TSTP Solution File: GRP683+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP683+1 : 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 : n015.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 01:19:41 EDT 2023
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP683+1 : 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
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 20:37:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.50 Command-line arguments: --no-flatten-goal
% 0.20/0.50
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 Take the following subset of the input axioms:
% 0.20/0.53 fof(f01, axiom, ![A]: ld(A, mult(A, A))=A).
% 0.20/0.53 fof(f02, axiom, ![A2]: rd(mult(A2, A2), A2)=A2).
% 0.20/0.53 fof(f03, axiom, ![B, A2]: mult(A2, ld(A2, B))=ld(A2, mult(A2, B))).
% 0.20/0.53 fof(f04, axiom, ![A2, B2]: mult(rd(A2, B2), B2)=rd(mult(A2, B2), B2)).
% 0.20/0.53 fof(f05, axiom, ![D, C, A2, B2]: ld(ld(A2, B2), mult(ld(A2, B2), mult(C, D)))=mult(ld(A2, mult(A2, C)), D)).
% 0.20/0.53 fof(f06, axiom, ![A2, B2, D2, C2]: rd(mult(mult(A2, B2), rd(C2, D2)), rd(C2, D2))=mult(A2, rd(mult(B2, D2), D2))).
% 0.20/0.53 fof(f07, axiom, ![A2, B2]: ld(A2, mult(A2, ld(B2, B2)))=rd(mult(rd(A2, A2), B2), B2)).
% 0.20/0.53 fof(goals, conjecture, ![X3, X4, X5]: (mult(X3, ld(X4, mult(X4, X5)))=mult(X3, X5) & mult(rd(mult(X3, X4), X4), X5)=mult(X3, X5))).
% 0.20/0.53
% 0.20/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.53 fresh(y, y, x1...xn) = u
% 0.20/0.53 C => fresh(s, t, x1...xn) = v
% 0.20/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.53 variables of u and v.
% 0.20/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.53 input problem has no model of domain size 1).
% 0.20/0.53
% 0.20/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.53
% 0.20/0.53 Axiom 1 (f01): ld(X, mult(X, X)) = X.
% 0.20/0.53 Axiom 2 (f02): rd(mult(X, X), X) = X.
% 0.20/0.53 Axiom 3 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.20/0.53 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.20/0.53 Axiom 5 (f07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 0.20/0.53 Axiom 6 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 0.20/0.53 Axiom 7 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 0.20/0.53
% 0.20/0.53 Lemma 8: rd(X, X) = ld(X, X).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(X, X)
% 0.20/0.53 = { by axiom 2 (f02) R->L }
% 0.20/0.53 rd(rd(mult(X, X), X), X)
% 0.20/0.53 = { by axiom 4 (f04) R->L }
% 0.20/0.53 rd(mult(rd(X, X), X), X)
% 0.20/0.53 = { by axiom 5 (f07) R->L }
% 0.20/0.53 ld(X, mult(X, ld(X, X)))
% 0.20/0.53 = { by axiom 3 (f03) }
% 0.20/0.53 ld(X, ld(X, mult(X, X)))
% 0.20/0.53 = { by axiom 1 (f01) }
% 0.20/0.53 ld(X, X)
% 0.20/0.53
% 0.20/0.53 Lemma 9: mult(ld(X, mult(X, Y)), Z) = ld(X, mult(X, mult(Y, Z))).
% 0.20/0.53 Proof:
% 0.20/0.53 mult(ld(X, mult(X, Y)), Z)
% 0.20/0.53 = { by axiom 6 (f05) R->L }
% 0.20/0.53 ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), mult(Y, Z)))
% 0.20/0.53 = { by axiom 1 (f01) }
% 0.20/0.53 ld(X, mult(ld(X, mult(X, X)), mult(Y, Z)))
% 0.20/0.53 = { by axiom 1 (f01) }
% 0.20/0.53 ld(X, mult(X, mult(Y, Z)))
% 0.20/0.53
% 0.20/0.53 Lemma 10: ld(X, mult(X, mult(X, Y))) = mult(X, Y).
