TSTP Solution File: GRP778+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP778+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:20:05 EDT 2023
% Result : Theorem 34.13s 4.78s
% Output : Proof 38.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP778+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 00:33:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 34.13/4.78 Command-line arguments: --ground-connectedness --complete-subsets
% 34.13/4.78
% 34.13/4.78 % SZS status Theorem
% 34.13/4.78
% 37.99/5.21 % SZS output start Proof
% 37.99/5.21 Take the following subset of the input axioms:
% 37.99/5.21 fof(goals, conjecture, m(b1, b, b2)).
% 37.99/5.21 fof(sos01, axiom, ![B, A]: difference(A, product(A, B))=B).
% 37.99/5.21 fof(sos02, axiom, ![B2, A2]: product(A2, difference(A2, B2))=B2).
% 37.99/5.21 fof(sos03, axiom, ![B2, A2]: quotient(product(A2, B2), B2)=A2).
% 37.99/5.21 fof(sos04, axiom, ![B2, A2]: product(quotient(A2, B2), B2)=A2).
% 37.99/5.21 fof(sos05, axiom, ![D, C, B2, A2]: product(product(A2, B2), product(C, D))=product(product(A2, C), product(B2, D))).
% 37.99/5.21 fof(sos06, axiom, ![A2]: product(A2, A2)=A2).
% 37.99/5.21 fof(sos07, axiom, ![B2, A2]: product(product(product(A2, B2), B2), product(B2, product(B2, A2)))=B2).
% 37.99/5.21 fof(sos08, axiom, ![X0, X1, X2]: (d(X0, X1, X2) <=> product(X0, X1)=product(X1, X2))).
% 37.99/5.21 fof(sos09, axiom, ![X3, X4, X5]: (m(X3, X4, X5) <=> product(product(X3, X4), product(X4, X5))=product(X3, X5))).
% 37.99/5.21 fof(sos10, axiom, d(a1, b, c)).
% 37.99/5.21 fof(sos11, axiom, d(a, b1, c)).
% 37.99/5.21 fof(sos12, axiom, d(a, b, c1)).
% 37.99/5.21 fof(sos13, axiom, d(a2, b1, c1)).
% 37.99/5.21 fof(sos14, axiom, d(a1, b2, c1)).
% 37.99/5.21 fof(sos15, axiom, d(a1, b1, c2)).
% 37.99/5.21
% 37.99/5.21 Now clausify the problem and encode Horn clauses using encoding 3 of
% 37.99/5.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 37.99/5.21 We repeatedly replace C & s=t => u=v by the two clauses:
% 37.99/5.21 fresh(y, y, x1...xn) = u
% 37.99/5.21 C => fresh(s, t, x1...xn) = v
% 37.99/5.21 where fresh is a fresh function symbol and x1..xn are the free
% 37.99/5.21 variables of u and v.
% 37.99/5.21 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 37.99/5.21 input problem has no model of domain size 1).
% 37.99/5.21
% 37.99/5.21 The encoding turns the above axioms into the following unit equations and goals:
% 37.99/5.21
% 37.99/5.21 Axiom 1 (sos06): product(X, X) = X.
% 37.99/5.21 Axiom 2 (sos13): d(a2, b1, c1) = true.
% 37.99/5.21 Axiom 3 (sos12): d(a, b, c1) = true.
% 37.99/5.21 Axiom 4 (sos11): d(a, b1, c) = true.
% 37.99/5.21 Axiom 5 (sos14): d(a1, b2, c1) = true.
% 37.99/5.21 Axiom 6 (sos10): d(a1, b, c) = true.
% 37.99/5.21 Axiom 7 (sos15): d(a1, b1, c2) = true.
% 37.99/5.21 Axiom 8 (sos01): difference(X, product(X, Y)) = Y.
% 37.99/5.21 Axiom 9 (sos03): quotient(product(X, Y), Y) = X.
% 37.99/5.21 Axiom 10 (sos02): product(X, difference(X, Y)) = Y.
% 37.99/5.21 Axiom 11 (sos04): product(quotient(X, Y), Y) = X.
% 37.99/5.21 Axiom 12 (sos08_1): fresh4(X, X, Y, Z, W) = product(Z, W).
% 37.99/5.21 Axiom 13 (sos09): fresh2(X, X, Y, Z, W) = true.
% 37.99/5.21 Axiom 14 (sos05): product(product(X, Y), product(Z, W)) = product(product(X, Z), product(Y, W)).
% 37.99/5.21 Axiom 15 (sos08_1): fresh4(d(X, Y, Z), true, X, Y, Z) = product(X, Y).
% 37.99/5.21 Axiom 16 (sos07): product(product(product(X, Y), Y), product(Y, product(Y, X))) = Y.
% 37.99/5.21 Axiom 17 (sos09): fresh2(product(product(X, Y), product(Y, Z)), product(X, Z), X, Y, Z) = m(X, Y, Z).
% 37.99/5.21
% 37.99/5.21 Lemma 18: product(b, c) = product(a1, b).
% 37.99/5.21 Proof:
% 37.99/5.21 product(b, c)
% 37.99/5.21 = { by axiom 12 (sos08_1) R->L }
% 37.99/5.21 fresh4(true, true, a1, b, c)
% 37.99/5.21 = { by axiom 6 (sos10) R->L }
% 37.99/5.21 fresh4(d(a1, b, c), true, a1, b, c)
% 37.99/5.21 = { by axiom 15 (sos08_1) }
% 37.99/5.21 product(a1, b)
% 37.99/5.21
% 37.99/5.21 Lemma 19: product(product(X, Y), product(X, Z)) = product(X, product(Y, Z)).
% 37.99/5.21 Proof:
% 37.99/5.21 product(product(X, Y), product(X, Z))
% 37.99/5.21 = { by axiom 14 (sos05) R->L }
% 37.99/5.21 product(product(X, X), product(Y, Z))
% 37.99/5.21 = { by axiom 1 (sos06) }
% 37.99/5.21 product(X, product(Y, Z))
% 37.99/5.21
% 37.99/5.21 Lemma 20: difference(X, product(Y, product(X, Z))) = product(difference(X, Y), Z).
% 37.99/5.21 Proof:
% 37.99/5.21 difference(X, product(Y, product(X, Z)))
% 37.99/5.21 = { by axiom 10 (sos02) R->L }
% 37.99/5.21 difference(X, product(product(X, difference(X, Y)), product(X, Z)))
% 37.99/5.21 = { by lemma 19 }
% 37.99/5.21 difference(X, product(X, product(difference(X, Y), Z)))
% 37.99/5.21 = { by axiom 8 (sos01) }
% 37.99/5.21 product(difference(X, Y), Z)
% 37.99/5.21
% 37.99/5.21 Lemma 21: product(difference(X, Y), X) = difference(X, product(Y, X)).
