TSTP Solution File: GRP654+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP654+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n025.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 01:19:27 EDT 2023
% Result : Theorem 11.39s 1.85s
% Output : Proof 12.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP654+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 22:10:24 EDT 2023
% 0.17/0.34 % CPUTime :
% 11.39/1.85 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 11.39/1.85
% 11.39/1.85 % SZS status Theorem
% 11.39/1.85
% 11.95/1.93 % SZS output start Proof
% 11.95/1.93 Take the following subset of the input axioms:
% 11.95/1.93 fof(f01, axiom, ![B, A]: mult(A, ld(A, B))=B).
% 11.95/1.93 fof(f02, axiom, ![B2, A2]: ld(A2, mult(A2, B2))=B2).
% 11.95/1.93 fof(f03, axiom, ![B2, A2]: mult(rd(A2, B2), B2)=A2).
% 11.95/1.93 fof(f04, axiom, ![B2, A2]: rd(mult(A2, B2), B2)=A2).
% 11.95/1.93 fof(f05, axiom, ![C, B2, A2]: mult(A2, mult(B2, mult(A2, C)))=mult(mult(mult(A2, B2), A2), C)).
% 11.95/1.93 fof(goals, conjecture, ![X0, X1]: (mult(X0, rd(X1, X1))=X0 & mult(rd(X1, X1), X0)=X0)).
% 11.95/1.93
% 11.95/1.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.95/1.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.95/1.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.95/1.93 fresh(y, y, x1...xn) = u
% 11.95/1.93 C => fresh(s, t, x1...xn) = v
% 11.95/1.93 where fresh is a fresh function symbol and x1..xn are the free
% 11.95/1.93 variables of u and v.
% 11.95/1.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.95/1.93 input problem has no model of domain size 1).
% 11.95/1.93
% 11.95/1.93 The encoding turns the above axioms into the following unit equations and goals:
% 11.95/1.93
% 11.95/1.93 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 11.95/1.93 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 11.95/1.93 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 11.95/1.93 Axiom 4 (f02): ld(X, mult(X, Y)) = Y.
% 11.95/1.93 Axiom 5 (f05): mult(X, mult(Y, mult(X, Z))) = mult(mult(mult(X, Y), X), Z).
% 11.95/1.93
% 11.95/1.93 Lemma 6: rd(mult(X, mult(Y, mult(X, Z))), Z) = mult(mult(X, Y), X).
% 11.95/1.93 Proof:
% 11.95/1.93 rd(mult(X, mult(Y, mult(X, Z))), Z)
% 11.95/1.93 = { by axiom 5 (f05) }
% 11.95/1.93 rd(mult(mult(mult(X, Y), X), Z), Z)
% 11.95/1.93 = { by axiom 3 (f04) }
% 11.95/1.93 mult(mult(X, Y), X)
% 11.95/1.93
% 11.95/1.93 Lemma 7: mult(X, mult(ld(X, Y), mult(X, Z))) = mult(mult(Y, X), Z).
% 11.95/1.93 Proof:
% 11.95/1.93 mult(X, mult(ld(X, Y), mult(X, Z)))
% 11.95/1.93 = { by axiom 5 (f05) }
% 11.95/1.93 mult(mult(mult(X, ld(X, Y)), X), Z)
% 11.95/1.93 = { by axiom 1 (f01) }
% 11.95/1.93 mult(mult(Y, X), Z)
% 11.95/1.93
% 11.95/1.93 Lemma 8: mult(mult(X, Y), ld(Y, Z)) = mult(Y, mult(ld(Y, X), Z)).
% 11.95/1.93 Proof:
% 11.95/1.93 mult(mult(X, Y), ld(Y, Z))
% 11.95/1.93 = { by lemma 7 R->L }
% 11.95/1.93 mult(Y, mult(ld(Y, X), mult(Y, ld(Y, Z))))
% 11.95/1.93 = { by axiom 1 (f01) }
% 11.95/1.93 mult(Y, mult(ld(Y, X), Z))
% 11.95/1.93
% 11.95/1.93 Lemma 9: mult(X, mult(ld(X, rd(X, X)), Y)) = Y.
