0.00/0.04	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.03/0.28	% Computer   : n010.star.cs.uiowa.edu
0.03/0.28	% Model      : x86_64 x86_64
0.03/0.28	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.28	% Memory     : 32218.625MB
0.03/0.28	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.28	% CPULimit   : 300
0.03/0.28	% DateTime   : Sat Jul 14 04:17:25 CDT 2018
0.03/0.28	% CPUTime    : 
13.16/13.44	% SZS status Theorem
13.16/13.44	
13.21/13.44	% SZS output start Proof
13.21/13.44	Take the following subset of the input axioms:
13.22/13.49	  fof(axiom_1, axiom,
13.22/13.49	      ![B, C, A]: times(times(A, B), C)=times(B, times(C, A))).
13.22/13.49	  fof(axiom_2, axiom,
13.22/13.49	      ![B]: (element(B) <=> ?[C]: (times(B, C)=B & C=times(B, B)))).
13.22/13.49	  fof(conjecture_1, conjecture,
13.22/13.49	      ![B, A]: ((element(B) & element(A)) => element(times(A, B)))).
13.22/13.49	
13.22/13.49	Now clausify the problem and encode Horn clauses using encoding 3 of
13.22/13.49	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
13.22/13.49	We repeatedly replace C & s=t => u=v by the two clauses:
13.22/13.49	  $$fresh(y, y, x1...xn) = u
13.22/13.49	  C => $$fresh(s, t, x1...xn) = v
13.22/13.49	where $$fresh is a fresh function symbol and x1..xn are the free
13.22/13.49	variables of u and v.
13.22/13.49	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
13.22/13.49	input problem has no model of domain size 1).
13.22/13.49	
13.22/13.49	The encoding turns the above axioms into the following unit equations and goals:
13.22/13.49	
13.22/13.49	Axiom 1 (axiom_2): $$fresh4(X, X, Y, Z) = element(Y).
13.22/13.49	Axiom 2 (axiom_2): $$fresh3(X, X, Y) = $$true.
13.22/13.49	Axiom 3 (axiom_2_1): $$fresh(X, X, Y) = Y.
13.22/13.49	Axiom 4 (axiom_2_2): $$fresh2(X, X, Y) = sK1_axiom_2_C(Y).
13.22/13.49	Axiom 5 (axiom_1): times(times(X, Y), Z) = times(Y, times(Z, X)).
13.22/13.49	Axiom 6 (axiom_2_2): $$fresh2(element(X), $$true, X) = times(X, X).
13.22/13.49	Axiom 7 (axiom_2_1): $$fresh(element(X), $$true, X) = times(X, sK1_axiom_2_C(X)).
13.22/13.49	Axiom 8 (axiom_2): $$fresh4(X, times(Y, Y), Y, X) = $$fresh3(times(Y, X), Y, Y).
13.22/13.49	Axiom 9 (conjecture_1): element(sK3_conjecture_1_B) = $$true.
13.22/13.49	Axiom 10 (conjecture_1_1): element(sK2_conjecture_1_A) = $$true.
13.22/13.49	
13.22/13.49	Lemma 11: times(sK3_conjecture_1_B, sK3_conjecture_1_B) = sK1_axiom_2_C(sK3_conjecture_1_B).
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, sK3_conjecture_1_B)
13.22/13.49	= { by axiom 6 (axiom_2_2) }
13.22/13.49	  $$fresh2(element(sK3_conjecture_1_B), $$true, sK3_conjecture_1_B)
13.22/13.49	= { by axiom 9 (conjecture_1) }
13.22/13.49	  $$fresh2($$true, $$true, sK3_conjecture_1_B)
13.22/13.49	= { by axiom 4 (axiom_2_2) }
13.22/13.49	  sK1_axiom_2_C(sK3_conjecture_1_B)
13.22/13.49	
13.22/13.49	Lemma 12: times(sK2_conjecture_1_A, sK2_conjecture_1_A) = sK1_axiom_2_C(sK2_conjecture_1_A).
13.22/13.49	Proof:
13.22/13.49	  times(sK2_conjecture_1_A, sK2_conjecture_1_A)
13.22/13.49	= { by axiom 6 (axiom_2_2) }
13.22/13.49	  $$fresh2(element(sK2_conjecture_1_A), $$true, sK2_conjecture_1_A)
13.22/13.49	= { by axiom 10 (conjecture_1_1) }
13.22/13.49	  $$fresh2($$true, $$true, sK2_conjecture_1_A)
13.22/13.49	= { by axiom 4 (axiom_2_2) }
13.22/13.49	  sK1_axiom_2_C(sK2_conjecture_1_A)
13.22/13.49	
13.22/13.49	Lemma 13: times(sK3_conjecture_1_B, sK1_axiom_2_C(sK3_conjecture_1_B)) = sK3_conjecture_1_B.