% 37.99/5.21 Proof:
% 37.99/5.21 product(difference(X, Y), X)
% 37.99/5.21 = { by lemma 20 R->L }
% 37.99/5.21 difference(X, product(Y, product(X, X)))
% 37.99/5.21 = { by axiom 1 (sos06) }
% 37.99/5.21 difference(X, product(Y, X))
% 37.99/5.21
% 37.99/5.21 Lemma 22: quotient(quotient(X, product(X, Y)), X) = difference(X, product(Y, X)).
% 37.99/5.21 Proof:
% 37.99/5.21 quotient(quotient(X, product(X, Y)), X)
% 37.99/5.21 = { by axiom 10 (sos02) R->L }
% 37.99/5.21 quotient(quotient(X, product(X, product(X, difference(X, Y)))), X)
% 37.99/5.21 = { by axiom 16 (sos07) R->L }
% 37.99/5.21 quotient(quotient(product(product(product(difference(X, Y), X), X), product(X, product(X, difference(X, Y)))), product(X, product(X, difference(X, Y)))), X)
% 37.99/5.21 = { by axiom 9 (sos03) }
% 37.99/5.21 quotient(product(product(difference(X, Y), X), X), X)
% 37.99/5.21 = { by axiom 9 (sos03) }
% 37.99/5.21 product(difference(X, Y), X)
% 37.99/5.21 = { by lemma 21 }
% 37.99/5.21 difference(X, product(Y, X))
% 37.99/5.21
% 37.99/5.21 Lemma 23: product(product(X, Y), product(Z, Y)) = product(product(X, Z), Y).
% 37.99/5.21 Proof:
% 37.99/5.21 product(product(X, Y), product(Z, Y))
% 37.99/5.21 = { by axiom 14 (sos05) R->L }
% 37.99/5.21 product(product(X, Z), product(Y, Y))
% 37.99/5.21 = { by axiom 1 (sos06) }
% 37.99/5.21 product(product(X, Z), Y)
% 37.99/5.21
% 37.99/5.22 Lemma 24: quotient(product(product(X, Y), Z), Y) = product(X, quotient(Z, Y)).
% 37.99/5.22 Proof:
% 37.99/5.22 quotient(product(product(X, Y), Z), Y)
% 37.99/5.22 = { by axiom 11 (sos04) R->L }
% 37.99/5.22 quotient(product(product(X, Y), product(quotient(Z, Y), Y)), Y)
% 37.99/5.22 = { by lemma 23 }
% 37.99/5.22 quotient(product(product(X, quotient(Z, Y)), Y), Y)
% 37.99/5.22 = { by axiom 9 (sos03) }
% 37.99/5.22 product(X, quotient(Z, Y))
% 37.99/5.22
% 37.99/5.22 Lemma 25: product(b1, c2) = product(a1, b1).
% 37.99/5.22 Proof:
% 37.99/5.22 product(b1, c2)
% 37.99/5.22 = { by axiom 12 (sos08_1) R->L }
% 37.99/5.22 fresh4(true, true, a1, b1, c2)
% 37.99/5.22 = { by axiom 7 (sos15) R->L }
% 37.99/5.22 fresh4(d(a1, b1, c2), true, a1, b1, c2)
% 37.99/5.22 = { by axiom 15 (sos08_1) }
% 37.99/5.22 product(a1, b1)
% 37.99/5.22
% 37.99/5.22 Lemma 26: product(b1, c) = product(a, b1).
% 37.99/5.22 Proof:
% 37.99/5.22 product(b1, c)
% 37.99/5.22 = { by axiom 12 (sos08_1) R->L }
% 37.99/5.22 fresh4(true, true, a, b1, c)
% 37.99/5.22 = { by axiom 4 (sos11) R->L }
% 37.99/5.22 fresh4(d(a, b1, c), true, a, b1, c)
% 37.99/5.22 = { by axiom 15 (sos08_1) }
% 37.99/5.22 product(a, b1)
% 37.99/5.22
% 37.99/5.22 Lemma 27: product(product(b1, X), c) = product(a, product(X, b1)).
% 37.99/5.22 Proof:
% 37.99/5.22 product(product(b1, X), c)
% 37.99/5.22 = { by lemma 23 R->L }
% 37.99/5.22 product(product(b1, c), product(X, c))
% 37.99/5.22 = { by lemma 26 }
% 37.99/5.22 product(product(a, b1), product(X, c))
% 37.99/5.22 = { by axiom 14 (sos05) }
% 37.99/5.22 product(product(a, X), product(b1, c))
% 37.99/5.22 = { by lemma 26 }
% 37.99/5.22 product(product(a, X), product(a, b1))
% 37.99/5.22 = { by lemma 19 }
% 37.99/5.22 product(a, product(X, b1))
% 37.99/5.22
% 37.99/5.22 Lemma 28: product(product(quotient(X, Y), Z), Y) = product(X, product(Z, Y)).
% 37.99/5.22 Proof:
% 37.99/5.22 product(product(quotient(X, Y), Z), Y)
% 37.99/5.22 = { by lemma 23 R->L }
% 37.99/5.22 product(product(quotient(X, Y), Y), product(Z, Y))
% 37.99/5.22 = { by axiom 11 (sos04) }
% 37.99/5.22 product(X, product(Z, Y))
% 37.99/5.22
% 37.99/5.22 Lemma 29: quotient(product(X, product(Y, Z)), Z) = product(quotient(X, Z), Y).
% 37.99/5.22 Proof:
% 37.99/5.22 quotient(product(X, product(Y, Z)), Z)
% 37.99/5.22 = { by lemma 28 R->L }
% 37.99/5.22 quotient(product(product(quotient(X, Z), Y), Z), Z)
% 37.99/5.22 = { by axiom 9 (sos03) }
% 37.99/5.22 product(quotient(X, Z), Y)
% 37.99/5.22
% 37.99/5.22 Lemma 30: product(product(X, c2), product(a1, b1)) = product(product(X, b1), c2).
% 37.99/5.22 Proof:
% 37.99/5.22 product(product(X, c2), product(a1, b1))
% 37.99/5.22 = { by lemma 25 R->L }
% 37.99/5.22 product(product(X, c2), product(b1, c2))
% 37.99/5.22 = { by lemma 23 }
% 37.99/5.22 product(product(X, b1), c2)
% 37.99/5.22
% 37.99/5.22 Lemma 31: product(a1, c) = product(a, c2).
