 (additive_idempotence): addition(X, X) = X.
29.93/30.10	Axiom 16 (star_unfold_left): true = leq(addition(one, multiplication(star(X), X)), star(X)).
29.93/30.10	
29.93/30.10	Lemma 17: leq(X, X) = true.
29.93/30.10	Proof:
29.93/30.10	  leq(X, X)
29.93/30.10	= { by axiom 3 (ifeq_axiom) }
29.93/30.10	  ifeq3(X, X, leq(X, X), true)
29.93/30.10	= { by axiom 15 (additive_idempotence) }
29.93/30.10	  ifeq3(addition(X, X), X, leq(X, X), true)
29.93/30.10	= { by axiom 6 (order) }
29.93/30.10	  true
29.93/30.10	
29.93/30.10	Lemma 18: multiplication(addition(X, one), Y) = addition(Y, multiplication(X, Y)).
29.93/30.10	Proof:
29.93/30.10	  multiplication(addition(X, one), Y)
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  multiplication(addition(one, X), Y)
29.93/30.10	= { by axiom 2 (left_distributivity) }
29.93/30.10	  addition(multiplication(one, Y), multiplication(X, Y))
29.93/30.10	= { by axiom 9 (multiplicative_left_identity) }
29.93/30.10	  addition(Y, multiplication(X, Y))
29.93/30.10	
29.93/30.10	Lemma 19: addition(X, multiplication(Y, X)) = multiplication(addition(one, Y), X).
29.93/30.10	Proof:
29.93/30.10	  addition(X, multiplication(Y, X))
29.93/30.10	= { by lemma 18 }
29.93/30.10	  multiplication(addition(Y, one), X)
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  multiplication(addition(one, Y), X)
29.93/30.10	
29.93/30.10	Lemma 20: addition(one, multiplication(addition(X, one), star(X))) = star(X).
29.93/30.10	Proof:
29.93/30.10	  addition(one, multiplication(addition(X, one), star(X)))
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  addition(one, multiplication(addition(one, X), star(X)))
29.93/30.10	= { by lemma 19 }
29.93/30.10	  addition(one, addition(star(X), multiplication(X, star(X))))
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  addition(one, addition(multiplication(X, star(X)), star(X)))
29.93/30.10	= { by axiom 7 (additive_associativity) }
29.93/30.10	  addition(addition(one, multiplication(X, star(X))), star(X))
29.93/30.10	= { by axiom 11 (ifeq_axiom_001) }
29.93/30.10	  ifeq2(true, true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
29.93/30.10	= { by axiom 12 (star_unfold_right) }
29.93/30.10	  ifeq2(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
29.93/30.10	= { by axiom 4 (order_1) }
29.93/30.10	  star(X)
29.93/30.10	
29.93/30.10	Lemma 21: addition(X, addition(X, Y)) = addition(X, Y).
29.93/30.10	Proof:
29.93/30.10	  addition(X, addition(X, Y))
29.93/30.10	= { by axiom 7 (additive_associativity) }
29.93/30.10	  addition(addition(X, X), Y)
29.93/30.10	= { by axiom 15 (additive_idempotence) }
29.93/30.10	  addition(X, Y)
29.93/30.10	
29.93/30.10	Lemma 22: addition(one, star(X)) = star(X).
29.93/30.10	Proof:
29.93/30.10	  addition(one, star(X))
29.93/30.10	= { by lemma 20 }
29.93/30.10	  addition(one, addition(one, multiplication(addition(X, one), star(X))))
29.93/30.10	= { by lemma 21 }
29.93/30.10	  addition(one, multiplication(addition(X, one), star(X)))
29.93/30.10	= { by lemma 20 }
29.93/30.10	  star(X)
29.93/30.10	
29.93/30.10	Lemma 23: addition(X, multiplication(X, Y)) = multiplication(X, addition(one, Y)).
29.93/30.10	Proof:
29.93/30.10	  addition(X, multiplication(X, Y))
29.93/30.10	= { by axiom 14 (multiplicative_right_identity) }
29.93/30.10	  addition(multiplication(X, one), multiplication(X, Y))
29.93/30.10	= { by axiom 13 (right_distributivity) }
29.93/30.10	  multiplication(X, addition(one, Y))
29.93/30.10	
29.93/30.10	Lemma 24: addition(one, multiplication(star(X), addition(X, one))) = star(X).