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.49	= { by axiom 7 (axiom_2_1) }
13.22/13.49	  $$fresh(element(sK3_conjecture_1_B), $$true, sK3_conjecture_1_B)
13.22/13.49	= { by axiom 9 (conjecture_1) }
13.22/13.49	  $$fresh($$true, $$true, sK3_conjecture_1_B)
13.22/13.49	= { by axiom 3 (axiom_2_1) }
13.22/13.49	  sK3_conjecture_1_B
13.22/13.49	
13.22/13.49	Lemma 14: times(sK2_conjecture_1_A, sK1_axiom_2_C(sK2_conjecture_1_A)) = sK2_conjecture_1_A.
13.22/13.49	Proof:
13.22/13.49	  times(sK2_conjecture_1_A, sK1_axiom_2_C(sK2_conjecture_1_A))
13.22/13.49	= { by axiom 7 (axiom_2_1) }
13.22/13.49	  $$fresh(element(sK2_conjecture_1_A), $$true, sK2_conjecture_1_A)
13.22/13.49	= { by axiom 10 (conjecture_1_1) }
13.22/13.49	  $$fresh($$true, $$true, sK2_conjecture_1_A)
13.22/13.49	= { by axiom 3 (axiom_2_1) }
13.22/13.49	  sK2_conjecture_1_A
13.22/13.49	
13.22/13.49	Lemma 15: times(sK3_conjecture_1_B, times(X, sK3_conjecture_1_B)) = times(sK1_axiom_2_C(sK3_conjecture_1_B), X).
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, times(X, sK3_conjecture_1_B))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK3_conjecture_1_B, sK3_conjecture_1_B), X)
13.22/13.49	= { by lemma 11 }
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), X)
13.22/13.49	
13.22/13.49	Lemma 16: times(sK1_axiom_2_C(sK3_conjecture_1_B), sK3_conjecture_1_B) = sK3_conjecture_1_B.
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), sK3_conjecture_1_B)
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 11 }
13.22/13.49	  times(sK3_conjecture_1_B, sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.49	= { by lemma 13 }
13.22/13.49	  sK3_conjecture_1_B
13.22/13.49	
13.22/13.49	Lemma 17: times(sK2_conjecture_1_A, times(X, sK2_conjecture_1_A)) = times(sK1_axiom_2_C(sK2_conjecture_1_A), X).
13.22/13.49	Proof:
13.22/13.49	  times(sK2_conjecture_1_A, times(X, sK2_conjecture_1_A))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK2_conjecture_1_A, sK2_conjecture_1_A), X)
13.22/13.49	= { by lemma 12 }
13.22/13.49	  times(sK1_axiom_2_C(sK2_conjecture_1_A), X)
13.22/13.49	
13.22/13.49	Lemma 18: times(sK1_axiom_2_C(sK2_conjecture_1_A), sK2_conjecture_1_A) = sK2_conjecture_1_A.
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK2_conjecture_1_A), sK2_conjecture_1_A)
13.22/13.49	= { by lemma 17 }
13.22/13.49	  times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, sK2_conjecture_1_A))
13.22/13.49	= { by lemma 12 }
13.22/13.49	  times(sK2_conjecture_1_A, sK1_axiom_2_C(sK2_conjecture_1_A))
13.22/13.49	= { by lemma 14 }
13.22/13.49	  sK2_conjecture_1_A
13.22/13.49	
13.22/13.49	Lemma 19: times(sK1_axiom_2_C(sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B)) = sK1_axiom_2_C(sK3_conjecture_1_B).
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK3_conjecture_1_B))
13.22/13.49	= { by lemma 16 }
13.22/13.49	  times(sK3_conjecture_1_B, sK3_conjecture_1_B)
13.22/13.49	= { by lemma 11 }
13.22/13.49	  sK1_axiom_2_C(sK3_conjecture_1_B)
13.22/13.49	
13.22/13.49	Lemma 20: times(sK1_axiom_2_C(sK2_conjecture_1_A), sK1_axiom_2_C(sK2_conjecture_1_A)) = sK1_axiom_2_C(sK2_conjecture_1_A).
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK2_conjecture_1_A), sK1_axiom_2_C(sK2_conjecture_1_A))
13.22/13.49	= { by lemma 17 }
13.22/13.49	  times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK2_conjecture_1_A), sK2_conjecture_1_A))
13.22/13.49	= { by lemma 18 }
13.22/13.49	  times(sK2_conjecture_1_A, sK2_conjecture_1_A)
13.22/13.49	= { by lemma 12 }
13.22/13.49	  sK1_axiom_2_C(sK2_conjecture_1_A)
13.22/13.49	
13.22/13.49	Lemma 21: times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, sK3_conjecture_1_B)) = times(sK3_conjecture_1_B, X).
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, sK3_conjecture_1_B))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK3_conjecture_1_B, sK1_axiom_2_C(sK3_conjecture_1_B)), X)
13.22/13.49	= { by lemma 13 }
13.22/13.49	  times(sK3_conjecture_1_B, X)
13.22/13.49	
13.22/13.49	Lemma 22: times(X, times(Y, times(Z, W))) = times(Z, times(W, times(X, Y))).