% 37.99/5.22 Proof:
% 37.99/5.22 product(a1, c)
% 37.99/5.22 = { by axiom 11 (sos04) R->L }
% 37.99/5.22 product(a1, product(quotient(c, b1), b1))
% 37.99/5.22 = { by lemma 19 R->L }
% 37.99/5.22 product(product(a1, quotient(c, b1)), product(a1, b1))
% 37.99/5.22 = { by lemma 24 R->L }
% 37.99/5.22 product(quotient(product(product(a1, b1), c), b1), product(a1, b1))
% 37.99/5.22 = { by lemma 25 R->L }
% 37.99/5.22 product(quotient(product(product(b1, c2), c), b1), product(a1, b1))
% 37.99/5.22 = { by lemma 27 }
% 37.99/5.22 product(quotient(product(a, product(c2, b1)), b1), product(a1, b1))
% 37.99/5.22 = { by lemma 29 }
% 37.99/5.22 product(product(quotient(a, b1), c2), product(a1, b1))
% 37.99/5.22 = { by lemma 30 }
% 37.99/5.22 product(product(quotient(a, b1), b1), c2)
% 37.99/5.22 = { by axiom 11 (sos04) }
% 37.99/5.22 product(a, c2)
% 37.99/5.22
% 37.99/5.22 Lemma 32: difference(product(product(X, Y), Y), Y) = product(Y, product(Y, X)).
% 37.99/5.22 Proof:
% 37.99/5.22 difference(product(product(X, Y), Y), Y)
% 37.99/5.22 = { by axiom 16 (sos07) R->L }
% 37.99/5.22 difference(product(product(X, Y), Y), product(product(product(X, Y), Y), product(Y, product(Y, X))))
% 37.99/5.22 = { by axiom 8 (sos01) }
% 37.99/5.22 product(Y, product(Y, X))
% 37.99/5.22
% 37.99/5.22 Lemma 33: product(product(a, c2), product(c, b)) = c.
% 37.99/5.22 Proof:
% 37.99/5.22 product(product(a, c2), product(c, b))
% 37.99/5.22 = { by lemma 31 R->L }
% 37.99/5.22 product(product(a1, c), product(c, b))
% 37.99/5.22 = { by lemma 23 R->L }
% 37.99/5.22 product(product(a1, product(c, b)), product(c, product(c, b)))
% 37.99/5.22 = { by lemma 32 R->L }
% 37.99/5.22 product(product(a1, product(c, b)), difference(product(product(b, c), c), c))
% 37.99/5.22 = { by lemma 23 R->L }
% 37.99/5.22 product(product(a1, product(c, b)), difference(product(product(b, c), product(c, c)), c))
% 37.99/5.22 = { by lemma 18 }
% 37.99/5.22 product(product(a1, product(c, b)), difference(product(product(a1, b), product(c, c)), c))
% 37.99/5.22 = { by axiom 14 (sos05) }
% 37.99/5.22 product(product(a1, product(c, b)), difference(product(product(a1, c), product(b, c)), c))
% 37.99/5.22 = { by lemma 18 }
% 37.99/5.22 product(product(a1, product(c, b)), difference(product(product(a1, c), product(a1, b)), c))
% 37.99/5.22 = { by lemma 19 }
% 37.99/5.22 product(product(a1, product(c, b)), difference(product(a1, product(c, b)), c))
% 37.99/5.22 = { by axiom 10 (sos02) }
% 37.99/5.22 c
% 37.99/5.22
% 37.99/5.22 Lemma 34: product(a1, b) = product(c, a1).
% 37.99/5.22 Proof:
% 37.99/5.22 product(a1, b)
% 37.99/5.22 = { by axiom 10 (sos02) R->L }
% 37.99/5.22 product(c, difference(c, product(a1, b)))
% 37.99/5.22 = { by lemma 18 R->L }
% 37.99/5.22 product(c, difference(c, product(b, c)))
% 37.99/5.22 = { by lemma 22 R->L }
% 37.99/5.22 product(c, quotient(quotient(c, product(c, b)), c))
% 37.99/5.22 = { by lemma 33 R->L }
% 37.99/5.22 product(c, quotient(quotient(product(product(a, c2), product(c, b)), product(c, b)), c))
% 37.99/5.22 = { by axiom 9 (sos03) }
% 37.99/5.22 product(c, quotient(product(a, c2), c))
% 37.99/5.22 = { by lemma 31 R->L }
% 37.99/5.22 product(c, quotient(product(a1, c), c))
% 37.99/5.22 = { by axiom 9 (sos03) }
% 37.99/5.22 product(c, a1)
% 37.99/5.22
% 37.99/5.22 Lemma 35: product(X, product(X, quotient(Y, X))) = difference(product(Y, X), X).
% 37.99/5.22 Proof:
% 37.99/5.22 product(X, product(X, quotient(Y, X)))
% 37.99/5.22 = { by lemma 32 R->L }
% 37.99/5.22 difference(product(product(quotient(Y, X), X), X), X)
% 37.99/5.22 = { by axiom 11 (sos04) }
% 37.99/5.22 difference(product(Y, X), X)
% 37.99/5.22
% 37.99/5.22 Lemma 36: product(X, quotient(Y, X)) = quotient(product(X, Y), X).
% 37.99/5.22 Proof:
% 37.99/5.22 product(X, quotient(Y, X))
% 37.99/5.22 = { by axiom 9 (sos03) R->L }
% 37.99/5.22 quotient(product(product(X, quotient(Y, X)), X), X)
% 37.99/5.22 = { by axiom 1 (sos06) R->L }
% 37.99/5.22 quotient(product(product(X, quotient(Y, X)), product(X, X)), X)
% 37.99/5.22 = { by lemma 19 }
% 37.99/5.22 quotient(product(X, product(quotient(Y, X), X)), X)
% 37.99/5.22 = { by axiom 11 (sos04) }
% 37.99/5.22 quotient(product(X, Y), X)
% 37.99/5.22
% 37.99/5.22 Lemma 37: difference(X, difference(product(Y, X), X)) = quotient(product(X, Y), X).
