TSTP Solution File: GRP779+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP779+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 : n028.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 97.46s 12.72s
% Output : Proof 98.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : GRP779+1 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.30 % Computer : n028.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Aug 28 20:13:40 EDT 2023
% 0.09/0.30 % CPUTime :
% 97.46/12.72 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 97.46/12.72
% 97.46/12.72 % SZS status Theorem
% 97.46/12.72
% 98.04/12.81 % SZS output start Proof
% 98.04/12.81 Take the following subset of the input axioms:
% 98.04/12.81 fof(goals, conjecture, m(bigA, b1, bigC)).
% 98.04/12.81 fof(sos01, axiom, ![B, A]: difference(A, product(A, B))=B).
% 98.04/12.81 fof(sos02, axiom, ![B2, A2]: product(A2, difference(A2, B2))=B2).
% 98.04/12.81 fof(sos03, axiom, ![B2, A2]: quotient(product(A2, B2), B2)=A2).
% 98.04/12.81 fof(sos04, axiom, ![B2, A2]: product(quotient(A2, B2), B2)=A2).
% 98.04/12.81 fof(sos05, axiom, ![D, C, B2, A2]: product(product(A2, B2), product(C, D))=product(product(A2, C), product(B2, D))).
% 98.04/12.81 fof(sos06, axiom, ![A2]: product(A2, A2)=A2).
% 98.04/12.81 fof(sos07, axiom, ![B2, A2]: product(product(product(A2, B2), B2), product(B2, product(B2, A2)))=B2).
% 98.04/12.81 fof(sos08, axiom, ![X0, X1, X2]: (d(X0, X1, X2) <=> product(X0, X1)=product(X1, X2))).
% 98.04/12.81 fof(sos09, axiom, ![X3, X4, X5]: (m(X3, X4, X5) <=> product(product(X3, X4), product(X4, X5))=product(X3, X5))).
% 98.04/12.81 fof(sos10, axiom, d(b, bigA, c)).
% 98.04/12.81 fof(sos11, axiom, d(bigB, a, c)).
% 98.04/12.81 fof(sos12, axiom, d(b, a, bigC)).
% 98.04/12.81 fof(sos13, axiom, d(a, b1, c1)).
% 98.04/12.81 fof(sos14, axiom, d(a1, b, c1)).
% 98.04/12.81 fof(sos15, axiom, d(a1, b1, c)).
% 98.04/12.81
% 98.04/12.81 Now clausify the problem and encode Horn clauses using encoding 3 of
% 98.04/12.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 98.04/12.81 We repeatedly replace C & s=t => u=v by the two clauses:
% 98.04/12.81 fresh(y, y, x1...xn) = u
% 98.04/12.81 C => fresh(s, t, x1...xn) = v
% 98.04/12.81 where fresh is a fresh function symbol and x1..xn are the free
% 98.04/12.81 variables of u and v.
% 98.04/12.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 98.04/12.81 input problem has no model of domain size 1).
% 98.04/12.81
% 98.04/12.81 The encoding turns the above axioms into the following unit equations and goals:
% 98.04/12.81
% 98.04/12.81 Axiom 1 (sos06): product(X, X) = X.
% 98.04/12.81 Axiom 2 (sos11): d(bigB, a, c) = true.
% 98.04/12.81 Axiom 3 (sos14): d(a1, b, c1) = true.
% 98.04/12.81 Axiom 4 (sos15): d(a1, b1, c) = true.
% 98.04/12.81 Axiom 5 (sos10): d(b, bigA, c) = true.
% 98.04/12.81 Axiom 6 (sos12): d(b, a, bigC) = true.
% 98.04/12.81 Axiom 7 (sos13): d(a, b1, c1) = true.
% 98.04/12.81 Axiom 8 (sos01): difference(X, product(X, Y)) = Y.
% 98.04/12.81 Axiom 9 (sos03): quotient(product(X, Y), Y) = X.
% 98.04/12.81 Axiom 10 (sos02): product(X, difference(X, Y)) = Y.
% 98.04/12.81 Axiom 11 (sos04): product(quotient(X, Y), Y) = X.
% 98.04/12.81 Axiom 12 (sos08_1): fresh4(X, X, Y, Z, W) = product(Z, W).
% 98.04/12.81 Axiom 13 (sos09): fresh2(X, X, Y, Z, W) = true.
% 98.04/12.81 Axiom 14 (sos05): product(product(X, Y), product(Z, W)) = product(product(X, Z), product(Y, W)).
% 98.04/12.81 Axiom 15 (sos08_1): fresh4(d(X, Y, Z), true, X, Y, Z) = product(X, Y).
% 98.04/12.81 Axiom 16 (sos07): product(product(product(X, Y), Y), product(Y, product(Y, X))) = Y.
% 98.04/12.81 Axiom 17 (sos09): fresh2(product(product(X, Y), product(Y, Z)), product(X, Z), X, Y, Z) = m(X, Y, Z).
% 98.04/12.81
% 98.04/12.81 Lemma 18: product(b, bigA) = product(bigA, c).
% 98.04/12.81 Proof:
% 98.04/12.81 product(b, bigA)
% 98.04/12.81 = { by axiom 15 (sos08_1) R->L }
% 98.04/12.81 fresh4(d(b, bigA, c), true, b, bigA, c)
% 98.04/12.81 = { by axiom 5 (sos10) }
% 98.04/12.81 fresh4(true, true, b, bigA, c)
% 98.04/12.81 = { by axiom 12 (sos08_1) }
% 98.04/12.81 product(bigA, c)
% 98.04/12.81
% 98.04/12.81 Lemma 19: product(product(X, Y), product(X, Z)) = product(X, product(Y, Z)).