13.22/13.49	Proof:
13.22/13.49	  times(X, times(Y, times(Z, W)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(times(Z, W), X), Y)
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(W, times(X, Z)), Y)
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(X, Z), times(Y, W))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(Z, times(times(Y, W), X))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(Z, times(W, times(X, Y)))
13.22/13.49	
13.22/13.49	Lemma 23: times(sK3_conjecture_1_B, times(X, sK1_axiom_2_C(sK3_conjecture_1_B))) = times(sK3_conjecture_1_B, X).
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, times(X, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK1_axiom_2_C(sK3_conjecture_1_B), sK3_conjecture_1_B), X)
13.22/13.49	= { by lemma 16 }
13.22/13.49	  times(sK3_conjecture_1_B, X)
13.22/13.49	
13.22/13.49	Lemma 24: times(sK2_conjecture_1_A, times(X, sK1_axiom_2_C(sK2_conjecture_1_A))) = times(sK2_conjecture_1_A, X).
13.22/13.49	Proof:
13.22/13.49	  times(sK2_conjecture_1_A, times(X, sK1_axiom_2_C(sK2_conjecture_1_A)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK1_axiom_2_C(sK2_conjecture_1_A), sK2_conjecture_1_A), X)
13.22/13.49	= { by lemma 18 }
13.22/13.49	  times(sK2_conjecture_1_A, X)
13.22/13.49	
13.22/13.49	Lemma 25: times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y)) = times(Y, times(sK1_axiom_2_C(sK3_conjecture_1_B), X)).
13.22/13.49	Proof:
13.22/13.49	  times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y))
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(X, times(sK3_conjecture_1_B, times(Y, sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 22 }
13.22/13.49	  times(Y, times(sK3_conjecture_1_B, times(X, sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(Y, times(sK1_axiom_2_C(sK3_conjecture_1_B), X))
13.22/13.49	
13.22/13.49	Lemma 26: times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), X)) = times(X, sK3_conjecture_1_B).
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), X))
13.22/13.49	= { by lemma 25 }
13.22/13.49	  times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK3_conjecture_1_B))
13.22/13.49	= { by lemma 16 }
13.22/13.49	  times(X, sK3_conjecture_1_B)
13.22/13.49	
13.22/13.49	Lemma 28: times(X, sK3_conjecture_1_B) = times(sK3_conjecture_1_B, X).
13.22/13.49	Proof:
13.22/13.49	  times(X, sK3_conjecture_1_B)
13.22/13.49	= { by lemma 13 }
13.22/13.49	  times(X, times(sK3_conjecture_1_B, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK1_axiom_2_C(sK3_conjecture_1_B), X), sK3_conjecture_1_B)
13.22/13.49	= { by lemma 26 }
13.22/13.49	  times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(sK1_axiom_2_C(sK3_conjecture_1_B), X)))
13.22/13.49	= { by lemma 25 }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B))))
13.22/13.49	= { by lemma 19 }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 23 }
13.22/13.49	  times(sK3_conjecture_1_B, X)
13.22/13.49	
13.22/13.49	Lemma 28: times(sK3_conjecture_1_B, X) = times(X, sK3_conjecture_1_B).
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, X)
13.22/13.49	= { by lemma 23 }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 19 }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B))))
13.22/13.49	= { by lemma 25 }
13.22/13.49	  times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(sK1_axiom_2_C(sK3_conjecture_1_B), X)))
13.22/13.49	= { by lemma 26 }
13.22/13.49	  times(times(sK1_axiom_2_C(sK3_conjecture_1_B), X), sK3_conjecture_1_B)
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(X, times(sK3_conjecture_1_B, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 13 }
13.22/13.49	  times(X, sK3_conjecture_1_B)
13.22/13.49	
13.22/13.49	Lemma 29: times(X, times(sK1_axiom_2_C(sK2_conjecture_1_A), Y)) = times(Y, times(sK1_axiom_2_C(sK2_conjecture_1_A), X)).
13.22/13.49	Proof:
13.22/13.49	  times(X, times(sK1_axiom_2_C(sK2_conjecture_1_A), Y))
13.22/13.49	= { by lemma 17 }
13.22/13.49	  times(X, times(sK2_conjecture_1_A, times(Y, sK2_conjecture_1_A)))
13.22/13.49	= { by lemma 22 }
13.22/13.49	  times(Y, times(sK2_conjecture_1_A, times(X, sK2_conjecture_1_A)))
13.22/13.49	= { by lemma 17 }
13.22/13.49	  times(Y, times(sK1_axiom_2_C(sK2_conjecture_1_A), X))
13.22/13.49	
13.22/13.49	Lemma 30: times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK2_conjecture_1_A), X)) = times(X, sK2_conjecture_1_A).
13.22/13.49	Proof:
13.22/13.49	  times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK2_conjecture_1_A), X))
13.22/13.49	= { by lemma 29 }
13.22/13.49	  times(X, times(sK1_axiom_2_C(sK2_conjecture_1_A), sK2_conjecture_1_A))
13.22/13.49	= { by lemma 18 }
13.22/13.49	  times(X, sK2_conjecture_1_A)
13.22/13.49	
13.22/13.49	Lemma 32: times(X, sK2_conjecture_1_A) = times(sK2_conjecture_1_A, X).