% 37.99/5.22 Proof:
% 37.99/5.22 difference(X, difference(product(Y, X), X))
% 37.99/5.22 = { by lemma 35 R->L }
% 37.99/5.22 difference(X, product(X, product(X, quotient(Y, X))))
% 37.99/5.22 = { by axiom 8 (sos01) }
% 37.99/5.22 product(X, quotient(Y, X))
% 37.99/5.22 = { by lemma 36 }
% 37.99/5.22 quotient(product(X, Y), X)
% 37.99/5.22
% 37.99/5.22 Lemma 38: product(a1, b1) = product(c2, a1).
% 37.99/5.22 Proof:
% 37.99/5.22 product(a1, b1)
% 37.99/5.22 = { by lemma 25 R->L }
% 37.99/5.22 product(b1, c2)
% 37.99/5.22 = { by axiom 8 (sos01) R->L }
% 37.99/5.22 product(difference(c2, product(c2, b1)), c2)
% 37.99/5.22 = { by axiom 8 (sos01) R->L }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, c2), product(c2, b1)))), c2)
% 37.99/5.22 = { by lemma 23 R->L }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, product(c2, b1)), product(c2, product(c2, b1))))), c2)
% 37.99/5.22 = { by lemma 32 R->L }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, product(c2, b1)), difference(product(product(b1, c2), c2), c2)))), c2)
% 37.99/5.22 = { by lemma 23 R->L }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, product(c2, b1)), difference(product(product(b1, c2), product(c2, c2)), c2)))), c2)
% 37.99/5.22 = { by lemma 25 }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, product(c2, b1)), difference(product(product(a1, b1), product(c2, c2)), c2)))), c2)
% 37.99/5.22 = { by axiom 14 (sos05) }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, product(c2, b1)), difference(product(product(a1, c2), product(b1, c2)), c2)))), c2)
% 37.99/5.22 = { by lemma 25 }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, product(c2, b1)), difference(product(product(a1, c2), product(a1, b1)), c2)))), c2)
% 37.99/5.22 = { by lemma 19 }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), product(product(a1, product(c2, b1)), difference(product(a1, product(c2, b1)), c2)))), c2)
% 37.99/5.22 = { by axiom 10 (sos02) }
% 37.99/5.22 product(difference(c2, difference(product(a1, c2), c2)), c2)
% 37.99/5.22 = { by lemma 37 }
% 37.99/5.22 product(quotient(product(c2, a1), c2), c2)
% 37.99/5.22 = { by axiom 11 (sos04) }
% 37.99/5.22 product(c2, a1)
% 37.99/5.22
% 37.99/5.22 Lemma 39: product(b1, c1) = product(a2, b1).
% 37.99/5.22 Proof:
% 37.99/5.22 product(b1, c1)
% 37.99/5.22 = { by axiom 12 (sos08_1) R->L }
% 37.99/5.22 fresh4(true, true, a2, b1, c1)
% 37.99/5.22 = { by axiom 2 (sos13) R->L }
% 37.99/5.22 fresh4(d(a2, b1, c1), true, a2, b1, c1)
% 37.99/5.22 = { by axiom 15 (sos08_1) }
% 37.99/5.23 product(a2, b1)
% 37.99/5.23
% 37.99/5.23 Lemma 40: product(a1, c1) = product(a2, c2).
% 37.99/5.23 Proof:
% 37.99/5.23 product(a1, c1)
% 37.99/5.23 = { by axiom 11 (sos04) R->L }
% 37.99/5.23 product(a1, product(quotient(c1, b1), b1))
% 37.99/5.23 = { by lemma 19 R->L }
% 37.99/5.23 product(product(a1, quotient(c1, b1)), product(a1, b1))
% 37.99/5.23 = { by lemma 24 R->L }
% 37.99/5.23 product(quotient(product(product(a1, b1), c1), b1), product(a1, b1))
% 37.99/5.23 = { by lemma 25 R->L }
% 37.99/5.23 product(quotient(product(product(b1, c2), c1), b1), product(a1, b1))
% 37.99/5.23 = { by lemma 23 R->L }
% 37.99/5.23 product(quotient(product(product(b1, c1), product(c2, c1)), b1), product(a1, b1))
% 37.99/5.23 = { by lemma 39 }
% 37.99/5.23 product(quotient(product(product(a2, b1), product(c2, c1)), b1), product(a1, b1))
% 37.99/5.23 = { by axiom 14 (sos05) }
% 37.99/5.23 product(quotient(product(product(a2, c2), product(b1, c1)), b1), product(a1, b1))
% 37.99/5.23 = { by lemma 39 }
% 37.99/5.23 product(quotient(product(product(a2, c2), product(a2, b1)), b1), product(a1, b1))
% 37.99/5.23 = { by lemma 19 }
% 37.99/5.23 product(quotient(product(a2, product(c2, b1)), b1), product(a1, b1))
% 37.99/5.23 = { by lemma 29 }
% 37.99/5.23 product(product(quotient(a2, b1), c2), product(a1, b1))
% 37.99/5.23 = { by lemma 30 }
% 37.99/5.23 product(product(quotient(a2, b1), b1), c2)
% 37.99/5.23 = { by axiom 11 (sos04) }
% 37.99/5.23 product(a2, c2)
% 37.99/5.23
% 37.99/5.23 Lemma 41: product(b, c1) = product(a, b).
% 37.99/5.23 Proof:
% 37.99/5.23 product(b, c1)
% 37.99/5.23 = { by axiom 12 (sos08_1) R->L }
% 37.99/5.23 fresh4(true, true, a, b, c1)
% 37.99/5.23 = { by axiom 3 (sos12) R->L }
% 37.99/5.23 fresh4(d(a, b, c1), true, a, b, c1)
% 37.99/5.23 = { by axiom 15 (sos08_1) }
% 37.99/5.23 product(a, b)
% 37.99/5.23
% 37.99/5.23 Lemma 42: product(product(a, b), product(X, c1)) = product(product(b, X), c1).
% 37.99/5.23 Proof:
% 37.99/5.23 product(product(a, b), product(X, c1))
% 37.99/5.23 = { by lemma 41 R->L }
% 37.99/5.23 product(product(b, c1), product(X, c1))
% 37.99/5.23 = { by lemma 23 }
% 37.99/5.23 product(product(b, X), c1)
% 37.99/5.23
% 37.99/5.23 Lemma 43: product(product(b, X), c1) = product(a, product(X, b)).
% 37.99/5.23 Proof:
% 37.99/5.23 product(product(b, X), c1)
% 37.99/5.23 = { by lemma 42 R->L }
% 37.99/5.23 product(product(a, b), product(X, c1))
% 37.99/5.23 = { by axiom 14 (sos05) }
% 37.99/5.23 product(product(a, X), product(b, c1))
% 37.99/5.23 = { by lemma 41 }
% 37.99/5.23 product(product(a, X), product(a, b))
% 37.99/5.23 = { by lemma 19 }
% 37.99/5.23 product(a, product(X, b))
% 37.99/5.23
% 37.99/5.23 Lemma 44: product(a, c) = product(a2, c2).