% 11.95/1.93 Proof:
% 11.95/1.93 mult(X, mult(ld(X, rd(X, X)), Y))
% 11.95/1.93 = { by lemma 8 R->L }
% 11.95/1.93 mult(mult(rd(X, X), X), ld(X, Y))
% 11.95/1.93 = { by axiom 2 (f03) }
% 11.95/1.93 mult(X, ld(X, Y))
% 11.95/1.93 = { by axiom 1 (f01) }
% 11.95/1.93 Y
% 11.95/1.93
% 11.95/1.93 Lemma 10: ld(ld(X, rd(X, X)), Y) = mult(X, Y).
% 11.95/1.93 Proof:
% 11.95/1.93 ld(ld(X, rd(X, X)), Y)
% 11.95/1.93 = { by lemma 9 R->L }
% 11.95/1.93 mult(X, mult(ld(X, rd(X, X)), ld(ld(X, rd(X, X)), Y)))
% 11.95/1.93 = { by axiom 1 (f01) }
% 11.95/1.93 mult(X, Y)
% 11.95/1.93
% 11.95/1.93 Lemma 11: mult(rd(X, X), mult(X, X)) = mult(X, X).
% 11.95/1.93 Proof:
% 11.95/1.93 mult(rd(X, X), mult(X, X))
% 11.95/1.93 = { by axiom 2 (f03) R->L }
% 11.95/1.93 mult(rd(X, X), mult(X, mult(rd(X, X), X)))
% 11.95/1.93 = { by axiom 5 (f05) }
% 11.95/1.93 mult(mult(mult(rd(X, X), X), rd(X, X)), X)
% 11.95/1.93 = { by axiom 2 (f03) }
% 11.95/1.93 mult(mult(X, rd(X, X)), X)
% 11.95/1.93 = { by lemma 6 R->L }
% 11.95/1.93 rd(mult(X, mult(rd(X, X), mult(X, Y))), Y)
% 11.95/1.93 = { by lemma 10 R->L }
% 11.95/1.93 rd(mult(X, mult(rd(X, X), ld(ld(X, rd(X, X)), Y))), Y)
% 11.95/1.93 = { by axiom 1 (f01) R->L }
% 11.95/1.93 rd(mult(X, mult(mult(X, ld(X, rd(X, X))), ld(ld(X, rd(X, X)), Y))), Y)
% 11.95/1.93 = { by lemma 8 }
% 11.95/1.93 rd(mult(X, mult(ld(X, rd(X, X)), mult(ld(ld(X, rd(X, X)), X), Y))), Y)
% 11.95/1.93 = { by lemma 9 }
% 11.95/1.93 rd(mult(ld(ld(X, rd(X, X)), X), Y), Y)
% 11.95/1.93 = { by lemma 10 }
% 11.95/1.93 rd(mult(mult(X, X), Y), Y)
% 11.95/1.93 = { by axiom 3 (f04) }
% 11.95/1.93 mult(X, X)
% 11.95/1.93
% 11.95/1.93 Lemma 12: rd(mult(rd(X, Y), mult(Z, X)), Y) = mult(mult(rd(X, Y), Z), rd(X, Y)).
% 11.95/1.93 Proof:
% 11.95/1.93 rd(mult(rd(X, Y), mult(Z, X)), Y)
% 11.95/1.93 = { by axiom 2 (f03) R->L }
% 11.95/1.93 rd(mult(rd(X, Y), mult(Z, mult(rd(X, Y), Y))), Y)
% 11.95/1.93 = { by lemma 6 }
% 11.95/1.93 mult(mult(rd(X, Y), Z), rd(X, Y))
% 11.95/1.93
% 11.95/1.93 Lemma 13: ld(X, X) = rd(X, X).