% 0.20/0.53 Proof:
% 0.20/0.53 ld(X, mult(X, mult(X, Y)))
% 0.20/0.53 = { by lemma 9 R->L }
% 0.20/0.53 mult(ld(X, mult(X, X)), Y)
% 0.20/0.53 = { by axiom 1 (f01) }
% 0.20/0.53 mult(X, Y)
% 0.20/0.53
% 0.20/0.53 Lemma 11: mult(X, rd(mult(Y, Z), Z)) = rd(mult(mult(X, Y), Z), Z).
% 0.20/0.53 Proof:
% 0.20/0.53 mult(X, rd(mult(Y, Z), Z))
% 0.20/0.53 = { by axiom 7 (f06) R->L }
% 0.20/0.53 rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 0.20/0.53 = { by axiom 2 (f02) }
% 0.20/0.53 rd(mult(mult(X, Y), Z), rd(mult(Z, Z), Z))
% 0.20/0.53 = { by axiom 2 (f02) }
% 0.20/0.53 rd(mult(mult(X, Y), Z), Z)
% 0.20/0.53
% 0.20/0.53 Lemma 12: mult(X, ld(Y, Y)) = rd(mult(X, Y), Y).
% 0.20/0.53 Proof:
% 0.20/0.53 mult(X, ld(Y, Y))
% 0.20/0.53 = { by lemma 10 R->L }
% 0.20/0.53 ld(X, mult(X, mult(X, ld(Y, Y))))
% 0.20/0.53 = { by axiom 3 (f03) R->L }
% 0.20/0.53 mult(X, ld(X, mult(X, ld(Y, Y))))
% 0.20/0.53 = { by axiom 5 (f07) }
% 0.20/0.53 mult(X, rd(mult(rd(X, X), Y), Y))
% 0.20/0.53 = { by lemma 11 }
% 0.20/0.53 rd(mult(mult(X, rd(X, X)), Y), Y)
% 0.20/0.53 = { by lemma 8 }
% 0.20/0.53 rd(mult(mult(X, ld(X, X)), Y), Y)
% 0.20/0.53 = { by axiom 3 (f03) }
% 0.20/0.53 rd(mult(ld(X, mult(X, X)), Y), Y)
% 0.20/0.53 = { by lemma 9 }
% 0.20/0.53 rd(ld(X, mult(X, mult(X, Y))), Y)
% 0.20/0.53 = { by lemma 10 }
% 0.20/0.53 rd(mult(X, Y), Y)
% 0.20/0.53
% 0.20/0.53 Lemma 13: mult(ld(X, X), X) = X.
% 0.20/0.53 Proof:
% 0.20/0.53 mult(ld(X, X), X)
% 0.20/0.53 = { by lemma 8 R->L }
% 0.20/0.53 mult(rd(X, X), X)
% 0.20/0.53 = { by axiom 4 (f04) }
% 0.20/0.53 rd(mult(X, X), X)
% 0.20/0.53 = { by axiom 2 (f02) }
% 0.20/0.53 X
% 0.20/0.53
% 0.20/0.53 Lemma 14: rd(mult(mult(X, Y), Y), Y) = mult(X, Y).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(mult(mult(X, Y), Y), Y)
% 0.20/0.53 = { by lemma 11 R->L }
% 0.20/0.53 mult(X, rd(mult(Y, Y), Y))
% 0.20/0.53 = { by axiom 2 (f02) }
% 0.20/0.53 mult(X, Y)
% 0.20/0.53
% 0.20/0.53 Lemma 15: rd(mult(ld(X, X), Y), Y) = ld(X, mult(X, ld(Y, Y))).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(mult(ld(X, X), Y), Y)
% 0.20/0.53 = { by lemma 8 R->L }
% 0.20/0.53 rd(mult(rd(X, X), Y), Y)
% 0.20/0.53 = { by axiom 5 (f07) R->L }
% 0.20/0.53 ld(X, mult(X, ld(Y, Y)))
% 0.20/0.53
% 0.20/0.53 Lemma 16: mult(ld(X, X), Y) = ld(X, mult(X, Y)).