13.22/13.49	Proof:
13.22/13.49	  times(X, sK2_conjecture_1_A)
13.22/13.49	= { by lemma 14 }
13.22/13.49	  times(X, times(sK2_conjecture_1_A, sK1_axiom_2_C(sK2_conjecture_1_A)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK1_axiom_2_C(sK2_conjecture_1_A), X), sK2_conjecture_1_A)
13.22/13.49	= { by lemma 30 }
13.22/13.49	  times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK2_conjecture_1_A), times(sK1_axiom_2_C(sK2_conjecture_1_A), X)))
13.22/13.49	= { by lemma 29 }
13.22/13.49	  times(sK2_conjecture_1_A, times(X, times(sK1_axiom_2_C(sK2_conjecture_1_A), sK1_axiom_2_C(sK2_conjecture_1_A))))
13.22/13.49	= { by lemma 20 }
13.22/13.49	  times(sK2_conjecture_1_A, times(X, sK1_axiom_2_C(sK2_conjecture_1_A)))
13.22/13.49	= { by lemma 24 }
13.22/13.49	  times(sK2_conjecture_1_A, X)
13.22/13.49	
13.22/13.49	Lemma 32: times(sK2_conjecture_1_A, X) = times(X, sK2_conjecture_1_A).
13.22/13.49	Proof:
13.22/13.49	  times(sK2_conjecture_1_A, X)
13.22/13.49	= { by lemma 24 }
13.22/13.49	  times(sK2_conjecture_1_A, times(X, sK1_axiom_2_C(sK2_conjecture_1_A)))
13.22/13.49	= { by lemma 20 }
13.22/13.49	  times(sK2_conjecture_1_A, times(X, times(sK1_axiom_2_C(sK2_conjecture_1_A), sK1_axiom_2_C(sK2_conjecture_1_A))))
13.22/13.49	= { by lemma 29 }
13.22/13.49	  times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK2_conjecture_1_A), times(sK1_axiom_2_C(sK2_conjecture_1_A), X)))
13.22/13.49	= { by lemma 30 }
13.22/13.49	  times(times(sK1_axiom_2_C(sK2_conjecture_1_A), X), sK2_conjecture_1_A)
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(X, times(sK2_conjecture_1_A, sK1_axiom_2_C(sK2_conjecture_1_A)))
13.22/13.49	= { by lemma 14 }
13.22/13.49	  times(X, sK2_conjecture_1_A)
13.22/13.49	
13.22/13.49	Lemma 33: times(X, times(Y, sK3_conjecture_1_B)) = times(Y, times(X, sK3_conjecture_1_B)).
13.22/13.49	Proof:
13.22/13.49	  times(X, times(Y, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 28 }
13.22/13.49	  times(X, times(sK3_conjecture_1_B, Y))
13.22/13.49	= { by lemma 21 }
13.22/13.49	  times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Y, sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 22 }
13.22/13.49	  times(Y, times(sK3_conjecture_1_B, times(X, sK1_axiom_2_C(sK3_conjecture_1_B))))
13.22/13.49	= { by lemma 23 }
13.22/13.49	  times(Y, times(sK3_conjecture_1_B, X))
13.22/13.49	= { by lemma 28 }
13.22/13.49	  times(Y, times(X, sK3_conjecture_1_B))
13.22/13.49	
13.22/13.49	Lemma 35: times(X, sK1_axiom_2_C(sK3_conjecture_1_B)) = times(sK1_axiom_2_C(sK3_conjecture_1_B), X).
13.22/13.49	Proof:
13.22/13.49	  times(X, sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.49	= { by lemma 11 }
13.22/13.49	  times(X, times(sK3_conjecture_1_B, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 33 }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), X)
13.22/13.49	
13.22/13.49	Lemma 35: times(sK1_axiom_2_C(sK3_conjecture_1_B), X) = times(X, sK1_axiom_2_C(sK3_conjecture_1_B)).
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), X)
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 33 }
13.22/13.49	  times(X, times(sK3_conjecture_1_B, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 11 }
13.22/13.49	  times(X, sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.49	
13.22/13.49	Lemma 36: times(X, times(Y, sK2_conjecture_1_A)) = times(Y, times(X, sK2_conjecture_1_A)).
13.22/13.49	Proof:
13.22/13.49	  times(X, times(Y, sK2_conjecture_1_A))
13.22/13.49	= { by lemma 32 }
13.22/13.49	  times(X, times(sK2_conjecture_1_A, Y))
13.22/13.49	= { by lemma 14 }
13.22/13.49	  times(X, times(times(sK2_conjecture_1_A, sK1_axiom_2_C(sK2_conjecture_1_A)), Y))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(X, times(sK1_axiom_2_C(sK2_conjecture_1_A), times(Y, sK2_conjecture_1_A)))
13.22/13.49	= { by lemma 22 }
13.22/13.49	  times(Y, times(sK2_conjecture_1_A, times(X, sK1_axiom_2_C(sK2_conjecture_1_A))))
13.22/13.49	= { by lemma 24 }
13.22/13.49	  times(Y, times(sK2_conjecture_1_A, X))
13.22/13.49	= { by lemma 32 }
13.22/13.49	  times(Y, times(X, sK2_conjecture_1_A))
13.22/13.49	
13.22/13.49	Lemma 38: times(X, sK1_axiom_2_C(sK2_conjecture_1_A)) = times(sK1_axiom_2_C(sK2_conjecture_1_A), X).