29.93/30.10	Proof:
29.93/30.10	  addition(one, multiplication(star(X), addition(X, one)))
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  addition(one, multiplication(star(X), addition(one, X)))
29.93/30.10	= { by lemma 23 }
29.93/30.10	  addition(one, addition(star(X), multiplication(star(X), X)))
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  addition(one, addition(multiplication(star(X), X), star(X)))
29.93/30.10	= { by axiom 7 (additive_associativity) }
29.93/30.10	  addition(addition(one, multiplication(star(X), X)), star(X))
29.93/30.10	= { by axiom 11 (ifeq_axiom_001) }
29.93/30.10	  ifeq2(true, true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
29.93/30.10	= { by axiom 16 (star_unfold_left) }
29.93/30.10	  ifeq2(leq(addition(one, multiplication(star(X), X)), star(X)), true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
29.93/30.10	= { by axiom 4 (order_1) }
29.93/30.10	  star(X)
29.93/30.10	
29.93/30.10	Lemma 25: multiplication(addition(X, one), star(X)) = multiplication(star(X), addition(X, one)).
29.93/30.10	Proof:
29.93/30.10	  multiplication(addition(X, one), star(X))
29.93/30.10	= { by lemma 24 }
29.93/30.10	  multiplication(addition(X, one), addition(one, multiplication(star(X), addition(X, one))))
29.93/30.10	= { by axiom 13 (right_distributivity) }
29.93/30.10	  addition(multiplication(addition(X, one), one), multiplication(addition(X, one), multiplication(star(X), addition(X, one))))
29.93/30.10	= { by axiom 14 (multiplicative_right_identity) }
29.93/30.10	  addition(addition(X, one), multiplication(addition(X, one), multiplication(star(X), addition(X, one))))
29.93/30.10	= { by axiom 9 (multiplicative_left_identity) }
29.93/30.10	  addition(multiplication(one, addition(X, one)), multiplication(addition(X, one), multiplication(star(X), addition(X, one))))
29.93/30.10	= { by axiom 5 (multiplicative_associativity) }
29.93/30.10	  addition(multiplication(one, addition(X, one)), multiplication(multiplication(addition(X, one), star(X)), addition(X, one)))
29.93/30.10	= { by axiom 2 (left_distributivity) }
29.93/30.10	  multiplication(addition(one, multiplication(addition(X, one), star(X))), addition(X, one))
29.93/30.10	= { by lemma 20 }
29.93/30.10	  multiplication(star(X), addition(X, one))
29.93/30.10	
29.93/30.10	Lemma 26: addition(X, multiplication(star(Y), X)) = multiplication(star(Y), X).
29.93/30.10	Proof:
29.93/30.10	  addition(X, multiplication(star(Y), X))
29.93/30.10	= { by lemma 18 }
29.93/30.10	  multiplication(addition(star(Y), one), X)
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  multiplication(addition(one, star(Y)), X)
29.93/30.10	= { by lemma 22 }
29.93/30.10	  multiplication(star(Y), X)
29.93/30.10	
29.93/30.10	Lemma 27: addition(X, addition(Y, Z)) = addition(Y, addition(X, Z)).
29.93/30.10	Proof:
29.93/30.10	  addition(X, addition(Y, Z))
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  addition(addition(Y, Z), X)
29.93/30.10	= { by axiom 7 (additive_associativity) }
29.93/30.10	  addition(Y, addition(Z, X))
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  addition(Y, addition(X, Z))
29.93/30.10	
29.93/30.10	Lemma 28: leq(X, addition(X, Y)) = true.
29.93/30.10	Proof:
29.93/30.10	  leq(X, addition(X, Y))
29.93/30.10	= { by axiom 3 (ifeq_axiom) }
29.93/30.10	  ifeq3(addition(X, Y), addition(X, Y), leq(X, addition(X, Y)), true)
29.93/30.10	= { by lemma 21 }
29.93/30.10	  ifeq3(addition(X, addition(X, Y)), addition(X, Y), leq(X, addition(X, Y)), true)
29.93/30.10	= { by axiom 6 (order) }
29.93/30.10	  true
29.93/30.10	
29.93/30.10	Lemma 29: ifeq(leq(addition(one, multiplication(X, Y)), X), true, leq(star(Y), X), true) = true.