% 0.20/0.53 Proof:
% 0.20/0.53 mult(ld(X, X), Y)
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 rd(mult(mult(ld(X, X), Y), Y), Y)
% 0.20/0.53 = { by axiom 4 (f04) R->L }
% 0.20/0.53 mult(rd(mult(ld(X, X), Y), Y), Y)
% 0.20/0.53 = { by lemma 15 }
% 0.20/0.53 mult(ld(X, mult(X, ld(Y, Y))), Y)
% 0.20/0.53 = { by lemma 9 }
% 0.20/0.53 ld(X, mult(X, mult(ld(Y, Y), Y)))
% 0.20/0.53 = { by lemma 13 }
% 0.20/0.53 ld(X, mult(X, Y))
% 0.20/0.53
% 0.20/0.53 Lemma 17: rd(mult(mult(X, Y), ld(Z, Z)), ld(Z, Z)) = rd(mult(mult(X, Y), Z), Z).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(mult(mult(X, Y), ld(Z, Z)), ld(Z, Z))
% 0.20/0.53 = { by lemma 8 R->L }
% 0.20/0.53 rd(mult(mult(X, Y), ld(Z, Z)), rd(Z, Z))
% 0.20/0.53 = { by lemma 8 R->L }
% 0.20/0.53 rd(mult(mult(X, Y), rd(Z, Z)), rd(Z, Z))
% 0.20/0.53 = { by axiom 7 (f06) }
% 0.20/0.53 mult(X, rd(mult(Y, Z), Z))
% 0.20/0.53 = { by lemma 11 }
% 0.20/0.53 rd(mult(mult(X, Y), Z), Z)
% 0.20/0.53
% 0.20/0.53 Lemma 18: rd(mult(X, ld(Y, Y)), ld(Y, Y)) = rd(mult(X, Y), Y).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(mult(X, ld(Y, Y)), ld(Y, Y))
% 0.20/0.53 = { by lemma 13 R->L }
% 0.20/0.53 rd(mult(mult(ld(X, X), X), ld(Y, Y)), ld(Y, Y))
% 0.20/0.53 = { by lemma 17 }
% 0.20/0.53 rd(mult(mult(ld(X, X), X), Y), Y)
% 0.20/0.53 = { by lemma 13 }
% 0.20/0.53 rd(mult(X, Y), Y)
% 0.20/0.53
% 0.20/0.53 Lemma 19: rd(rd(mult(X, Y), Y), Y) = rd(X, Y).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(rd(mult(X, Y), Y), Y)
% 0.20/0.53 = { by axiom 4 (f04) R->L }
% 0.20/0.53 rd(mult(rd(X, Y), Y), Y)
% 0.20/0.53 = { by lemma 13 R->L }
% 0.20/0.53 rd(mult(mult(ld(rd(X, Y), rd(X, Y)), rd(X, Y)), Y), Y)
% 0.20/0.53 = { by lemma 11 R->L }
% 0.20/0.53 mult(ld(rd(X, Y), rd(X, Y)), rd(mult(rd(X, Y), Y), Y))
% 0.20/0.53 = { by axiom 7 (f06) R->L }
% 0.20/0.53 rd(mult(mult(ld(rd(X, Y), rd(X, Y)), rd(X, Y)), rd(X, Y)), rd(X, Y))
% 0.20/0.53 = { by lemma 14 }
% 0.20/0.53 mult(ld(rd(X, Y), rd(X, Y)), rd(X, Y))
% 0.20/0.53 = { by lemma 13 }
% 0.20/0.53 rd(X, Y)
% 0.20/0.53
% 0.20/0.53 Lemma 20: rd(mult(rd(X, ld(Y, Y)), Y), Y) = rd(X, ld(Y, Y)).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(mult(rd(X, ld(Y, Y)), Y), Y)
% 0.20/0.53 = { by lemma 18 R->L }
% 0.20/0.53 rd(mult(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 0.20/0.53 = { by axiom 4 (f04) }
% 0.20/0.53 rd(rd(mult(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 0.20/0.53 = { by lemma 19 }
% 0.20/0.53 rd(X, ld(Y, Y))
% 0.20/0.53
% 0.20/0.53 Lemma 21: ld(ld(X, X), ld(X, X)) = ld(X, X).