% 37.99/5.23 Proof:
% 37.99/5.23 product(a, c)
% 37.99/5.23 = { by axiom 11 (sos04) R->L }
% 37.99/5.23 product(product(quotient(a, b), b), c)
% 37.99/5.23 = { by lemma 23 R->L }
% 37.99/5.23 product(product(quotient(a, b), c), product(b, c))
% 37.99/5.23 = { by lemma 18 }
% 37.99/5.23 product(product(quotient(a, b), c), product(a1, b))
% 37.99/5.23 = { by lemma 29 R->L }
% 37.99/5.23 product(quotient(product(a, product(c, b)), b), product(a1, b))
% 37.99/5.23 = { by lemma 43 R->L }
% 37.99/5.23 product(quotient(product(product(b, c), c1), b), product(a1, b))
% 37.99/5.23 = { by lemma 18 }
% 37.99/5.23 product(quotient(product(product(a1, b), c1), b), product(a1, b))
% 37.99/5.23 = { by lemma 24 }
% 37.99/5.23 product(product(a1, quotient(c1, b)), product(a1, b))
% 37.99/5.23 = { by lemma 19 }
% 37.99/5.23 product(a1, product(quotient(c1, b), b))
% 37.99/5.23 = { by axiom 11 (sos04) }
% 37.99/5.23 product(a1, c1)
% 37.99/5.23 = { by lemma 40 }
% 37.99/5.23 product(a2, c2)
% 37.99/5.23
% 37.99/5.23 Lemma 45: product(product(a2, c2), product(c, b1)) = c.
% 37.99/5.23 Proof:
% 37.99/5.23 product(product(a2, c2), product(c, b1))
% 37.99/5.23 = { by lemma 44 R->L }
% 37.99/5.23 product(product(a, c), product(c, b1))
% 37.99/5.23 = { by lemma 23 R->L }
% 37.99/5.23 product(product(a, product(c, b1)), product(c, product(c, b1)))
% 37.99/5.23 = { by lemma 32 R->L }
% 37.99/5.23 product(product(a, product(c, b1)), difference(product(product(b1, c), c), c))
% 37.99/5.23 = { by lemma 27 }
% 37.99/5.23 product(product(a, product(c, b1)), difference(product(a, product(c, b1)), c))
% 37.99/5.23 = { by axiom 10 (sos02) }
% 37.99/5.23 c
% 37.99/5.23
% 37.99/5.23 Lemma 46: product(a, b1) = product(c, a).
% 37.99/5.23 Proof:
% 37.99/5.23 product(a, b1)
% 37.99/5.23 = { by axiom 10 (sos02) R->L }
% 37.99/5.23 product(c, difference(c, product(a, b1)))
% 37.99/5.23 = { by lemma 26 R->L }
% 37.99/5.23 product(c, difference(c, product(b1, c)))
% 37.99/5.23 = { by lemma 22 R->L }
% 37.99/5.23 product(c, quotient(quotient(c, product(c, b1)), c))
% 37.99/5.23 = { by lemma 45 R->L }
% 37.99/5.23 product(c, quotient(quotient(product(product(a2, c2), product(c, b1)), product(c, b1)), c))
% 37.99/5.23 = { by axiom 9 (sos03) }
% 37.99/5.23 product(c, quotient(product(a2, c2), c))
% 37.99/5.23 = { by lemma 44 R->L }
% 37.99/5.23 product(c, quotient(product(a, c), c))
% 37.99/5.23 = { by axiom 9 (sos03) }
% 37.99/5.23 product(c, a)
% 37.99/5.23
% 37.99/5.23 Lemma 47: product(b2, c1) = product(a1, b2).
% 37.99/5.23 Proof:
% 37.99/5.23 product(b2, c1)
% 37.99/5.23 = { by axiom 12 (sos08_1) R->L }
% 37.99/5.23 fresh4(true, true, a1, b2, c1)
% 37.99/5.23 = { by axiom 5 (sos14) R->L }
% 37.99/5.23 fresh4(d(a1, b2, c1), true, a1, b2, c1)
% 37.99/5.23 = { by axiom 15 (sos08_1) }
% 37.99/5.23 product(a1, b2)
% 37.99/5.23
% 37.99/5.23 Lemma 48: product(product(X, b), product(Y, c)) = product(product(X, Y), product(c, a1)).
% 37.99/5.23 Proof:
% 37.99/5.23 product(product(X, b), product(Y, c))
% 37.99/5.23 = { by axiom 14 (sos05) R->L }
% 37.99/5.23 product(product(X, Y), product(b, c))
% 37.99/5.23 = { by lemma 18 }
% 37.99/5.23 product(product(X, Y), product(a1, b))
% 37.99/5.23 = { by lemma 34 }
% 37.99/5.23 product(product(X, Y), product(c, a1))
% 37.99/5.23
% 37.99/5.23 Lemma 49: product(product(c, X), a1) = product(b, product(X, c)).
% 37.99/5.23 Proof:
% 37.99/5.23 product(product(c, X), a1)
% 37.99/5.23 = { by lemma 23 R->L }
% 37.99/5.23 product(product(c, a1), product(X, a1))
% 37.99/5.23 = { by lemma 34 R->L }
% 37.99/5.23 product(product(a1, b), product(X, a1))
% 37.99/5.23 = { by lemma 18 R->L }
% 37.99/5.23 product(product(b, c), product(X, a1))
% 37.99/5.23 = { by axiom 14 (sos05) }
% 37.99/5.23 product(product(b, X), product(c, a1))
% 37.99/5.23 = { by lemma 48 R->L }
% 37.99/5.23 product(product(b, b), product(X, c))
% 37.99/5.23 = { by axiom 1 (sos06) }
% 37.99/5.23 product(b, product(X, c))
% 37.99/5.23
% 37.99/5.23 Lemma 50: product(product(c2, X), a1) = product(b1, product(X, c2)).