% 98.04/12.81 Proof:
% 98.04/12.81 product(product(X, Y), product(X, Z))
% 98.04/12.81 = { by axiom 14 (sos05) R->L }
% 98.04/12.81 product(product(X, X), product(Y, Z))
% 98.04/12.81 = { by axiom 1 (sos06) }
% 98.04/12.81 product(X, product(Y, Z))
% 98.04/12.81
% 98.04/12.81 Lemma 20: product(product(X, Y), X) = product(X, product(Y, X)).
% 98.04/12.81 Proof:
% 98.04/12.81 product(product(X, Y), X)
% 98.04/12.81 = { by axiom 1 (sos06) R->L }
% 98.04/12.81 product(product(X, Y), product(X, X))
% 98.04/12.81 = { by lemma 19 }
% 98.04/12.81 product(X, product(Y, X))
% 98.04/12.81
% 98.04/12.81 Lemma 21: product(product(X, product(X, Y)), product(product(Y, X), Z)) = product(X, product(Y, Z)).
% 98.04/12.81 Proof:
% 98.04/12.81 product(product(X, product(X, Y)), product(product(Y, X), Z))
% 98.04/12.81 = { by axiom 14 (sos05) R->L }
% 98.04/12.81 product(product(X, product(Y, X)), product(product(X, Y), Z))
% 98.04/12.81 = { by lemma 20 R->L }
% 98.04/12.81 product(product(product(X, Y), X), product(product(X, Y), Z))
% 98.04/12.81 = { by lemma 19 }
% 98.04/12.81 product(product(X, Y), product(X, Z))
% 98.04/12.81 = { by lemma 19 }
% 98.04/12.81 product(X, product(Y, Z))
% 98.04/12.81
% 98.04/12.81 Lemma 22: difference(X, X) = X.
% 98.04/12.81 Proof:
% 98.04/12.81 difference(X, X)
% 98.04/12.81 = { by axiom 1 (sos06) R->L }
% 98.04/12.81 difference(X, product(X, X))
% 98.04/12.81 = { by axiom 8 (sos01) }
% 98.04/12.81 X
% 98.04/12.81
% 98.04/12.81 Lemma 23: product(product(c, bigA), product(bigA, b)) = bigA.
% 98.04/12.81 Proof:
% 98.04/12.82 product(product(c, bigA), product(bigA, b))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 difference(bigA, product(bigA, product(product(c, bigA), product(bigA, b))))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, product(c, bigA)), product(bigA, product(bigA, b))))
% 98.04/12.82 = { by lemma 20 R->L }
% 98.04/12.82 difference(bigA, product(product(product(bigA, c), bigA), product(bigA, product(bigA, b))))
% 98.04/12.82 = { by lemma 18 R->L }
% 98.04/12.82 difference(bigA, product(product(product(b, bigA), bigA), product(bigA, product(bigA, b))))
% 98.04/12.82 = { by axiom 16 (sos07) }
% 98.04/12.82 difference(bigA, bigA)
% 98.04/12.82 = { by lemma 22 }
% 98.04/12.82 bigA
% 98.04/12.82
% 98.04/12.82 Lemma 24: product(product(X, Y), product(Z, Y)) = product(product(X, Z), Y).
% 98.04/12.82 Proof:
% 98.04/12.82 product(product(X, Y), product(Z, Y))
% 98.04/12.82 = { by axiom 14 (sos05) R->L }
% 98.04/12.82 product(product(X, Z), product(Y, Y))
% 98.04/12.82 = { by axiom 1 (sos06) }
% 98.04/12.82 product(product(X, Z), Y)
% 98.04/12.82
% 98.04/12.82 Lemma 25: product(c, b) = product(bigA, c).
% 98.04/12.82 Proof:
% 98.04/12.82 product(c, b)
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 difference(bigA, product(bigA, product(c, b)))
% 98.04/12.82 = { by lemma 21 R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), product(product(c, bigA), b)))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(bigA, product(product(c, bigA), b)))))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(product(bigA, product(c, bigA)), product(bigA, b)))))
% 98.04/12.82 = { by lemma 23 R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(product(product(product(c, bigA), product(bigA, b)), product(c, bigA)), product(bigA, b)))))
% 98.04/12.82 = { by lemma 24 R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(product(product(product(c, bigA), product(bigA, b)), product(bigA, b)), product(product(c, bigA), product(bigA, b))))))
% 98.04/12.82 = { by lemma 20 }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(product(product(c, bigA), product(bigA, b)), product(product(bigA, b), product(product(c, bigA), product(bigA, b)))))))
% 98.04/12.82 = { by lemma 23 }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(bigA, product(product(bigA, b), product(product(c, bigA), product(bigA, b)))))))
% 98.04/12.82 = { by lemma 23 }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(bigA, product(product(bigA, b), bigA)))))
% 98.04/12.82 = { by lemma 20 }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(bigA, product(bigA, product(b, bigA))))))
% 98.04/12.82 = { by lemma 18 }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), difference(bigA, product(bigA, product(bigA, product(bigA, c))))))
% 98.04/12.82 = { by axiom 8 (sos01) }
% 98.04/12.82 difference(bigA, product(product(bigA, product(bigA, c)), product(bigA, product(bigA, c))))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 difference(bigA, product(bigA, product(product(bigA, c), product(bigA, c))))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 difference(bigA, product(bigA, product(bigA, product(c, c))))
% 98.04/12.82 = { by axiom 1 (sos06) }
% 98.04/12.82 difference(bigA, product(bigA, product(bigA, c)))
% 98.04/12.82 = { by axiom 8 (sos01) }
% 98.04/12.82 product(bigA, c)
% 98.04/12.82
% 98.04/12.82 Lemma 26: product(a, bigC) = product(b, a).