% 0.20/0.53 Proof:
% 0.20/0.53 ld(ld(X, X), ld(X, X))
% 0.20/0.53 = { by axiom 1 (f01) R->L }
% 0.20/0.53 ld(ld(X, X), ld(X, ld(X, mult(X, X))))
% 0.20/0.53 = { by axiom 3 (f03) R->L }
% 0.20/0.53 ld(ld(X, X), ld(X, mult(X, ld(X, X))))
% 0.20/0.53 = { by lemma 16 R->L }
% 0.20/0.53 ld(ld(X, X), mult(ld(X, X), ld(X, X)))
% 0.20/0.53 = { by axiom 1 (f01) }
% 0.20/0.53 ld(X, X)
% 0.20/0.53
% 0.20/0.53 Lemma 22: rd(rd(X, ld(Y, Y)), ld(Y, Y)) = rd(X, ld(Y, Y)).
% 0.20/0.53 Proof:
% 0.20/0.53 rd(rd(X, ld(Y, Y)), ld(Y, Y))
% 0.20/0.53 = { by lemma 20 R->L }
% 0.20/0.53 rd(rd(mult(rd(X, ld(Y, Y)), Y), Y), ld(Y, Y))
% 0.20/0.53 = { by lemma 21 R->L }
% 0.20/0.54 rd(rd(mult(rd(X, ld(ld(Y, Y), ld(Y, Y))), Y), Y), ld(Y, Y))
% 0.20/0.54 = { by lemma 12 R->L }
% 0.20/0.54 rd(mult(rd(X, ld(ld(Y, Y), ld(Y, Y))), ld(Y, Y)), ld(Y, Y))
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 rd(X, ld(ld(Y, Y), ld(Y, Y)))
% 0.20/0.54 = { by lemma 21 }
% 0.20/0.54 rd(X, ld(Y, Y))
% 0.20/0.54
% 0.20/0.54 Lemma 23: rd(mult(X, Y), Y) = rd(X, ld(Y, Y)).
% 0.20/0.54 Proof:
% 0.20/0.54 rd(mult(X, Y), Y)
% 0.20/0.54 = { by lemma 18 R->L }
% 0.20/0.54 rd(mult(X, ld(Y, Y)), ld(Y, Y))
% 0.20/0.54 = { by axiom 4 (f04) R->L }
% 0.20/0.54 mult(rd(X, ld(Y, Y)), ld(Y, Y))
% 0.20/0.54 = { by lemma 22 R->L }
% 0.20/0.54 mult(rd(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 0.20/0.54 = { by axiom 4 (f04) }
% 0.20/0.54 rd(mult(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 0.20/0.54 = { by lemma 18 }
% 0.20/0.54 rd(mult(rd(X, ld(Y, Y)), Y), Y)
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 rd(X, ld(Y, Y))
% 0.20/0.54
% 0.20/0.54 Lemma 24: mult(rd(X, ld(Y, Y)), Y) = mult(X, Y).
% 0.20/0.54 Proof:
% 0.20/0.54 mult(rd(X, ld(Y, Y)), Y)
% 0.20/0.54 = { by lemma 23 R->L }
% 0.20/0.54 mult(rd(mult(X, Y), Y), Y)
% 0.20/0.54 = { by axiom 4 (f04) }
% 0.20/0.54 rd(mult(mult(X, Y), Y), Y)
% 0.20/0.54 = { by lemma 14 }
% 0.20/0.54 mult(X, Y)
% 0.20/0.54
% 0.20/0.54 Lemma 25: mult(X, ld(Y, rd(Y, ld(Z, Z)))) = rd(rd(X, ld(Y, Y)), ld(Z, Z)).