% 11.95/1.93 Proof:
% 11.95/1.93 ld(X, X)
% 11.95/1.93 = { by axiom 2 (f03) R->L }
% 11.95/1.93 ld(mult(rd(X, X), X), X)
% 11.95/1.93 = { by axiom 3 (f04) R->L }
% 11.95/1.93 ld(mult(rd(X, X), rd(mult(X, X), X)), X)
% 11.95/1.93 = { by axiom 3 (f04) R->L }
% 11.95/1.94 ld(mult(rd(X, X), rd(mult(X, X), X)), rd(mult(X, X), X))
% 11.95/1.94 = { by lemma 11 R->L }
% 11.95/1.94 ld(mult(rd(X, X), rd(mult(X, X), X)), rd(mult(rd(X, X), mult(X, X)), X))
% 11.95/1.94 = { by axiom 2 (f03) R->L }
% 11.95/1.94 ld(mult(rd(X, X), rd(mult(X, X), X)), rd(mult(rd(X, X), mult(rd(mult(X, X), X), X)), X))
% 11.95/1.94 = { by lemma 12 }
% 11.95/1.94 ld(mult(rd(X, X), rd(mult(X, X), X)), mult(mult(rd(X, X), rd(mult(X, X), X)), rd(X, X)))
% 11.95/1.94 = { by axiom 4 (f02) }
% 11.95/1.94 rd(X, X)
% 11.95/1.94
% 11.95/1.94 Lemma 14: mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)) = rd(X, Y).
% 11.95/1.94 Proof:
% 11.95/1.94 mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y))
% 11.95/1.94 = { by lemma 12 R->L }
% 11.95/1.94 rd(mult(rd(X, Y), mult(rd(Y, X), X)), Y)
% 11.95/1.94 = { by axiom 2 (f03) }
% 11.95/1.94 rd(mult(rd(X, Y), Y), Y)
% 11.95/1.94 = { by axiom 3 (f04) }
% 11.95/1.94 rd(X, Y)
% 11.95/1.94
% 11.95/1.94 Lemma 15: mult(rd(X, Y), mult(rd(Y, X), Z)) = Z.
% 11.95/1.94 Proof:
% 11.95/1.94 mult(rd(X, Y), mult(rd(Y, X), Z))
% 11.95/1.94 = { by axiom 1 (f01) R->L }
% 11.95/1.94 mult(rd(X, Y), mult(rd(Y, X), mult(rd(X, Y), ld(rd(X, Y), Z))))
% 11.95/1.94 = { by lemma 14 R->L }
% 11.95/1.94 mult(rd(X, Y), mult(rd(Y, X), mult(rd(X, Y), ld(mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)), Z))))
% 11.95/1.94 = { by axiom 5 (f05) }
% 11.95/1.94 mult(mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)), ld(mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)), Z))
% 11.95/1.94 = { by axiom 1 (f01) }
% 11.95/1.94 Z
% 11.95/1.94
% 11.95/1.94 Lemma 16: ld(rd(X, Y), Z) = mult(rd(Y, X), Z).
% 11.95/1.94 Proof:
% 11.95/1.94 ld(rd(X, Y), Z)
% 11.95/1.94 = { by lemma 15 R->L }
% 11.95/1.94 mult(rd(Y, X), mult(rd(X, Y), ld(rd(X, Y), Z)))
% 11.95/1.94 = { by axiom 1 (f01) }
% 11.95/1.94 mult(rd(Y, X), Z)
% 11.95/1.94
% 11.95/1.94 Lemma 17: ld(mult(mult(X, Y), X), mult(X, mult(Y, mult(X, Z)))) = Z.
% 11.95/1.94 Proof:
% 11.95/1.94 ld(mult(mult(X, Y), X), mult(X, mult(Y, mult(X, Z))))
% 11.95/1.94 = { by axiom 5 (f05) }
% 11.95/1.94 ld(mult(mult(X, Y), X), mult(mult(mult(X, Y), X), Z))
% 11.95/1.94 = { by axiom 4 (f02) }
% 11.95/1.94 Z
% 11.95/1.94
% 11.95/1.94 Lemma 18: ld(mult(mult(X, Y), X), mult(X, mult(Y, Z))) = ld(X, Z).
% 11.95/1.94 Proof:
% 11.95/1.94 ld(mult(mult(X, Y), X), mult(X, mult(Y, Z)))
% 11.95/1.94 = { by axiom 1 (f01) R->L }
% 11.95/1.94 ld(mult(mult(X, Y), X), mult(X, mult(Y, mult(X, ld(X, Z)))))
% 11.95/1.94 = { by lemma 17 }
% 11.95/1.94 ld(X, Z)
% 11.95/1.94
% 11.95/1.94 Lemma 19: ld(mult(X, rd(X, Y)), mult(rd(X, Y), mult(Y, Z))) = mult(rd(Y, X), Z).