% 98.04/12.82 Proof:
% 98.04/12.82 product(a, bigC)
% 98.04/12.82 = { by axiom 12 (sos08_1) R->L }
% 98.04/12.82 fresh4(true, true, b, a, bigC)
% 98.04/12.82 = { by axiom 6 (sos12) R->L }
% 98.04/12.82 fresh4(d(b, a, bigC), true, b, a, bigC)
% 98.04/12.82 = { by axiom 15 (sos08_1) }
% 98.04/12.82 product(b, a)
% 98.04/12.82
% 98.04/12.82 Lemma 27: product(product(a, X), product(b, a)) = product(a, product(X, bigC)).
% 98.04/12.82 Proof:
% 98.04/12.82 product(product(a, X), product(b, a))
% 98.04/12.82 = { by lemma 26 R->L }
% 98.04/12.82 product(product(a, X), product(a, bigC))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 product(a, product(X, bigC))
% 98.04/12.82
% 98.04/12.82 Lemma 28: product(product(bigC, a), product(a, b)) = a.
% 98.04/12.82 Proof:
% 98.04/12.82 product(product(bigC, a), product(a, b))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 difference(a, product(a, product(product(bigC, a), product(a, b))))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 difference(a, product(product(a, product(bigC, a)), product(a, product(a, b))))
% 98.04/12.82 = { by lemma 20 R->L }
% 98.04/12.82 difference(a, product(product(product(a, bigC), a), product(a, product(a, b))))
% 98.04/12.82 = { by lemma 26 }
% 98.04/12.82 difference(a, product(product(product(b, a), a), product(a, product(a, b))))
% 98.04/12.82 = { by axiom 16 (sos07) }
% 98.04/12.82 difference(a, a)
% 98.04/12.82 = { by lemma 22 }
% 98.04/12.82 a
% 98.04/12.82
% 98.04/12.82 Lemma 29: product(a, c) = product(bigB, a).
% 98.04/12.82 Proof:
% 98.04/12.82 product(a, c)
% 98.04/12.82 = { by axiom 12 (sos08_1) R->L }
% 98.04/12.82 fresh4(true, true, bigB, a, c)
% 98.04/12.82 = { by axiom 2 (sos11) R->L }
% 98.04/12.82 fresh4(d(bigB, a, c), true, bigB, a, c)
% 98.04/12.82 = { by axiom 15 (sos08_1) }
% 98.04/12.82 product(bigB, a)
% 98.04/12.82
% 98.04/12.82 Lemma 30: product(a, b) = product(bigA, bigB).
% 98.04/12.82 Proof:
% 98.04/12.82 product(a, b)
% 98.04/12.82 = { by axiom 9 (sos03) R->L }
% 98.04/12.82 quotient(product(product(a, b), product(b, bigC)), product(b, bigC))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 quotient(difference(a, product(a, product(product(a, b), product(b, bigC)))), product(b, bigC))
% 98.04/12.82 = { by axiom 1 (sos06) R->L }
% 98.04/12.82 quotient(difference(a, product(a, product(product(a, b), product(b, product(bigC, bigC))))), product(b, bigC))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 quotient(difference(a, product(product(a, product(a, b)), product(a, product(b, product(bigC, bigC))))), product(b, bigC))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 quotient(difference(a, product(product(a, product(a, b)), product(product(a, b), product(a, product(bigC, bigC))))), product(b, bigC))
% 98.04/12.82 = { by lemma 27 R->L }
% 98.04/12.82 quotient(difference(a, product(product(a, product(a, b)), product(product(a, b), product(product(a, bigC), product(b, a))))), product(b, bigC))
% 98.04/12.82 = { by axiom 14 (sos05) }
% 98.04/12.82 quotient(difference(a, product(product(a, product(a, b)), product(product(a, b), product(product(a, b), product(bigC, a))))), product(b, bigC))
% 98.04/12.82 = { by lemma 28 R->L }
% 98.04/12.82 quotient(difference(a, product(product(product(product(bigC, a), product(a, b)), product(a, b)), product(product(a, b), product(product(a, b), product(bigC, a))))), product(b, bigC))
% 98.04/12.82 = { by axiom 16 (sos07) }
% 98.04/12.82 quotient(difference(a, product(a, b)), product(b, bigC))
% 98.04/12.82 = { by axiom 8 (sos01) }
% 98.04/12.82 quotient(b, product(b, bigC))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 quotient(difference(bigA, product(bigA, b)), product(b, bigC))
% 98.04/12.82 = { by axiom 16 (sos07) R->L }
% 98.04/12.82 quotient(difference(bigA, product(product(product(product(c, bigA), product(bigA, b)), product(bigA, b)), product(product(bigA, b), product(product(bigA, b), product(c, bigA))))), product(b, bigC))
% 98.04/12.82 = { by lemma 23 }
% 98.04/12.82 quotient(difference(bigA, product(product(bigA, product(bigA, b)), product(product(bigA, b), product(product(bigA, b), product(c, bigA))))), product(b, bigC))
% 98.04/12.82 = { by axiom 14 (sos05) R->L }
% 98.04/12.82 quotient(difference(bigA, product(product(bigA, product(bigA, b)), product(product(bigA, b), product(product(bigA, c), product(b, bigA))))), product(b, bigC))
% 98.04/12.82 = { by lemma 18 R->L }
% 98.04/12.82 quotient(difference(bigA, product(product(bigA, product(bigA, b)), product(product(bigA, b), product(product(b, bigA), product(b, bigA))))), product(b, bigC))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 quotient(difference(bigA, product(product(bigA, product(bigA, b)), product(product(bigA, b), product(b, product(bigA, bigA))))), product(b, bigC))
% 98.04/12.82 = { by axiom 1 (sos06) }
% 98.04/12.82 quotient(difference(bigA, product(product(bigA, product(bigA, b)), product(product(bigA, b), product(b, bigA)))), product(b, bigC))