% 37.99/5.23 Proof:
% 37.99/5.23 product(product(c2, X), a1)
% 37.99/5.23 = { by lemma 23 R->L }
% 37.99/5.23 product(product(c2, a1), product(X, a1))
% 37.99/5.23 = { by lemma 38 R->L }
% 37.99/5.23 product(product(a1, b1), product(X, a1))
% 37.99/5.23 = { by lemma 25 R->L }
% 37.99/5.23 product(product(b1, c2), product(X, a1))
% 37.99/5.23 = { by axiom 14 (sos05) }
% 37.99/5.23 product(product(b1, X), product(c2, a1))
% 37.99/5.23 = { by lemma 38 R->L }
% 37.99/5.23 product(product(b1, X), product(a1, b1))
% 37.99/5.23 = { by lemma 25 R->L }
% 37.99/5.23 product(product(b1, X), product(b1, c2))
% 37.99/5.23 = { by axiom 14 (sos05) }
% 37.99/5.23 product(product(b1, b1), product(X, c2))
% 37.99/5.23 = { by axiom 1 (sos06) }
% 37.99/5.23 product(b1, product(X, c2))
% 37.99/5.23
% 37.99/5.23 Lemma 51: difference(X, difference(X, product(Y, X))) = quotient(quotient(X, Y), X).
% 37.99/5.23 Proof:
% 37.99/5.23 difference(X, difference(X, product(Y, X)))
% 37.99/5.23 = { by lemma 21 R->L }
% 37.99/5.23 difference(X, product(difference(X, Y), X))
% 37.99/5.23 = { by lemma 22 R->L }
% 37.99/5.23 quotient(quotient(X, product(X, difference(X, Y))), X)
% 37.99/5.23 = { by axiom 10 (sos02) }
% 37.99/5.23 quotient(quotient(X, Y), X)
% 37.99/5.23
% 37.99/5.23 Lemma 52: product(X, product(Y, difference(X, Z))) = product(product(X, Y), Z).
% 37.99/5.23 Proof:
% 37.99/5.23 product(X, product(Y, difference(X, Z)))
% 37.99/5.23 = { by lemma 19 R->L }
% 37.99/5.23 product(product(X, Y), product(X, difference(X, Z)))
% 37.99/5.23 = { by axiom 10 (sos02) }
% 37.99/5.23 product(product(X, Y), Z)
% 37.99/5.23
% 37.99/5.23 Lemma 53: difference(product(X, Y), product(product(X, Z), Y)) = product(Z, Y).
% 37.99/5.23 Proof:
% 37.99/5.23 difference(product(X, Y), product(product(X, Z), Y))
% 37.99/5.23 = { by lemma 23 R->L }
% 37.99/5.23 difference(product(X, Y), product(product(X, Y), product(Z, Y)))
% 37.99/5.23 = { by axiom 8 (sos01) }
% 37.99/5.23 product(Z, Y)
% 37.99/5.23
% 37.99/5.23 Lemma 54: quotient(product(Y, X), Y) = difference(X, product(Y, X)).
% 37.99/5.23 Proof:
% 37.99/5.23 quotient(product(Y, X), Y)
% 37.99/5.23 = { by lemma 36 R->L }
% 37.99/5.23 product(Y, quotient(X, Y))
% 37.99/5.23 = { by axiom 9 (sos03) R->L }
% 37.99/5.23 product(Y, quotient(X, quotient(product(Y, X), X)))
% 37.99/5.23 = { by axiom 11 (sos04) R->L }
% 37.99/5.23 product(Y, product(quotient(quotient(X, quotient(product(Y, X), X)), X), X))
% 37.99/5.23 = { by lemma 51 R->L }
% 37.99/5.23 product(Y, product(difference(X, difference(X, product(quotient(product(Y, X), X), X))), X))
% 37.99/5.23 = { by lemma 21 }
% 37.99/5.23 product(Y, difference(X, product(difference(X, product(quotient(product(Y, X), X), X)), X)))
% 37.99/5.23 = { by lemma 21 }
% 37.99/5.23 product(Y, difference(X, difference(X, product(product(quotient(product(Y, X), X), X), X))))
% 37.99/5.23 = { by lemma 51 }
% 37.99/5.23 product(Y, quotient(quotient(X, product(quotient(product(Y, X), X), X)), X))
% 37.99/5.23 = { by axiom 11 (sos04) }
% 37.99/5.23 product(Y, quotient(quotient(X, product(Y, X)), X))
% 37.99/5.23 = { by axiom 10 (sos02) R->L }
% 37.99/5.24 product(Y, quotient(quotient(X, product(X, difference(X, product(Y, X)))), X))
% 37.99/5.24 = { by lemma 22 }
% 37.99/5.24 product(Y, difference(X, product(difference(X, product(Y, X)), X)))
% 37.99/5.24 = { by lemma 21 }
% 37.99/5.24 product(Y, difference(X, difference(X, product(product(Y, X), X))))
% 37.99/5.24 = { by lemma 52 R->L }
% 37.99/5.24 product(Y, difference(X, difference(X, product(Y, product(X, difference(Y, X))))))
% 37.99/5.24 = { by lemma 20 }
% 37.99/5.24 product(Y, difference(X, product(difference(X, Y), difference(Y, X))))
% 37.99/5.24 = { by axiom 10 (sos02) R->L }
% 37.99/5.24 product(Y, difference(product(Y, difference(Y, X)), product(difference(X, Y), difference(Y, X))))
% 37.99/5.24 = { by axiom 10 (sos02) R->L }
% 37.99/5.24 product(Y, difference(product(Y, difference(Y, X)), product(product(Y, difference(Y, difference(X, Y))), difference(Y, X))))
% 37.99/5.24 = { by lemma 53 }
% 37.99/5.24 product(Y, product(difference(Y, difference(X, Y)), difference(Y, X)))
% 37.99/5.24 = { by lemma 20 R->L }
% 37.99/5.24 product(Y, difference(Y, product(difference(X, Y), product(Y, difference(Y, X)))))
% 37.99/5.24 = { by axiom 10 (sos02) }
% 37.99/5.24 product(Y, difference(Y, product(difference(X, Y), X)))
% 37.99/5.24 = { by lemma 21 }
% 37.99/5.24 product(Y, difference(Y, difference(X, product(Y, X))))
% 37.99/5.24 = { by axiom 10 (sos02) }
% 37.99/5.24 difference(X, product(Y, X))
% 37.99/5.24
% 37.99/5.24 Lemma 55: difference(X, product(product(X, Y), Z)) = product(Y, difference(X, Z)).
% 37.99/5.24 Proof:
% 37.99/5.24 difference(X, product(product(X, Y), Z))
% 37.99/5.24 = { by lemma 52 R->L }
% 37.99/5.24 difference(X, product(X, product(Y, difference(X, Z))))
% 37.99/5.24 = { by axiom 8 (sos01) }
% 37.99/5.24 product(Y, difference(X, Z))
% 37.99/5.24
% 37.99/5.24 Goal 1 (goals): m(b1, b, b2) = true.