% 11.95/1.94 Proof:
% 11.95/1.94 ld(mult(X, rd(X, Y)), mult(rd(X, Y), mult(Y, Z)))
% 11.95/1.94 = { by axiom 2 (f03) R->L }
% 11.95/1.94 ld(mult(mult(rd(X, Y), Y), rd(X, Y)), mult(rd(X, Y), mult(Y, Z)))
% 11.95/1.94 = { by lemma 18 }
% 11.95/1.94 ld(rd(X, Y), Z)
% 11.95/1.94 = { by lemma 16 }
% 11.95/1.94 mult(rd(Y, X), Z)
% 11.95/1.94
% 11.95/1.94 Lemma 20: mult(X, rd(X, X)) = X.
% 11.95/1.94 Proof:
% 11.95/1.94 mult(X, rd(X, X))
% 11.95/1.94 = { by axiom 3 (f04) R->L }
% 11.95/1.94 rd(mult(mult(X, rd(X, X)), ld(mult(X, rd(X, X)), mult(rd(X, X), mult(X, X)))), ld(mult(X, rd(X, X)), mult(rd(X, X), mult(X, X))))
% 11.95/1.94 = { by axiom 1 (f01) }
% 11.95/1.94 rd(mult(rd(X, X), mult(X, X)), ld(mult(X, rd(X, X)), mult(rd(X, X), mult(X, X))))
% 11.95/1.94 = { by lemma 19 }
% 11.95/1.94 rd(mult(rd(X, X), mult(X, X)), mult(rd(X, X), X))
% 11.95/1.94 = { by lemma 11 }
% 11.95/1.94 rd(mult(X, X), mult(rd(X, X), X))
% 11.95/1.94 = { by axiom 2 (f03) }
% 11.95/1.94 rd(mult(X, X), X)
% 11.95/1.94 = { by axiom 3 (f04) }
% 11.95/1.94 X
% 11.95/1.94
% 11.95/1.94 Lemma 21: mult(rd(X, X), rd(X, X)) = rd(X, X).
% 11.95/1.94 Proof:
% 11.95/1.94 mult(rd(X, X), rd(X, X))
% 11.95/1.94 = { by lemma 13 R->L }
% 11.95/1.94 mult(rd(X, X), ld(X, X))
% 11.95/1.94 = { by lemma 19 R->L }
% 11.95/1.94 ld(mult(X, rd(X, X)), mult(rd(X, X), mult(X, ld(X, X))))
% 11.95/1.94 = { by axiom 1 (f01) }
% 11.95/1.94 ld(mult(X, rd(X, X)), mult(rd(X, X), X))
% 11.95/1.94 = { by axiom 2 (f03) }
% 11.95/1.94 ld(mult(X, rd(X, X)), X)
% 11.95/1.94 = { by lemma 20 }
% 11.95/1.94 ld(X, X)
% 11.95/1.94 = { by lemma 13 }
% 11.95/1.94 rd(X, X)
% 11.95/1.94
% 11.95/1.94 Lemma 22: mult(mult(X, rd(Y, mult(X, Z))), X) = rd(mult(X, Y), Z).
% 11.95/1.94 Proof:
% 11.95/1.94 mult(mult(X, rd(Y, mult(X, Z))), X)
% 11.95/1.94 = { by lemma 6 R->L }
% 11.95/1.94 rd(mult(X, mult(rd(Y, mult(X, Z)), mult(X, Z))), Z)
% 11.95/1.94 = { by axiom 2 (f03) }
% 11.95/1.94 rd(mult(X, Y), Z)
% 11.95/1.94
% 11.95/1.94 Lemma 23: rd(X, mult(Y, mult(Z, ld(mult(mult(Z, Y), Z), X)))) = Z.