% 98.04/12.82 = { by lemma 18 }
% 98.04/12.82 quotient(difference(bigA, product(product(bigA, product(bigA, b)), product(product(bigA, b), product(bigA, c)))), product(b, bigC))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 quotient(difference(bigA, product(product(bigA, product(bigA, b)), product(bigA, product(b, c)))), product(b, bigC))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, b), product(b, c)))), product(b, bigC))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, b), difference(a, product(a, product(b, c)))))), product(b, bigC))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, b), difference(a, product(product(a, b), product(a, c)))))), product(b, bigC))
% 98.04/12.82 = { by lemma 29 }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, b), difference(a, product(product(a, b), product(bigB, a)))))), product(b, bigC))
% 98.04/12.82 = { by axiom 14 (sos05) }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, b), difference(a, product(product(a, bigB), product(b, a)))))), product(b, bigC))
% 98.04/12.82 = { by lemma 27 }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, b), difference(a, product(a, product(bigB, bigC)))))), product(b, bigC))
% 98.04/12.82 = { by axiom 8 (sos01) }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, b), product(bigB, bigC)))), product(b, bigC))
% 98.04/12.82 = { by axiom 14 (sos05) }
% 98.04/12.82 quotient(difference(bigA, product(bigA, product(product(bigA, bigB), product(b, bigC)))), product(b, bigC))
% 98.04/12.82 = { by axiom 8 (sos01) }
% 98.04/12.82 quotient(product(product(bigA, bigB), product(b, bigC)), product(b, bigC))
% 98.04/12.82 = { by axiom 9 (sos03) }
% 98.04/12.82 product(bigA, bigB)
% 98.04/12.82
% 98.04/12.82 Lemma 31: product(c, bigB) = product(bigB, a).
% 98.04/12.82 Proof:
% 98.04/12.82 product(c, bigB)
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 difference(bigA, product(bigA, product(c, bigB)))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, c), product(bigA, bigB)))
% 98.04/12.82 = { by lemma 30 R->L }
% 98.04/12.82 difference(bigA, product(product(bigA, c), product(a, b)))
% 98.04/12.82 = { by axiom 14 (sos05) }
% 98.04/12.82 difference(bigA, product(product(bigA, a), product(c, b)))
% 98.04/12.82 = { by lemma 25 }
% 98.04/12.82 difference(bigA, product(product(bigA, a), product(bigA, c)))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 difference(bigA, product(bigA, product(a, c)))
% 98.04/12.82 = { by lemma 29 }
% 98.04/12.82 difference(bigA, product(bigA, product(bigB, a)))
% 98.04/12.82 = { by axiom 8 (sos01) }
% 98.04/12.82 product(bigB, a)
% 98.04/12.82
% 98.04/12.82 Lemma 32: product(c, a) = product(bigC, bigA).
% 98.04/12.82 Proof:
% 98.04/12.82 product(c, a)
% 98.04/12.82 = { by axiom 9 (sos03) R->L }
% 98.04/12.82 quotient(product(product(c, a), product(a, bigB)), product(a, bigB))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 quotient(difference(a, product(a, product(product(c, a), product(a, bigB)))), product(a, bigB))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 quotient(difference(a, product(product(a, product(c, a)), product(a, product(a, bigB)))), product(a, bigB))
% 98.04/12.82 = { by lemma 20 R->L }
% 98.04/12.82 quotient(difference(a, product(product(product(a, c), a), product(a, product(a, bigB)))), product(a, bigB))
% 98.04/12.82 = { by lemma 29 }
% 98.04/12.82 quotient(difference(a, product(product(product(bigB, a), a), product(a, product(a, bigB)))), product(a, bigB))
% 98.04/12.82 = { by axiom 16 (sos07) }
% 98.04/12.82 quotient(difference(a, a), product(a, bigB))
% 98.04/12.82 = { by lemma 22 }
% 98.04/12.82 quotient(a, product(a, bigB))
% 98.04/12.82 = { by lemma 28 R->L }
% 98.04/12.82 quotient(product(product(bigC, a), product(a, b)), product(a, bigB))
% 98.04/12.82 = { by lemma 30 }
% 98.04/12.82 quotient(product(product(bigC, a), product(bigA, bigB)), product(a, bigB))
% 98.04/12.82 = { by axiom 14 (sos05) }
% 98.04/12.82 quotient(product(product(bigC, bigA), product(a, bigB)), product(a, bigB))
% 98.04/12.82 = { by axiom 9 (sos03) }
% 98.04/12.82 product(bigC, bigA)
% 98.04/12.82
% 98.04/12.82 Lemma 33: product(b1, c) = product(a1, b1).
% 98.04/12.82 Proof:
% 98.04/12.82 product(b1, c)
% 98.04/12.82 = { by axiom 12 (sos08_1) R->L }
% 98.04/12.82 fresh4(true, true, a1, b1, c)
% 98.04/12.82 = { by axiom 4 (sos15) R->L }
% 98.04/12.82 fresh4(d(a1, b1, c), true, a1, b1, c)
% 98.04/12.82 = { by axiom 15 (sos08_1) }
% 98.04/12.82 product(a1, b1)
% 98.04/12.82
% 98.04/12.82 Lemma 34: product(b1, c1) = product(a, b1).
% 98.04/12.82 Proof:
% 98.04/12.82 product(b1, c1)
% 98.04/12.82 = { by axiom 12 (sos08_1) R->L }
% 98.04/12.82 fresh4(true, true, a, b1, c1)
% 98.04/12.82 = { by axiom 7 (sos13) R->L }
% 98.04/12.82 fresh4(d(a, b1, c1), true, a, b1, c1)
% 98.04/12.82 = { by axiom 15 (sos08_1) }
% 98.04/12.82 product(a, b1)
% 98.04/12.82
% 98.04/12.82 Lemma 35: product(product(b1, X), product(a, b1)) = product(b1, product(X, c1)).