29.93/30.10	Proof:
29.93/30.10	  ifeq(leq(addition(one, multiplication(X, Y)), X), true, leq(star(Y), X), true)
29.93/30.10	= { by axiom 10 (additive_commutativity) }
29.93/30.10	  ifeq(leq(addition(multiplication(X, Y), one), X), true, leq(star(Y), X), true)
29.93/30.10	= { by axiom 9 (multiplicative_left_identity) }
29.93/30.10	  ifeq(leq(addition(multiplication(X, Y), one), X), true, leq(multiplication(one, star(Y)), X), true)
29.93/30.10	= { by axiom 8 (star_induction_right) }
29.93/30.10	  true
29.93/30.10	
29.93/30.10	Lemma 30: leq(star(addition(X, one)), star(X)) = true.
29.93/30.10	Proof:
29.93/30.10	  leq(star(addition(X, one)), star(X))
29.93/30.10	= { by axiom 1 (ifeq_axiom_002) }
29.93/30.10	  ifeq(true, true, leq(star(addition(X, one)), star(X)), true)
29.93/30.10	= { by lemma 17 }
29.93/30.11	  ifeq(leq(star(X), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 22 }
29.93/30.11	  ifeq(leq(addition(one, star(X)), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by axiom 4 (order_1) }
29.93/30.11	  ifeq(leq(addition(one, ifeq2(leq(addition(X, one), star(X)), true, addition(addition(X, one), star(X)), star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 24 }
29.93/30.11	  ifeq(leq(addition(one, ifeq2(leq(addition(X, one), addition(one, multiplication(star(X), addition(X, one)))), true, addition(addition(X, one), star(X)), star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 26 }
29.93/30.11	  ifeq(leq(addition(one, ifeq2(leq(addition(X, one), addition(one, addition(addition(X, one), multiplication(star(X), addition(X, one))))), true, addition(addition(X, one), star(X)), star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 27 }
29.93/30.11	  ifeq(leq(addition(one, ifeq2(leq(addition(X, one), addition(addition(X, one), addition(one, multiplication(star(X), addition(X, one))))), true, addition(addition(X, one), star(X)), star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 28 }
29.93/30.11	  ifeq(leq(addition(one, ifeq2(true, true, addition(addition(X, one), star(X)), star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by axiom 11 (ifeq_axiom_001) }
29.93/30.11	  ifeq(leq(addition(one, addition(addition(X, one), star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by axiom 7 (additive_associativity) }
29.93/30.11	  ifeq(leq(addition(one, addition(X, addition(one, star(X)))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 22 }
29.93/30.11	  ifeq(leq(addition(one, addition(X, star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 24 }
29.93/30.11	  ifeq(leq(addition(one, addition(X, addition(one, multiplication(star(X), addition(X, one))))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by axiom 7 (additive_associativity) }
29.93/30.11	  ifeq(leq(addition(one, addition(addition(X, one), multiplication(star(X), addition(X, one)))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 25 }
29.93/30.11	  ifeq(leq(addition(one, addition(addition(X, one), multiplication(addition(X, one), star(X)))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 23 }
29.93/30.11	  ifeq(leq(addition(one, multiplication(addition(X, one), addition(one, star(X)))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 22 }
29.93/30.11	  ifeq(leq(addition(one, multiplication(addition(X, one), star(X))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 25 }
29.93/30.11	  ifeq(leq(addition(one, multiplication(star(X), addition(X, one))), star(X)), true, leq(star(addition(X, one)), star(X)), true)
29.93/30.11	= { by lemma 29 }
29.93/30.11	  true
29.93/30.11	
29.93/30.11	Lemma 31: multiplication(addition(X, one), X) = multiplication(X, addition(X, one)).
29.93/30.11	Proof:
29.93/30.11	  multiplication(addition(X, one), X)
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  multiplication(addition(one, X), X)
29.93/30.11	= { by axiom 2 (left_distributivity) }
29.93/30.11	  addition(multiplication(one, X), multiplication(X, X))
29.93/30.11	= { by axiom 9 (multiplicative_left_identity) }
29.93/30.11	  addition(X, multiplication(X, X))
29.93/30.11	= { by axiom 14 (multiplicative_right_identity) }
29.93/30.11	  addition(multiplication(X, one), multiplication(X, X))
29.93/30.11	= { by axiom 13 (right_distributivity) }
29.93/30.11	  multiplication(X, addition(one, X))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  multiplication(X, addition(X, one))
29.93/30.11	
29.93/30.11	Lemma 32: addition(one, multiplication(addition(X, one), star(addition(X, one)))) = star(addition(X, one)).