% 11.95/1.94 Proof:
% 11.95/1.94 rd(X, mult(Y, mult(Z, ld(mult(mult(Z, Y), Z), X))))
% 11.95/1.94 = { by axiom 1 (f01) R->L }
% 11.95/1.94 rd(mult(mult(mult(Z, Y), Z), ld(mult(mult(Z, Y), Z), X)), mult(Y, mult(Z, ld(mult(mult(Z, Y), Z), X))))
% 11.95/1.94 = { by axiom 5 (f05) R->L }
% 11.95/1.94 rd(mult(Z, mult(Y, mult(Z, ld(mult(mult(Z, Y), Z), X)))), mult(Y, mult(Z, ld(mult(mult(Z, Y), Z), X))))
% 11.95/1.94 = { by axiom 3 (f04) }
% 11.95/1.94 Z
% 11.95/1.94
% 11.95/1.94 Lemma 24: rd(mult(rd(X, Y), mult(Z, W)), mult(rd(Y, X), W)) = mult(rd(X, Y), rd(Z, rd(Y, X))).
% 11.95/1.94 Proof:
% 11.95/1.94 rd(mult(rd(X, Y), mult(Z, W)), mult(rd(Y, X), W))
% 11.95/1.94 = { by lemma 16 R->L }
% 11.95/1.94 rd(mult(rd(X, Y), mult(Z, W)), ld(rd(X, Y), W))
% 11.95/1.94 = { by axiom 1 (f01) R->L }
% 11.95/1.94 rd(mult(rd(X, Y), mult(Z, W)), ld(rd(X, Y), mult(mult(mult(rd(X, Y), V), rd(X, Y)), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W))))
% 11.95/1.94 = { by axiom 5 (f05) R->L }
% 11.95/1.94 rd(mult(rd(X, Y), mult(Z, W)), ld(rd(X, Y), mult(rd(X, Y), mult(V, mult(rd(X, Y), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W))))))
% 11.95/1.94 = { by axiom 4 (f02) }
% 11.95/1.94 rd(mult(rd(X, Y), mult(Z, W)), mult(V, mult(rd(X, Y), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W))))
% 11.95/1.94 = { by lemma 23 R->L }
% 11.95/1.94 rd(mult(rd(W, mult(V, mult(rd(X, Y), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W)))), mult(Z, W)), mult(V, mult(rd(X, Y), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W))))
% 11.95/1.94 = { by lemma 12 }
% 11.95/1.94 mult(mult(rd(W, mult(V, mult(rd(X, Y), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W)))), Z), rd(W, mult(V, mult(rd(X, Y), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W)))))
% 11.95/1.94 = { by lemma 23 }
% 11.95/1.94 mult(mult(rd(X, Y), Z), rd(W, mult(V, mult(rd(X, Y), ld(mult(mult(rd(X, Y), V), rd(X, Y)), W)))))
% 11.95/1.94 = { by lemma 23 }
% 11.95/1.94 mult(mult(rd(X, Y), Z), rd(X, Y))
% 11.95/1.94 = { by axiom 2 (f03) R->L }
% 11.95/1.94 mult(mult(rd(X, Y), mult(rd(Z, rd(Y, X)), rd(Y, X))), rd(X, Y))
% 11.95/1.94 = { by lemma 6 R->L }
% 11.95/1.94 rd(mult(rd(X, Y), mult(mult(rd(Z, rd(Y, X)), rd(Y, X)), mult(rd(X, Y), ld(rd(X, Y), U)))), ld(rd(X, Y), U))
% 11.95/1.94 = { by axiom 1 (f01) }
% 11.95/1.94 rd(mult(rd(X, Y), mult(mult(rd(Z, rd(Y, X)), rd(Y, X)), U)), ld(rd(X, Y), U))
% 11.95/1.94 = { by lemma 16 R->L }
% 11.95/1.94 rd(ld(rd(Y, X), mult(mult(rd(Z, rd(Y, X)), rd(Y, X)), U)), ld(rd(X, Y), U))
% 11.95/1.94 = { by lemma 7 R->L }
% 11.95/1.94 rd(ld(rd(Y, X), mult(rd(Y, X), mult(ld(rd(Y, X), rd(Z, rd(Y, X))), mult(rd(Y, X), U)))), ld(rd(X, Y), U))
% 11.95/1.94 = { by axiom 4 (f02) }
% 11.95/1.94 rd(mult(ld(rd(Y, X), rd(Z, rd(Y, X))), mult(rd(Y, X), U)), ld(rd(X, Y), U))
% 11.95/1.94 = { by lemma 16 }
% 11.95/1.94 rd(mult(mult(rd(X, Y), rd(Z, rd(Y, X))), mult(rd(Y, X), U)), ld(rd(X, Y), U))
% 11.95/1.94 = { by lemma 16 }
% 11.95/1.94 rd(mult(mult(rd(X, Y), rd(Z, rd(Y, X))), mult(rd(Y, X), U)), mult(rd(Y, X), U))
% 11.95/1.94 = { by axiom 3 (f04) }
% 11.95/1.94 mult(rd(X, Y), rd(Z, rd(Y, X)))
% 11.95/1.94
% 11.95/1.95 Lemma 25: ld(mult(X, mult(Y, mult(X, mult(X, Y)))), mult(mult(X, Y), mult(X, mult(mult(X, Y), Z)))) = Z.