13.22/13.49	Proof:
13.22/13.49	  times(X, sK1_axiom_2_C(sK2_conjecture_1_A))
13.22/13.49	= { by lemma 12 }
13.22/13.49	  times(X, times(sK2_conjecture_1_A, sK2_conjecture_1_A))
13.22/13.49	= { by lemma 36 }
13.22/13.49	  times(sK2_conjecture_1_A, times(X, sK2_conjecture_1_A))
13.22/13.49	= { by lemma 17 }
13.22/13.49	  times(sK1_axiom_2_C(sK2_conjecture_1_A), X)
13.22/13.49	
13.22/13.49	Lemma 38: times(sK1_axiom_2_C(sK2_conjecture_1_A), X) = times(X, sK1_axiom_2_C(sK2_conjecture_1_A)).
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK2_conjecture_1_A), X)
13.22/13.49	= { by lemma 17 }
13.22/13.49	  times(sK2_conjecture_1_A, times(X, sK2_conjecture_1_A))
13.22/13.49	= { by lemma 36 }
13.22/13.49	  times(X, times(sK2_conjecture_1_A, sK2_conjecture_1_A))
13.22/13.49	= { by lemma 12 }
13.22/13.49	  times(X, sK1_axiom_2_C(sK2_conjecture_1_A))
13.22/13.49	
13.22/13.49	Lemma 40: times(X, times(Y, sK3_conjecture_1_B)) = times(sK3_conjecture_1_B, times(X, Y)).
13.22/13.49	Proof:
13.22/13.49	  times(X, times(Y, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 33 }
13.22/13.49	  times(Y, times(X, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 26 }
13.22/13.49	  times(Y, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), X)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(Y, times(times(X, sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK1_axiom_2_C(sK3_conjecture_1_B), Y), times(X, sK3_conjecture_1_B))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y)), X)
13.22/13.49	= { by lemma 26 }
13.22/13.49	  times(times(Y, sK3_conjecture_1_B), X)
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, Y))
13.22/13.49	
13.22/13.49	Lemma 40: times(sK3_conjecture_1_B, times(X, Y)) = times(X, times(Y, sK3_conjecture_1_B)).
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, times(X, Y))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(Y, sK3_conjecture_1_B), X)
13.22/13.49	= { by lemma 26 }
13.22/13.49	  times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y)), X)
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(times(sK1_axiom_2_C(sK3_conjecture_1_B), Y), times(X, sK3_conjecture_1_B))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(Y, times(times(X, sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by axiom 5 (axiom_1) }
13.22/13.49	  times(Y, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), X)))
13.22/13.49	= { by lemma 26 }
13.22/13.49	  times(Y, times(X, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 33 }
13.22/13.49	  times(X, times(Y, sK3_conjecture_1_B))
13.22/13.49	
13.22/13.49	Lemma 41: times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(X, Y))) = times(X, times(Y, sK1_axiom_2_C(sK3_conjecture_1_B))).
13.22/13.49	Proof:
13.22/13.49	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(X, Y)))
13.22/13.49	= { by lemma 22 }
13.22/13.49	  times(X, times(Y, times(sK3_conjecture_1_B, sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 11 }
13.22/13.49	  times(X, times(Y, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	
13.22/13.49	Lemma 42: times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, sK1_axiom_2_C(sK3_conjecture_1_B))) = times(X, sK1_axiom_2_C(sK3_conjecture_1_B)).
13.22/13.49	Proof:
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 41 }
13.22/13.49	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), X)))
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(X, sK3_conjecture_1_B))))
13.22/13.49	= { by lemma 41 }
13.22/13.49	  times(sK3_conjecture_1_B, times(times(X, sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.49	= { by lemma 23 }
13.22/13.49	  times(sK3_conjecture_1_B, times(X, sK3_conjecture_1_B))
13.22/13.49	= { by lemma 15 }
13.22/13.49	  times(sK1_axiom_2_C(sK3_conjecture_1_B), X)
13.22/13.49	= { by lemma 35 }
13.22/13.49	  times(X, sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.49	
13.22/13.50	Lemma 43: times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(X, Y))) = times(X, times(Y, sK1_axiom_2_C(sK2_conjecture_1_A))).
13.22/13.50	Proof:
13.22/13.50	  times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(X, Y)))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(X, times(Y, times(sK2_conjecture_1_A, sK2_conjecture_1_A)))
13.22/13.50	= { by lemma 12 }
13.22/13.50	  times(X, times(Y, sK1_axiom_2_C(sK2_conjecture_1_A)))
13.22/13.50	
13.22/13.50	Lemma 45: times(X, times(Y, sK3_conjecture_1_B)) = times(Y, times(sK3_conjecture_1_B, X)).