29.93/30.11	Proof:
29.93/30.11	  addition(one, multiplication(addition(X, one), star(addition(X, one))))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  addition(one, multiplication(addition(one, X), star(addition(X, one))))
29.93/30.11	= { by lemma 21 }
29.93/30.11	  addition(one, multiplication(addition(one, addition(one, X)), star(addition(X, one))))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  addition(one, multiplication(addition(addition(one, X), one), star(addition(X, one))))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  addition(one, multiplication(addition(addition(one, X), one), star(addition(one, X))))
29.93/30.11	= { by lemma 20 }
29.93/30.11	  star(addition(one, X))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  star(addition(X, one))
29.93/30.11	
29.93/30.11	Lemma 33: multiplication(star(addition(X, one)), addition(X, one)) = star(addition(X, one)).
29.93/30.11	Proof:
29.93/30.11	  multiplication(star(addition(X, one)), addition(X, one))
29.93/30.11	= { by lemma 22 }
29.93/30.11	  multiplication(addition(one, star(addition(X, one))), addition(X, one))
29.93/30.11	= { by axiom 2 (left_distributivity) }
29.93/30.11	  addition(multiplication(one, addition(X, one)), multiplication(star(addition(X, one)), addition(X, one)))
29.93/30.11	= { by axiom 9 (multiplicative_left_identity) }
29.93/30.11	  addition(addition(X, one), multiplication(star(addition(X, one)), addition(X, one)))
29.93/30.11	= { by axiom 7 (additive_associativity) }
29.93/30.11	  addition(X, addition(one, multiplication(star(addition(X, one)), addition(X, one))))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  addition(X, addition(one, multiplication(star(addition(one, X)), addition(X, one))))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  addition(X, addition(one, multiplication(star(addition(one, X)), addition(one, X))))
29.93/30.11	= { by lemma 21 }
29.93/30.11	  addition(X, addition(one, multiplication(star(addition(one, X)), addition(one, addition(one, X)))))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  addition(X, addition(one, multiplication(star(addition(one, X)), addition(addition(one, X), one))))
29.93/30.11	= { by lemma 24 }
29.93/30.11	  addition(X, star(addition(one, X)))
29.93/30.11	= { by axiom 10 (additive_commutativity) }
29.93/30.11	  addition(X, star(addition(X, one)))
29.93/30.11	= { by lemma 22 }
29.93/30.11	  addition(X, addition(one, star(addition(X, one))))
29.93/30.11	= { by axiom 7 (additive_associativity) }
29.93/30.11	  addition(addition(X, one), star(addition(X, one)))
29.93/30.11	= { by lemma 32 }
29.93/30.11	  addition(addition(X, one), addition(one, multiplication(addition(X, one), star(addition(X, one)))))
29.93/30.11	= { by lemma 27 }
29.93/30.11	  addition(one, addition(addition(X, one), multiplication(addition(X, one), star(addition(X, one)))))
29.93/30.11	= { by lemma 23 }
29.93/30.11	  addition(one, multiplication(addition(X, one), addition(one, star(addition(X, one)))))
29.93/30.11	= { by lemma 22 }
29.93/30.11	  addition(one, multiplication(addition(X, one), star(addition(X, one))))
29.93/30.11	= { by lemma 32 }
29.93/30.11	  star(addition(X, one))
29.93/30.11	
29.93/30.11	Lemma 34: multiplication(star(addition(X, one)), multiplication(addition(X, one), Y)) = multiplication(star(addition(X, one)), Y).
29.93/30.11	Proof:
29.93/30.11	  multiplication(star(addition(X, one)), multiplication(addition(X, one), Y))
29.93/30.11	= { by axiom 5 (multiplicative_associativity) }
29.93/30.11	  multiplication(multiplication(star(addition(X, one)), addition(X, one)), Y)
29.93/30.11	= { by lemma 33 }
30.23/30.39	  multiplication(star(addition(X, one)), Y)
30.23/30.39	
30.23/30.39	Goal 1 (goals): tuple(leq(star(addition(one, sK2_goals_X0)), star(sK2_goals_X0)), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0)))) = tuple(true, true).