% 11.95/1.95 Proof:
% 11.95/1.95 ld(mult(X, mult(Y, mult(X, mult(X, Y)))), mult(mult(X, Y), mult(X, mult(mult(X, Y), Z))))
% 11.95/1.95 = { by axiom 5 (f05) }
% 11.95/1.95 ld(mult(mult(mult(X, Y), X), mult(X, Y)), mult(mult(X, Y), mult(X, mult(mult(X, Y), Z))))
% 11.95/1.95 = { by lemma 17 }
% 11.95/1.95 Z
% 11.95/1.95
% 11.95/1.95 Goal 1 (goals): tuple(mult(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2))) = tuple(x0, x0_2).
% 11.95/1.95 Proof:
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2)))
% 11.95/1.95 = { by axiom 4 (f02) R->L }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))
% 11.95/1.95 = { by axiom 4 (f02) R->L }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(x0_2, mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.95 = { by lemma 18 R->L }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(mult(mult(x0_2, rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2)))), x0_2), mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))))
% 11.95/1.95 = { by axiom 3 (f04) R->L }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(mult(rd(mult(mult(x0_2, rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2)))), x0_2), x0_2), x0_2), mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))))
% 11.95/1.95 = { by lemma 22 }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(mult(rd(rd(mult(x0_2, rd(x1_2, x1_2)), rd(x1_2, x1_2)), x0_2), x0_2), mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))))
% 11.95/1.95 = { by axiom 3 (f04) }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(mult(rd(x0_2, x0_2), x0_2), mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))))
% 11.95/1.95 = { by axiom 2 (f03) }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(x0_2, mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))))
% 11.95/1.95 = { by axiom 4 (f02) }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.95 = { by axiom 4 (f02) R->L }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), mult(rd(x0_2, x0_2), rd(x1_2, x1_2))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.95 = { by axiom 3 (f04) R->L }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(ld(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), rd(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(rd(x0_2, x0_2), rd(x1_2, x1_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X))), mult(ld(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), rd(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(rd(x0_2, x0_2), rd(x1_2, x1_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.95 = { by lemma 7 }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(rd(x0_2, x0_2), rd(x1_2, x1_2))), mult(rd(x0_2, x0_2), rd(x1_2, x1_2))), X), mult(ld(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), rd(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(rd(x0_2, x0_2), rd(x1_2, x1_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.95 = { by axiom 2 (f03) }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), rd(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(rd(x0_2, x0_2), rd(x1_2, x1_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.95 = { by lemma 14 R->L }
% 11.95/1.95 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), rd(mult(rd(x0_2, x0_2), mult(mult(rd(x1_2, x1_2), rd(x1_2, x1_2)), rd(x1_2, x1_2))), mult(rd(x0_2, x0_2), rd(x1_2, x1_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 24 }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(rd(x0_2, x0_2), rd(mult(rd(x1_2, x1_2), rd(x1_2, x1_2)), rd(x0_2, x0_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 21 }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), mult(rd(x0_2, x0_2), rd(rd(x1_2, x1_2), rd(x0_2, x0_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by axiom 3 (f04) R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(mult(rd(x1_2, x1_2), Y), Y)), mult(rd(x0_2, x0_2), rd(rd(x1_2, x1_2), rd(x0_2, x0_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 15 R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(mult(rd(x1_2, x1_2), Y), mult(rd(x0_2, x0_2), mult(rd(x0_2, x0_2), Y)))), mult(rd(x0_2, x0_2), rd(rd(x1_2, x1_2), rd(x0_2, x0_2)))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 24 R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(mult(rd(x1_2, x1_2), Y), mult(rd(x0_2, x0_2), mult(rd(x0_2, x0_2), Y)))), rd(mult(rd(x0_2, x0_2), mult(rd(x1_2, x1_2), Y)), mult(rd(x0_2, x0_2), Y))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 22 