% 37.99/5.24 Proof:
% 37.99/5.24 m(b1, b, b2)
% 37.99/5.24 = { by axiom 17 (sos09) R->L }
% 37.99/5.24 fresh2(product(product(b1, b), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by axiom 9 (sos03) R->L }
% 37.99/5.24 fresh2(product(product(b1, quotient(product(b, c1), c1)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 41 }
% 37.99/5.24 fresh2(product(product(b1, quotient(product(a, b), c1)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 24 R->L }
% 37.99/5.24 fresh2(product(quotient(product(product(b1, c1), product(a, b)), c1), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 39 }
% 37.99/5.24 fresh2(product(quotient(product(product(a2, b1), product(a, b)), c1), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 41 R->L }
% 37.99/5.24 fresh2(product(quotient(product(product(a2, b1), product(b, c1)), c1), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 29 }
% 37.99/5.24 fresh2(product(product(quotient(product(a2, b1), c1), b), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by axiom 8 (sos01) R->L }
% 37.99/5.24 fresh2(product(difference(a, product(a, product(quotient(product(a2, b1), c1), b))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 43 R->L }
% 37.99/5.24 fresh2(product(difference(a, product(product(b, quotient(product(a2, b1), c1)), c1)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 42 R->L }
% 37.99/5.24 fresh2(product(difference(a, product(product(a, b), product(quotient(product(a2, b1), c1), c1))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.24 = { by lemma 55 }
% 37.99/5.25 fresh2(product(product(b, difference(a, product(quotient(product(a2, b1), c1), c1))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 11 (sos04) }
% 37.99/5.25 fresh2(product(product(b, difference(a, product(a2, b1))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 39 R->L }
% 37.99/5.25 fresh2(product(product(b, difference(a, product(b1, c1))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 10 (sos02) R->L }
% 37.99/5.25 fresh2(product(product(b, difference(a, product(product(b, difference(b, b1)), c1))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 43 }
% 37.99/5.25 fresh2(product(product(b, difference(a, product(a, product(difference(b, b1), b)))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 21 }
% 37.99/5.25 fresh2(product(product(b, difference(a, product(a, difference(b, product(b1, b))))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 8 (sos01) }
% 37.99/5.25 fresh2(product(product(b, difference(b, product(b1, b))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 54 R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(b1, b), b1)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 36 R->L }
% 37.99/5.25 fresh2(product(product(b, product(b1, quotient(b, b1))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 9 (sos03) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(product(b1, quotient(b, b1)), c), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 27 }
% 37.99/5.25 fresh2(product(product(b, quotient(product(a, product(quotient(b, b1), b1)), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 11 (sos04) }
% 37.99/5.25 fresh2(product(product(b, quotient(product(a, b), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 8 (sos01) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(c2, product(a, b))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 1 (sos06) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, c2), product(a, b))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 14 (sos05) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, a), product(c2, b))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 8 (sos01) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, a), difference(product(a2, c2), product(product(a2, c2), product(c2, b))))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 44 R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, a), difference(product(a2, c2), product(product(a, c), product(c2, b))))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 14 (sos05) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, a), difference(product(a2, c2), product(product(a, c2), product(c, b))))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 33 }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, a), difference(product(a2, c2), c))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 45 R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, a), difference(product(a2, c2), product(product(a2, c2), product(c, b1))))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 8 (sos01) }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, a), product(c, b1))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 14 (sos05) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, c), product(a, b1))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 26 R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, c), product(b1, c))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 23 }
% 37.99/5.25 fresh2(product(product(b, quotient(difference(c2, product(product(c2, b1), c)), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 55 }
% 37.99/5.25 fresh2(product(product(b, quotient(product(b1, difference(c2, c)), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 11 (sos04) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(b1, difference(c2, product(quotient(c, c2), c2))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 21 R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(b1, product(difference(c2, quotient(c, c2)), c2)), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 50 R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(product(c2, difference(c2, quotient(c, c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 10 (sos02) }
% 37.99/5.25 fresh2(product(product(b, quotient(product(quotient(c, c2), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 8 (sos01) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(c, c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 8 (sos01) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(difference(b, product(b, c)), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 18 }
% 37.99/5.25 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(difference(b, product(a1, b)), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 34 }
% 37.99/5.25 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(difference(b, product(c, a1)), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by axiom 1 (sos06) R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(difference(b, product(product(c, a1), product(c, a1))), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 48 R->L }
% 37.99/5.25 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(difference(b, product(product(c, b), product(a1, c))), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.25 = { by lemma 31 }
% 37.99/5.25 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(difference(b, product(product(c, b), product(a, c2))), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 14 (sos05) }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(difference(b, product(product(c, a), product(b, c2))), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 20 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, product(b2, quotient(product(difference(b, product(c, a)), c2), c2))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 9 (sos03) }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, product(b2, difference(b, product(c, a)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 46 R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, product(b2, difference(b, product(a, b1)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 55 R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(b, product(product(b, b2), product(a, b1)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 14 (sos05) R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(b, product(product(b, a), product(b2, b1)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 55 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, product(a, difference(b, product(b2, b1)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 8 (sos01) R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(a, b), product(a, difference(b, product(b2, b1)))))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 19 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(a, product(b, difference(b, product(b2, b1)))))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 10 (sos02) }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(a, product(b2, b1)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 11 (sos04) R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(a, product(b2, b1)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 27 R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(b1, b2), c), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 9 (sos03) R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(quotient(product(b1, c), c), b2), c), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 26 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(quotient(product(a, b1), c), b2), c), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 28 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(a, b1), product(b2, c)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 46 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(c, a), product(b2, c)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 14 (sos05) }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(c, b2), product(a, c)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 44 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(c, b2), product(a2, c2)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 40 R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(c, b2), product(a1, c1)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 14 (sos05) R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(c, a1), product(b2, c1)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 47 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(quotient(product(product(c, a1), product(a1, b2)), a1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 24 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), a1)), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by axiom 9 (sos03) R->L }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(product(a1, c1), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.26 = { by lemma 40 }