% 0.20/0.54 Proof:
% 0.20/0.54 mult(X, ld(Y, rd(Y, ld(Z, Z))))
% 0.20/0.54 = { by lemma 23 R->L }
% 0.20/0.54 mult(X, ld(Y, rd(mult(Y, Z), Z)))
% 0.20/0.54 = { by lemma 12 R->L }
% 0.20/0.54 mult(X, ld(Y, mult(Y, ld(Z, Z))))
% 0.20/0.54 = { by lemma 15 R->L }
% 0.20/0.54 mult(X, rd(mult(ld(Y, Y), Z), Z))
% 0.20/0.54 = { by lemma 11 }
% 0.20/0.54 rd(mult(mult(X, ld(Y, Y)), Z), Z)
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 rd(mult(X, ld(Y, Y)), ld(Z, Z))
% 0.20/0.54 = { by lemma 12 }
% 0.20/0.54 rd(rd(mult(X, Y), Y), ld(Z, Z))
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 rd(rd(X, ld(Y, Y)), ld(Z, Z))
% 0.20/0.54
% 0.20/0.54 Lemma 26: ld(mult(X, Y), mult(mult(X, Y), Z)) = ld(X, mult(X, Z)).
% 0.20/0.54 Proof:
% 0.20/0.54 ld(mult(X, Y), mult(mult(X, Y), Z))
% 0.20/0.54 = { by lemma 10 R->L }
% 0.20/0.54 ld(mult(X, Y), mult(ld(X, mult(X, mult(X, Y))), Z))
% 0.20/0.54 = { by lemma 10 R->L }
% 0.20/0.54 ld(ld(X, mult(X, mult(X, Y))), mult(ld(X, mult(X, mult(X, Y))), Z))
% 0.20/0.54 = { by lemma 13 R->L }
% 0.20/0.54 ld(ld(X, mult(X, mult(X, Y))), mult(ld(X, mult(X, mult(X, Y))), mult(ld(Z, Z), Z)))
% 0.20/0.54 = { by axiom 6 (f05) }
% 0.20/0.54 mult(ld(X, mult(X, ld(Z, Z))), Z)
% 0.20/0.54 = { by lemma 9 }
% 0.20/0.54 ld(X, mult(X, mult(ld(Z, Z), Z)))
% 0.20/0.54 = { by lemma 13 }
% 0.20/0.54 ld(X, mult(X, Z))
% 0.20/0.54
% 0.20/0.54 Lemma 27: rd(mult(X, mult(Y, Z)), mult(Y, Z)) = rd(mult(X, Z), Z).
% 0.20/0.54 Proof:
% 0.20/0.54 rd(mult(X, mult(Y, Z)), mult(Y, Z))
% 0.20/0.54 = { by lemma 14 R->L }
% 0.20/0.54 rd(mult(X, mult(Y, Z)), rd(mult(mult(Y, Z), Z), Z))
% 0.20/0.54 = { by lemma 14 R->L }
% 0.20/0.54 rd(mult(X, rd(mult(mult(Y, Z), Z), Z)), rd(mult(mult(Y, Z), Z), Z))
% 0.20/0.54 = { by lemma 13 R->L }
% 0.20/0.54 rd(mult(mult(ld(X, X), X), rd(mult(mult(Y, Z), Z), Z)), rd(mult(mult(Y, Z), Z), Z))
% 0.20/0.54 = { by axiom 7 (f06) }
% 0.20/0.54 mult(ld(X, X), rd(mult(X, Z), Z))
% 0.20/0.54 = { by axiom 7 (f06) R->L }
% 0.20/0.54 rd(mult(mult(ld(X, X), X), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 0.20/0.54 = { by lemma 13 }
% 0.20/0.54 rd(mult(X, rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 0.20/0.54 = { by axiom 2 (f02) }
% 0.20/0.54 rd(mult(X, Z), rd(mult(Z, Z), Z))
% 0.20/0.54 = { by axiom 2 (f02) }
% 0.20/0.54 rd(mult(X, Z), Z)
% 0.20/0.54
% 0.20/0.54 Lemma 28: rd(X, ld(Y, rd(Y, ld(Z, Z)))) = rd(X, ld(Z, Z)).