13.22/13.50	Proof:
13.22/13.50	  times(X, times(Y, sK3_conjecture_1_B))
13.22/13.50	= { by lemma 33 }
13.22/13.50	  times(Y, times(X, sK3_conjecture_1_B))
13.22/13.50	= { by lemma 28 }
13.22/13.50	  times(Y, times(sK3_conjecture_1_B, X))
13.22/13.50	
13.22/13.50	Lemma 45: times(Y, times(sK3_conjecture_1_B, X)) = times(X, times(Y, sK3_conjecture_1_B)).
13.22/13.50	Proof:
13.22/13.50	  times(Y, times(sK3_conjecture_1_B, X))
13.22/13.50	= { by lemma 28 }
13.22/13.50	  times(Y, times(X, sK3_conjecture_1_B))
13.22/13.50	= { by lemma 33 }
13.22/13.50	  times(X, times(Y, sK3_conjecture_1_B))
13.22/13.50	
13.22/13.50	Lemma 46: times(sK3_conjecture_1_B, times(Y, times(sK3_conjecture_1_B, X))) = times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y)).
13.22/13.50	Proof:
13.22/13.50	  times(sK3_conjecture_1_B, times(Y, times(sK3_conjecture_1_B, X)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(sK3_conjecture_1_B, times(times(X, Y), sK3_conjecture_1_B))
13.22/13.50	= { by lemma 15 }
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y))
13.22/13.50	
13.22/13.50	Lemma 47: times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y)) = times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Y, X)).
13.22/13.50	Proof:
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y))
13.22/13.50	= { by lemma 46 }
13.22/13.50	  times(sK3_conjecture_1_B, times(Y, times(sK3_conjecture_1_B, X)))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(sK3_conjecture_1_B, times(X, times(sK3_conjecture_1_B, Y)))
13.22/13.50	= { by lemma 46 }
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Y, X))
13.22/13.50	
13.22/13.50	Lemma 49: times(X, times(Y, sK1_axiom_2_C(sK3_conjecture_1_B))) = times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y)).
13.22/13.50	Proof:
13.22/13.50	  times(X, times(Y, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 35 }
13.22/13.50	  times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(times(Y, X), sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.50	= { by lemma 42 }
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(times(Y, X), sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 41 }
13.22/13.50	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Y, X))))
13.22/13.50	= { by lemma 46 }
13.22/13.50	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(X, times(sK3_conjecture_1_B, Y)))))
13.22/13.50	= { by lemma 41 }
13.22/13.50	  times(sK3_conjecture_1_B, times(times(X, times(sK3_conjecture_1_B, Y)), sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 23 }
13.22/13.50	  times(sK3_conjecture_1_B, times(X, times(sK3_conjecture_1_B, Y)))
13.22/13.50	= { by lemma 46 }
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Y, X))
13.22/13.50	= { by lemma 47 }
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y))
13.22/13.50	
13.22/13.50	Lemma 49: times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y)) = times(X, times(Y, sK1_axiom_2_C(sK3_conjecture_1_B))).
13.22/13.50	Proof:
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, Y))
13.22/13.50	= { by lemma 47 }
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Y, X))
13.22/13.50	= { by lemma 46 }
13.22/13.50	  times(sK3_conjecture_1_B, times(X, times(sK3_conjecture_1_B, Y)))
13.22/13.50	= { by lemma 23 }
13.22/13.50	  times(sK3_conjecture_1_B, times(times(X, times(sK3_conjecture_1_B, Y)), sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 41 }
13.22/13.50	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(X, times(sK3_conjecture_1_B, Y)))))
13.22/13.50	= { by lemma 46 }
13.22/13.50	  times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Y, X))))
13.22/13.50	= { by lemma 41 }
13.22/13.50	  times(sK1_axiom_2_C(sK3_conjecture_1_B), times(times(Y, X), sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 42 }
13.22/13.50	  times(times(Y, X), sK1_axiom_2_C(sK3_conjecture_1_B))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y))
13.22/13.50	= { by lemma 35 }
13.22/13.50	  times(X, times(Y, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	
13.22/13.50	Lemma 50: times(sK2_conjecture_1_A, times(Y, times(sK2_conjecture_1_A, X))) = times(sK1_axiom_2_C(sK2_conjecture_1_A), times(X, Y)).
13.22/13.50	Proof:
13.22/13.50	  times(sK2_conjecture_1_A, times(Y, times(sK2_conjecture_1_A, X)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(sK2_conjecture_1_A, times(times(X, Y), sK2_conjecture_1_A))
13.22/13.50	= { by lemma 17 }
13.22/13.50	  times(sK1_axiom_2_C(sK2_conjecture_1_A), times(X, Y))
13.22/13.50	
13.22/13.50	Lemma 52: times(X, times(Y, times(W, times(V, Z)))) = times(Z, times(V, times(X, times(Y, W)))).