% 98.04/12.82 Proof:
% 98.04/12.82 product(product(b1, X), product(a, b1))
% 98.04/12.82 = { by lemma 34 R->L }
% 98.04/12.82 product(product(b1, X), product(b1, c1))
% 98.04/12.82 = { by lemma 19 }
% 98.04/12.82 product(b1, product(X, c1))
% 98.04/12.82
% 98.04/12.82 Lemma 36: product(product(c1, b1), product(b1, a)) = b1.
% 98.04/12.82 Proof:
% 98.04/12.82 product(product(c1, b1), product(b1, a))
% 98.04/12.82 = { by axiom 8 (sos01) R->L }
% 98.04/12.82 difference(b1, product(b1, product(product(c1, b1), product(b1, a))))
% 98.04/12.82 = { by lemma 19 R->L }
% 98.04/12.82 difference(b1, product(product(b1, product(c1, b1)), product(b1, product(b1, a))))
% 98.04/12.82 = { by lemma 20 R->L }
% 98.04/12.82 difference(b1, product(product(product(b1, c1), b1), product(b1, product(b1, a))))
% 98.04/12.82 = { by lemma 34 }
% 98.04/12.82 difference(b1, product(product(product(a, b1), b1), product(b1, product(b1, a))))
% 98.04/12.82 = { by axiom 16 (sos07) }
% 98.04/12.82 difference(b1, b1)
% 98.04/12.82 = { by lemma 22 }
% 98.04/12.82 b1
% 98.04/12.82
% 98.04/12.82 Lemma 37: product(product(b1, X), c1) = product(a, product(X, b1)).
% 98.04/12.82 Proof:
% 98.04/12.82 product(product(b1, X), c1)
% 98.04/12.82 = { by lemma 24 R->L }
% 98.04/12.82 product(product(b1, c1), product(X, c1))
% 98.04/12.83 = { by lemma 34 }
% 98.04/12.83 product(product(a, b1), product(X, c1))
% 98.04/12.83 = { by axiom 14 (sos05) }
% 98.04/12.83 product(product(a, X), product(b1, c1))
% 98.04/12.83 = { by lemma 34 }
% 98.04/12.83 product(product(a, X), product(a, b1))
% 98.04/12.83 = { by lemma 19 }
% 98.04/12.83 product(a, product(X, b1))
% 98.04/12.83
% 98.04/12.83 Lemma 38: product(product(X, product(Y, X)), product(Z, X)) = product(product(product(X, Y), Z), X).
% 98.04/12.83 Proof:
% 98.04/12.83 product(product(X, product(Y, X)), product(Z, X))
% 98.04/12.83 = { by lemma 20 R->L }
% 98.04/12.83 product(product(product(X, Y), X), product(Z, X))
% 98.04/12.83 = { by lemma 24 }
% 98.04/12.83 product(product(product(X, Y), Z), X)
% 98.04/12.83
% 98.04/12.83 Lemma 39: product(product(X, Y), product(product(Z, X), X)) = product(product(product(X, Z), Y), X).
% 98.04/12.83 Proof:
% 98.04/12.83 product(product(X, Y), product(product(Z, X), X))
% 98.04/12.83 = { by axiom 14 (sos05) R->L }
% 98.04/12.83 product(product(X, product(Z, X)), product(Y, X))
% 98.04/12.83 = { by lemma 38 }
% 98.04/12.83 product(product(product(X, Z), Y), X)
% 98.04/12.83
% 98.04/12.83 Lemma 40: product(c, product(bigB, a)) = product(a1, product(b1, bigA)).
% 98.04/12.83 Proof:
% 98.04/12.83 product(c, product(bigB, a))
% 98.04/12.83 = { by lemma 31 R->L }
% 98.04/12.83 product(c, product(c, bigB))
% 98.04/12.83 = { by lemma 19 R->L }
% 98.04/12.83 product(product(c, c), product(c, bigB))
% 98.04/12.83 = { by lemma 31 }
% 98.04/12.83 product(product(c, c), product(bigB, a))
% 98.04/12.83 = { by axiom 14 (sos05) }
% 98.04/12.83 product(product(c, bigB), product(c, a))
% 98.04/12.83 = { by lemma 31 }
% 98.04/12.83 product(product(bigB, a), product(c, a))
% 98.04/12.83 = { by axiom 8 (sos01) R->L }
% 98.04/12.83 product(difference(b1, product(b1, product(bigB, a))), product(c, a))
% 98.04/12.83 = { by lemma 29 R->L }
% 98.04/12.83 product(difference(b1, product(b1, product(a, c))), product(c, a))
% 98.04/12.83 = { by lemma 19 R->L }
% 98.04/12.83 product(difference(b1, product(product(b1, a), product(b1, c))), product(c, a))
% 98.04/12.83 = { by lemma 33 }
% 98.04/12.83 product(difference(b1, product(product(b1, a), product(a1, b1))), product(c, a))
% 98.04/12.83 = { by axiom 14 (sos05) }
% 98.04/12.83 product(difference(b1, product(product(b1, a1), product(a, b1))), product(c, a))
% 98.04/12.83 = { by lemma 35 }
% 98.04/12.83 product(difference(b1, product(b1, product(a1, c1))), product(c, a))
% 98.04/12.83 = { by axiom 8 (sos01) }
% 98.04/12.83 product(product(a1, c1), product(c, a))
% 98.04/12.83 = { by axiom 14 (sos05) }
% 98.04/12.83 product(product(a1, c), product(c1, a))
% 98.04/12.83 = { by axiom 8 (sos01) R->L }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(b1, a))))
% 98.04/12.83 = { by axiom 16 (sos07) R->L }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(product(product(product(c1, b1), product(b1, a)), product(b1, a)), product(product(b1, a), product(product(b1, a), product(c1, b1)))))))
% 98.04/12.83 = { by lemma 36 }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(product(b1, product(b1, a)), product(product(b1, a), product(product(b1, a), product(c1, b1)))))))
% 98.04/12.83 = { by axiom 14 (sos05) R->L }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(product(b1, product(b1, a)), product(product(b1, a), product(product(b1, c1), product(a, b1)))))))