% 0.20/0.54 Proof:
% 0.20/0.54 rd(X, ld(Y, rd(Y, ld(Z, Z))))
% 0.20/0.54 = { by lemma 23 R->L }
% 0.20/0.54 rd(X, ld(Y, rd(mult(Y, Z), Z)))
% 0.20/0.54 = { by lemma 12 R->L }
% 0.20/0.54 rd(X, ld(Y, mult(Y, ld(Z, Z))))
% 0.20/0.54 = { by lemma 26 R->L }
% 0.20/0.54 rd(X, ld(mult(Y, Z), mult(mult(Y, Z), ld(Z, Z))))
% 0.20/0.54 = { by lemma 15 R->L }
% 0.20/0.54 rd(X, rd(mult(ld(mult(Y, Z), mult(Y, Z)), Z), Z))
% 0.20/0.54 = { by lemma 27 R->L }
% 0.20/0.54 rd(X, rd(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))
% 0.20/0.54 = { by lemma 13 }
% 0.20/0.54 rd(X, rd(mult(Y, Z), mult(Y, Z)))
% 0.20/0.54 = { by lemma 8 }
% 0.20/0.54 rd(X, ld(mult(Y, Z), mult(Y, Z)))
% 0.20/0.54 = { by lemma 22 R->L }
% 0.20/0.54 rd(rd(X, ld(mult(Y, Z), mult(Y, Z))), ld(mult(Y, Z), mult(Y, Z)))
% 0.20/0.54 = { by lemma 25 R->L }
% 0.20/0.54 mult(X, ld(mult(Y, Z), rd(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z)))))
% 0.20/0.54 = { by axiom 1 (f01) R->L }
% 0.20/0.54 mult(X, ld(mult(Y, Z), rd(ld(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z))), ld(mult(Y, Z), mult(Y, Z)))))
% 0.20/0.54 = { by axiom 3 (f03) R->L }
% 0.20/0.54 mult(X, ld(mult(Y, Z), rd(mult(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z))), ld(mult(Y, Z), mult(Y, Z)))))
% 0.20/0.54 = { by lemma 17 }
% 0.20/0.54 mult(X, ld(mult(Y, Z), rd(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z))))
% 0.20/0.54 = { by axiom 2 (f02) }
% 0.20/0.54 mult(X, ld(mult(Y, Z), mult(Y, Z)))
% 0.20/0.54 = { by lemma 12 }
% 0.20/0.54 rd(mult(X, mult(Y, Z)), mult(Y, Z))
% 0.20/0.54 = { by lemma 27 }
% 0.20/0.54 rd(mult(X, Z), Z)
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 rd(X, ld(Z, Z))
% 0.20/0.54
% 0.20/0.54 Goal 1 (goals): tuple(mult(rd(mult(x3, x4), x4), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2)))) = tuple(mult(x3, x5), mult(x3_2, x5_2)).