13.22/13.50	Proof:
13.22/13.50	  times(X, times(Y, times(W, times(V, Z))))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(X, times(Y, times(times(Z, W), V)))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(times(Z, W), times(V, times(X, Y)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(times(V, times(X, Y)), Z))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(times(X, Y), times(Z, V)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(Y, times(times(Z, V), X)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(Y, times(V, times(X, Z))))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(W, times(X, times(Z, times(Y, V))))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(Z, times(times(Y, V), times(W, X)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(Z, times(V, times(times(W, X), Y)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(Z, times(V, times(X, times(Y, W))))
13.22/13.50	
13.22/13.50	Lemma 52: times(Z, times(V, times(X, times(Y, W)))) = times(X, times(Y, times(W, times(V, Z)))).
13.22/13.50	Proof:
13.22/13.50	  times(Z, times(V, times(X, times(Y, W))))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(Z, times(V, times(times(W, X), Y)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(Z, times(times(Y, V), times(W, X)))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(W, times(X, times(Z, times(Y, V))))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(W, times(Y, times(V, times(X, Z))))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(Y, times(times(Z, V), X)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(times(X, Y), times(Z, V)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(times(V, times(X, Y)), Z))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(times(Z, W), times(V, times(X, Y)))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(X, times(Y, times(times(Z, W), V)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(X, times(Y, times(W, times(V, Z))))
13.22/13.50	
13.22/13.50	Lemma 53: times(X, times(Y, times(Z, times(W, V)))) = times(Z, times(V, times(X, times(Y, W)))).
13.22/13.50	Proof:
13.22/13.50	  times(X, times(Y, times(Z, times(W, V))))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(Z, times(times(W, V), times(X, Y)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(Z, times(V, times(times(X, Y), W)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(Z, times(V, times(Y, times(W, X))))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(Z, times(W, times(X, times(V, Y))))
13.22/13.50	= { by lemma 52 }
13.22/13.50	  times(X, times(V, times(Y, times(W, Z))))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(X, times(V, times(times(Z, Y), W)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(X, times(times(W, V), times(Z, Y)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(X, times(times(Y, times(W, V)), Z))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(times(Z, X), times(Y, times(W, V)))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(W, times(V, times(times(Z, X), Y)))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(W, times(V, times(X, times(Y, Z))))
13.22/13.50	= { by lemma 52 }
13.22/13.50	  times(Z, times(Y, times(W, times(V, X))))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(Z, times(V, times(X, times(Y, W))))
13.22/13.50	
13.22/13.50	Lemma 55: times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y)) = times(Y, times(X, sK1_axiom_2_C(sK3_conjecture_1_B))).
13.22/13.50	Proof:
13.22/13.50	  times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y))
13.22/13.50	= { by lemma 25 }
13.22/13.50	  times(Y, times(sK1_axiom_2_C(sK3_conjecture_1_B), X))
13.22/13.50	= { by lemma 35 }
13.22/13.50	  times(Y, times(X, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	
13.22/13.50	Lemma 55: times(Y, times(X, sK1_axiom_2_C(sK3_conjecture_1_B))) = times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y)).
13.22/13.50	Proof:
13.22/13.50	  times(Y, times(X, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 35 }
13.22/13.50	  times(Y, times(sK1_axiom_2_C(sK3_conjecture_1_B), X))
13.22/13.50	= { by lemma 25 }
13.22/13.50	  times(X, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y))
13.22/13.50	
13.22/13.50	Lemma 56: times(X, times(Y, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), Z)))) = times(X, times(Y, times(Z, sK3_conjecture_1_B))).
13.22/13.50	Proof:
13.22/13.50	  times(X, times(Y, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), Z))))
13.22/13.50	= { by lemma 52 }
13.22/13.50	  times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Z, times(Y, X))))
13.22/13.50	= { by lemma 53 }
13.22/13.50	  times(Z, times(X, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), Y))))
13.22/13.50	= { by lemma 52 }
13.22/13.50	  times(Y, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(Z, times(X, sK3_conjecture_1_B))))
13.22/13.50	= { by lemma 53 }
13.22/13.50	  times(Z, times(sK3_conjecture_1_B, times(Y, times(sK1_axiom_2_C(sK3_conjecture_1_B), X))))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(Z, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(X, times(sK3_conjecture_1_B, Y))))
13.22/13.50	= { by axiom 5 (axiom_1) }
13.22/13.50	  times(Z, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(times(Y, X), sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 21 }
13.22/13.50	  times(Z, times(sK3_conjecture_1_B, times(Y, X)))
13.22/13.50	= { by lemma 40 }
13.22/13.50	  times(Z, times(Y, times(X, sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 22 }
13.22/13.50	  times(X, times(sK3_conjecture_1_B, times(Z, Y)))
13.22/13.50	= { by lemma 40 }
13.22/13.50	  times(X, times(Z, times(Y, sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 33 }
13.22/13.50	  times(X, times(Y, times(Z, sK3_conjecture_1_B)))
13.22/13.50	
13.22/13.50	Lemma 57: times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), X)) = times(X, sK3_conjecture_1_B).