% 98.04/12.83 = { by lemma 35 }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(product(b1, product(b1, a)), product(product(b1, a), product(b1, product(c1, c1)))))))
% 98.04/12.83 = { by lemma 19 }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(product(b1, product(b1, a)), product(b1, product(a, product(c1, c1)))))))
% 98.04/12.83 = { by lemma 19 }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(b1, product(product(b1, a), product(a, product(c1, c1)))))))
% 98.04/12.83 = { by axiom 1 (sos06) }
% 98.04/12.83 product(product(a1, c), product(c1, difference(b1, product(b1, product(product(b1, a), product(a, c1))))))
% 98.04/12.83 = { by axiom 8 (sos01) }
% 98.04/12.83 product(product(a1, c), product(c1, product(product(b1, a), product(a, c1))))
% 98.04/12.83 = { by lemma 19 R->L }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), product(c1, product(a, c1))))
% 98.04/12.83 = { by axiom 8 (sos01) R->L }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), difference(c1, product(c1, product(c1, product(a, c1))))))
% 98.04/12.83 = { by lemma 20 R->L }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), difference(c1, product(c1, product(product(c1, a), c1)))))
% 98.04/12.83 = { by lemma 20 R->L }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), difference(c1, product(product(c1, product(c1, a)), c1))))
% 98.04/12.83 = { by axiom 16 (sos07) R->L }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), difference(c1, product(product(c1, product(c1, a)), product(product(product(b1, c1), c1), product(c1, product(c1, b1)))))))
% 98.04/12.83 = { by lemma 37 }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), difference(c1, product(product(c1, product(c1, a)), product(product(a, product(c1, b1)), product(c1, product(c1, b1)))))))
% 98.04/12.83 = { by lemma 24 }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), difference(c1, product(product(c1, product(c1, a)), product(product(a, c1), product(c1, b1))))))
% 98.04/12.83 = { by lemma 21 }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), difference(c1, product(c1, product(a, product(c1, b1))))))
% 98.04/12.83 = { by axiom 8 (sos01) }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), product(a, product(c1, b1))))
% 98.04/12.83 = { by lemma 37 R->L }
% 98.04/12.83 product(product(a1, c), product(product(c1, product(b1, a)), product(product(b1, c1), c1)))
% 98.04/12.83 = { by lemma 39 }
% 98.04/12.83 product(product(a1, c), product(product(product(c1, b1), product(b1, a)), c1))
% 98.04/12.83 = { by lemma 36 }
% 98.04/12.83 product(product(a1, c), product(b1, c1))
% 98.04/12.83 = { by axiom 14 (sos05) R->L }
% 98.04/12.83 product(product(a1, b1), product(c, c1))
% 98.04/12.83 = { by axiom 8 (sos01) R->L }
% 98.04/12.83 product(product(a1, b1), difference(b, product(b, product(c, c1))))
% 98.04/12.83 = { by lemma 19 R->L }
% 98.04/12.83 product(product(a1, b1), difference(b, product(product(b, c), product(b, c1))))
% 98.04/12.83 = { by axiom 12 (sos08_1) R->L }
% 98.04/12.83 product(product(a1, b1), difference(b, product(product(b, c), fresh4(true, true, a1, b, c1))))
% 98.04/12.83 = { by axiom 3 (sos14) R->L }
% 98.04/12.83 product(product(a1, b1), difference(b, product(product(b, c), fresh4(d(a1, b, c1), true, a1, b, c1))))
% 98.04/12.83 = { by axiom 15 (sos08_1) }
% 98.04/12.83 product(product(a1, b1), difference(b, product(product(b, c), product(a1, b))))
% 98.04/12.83 = { by axiom 14 (sos05) }
% 98.04/12.83 product(product(a1, b1), difference(b, product(product(b, a1), product(c, b))))
% 98.04/12.83 = { by lemma 25 }
% 98.04/12.83 product(product(a1, b1), difference(b, product(product(b, a1), product(bigA, c))))
% 98.04/12.83 = { by lemma 18 R->L }
% 98.04/12.83 product(product(a1, b1), difference(b, product(product(b, a1), product(b, bigA))))
% 98.04/12.83 = { by lemma 19 }
% 98.04/12.83 product(product(a1, b1), difference(b, product(b, product(a1, bigA))))
% 98.04/12.83 = { by axiom 8 (sos01) }
% 98.04/12.83 product(product(a1, b1), product(a1, bigA))
% 98.04/12.83 = { by lemma 19 }
% 98.04/12.83 product(a1, product(b1, bigA))
% 98.04/12.83
% 98.04/12.83 Lemma 41: product(product(b1, X), c) = product(a1, product(X, b1)).
% 98.04/12.83 Proof:
% 98.04/12.83 product(product(b1, X), c)
% 98.04/12.83 = { by lemma 24 R->L }
% 98.04/12.83 product(product(b1, c), product(X, c))
% 98.04/12.83 = { by lemma 33 }
% 98.04/12.83 product(product(a1, b1), product(X, c))
% 98.04/12.83 = { by axiom 14 (sos05) }
% 98.04/12.83 product(product(a1, X), product(b1, c))
% 98.04/12.83 = { by lemma 33 }
% 98.04/12.83 product(product(a1, X), product(a1, b1))
% 98.04/12.83 = { by lemma 19 }
% 98.04/12.83 product(a1, product(X, b1))
% 98.04/12.83
% 98.04/12.83 Lemma 42: product(difference(bigC, b1), bigA) = product(bigA, b1).