% 0.20/0.54 Proof:
% 0.20/0.54 tuple(mult(rd(mult(x3, x4), x4), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 tuple(mult(rd(x3, ld(x4, x4)), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 24 R->L }
% 0.20/0.54 tuple(mult(rd(rd(x3, ld(x4, x4)), ld(x5, x5)), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 22 R->L }
% 0.20/0.54 tuple(mult(rd(rd(rd(x3, ld(x4, x4)), ld(x5, x5)), ld(x5, x5)), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 25 R->L }
% 0.20/0.54 tuple(mult(rd(mult(x3, ld(x4, rd(x4, ld(x5, x5)))), ld(x5, x5)), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 22 R->L }
% 0.20/0.54 tuple(mult(rd(rd(mult(x3, ld(x4, rd(x4, ld(x5, x5)))), ld(x5, x5)), ld(x5, x5)), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 28 R->L }
% 0.20/0.54 tuple(mult(rd(rd(mult(x3, ld(x4, rd(x4, ld(x5, x5)))), ld(x5, x5)), ld(x4, rd(x4, ld(x5, x5)))), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 28 R->L }
% 0.20/0.54 tuple(mult(rd(rd(mult(x3, ld(x4, rd(x4, ld(x5, x5)))), ld(x4, rd(x4, ld(x5, x5)))), ld(x4, rd(x4, ld(x5, x5)))), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 19 }
% 0.20/0.54 tuple(mult(rd(x3, ld(x4, rd(x4, ld(x5, x5)))), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 28 }
% 0.20/0.54 tuple(mult(rd(x3, ld(x5, x5)), x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 24 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))
% 0.20/0.54 = { by lemma 10 R->L }
% 0.20/0.54 tuple(mult(x3, x5), ld(x3_2, mult(x3_2, mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))))
% 0.20/0.54 = { by axiom 3 (f03) R->L }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, ld(x3_2, mult(x3_2, ld(x4_2, mult(x4_2, x5_2))))))
% 0.20/0.54 = { by lemma 26 R->L }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, ld(mult(x3_2, ld(x4_2, x4_2)), mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, mult(x4_2, x5_2))))))
% 0.20/0.54 = { by lemma 26 R->L }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, ld(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), mult(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), ld(x4_2, mult(x4_2, x5_2))))))
% 0.20/0.54 = { by lemma 16 R->L }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, ld(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), mult(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), mult(ld(x4_2, x4_2), x5_2)))))
% 0.20/0.54 = { by lemma 9 R->L }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), mult(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), ld(x4_2, x4_2))), x5_2)))
% 0.20/0.54 = { by lemma 12 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), rd(mult(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), x4_2), x4_2)), x5_2)))
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), rd(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), ld(x4_2, x4_2))), x5_2)))
% 0.20/0.54 = { by lemma 14 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(mult(mult(x3_2, ld(x4_2, x4_2)), ld(x4_2, x4_2)), mult(x3_2, ld(x4_2, x4_2))), x5_2)))
% 0.20/0.54 = { by lemma 12 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(rd(mult(mult(x3_2, ld(x4_2, x4_2)), x4_2), x4_2), mult(x3_2, ld(x4_2, x4_2))), x5_2)))
% 0.20/0.54 = { by lemma 11 R->L }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(mult(x3_2, rd(mult(ld(x4_2, x4_2), x4_2), x4_2)), mult(x3_2, ld(x4_2, x4_2))), x5_2)))
% 0.20/0.54 = { by lemma 13 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(mult(x3_2, rd(x4_2, x4_2)), mult(x3_2, ld(x4_2, x4_2))), x5_2)))
% 0.20/0.54 = { by lemma 8 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, mult(ld(mult(x3_2, ld(x4_2, x4_2)), mult(x3_2, ld(x4_2, x4_2))), x5_2)))
% 0.20/0.54 = { by lemma 16 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, ld(mult(x3_2, ld(x4_2, x4_2)), mult(mult(x3_2, ld(x4_2, x4_2)), x5_2))))
% 0.20/0.54 = { by lemma 26 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, ld(x3_2, mult(x3_2, x5_2))))
% 0.20/0.54 = { by axiom 3 (f03) }
% 0.20/0.54 tuple(mult(x3, x5), ld(x3_2, mult(x3_2, mult(x3_2, x5_2))))
% 0.20/0.54 = { by lemma 10 }
% 0.20/0.54 tuple(mult(x3, x5), mult(x3_2, x5_2))
% 0.20/0.54 % SZS output end Proof
% 0.20/0.54
% 0.20/0.54 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------