R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(ld(mult(rd(x0_2, x0_2), rd(mult(rd(x1_2, x1_2), Y), mult(rd(x0_2, x0_2), mult(rd(x0_2, x0_2), Y)))), mult(mult(rd(x0_2, x0_2), rd(mult(rd(x1_2, x1_2), Y), mult(rd(x0_2, x0_2), mult(rd(x0_2, x0_2), Y)))), rd(x0_2, x0_2))), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by axiom 4 (f02) }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X), mult(rd(x0_2, x0_2), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 15 R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(mult(rd(x0_2, x0_2), mult(rd(x0_2, x0_2), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X))), mult(rd(x0_2, x0_2), mult(mult(rd(x0_2, x0_2), rd(x1_2, x1_2)), X)))), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by axiom 3 (f04) }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(ld(rd(x0_2, x0_2), rd(x0_2, x0_2)), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 16 }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(mult(rd(x0_2, x0_2), rd(x0_2, x0_2)), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 21 }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(rd(x0_2, x0_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), x0_2), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 20 R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), mult(rd(rd(x0_2, x0_2), mult(x0_2, rd(x1_2, x1_2))), mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x0_2, x0_2))), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 16 R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(rd(mult(x0_2, rd(x1_2, x1_2)), rd(x0_2, x0_2)), mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x0_2, x0_2))), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 22 R->L }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), ld(mult(mult(x0_2, rd(rd(x1_2, x1_2), mult(x0_2, rd(x0_2, x0_2)))), x0_2), mult(x0_2, mult(rd(rd(x1_2, x1_2), mult(x0_2, rd(x0_2, x0_2))), mult(x0_2, rd(x1_2, x1_2)))))))
% 11.95/1.96 = { by lemma 17 }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), ld(rd(rd(x1_2, x1_2), x0_2), rd(x1_2, x1_2)))
% 11.95/1.96 = { by lemma 16 }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), mult(rd(x0_2, rd(x1_2, x1_2)), rd(x1_2, x1_2)))
% 11.95/1.96 = { by axiom 2 (f03) }
% 11.95/1.96 tuple(mult(rd(x1, x1), x0), x0_2)
% 11.95/1.96 = { by axiom 2 (f03) R->L }
% 11.95/1.96 tuple(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), x0)), x0_2)
% 11.95/1.96 = { by axiom 4 (f02) R->L }
% 11.95/1.96 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), x0)))), x0_2)
% 12.56/1.97 = { by lemma 21 R->L }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), rd(x1, x1))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), x0)))), x0_2)
% 12.56/1.97 = { by lemma 15 R->L }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), x0)))), x0_2)
% 12.56/1.97 = { by lemma 25 R->L }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), ld(mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)))))), mult(mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(rd(x1, x1), mult(mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(rd(x1, x1), x0)))))))), x0_2)
% 12.56/1.97 = { by lemma 16 R->L }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), ld(mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)))))), mult(mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(rd(x1, x1), mult(ld(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(rd(x1, x1), x0)))))))), x0_2)
% 12.56/1.97 = { by lemma 7 }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), ld(mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)))))), mult(mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), x0)))))), x0_2)
% 12.56/1.97 = { by lemma 15 }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), ld(mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)))), mult(mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), x0)))))), x0_2)
% 12.56/1.97 = { by lemma 21 }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), ld(mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), x0)))))), x0_2)
% 12.56/1.97 = { by axiom 4 (f02) }
% 12.56/1.97 tuple(ld(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))))), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), mult(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1)), x0)))), x0_2)
% 12.56/1.97 = { by lemma 25 }
% 12.56/1.97 tuple(x0, x0_2)
% 12.56/1.97 % SZS output end Proof
% 12.56/1.97
% 12.56/1.97 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------