% 98.04/12.83 Proof:
% 98.04/12.83 product(difference(bigC, b1), bigA)
% 98.04/12.83 = { by axiom 8 (sos01) R->L }
% 98.04/12.83 difference(product(bigC, bigA), product(product(bigC, bigA), product(difference(bigC, b1), bigA)))
% 98.04/12.83 = { by lemma 24 }
% 98.04/12.83 difference(product(bigC, bigA), product(product(bigC, difference(bigC, b1)), bigA))
% 98.04/12.83 = { by axiom 10 (sos02) }
% 98.04/12.83 difference(product(bigC, bigA), product(b1, bigA))
% 98.04/12.83 = { by axiom 8 (sos01) R->L }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(a1, product(b1, bigA))))
% 98.04/12.83 = { by lemma 40 R->L }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(c, product(bigB, a))))
% 98.04/12.83 = { by lemma 29 R->L }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(c, product(a, c))))
% 98.04/12.83 = { by lemma 20 R->L }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(c, a), c)))
% 98.04/12.83 = { by lemma 32 }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(bigC, bigA), c)))
% 98.04/12.83 = { by axiom 1 (sos06) R->L }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(product(bigC, bigA), product(bigC, bigA)), c)))
% 98.04/12.83 = { by lemma 32 R->L }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(product(c, a), product(bigC, bigA)), c)))
% 98.04/12.83 = { by lemma 38 R->L }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(c, product(a, c)), product(product(bigC, bigA), c))))
% 98.04/12.83 = { by lemma 29 }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(c, product(bigB, a)), product(product(bigC, bigA), c))))
% 98.04/12.83 = { by lemma 40 }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(a1, product(b1, bigA)), product(product(bigC, bigA), c))))
% 98.04/12.83 = { by axiom 14 (sos05) }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(a1, product(bigC, bigA)), product(product(b1, bigA), c))))
% 98.04/12.83 = { by lemma 41 }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(product(a1, product(bigC, bigA)), product(a1, product(bigA, b1)))))
% 98.04/12.83 = { by lemma 19 }
% 98.04/12.83 difference(product(bigC, bigA), difference(a1, product(a1, product(product(bigC, bigA), product(bigA, b1)))))
% 98.04/12.83 = { by axiom 8 (sos01) }
% 98.04/12.83 difference(product(bigC, bigA), product(product(bigC, bigA), product(bigA, b1)))
% 98.04/12.83 = { by axiom 8 (sos01) }
% 98.04/12.83 product(bigA, b1)
% 98.04/12.83
% 98.04/12.83 Lemma 43: product(X, product(difference(X, Y), X)) = product(Y, X).
% 98.04/12.83 Proof:
% 98.04/12.83 product(X, product(difference(X, Y), X))
% 98.04/12.83 = { by lemma 20 R->L }
% 98.04/12.83 product(product(X, difference(X, Y)), X)
% 98.04/12.83 = { by axiom 10 (sos02) }
% 98.04/12.83 product(Y, X)
% 98.04/12.83
% 98.04/12.83 Lemma 44: quotient(product(X, product(Y, X)), X) = product(X, Y).
% 98.04/12.83 Proof:
% 98.04/12.83 quotient(product(X, product(Y, X)), X)
% 98.04/12.83 = { by lemma 20 R->L }
% 98.04/12.83 quotient(product(product(X, Y), X), X)
% 98.04/12.83 = { by axiom 9 (sos03) }
% 98.04/12.83 product(X, Y)
% 98.04/12.83
% 98.04/12.83 Lemma 45: product(difference(X, product(Y, X)), Y) = product(Y, X).
% 98.04/12.83 Proof:
% 98.04/12.83 product(difference(X, product(Y, X)), Y)
% 98.04/12.83 = { by lemma 43 R->L }
% 98.04/12.83 product(difference(X, product(X, product(difference(X, Y), X))), Y)
% 98.04/12.83 = { by axiom 8 (sos01) }
% 98.04/12.83 product(product(difference(X, Y), X), Y)
% 98.04/12.83 = { by axiom 10 (sos02) R->L }
% 98.04/12.83 product(product(difference(X, Y), X), product(X, difference(X, Y)))
% 98.04/12.83 = { by axiom 9 (sos03) R->L }
% 98.04/12.83 quotient(product(product(product(difference(X, Y), X), product(X, difference(X, Y))), X), X)
% 98.04/12.83 = { by axiom 1 (sos06) R->L }
% 98.04/12.83 quotient(product(product(product(difference(X, Y), X), product(X, product(difference(X, Y), difference(X, Y)))), X), X)
% 98.04/12.83 = { by lemma 19 R->L }
% 98.04/12.83 quotient(product(product(product(difference(X, Y), X), product(product(X, difference(X, Y)), product(X, difference(X, Y)))), X), X)
% 98.04/12.83 = { by lemma 24 R->L }
% 98.04/12.83 quotient(product(product(product(difference(X, Y), X), X), product(product(product(X, difference(X, Y)), product(X, difference(X, Y))), X)), X)
% 98.04/12.83 = { by lemma 39 R->L }
% 98.04/12.83 quotient(product(product(product(difference(X, Y), X), X), product(product(X, product(X, difference(X, Y))), product(product(difference(X, Y), X), X))), X)
% 98.04/12.83 = { by axiom 8 (sos01) R->L }
% 98.04/12.83 quotient(product(product(product(difference(X, Y), X), X), product(difference(product(product(difference(X, Y), X), X), product(product(product(difference(X, Y), X), X), product(X, product(X, difference(X, Y))))), product(product(difference(X, Y), X), X))), X)
% 98.04/12.83 = { by axiom 16 (sos07) }
% 98.04/12.83 quotient(product(product(product(difference(X, Y), X), X), product(difference(product(product(difference(X, Y), X), X), X), product(product(difference(X, Y), X), X))), X)
% 98.04/12.83 = { by lemma 43 }
% 98.04/12.83 quotient(product(X, product(product(difference(X, Y), X), X)), X)
% 98.04/12.83 = { by lemma 44 }
% 98.04/12.83 product(X, product(difference(X, Y), X))
% 98.04/12.83 = { by lemma 43 }
% 98.04/12.83 product(Y, X)
% 98.04/12.83
% 98.04/12.83 Lemma 46: quotient(product(X, product(Y, Z)), product(X, Z)) = product(X, Y).