30.23/30.39	Proof:
30.23/30.39	  tuple(leq(star(addition(one, sK2_goals_X0)), star(sK2_goals_X0)), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
30.23/30.39	= { by lemma 30 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))))
30.23/30.39	= { by axiom 4 (order_1) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 1 (ifeq_axiom_002) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(true, true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 28 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 7 (additive_associativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), addition(one, multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one))))), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), addition(multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one))), one)), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 7 (additive_associativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), one), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 26 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one))), one), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 31 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(sK1_goals_X0, one), sK1_goals_X0))), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 34 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), addition(addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)))), multiplication(star(addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 7 (additive_associativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), addition(multiplication(star(addition(sK1_goals_X0, one)), multiplication(sK1_goals_X0, addition(sK1_goals_X0, one))), multiplication(star(addition(sK1_goals_X0, one)), one)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 13 (right_distributivity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), addition(addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one), multiplication(star(addition(sK1_goals_X0, one)), addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 26 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(multiplication(sK1_goals_X0, addition(sK1_goals_X0, one)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 31 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(multiplication(addition(sK1_goals_X0, one), sK1_goals_X0), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(multiplication(addition(one, sK1_goals_X0), sK1_goals_X0), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 2 (left_distributivity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(addition(multiplication(one, sK1_goals_X0), multiplication(sK1_goals_X0, sK1_goals_X0)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 9 (multiplicative_left_identity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(addition(sK1_goals_X0, multiplication(sK1_goals_X0, sK1_goals_X0)), one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 7 (additive_associativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(sK1_goals_X0, addition(multiplication(sK1_goals_X0, sK1_goals_X0), one)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(sK1_goals_X0, addition(one, multiplication(sK1_goals_X0, sK1_goals_X0))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 27 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(one, addition(sK1_goals_X0, multiplication(sK1_goals_X0, sK1_goals_X0))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 21 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(one, addition(sK1_goals_X0, addition(sK1_goals_X0, multiplication(sK1_goals_X0, sK1_goals_X0)))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 19 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(one, addition(sK1_goals_X0, multiplication(addition(one, sK1_goals_X0), sK1_goals_X0))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 7 (additive_associativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(addition(one, sK1_goals_X0), multiplication(addition(one, sK1_goals_X0), sK1_goals_X0)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 21 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(addition(one, sK1_goals_X0), addition(addition(one, sK1_goals_X0), multiplication(addition(one, sK1_goals_X0), sK1_goals_X0))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 9 (multiplicative_left_identity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(multiplication(one, addition(one, sK1_goals_X0)), addition(addition(one, sK1_goals_X0), multiplication(addition(one, sK1_goals_X0), sK1_goals_X0))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 23 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(multiplication(one, addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), addition(one, sK1_goals_X0))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 2 (left_distributivity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(one, addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(addition(one, sK1_goals_X0), one), addition(one, sK1_goals_X0)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 31 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(one, sK1_goals_X0), addition(addition(one, sK1_goals_X0), one)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(sK1_goals_X0, one), addition(addition(one, sK1_goals_X0), one)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 7 (additive_associativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(sK1_goals_X0, one), addition(one, addition(sK1_goals_X0, one))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(sK1_goals_X0, one), addition(one, addition(one, sK1_goals_X0))))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 21 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(sK1_goals_X0, one), addition(one, sK1_goals_X0)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), multiplication(addition(sK1_goals_X0, one), addition(sK1_goals_X0, one)))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 34 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), multiplication(star(addition(sK1_goals_X0, one)), addition(sK1_goals_X0, one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 33 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(ifeq(leq(addition(one, multiplication(star(addition(sK1_goals_X0, one)), sK1_goals_X0)), star(addition(sK1_goals_X0, one))), true, leq(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), true), true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by lemma 29 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(true, true, addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one))), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 11 (ifeq_axiom_001) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), addition(star(sK1_goals_X0), star(addition(sK1_goals_X0, one)))))
30.23/30.39	= { by axiom 10 (additive_commutativity) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), addition(star(addition(sK1_goals_X0, one)), star(sK1_goals_X0))))
30.23/30.39	= { by axiom 11 (ifeq_axiom_001) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(true, true, addition(star(addition(sK1_goals_X0, one)), star(sK1_goals_X0)), star(sK1_goals_X0))))
30.23/30.39	= { by lemma 30 }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), ifeq2(leq(star(addition(sK1_goals_X0, one)), star(sK1_goals_X0)), true, addition(star(addition(sK1_goals_X0, one)), star(sK1_goals_X0)), star(sK1_goals_X0))))
30.23/30.39	= { by axiom 4 (order_1) }
30.23/30.39	  tuple(true, leq(star(sK1_goals_X0), star(sK1_goals_X0)))
30.23/30.39	= { by lemma 17 }
30.23/30.39	  tuple(true, true)
30.23/30.39	% SZS output end Proof
30.23/30.39	
30.23/30.39	RESULT: Unsatisfiable (the axioms are contradictory).
30.23/30.40	EOF