% 37.99/5.26 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(product(a2, c2), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 9 (sos03) R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a2, c2), product(c1, b2)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 40 R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, c1), product(c1, b2)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 23 R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, product(c1, b2)), product(c1, product(c1, b2))), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 32 R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, product(c1, b2)), difference(product(product(b2, c1), c1), c1)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 23 R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, product(c1, b2)), difference(product(product(b2, c1), product(c1, c1)), c1)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 47 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, product(c1, b2)), difference(product(product(a1, b2), product(c1, c1)), c1)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 14 (sos05) }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, product(c1, b2)), difference(product(product(a1, c1), product(b2, c1)), c1)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 47 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, product(c1, b2)), difference(product(product(a1, c1), product(a1, b2)), c1)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 19 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(product(product(a1, product(c1, b2)), difference(product(a1, product(c1, b2)), c1)), product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 10 (sos02) }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), quotient(quotient(c1, product(c1, b2)), c1))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 22 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), difference(c1, product(b2, c1)))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 47 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(a1, b2), difference(c1, product(a1, b2)))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 10 (sos02) R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, quotient(product(c1, difference(c1, product(a1, b2))), difference(c1, product(a1, b2)))), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 9 (sos03) }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(c, c1), a1))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 49 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(b, product(c1, c)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 19 R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(b, c1), product(b, c)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 41 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(a, b), product(b, c)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 18 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(a, b), product(a1, b)))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 23 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, difference(product(a, b), product(product(a, a1), b))), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 53 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, product(a1, b)), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 34 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, product(c, a1)), a1), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 20 R->L }
% 37.99/5.27 fresh2(product(product(b, quotient(difference(b2, product(product(c, a1), product(b2, a1))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 23 }
% 37.99/5.27 fresh2(product(product(b, quotient(difference(b2, product(product(c, b2), a1)), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 49 }
% 37.99/5.27 fresh2(product(product(b, quotient(difference(b2, product(b, product(b2, c))), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 20 }
% 37.99/5.27 fresh2(product(product(b, quotient(product(difference(b2, b), c), c)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 9 (sos03) }
% 37.99/5.27 fresh2(product(product(b, difference(b2, b)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 1 (sos06) R->L }
% 37.99/5.27 fresh2(product(product(product(b, b), difference(b2, b)), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 52 R->L }
% 37.99/5.27 fresh2(product(product(b, product(b, difference(b, difference(b2, b)))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by axiom 11 (sos04) R->L }
% 37.99/5.27 fresh2(product(product(b, product(b, difference(b, difference(product(quotient(b2, b), b), b)))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 37 }
% 37.99/5.27 fresh2(product(product(b, product(b, quotient(product(b, quotient(b2, b)), b))), product(b, b2)), product(b1, b2), b1, b, b2)
% 37.99/5.27 = { by lemma 36 }
% 37.99/5.27 fresh2(product(product(b, product(b, quotient(quotient(product(b, b2), b), b))), product(b, b2)), product(b1, b2), b1, b, b2)
% 38.55/5.27 = { by lemma 35 }
% 38.55/5.27 fresh2(product(difference(product(quotient(product(b, b2), b), b), b), product(b, b2)), product(b1, b2), b1, b, b2)
% 38.55/5.27 = { by lemma 29 R->L }
% 38.55/5.27 fresh2(product(difference(quotient(product(product(b, b2), product(b, b)), b), b), product(b, b2)), product(b1, b2), b1, b, b2)
% 38.55/5.27 = { by lemma 19 }
% 38.55/5.27 fresh2(product(difference(quotient(product(b, product(b2, b)), b), b), product(b, b2)), product(b1, b2), b1, b, b2)
% 38.55/5.27 = { by lemma 29 }
% 38.55/5.27 fresh2(product(difference(product(quotient(b, b), b2), b), product(b, b2)), product(b1, b2), b1, b, b2)
% 38.55/5.27 = { by axiom 1 (sos06) R->L }
% 38.55/5.27 fresh2(product(difference(product(quotient(product(b, b), b), b2), b), product(b, b2)), product(b1, b2), b1, b, b2)
% 38.55/5.27 = { by axiom 9 (sos03) }
% 38.55/5.27 fresh2(product(difference(product(b, b2), b), product(b, b2)), product(b1, b2), b1, b, b2)
% 38.55/5.27 = { by lemma 21 }
% 38.55/5.28 fresh2(difference(product(b, b2), product(b, product(b, b2))), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 54 R->L }
% 38.55/5.28 fresh2(quotient(product(b, product(b, b2)), b), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 36 R->L }
% 38.55/5.28 fresh2(product(b, quotient(product(b, b2), b)), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 9 (sos03) R->L }
% 38.55/5.28 fresh2(quotient(product(product(b, quotient(product(b, b2), b)), c1), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 43 }
% 38.55/5.28 fresh2(quotient(product(a, product(quotient(product(b, b2), b), b)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 11 (sos04) }
% 38.55/5.28 fresh2(quotient(product(a, product(b, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 19 R->L }
% 38.55/5.28 fresh2(quotient(product(product(a, b), product(a, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 41 R->L }
% 38.55/5.28 fresh2(quotient(product(product(b, c1), product(a, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 14 (sos05) }
% 38.55/5.28 fresh2(quotient(product(product(b, a), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 9 (sos03) R->L }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(b, a), product(a1, c2)), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 14 (sos05) R->L }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(b, a1), product(a, c2)), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 31 R->L }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(b, a1), product(a1, c)), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 23 R->L }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(b, product(a1, c)), product(a1, product(a1, c))), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 49 R->L }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(product(c, a1), a1), product(a1, product(a1, c))), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 16 (sos07) }
% 38.55/5.28 fresh2(quotient(product(quotient(a1, product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 16 (sos07) R->L }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(product(c2, a1), a1), product(a1, product(a1, c2))), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 50 }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(b1, product(a1, c2)), product(a1, product(a1, c2))), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 23 }
% 38.55/5.28 fresh2(quotient(product(quotient(product(product(b1, a1), product(a1, c2)), product(a1, c2)), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 9 (sos03) }
% 38.55/5.28 fresh2(quotient(product(product(b1, a1), product(c1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 14 (sos05) R->L }
% 38.55/5.28 fresh2(quotient(product(product(b1, c1), product(a1, b2)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 47 R->L }
% 38.55/5.28 fresh2(quotient(product(product(b1, c1), product(b2, c1)), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by lemma 23 }
% 38.55/5.28 fresh2(quotient(product(product(b1, b2), c1), c1), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 9 (sos03) }
% 38.55/5.28 fresh2(product(b1, b2), product(b1, b2), b1, b, b2)
% 38.55/5.28 = { by axiom 13 (sos09) }
% 38.55/5.28 true
% 38.55/5.28 % SZS output end Proof
% 38.55/5.28
% 38.55/5.28 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------