% 98.04/12.83 Proof:
% 98.04/12.83 quotient(product(X, product(Y, Z)), product(X, Z))
% 98.04/12.83 = { by lemma 19 R->L }
% 98.04/12.83 quotient(product(product(X, Y), product(X, Z)), product(X, Z))
% 98.04/12.83 = { by axiom 9 (sos03) }
% 98.04/12.84 product(X, Y)
% 98.04/12.84
% 98.04/12.84 Goal 1 (goals): m(bigA, b1, bigC) = true.
% 98.04/12.84 Proof:
% 98.04/12.84 m(bigA, b1, bigC)
% 98.04/12.84 = { by axiom 17 (sos09) R->L }
% 98.04/12.84 fresh2(product(product(bigA, b1), product(b1, bigC)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 9 (sos03) R->L }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(product(product(b1, bigC), difference(product(b1, bigC), b1)), difference(product(b1, bigC), b1))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 10 (sos02) }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, difference(product(b1, bigC), b1))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 1 (sos06) R->L }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, difference(product(b1, bigC), product(b1, b1)))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 10 (sos02) R->L }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, difference(product(b1, bigC), product(b1, product(bigC, difference(bigC, b1)))))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 19 R->L }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, difference(product(b1, bigC), product(product(b1, bigC), product(b1, difference(bigC, b1)))))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 8 (sos01) }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, product(b1, difference(bigC, b1)))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 8 (sos01) R->L }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, product(difference(bigA, product(bigA, b1)), difference(bigC, b1)))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 42 R->L }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, product(difference(bigA, product(difference(bigC, b1), bigA)), difference(bigC, b1)))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 45 }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, product(difference(bigC, b1), bigA))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 42 }
% 98.04/12.84 fresh2(product(product(bigA, b1), quotient(b1, product(bigA, b1))), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 44 R->L }
% 98.04/12.84 fresh2(quotient(product(product(bigA, b1), product(quotient(b1, product(bigA, b1)), product(bigA, b1))), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 11 (sos04) }
% 98.04/12.84 fresh2(quotient(product(product(bigA, b1), b1), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 45 R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(product(bigA, b1), b1)), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 9 (sos03) R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, quotient(product(product(product(bigA, b1), b1), product(b1, product(b1, bigA))), product(b1, product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 16 (sos07) }
% 98.04/12.84 fresh2(quotient(product(difference(b1, quotient(b1, product(b1, product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 1 (sos06) R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, quotient(product(b1, b1), product(b1, product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 11 (sos04) R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, quotient(product(b1, product(quotient(b1, product(b1, bigA)), product(b1, bigA))), product(b1, product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 46 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(b1, product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 22 R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, b1), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 22 R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, b1)), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 16 (sos07) R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(product(product(bigC, bigA), b1), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 8 (sos01) R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(a1, product(product(bigC, bigA), b1))), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 41 R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(product(b1, product(bigC, bigA)), c)), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 32 R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(product(b1, product(c, a)), c)), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 24 R->L }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(product(b1, c), product(product(c, a), c))), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 20 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(product(b1, c), product(c, product(a, c)))), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 29 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(product(b1, c), product(c, product(bigB, a)))), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 40 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(product(b1, c), product(a1, product(b1, bigA)))), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 33 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(product(a1, b1), product(a1, product(b1, bigA)))), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 19 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(difference(a1, product(a1, product(b1, product(b1, bigA)))), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 8 (sos01) }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(product(b1, product(b1, bigA)), b1), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 20 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(product(b1, product(product(b1, bigA), b1)), product(b1, product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 19 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(b1, product(product(product(b1, bigA), b1), product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 20 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(b1, product(product(b1, product(bigA, b1)), product(b1, product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 19 }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(b1, product(b1, product(product(bigA, b1), product(bigC, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 14 (sos05) }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, difference(b1, product(b1, product(b1, product(product(bigA, bigC), product(b1, bigA)))))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 8 (sos01) }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(difference(b1, product(b1, product(product(bigA, bigC), product(b1, bigA)))), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 8 (sos01) }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, quotient(product(product(bigA, bigC), product(b1, bigA)), product(b1, bigA)))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 9 (sos03) }
% 98.04/12.84 fresh2(quotient(product(difference(b1, product(b1, product(bigA, bigC))), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 8 (sos01) }
% 98.04/12.84 fresh2(quotient(product(product(bigA, bigC), product(bigA, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 19 }
% 98.04/12.84 fresh2(quotient(product(bigA, product(bigC, b1)), product(bigA, b1)), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by lemma 46 }
% 98.04/12.84 fresh2(product(bigA, bigC), product(bigA, bigC), bigA, b1, bigC)
% 98.04/12.84 = { by axiom 13 (sos09) }
% 98.04/12.84 true
% 98.04/12.84 % SZS output end Proof
% 98.04/12.84
% 98.04/12.84 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------