13.22/13.50	Proof:
13.22/13.50	  times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), X))
13.22/13.50	= { by lemma 55 }
13.22/13.50	  times(X, times(sK3_conjecture_1_B, sK1_axiom_2_C(sK3_conjecture_1_B)))
13.22/13.50	= { by lemma 13 }
13.28/13.54	  times(X, sK3_conjecture_1_B)
13.28/13.54	
13.28/13.54	Goal 1 (conjecture_1_2): element(times(sK2_conjecture_1_A, sK3_conjecture_1_B)) = $$true.
13.28/13.54	Proof:
13.28/13.54	  element(times(sK2_conjecture_1_A, sK3_conjecture_1_B))
13.28/13.54	= { by lemma 28 }
13.28/13.54	  element(times(sK3_conjecture_1_B, sK2_conjecture_1_A))
13.28/13.54	= { by lemma 32 }
13.28/13.54	  element(times(sK2_conjecture_1_A, sK3_conjecture_1_B))
13.28/13.54	= { by lemma 57 }
13.28/13.54	  element(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 1 (axiom_2) }
13.28/13.54	  $$fresh4(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A))), times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A))))
13.28/13.54	= { by axiom 8 (axiom_2) }
13.28/13.54	  $$fresh3(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 56 }
13.28/13.54	  $$fresh3(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A), times(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), sK3_conjecture_1_B)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(times(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B))))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 40 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), sK3_conjecture_1_B))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 22 }
13.28/13.54	  $$fresh3(times(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), times(sK3_conjecture_1_B, times(sK2_conjecture_1_A, sK1_axiom_2_C(sK3_conjecture_1_B)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), times(times(sK1_axiom_2_C(sK3_conjecture_1_B), sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 16 }
13.28/13.54	  $$fresh3(times(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), times(sK3_conjecture_1_B, sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 28 }
13.28/13.54	  $$fresh3(times(times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 45 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK2_conjecture_1_A, sK3_conjecture_1_B)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A), times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK3_conjecture_1_B)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(sK2_conjecture_1_A, times(times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B))))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 49 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(sK2_conjecture_1_A, times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK3_conjecture_1_B))))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 26 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(times(sK2_conjecture_1_A, times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK3_conjecture_1_B)), sK3_conjecture_1_B)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK3_conjecture_1_B), times(sK3_conjecture_1_B, sK2_conjecture_1_A))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 45 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK3_conjecture_1_B), sK3_conjecture_1_B))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(sK3_conjecture_1_B, times(sK2_conjecture_1_A, sK3_conjecture_1_B))))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 28 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK3_conjecture_1_B)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 15 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK3_conjecture_1_B), times(sK2_conjecture_1_A, sK3_conjecture_1_B)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 35 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(times(sK2_conjecture_1_A, sK3_conjecture_1_B), sK1_axiom_2_C(sK3_conjecture_1_B)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 56 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, sK3_conjecture_1_B))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 32 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK2_conjecture_1_A, times(sK3_conjecture_1_B, sK2_conjecture_1_A))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 32 }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(times(sK3_conjecture_1_B, sK2_conjecture_1_A), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 17 }
13.28/13.54	  $$fresh3(times(sK1_axiom_2_C(sK2_conjecture_1_A), times(sK3_conjecture_1_B, sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 38 }
13.28/13.54	  $$fresh3(times(times(sK3_conjecture_1_B, sK2_conjecture_1_A), sK1_axiom_2_C(sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by axiom 5 (axiom_1) }
13.28/13.54	  $$fresh3(times(sK2_conjecture_1_A, times(sK1_axiom_2_C(sK2_conjecture_1_A), sK3_conjecture_1_B)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 29 }
13.28/13.54	  $$fresh3(times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK2_conjecture_1_A), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 38 }
13.28/13.54	  $$fresh3(times(sK3_conjecture_1_B, times(sK2_conjecture_1_A, sK1_axiom_2_C(sK2_conjecture_1_A))), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 14 }
13.28/13.54	  $$fresh3(times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 57 }
13.28/13.54	  $$fresh3(times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK2_conjecture_1_A, sK3_conjecture_1_B), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 32 }
13.28/13.54	  $$fresh3(times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK3_conjecture_1_B, times(sK1_axiom_2_C(sK3_conjecture_1_B), sK2_conjecture_1_A)))
13.28/13.54	= { by lemma 57 }
13.28/13.54	  $$fresh3(times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK2_conjecture_1_A, sK3_conjecture_1_B))
13.28/13.54	= { by lemma 32 }
13.28/13.54	  $$fresh3(times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK3_conjecture_1_B, sK2_conjecture_1_A), times(sK3_conjecture_1_B, sK2_conjecture_1_A))
13.28/13.54	= { by axiom 2 (axiom_2) }
13.28/13.54	  $$true
13.28/13.54	% SZS output end Proof
13.28/13.54	
13.28/13.54	RESULT: Theorem (the conjecture is true).
13.28/13.54	EOF