TSTP Solution File: GRP683-10 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP683-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n001.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 01:16:01 EDT 2023
% Result : Unsatisfiable 9.02s 9.26s
% Output : CNFRefutation 9.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP683-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 22:22:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 9.02/9.26 % SZS status Unsatisfiable
% 9.02/9.26 % SZS output start Proof
% 9.02/9.26 original problem:
% 9.02/9.26 axioms:
% 9.02/9.26 ld(A, mult(A, A)) = A
% 9.02/9.26 rd(mult(A, A), A) = A
% 9.02/9.26 mult(A, ld(A, B)) = ld(A, mult(A, B))
% 9.02/9.26 mult(rd(A, B), B) = rd(mult(A, B), B)
% 9.02/9.26 ld(ld(A, B), mult(ld(A, B), mult(C, D))) = mult(ld(A, mult(A, C)), D)
% 9.02/9.26 rd(mult(mult(A, B), rd(C, D)), rd(C, D)) = mult(A, rd(mult(B, D), D))
% 9.02/9.26 ld(A, mult(A, ld(B, B))) = rd(mult(rd(A, A), B), B)
% 9.02/9.26 goal:
% 9.02/9.26 mult(x3(), ld(x4(), mult(x4(), x5()))) != mult(x3(), x5())
% 9.02/9.26 To show the unsatisfiability of the original goal,
% 9.02/9.26 it suffices to show that mult(x3(), ld(x4(), mult(x4(), x5()))) = mult(x3(), x5()) (skolemized goal) is valid under the axioms.
% 9.02/9.26 Here is an equational proof:
% 9.02/9.26 0: ld(X0, mult(X0, X0)) = X0.
% 9.02/9.26 Proof: Axiom.
% 9.02/9.26
% 9.02/9.26 1: rd(mult(X0, X0), X0) = X0.
% 9.02/9.26 Proof: Axiom.
% 9.02/9.26
% 9.02/9.26 2: mult(X0, ld(X0, X1)) = ld(X0, mult(X0, X1)).
% 9.02/9.26 Proof: Axiom.
% 9.02/9.26
% 9.02/9.26 3: mult(rd(X0, X1), X1) = rd(mult(X0, X1), X1).
% 9.02/9.26 Proof: Axiom.
% 9.02/9.26
% 9.02/9.26 4: ld(ld(X0, X1), mult(ld(X0, X1), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 9.02/9.26 Proof: Axiom.
% 9.02/9.26
% 9.02/9.26 5: rd(mult(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 9.02/9.26 Proof: Axiom.
% 9.02/9.26
% 9.02/9.26 6: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 9.02/9.26 Proof: Axiom.
% 9.02/9.26
% 9.02/9.26 7: mult(X0, ld(X0, X0)) = X0.
% 9.02/9.26 Proof: Rewrite equation 0,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 8: mult(rd(X0, X0), X0) = X0.
% 9.02/9.26 Proof: Rewrite equation 1,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 9: mult(ld(X0, X1), ld(ld(X0, X1), mult(X2, X3))) = mult(mult(X0, ld(X0, X2)), X3).
% 9.02/9.26 Proof: Rewrite equation 4,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 10: mult(rd(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, mult(rd(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 5,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 11: mult(X0, ld(X0, ld(X1, X1))) = mult(rd(rd(X0, X0), X1), X1).
% 9.02/9.26 Proof: Rewrite equation 6,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 12: mult(X2, ld(X2, ld(X2, X2))) = ld(X2, X2).
% 9.02/9.26 Proof: A critical pair between equations 2 and 7.
% 9.02/9.26
% 9.02/9.26 13: mult(rd(rd(X2, X2), X2), X2) = rd(X2, X2).
% 9.02/9.26 Proof: A critical pair between equations 3 and 8.
% 9.02/9.26
% 9.02/9.26 18: mult(mult(X0, ld(X0, X4)), ld(X4, X4)) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 9.02/9.26 Proof: A critical pair between equations 9 and 7.
% 9.02/9.26
% 9.02/9.26 19: mult(mult(X0, ld(X0, rd(X4, X4))), X4) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 9.02/9.26 Proof: A critical pair between equations 9 and 8.
% 9.02/9.26
% 9.02/9.26 20: mult(X4, mult(rd(ld(X4, X4), X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: A critical pair between equations 10 and 7.
% 9.02/9.26
% 9.02/9.26 21: mult(rd(X4, X4), mult(rd(X4, X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: A critical pair between equations 10 and 8.
% 9.02/9.26
% 9.02/9.26 28: ld(X2, X2) = rd(X2, X2).
% 9.02/9.26 Proof: Rewrite equation 13,
% 9.02/9.26 lhs with equations [11,12]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 29: ld(X2, mult(X2, rd(X2, X2))) = rd(X2, X2).
% 9.02/9.26 Proof: Rewrite equation 12,
% 9.02/9.26 lhs with equations [28,2]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 30: ld(X0, mult(X0, rd(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 9.02/9.26 Proof: Rewrite equation 11,
% 9.02/9.26 lhs with equations [28,2]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 31: rd(mult(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 10,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 32: rd(mult(X0, X0), X0) = X0.
% 9.02/9.26 Proof: Rewrite equation 8,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 33: mult(X0, rd(X0, X0)) = X0.
% 9.02/9.26 Proof: Rewrite equation 7,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 35: mult(rd(X4, X4), rd(mult(X4, X3), X3)) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 21,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 36: ld(X4, mult(X4, mult(X4, rd(X3, X3)))) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 20,
% 9.02/9.26 lhs with equations [28,3,30,2]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 37: mult(ld(X0, mult(X0, rd(X4, X4))), X4) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 9.02/9.26 Proof: Rewrite equation 19,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 38: mult(ld(X0, mult(X0, X4)), rd(X4, X4)) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 9.02/9.26 Proof: Rewrite equation 18,
% 9.02/9.26 lhs with equations [2,28]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 39: ld(ld(X0, X1), mult(ld(X0, X1), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 9.02/9.26 Proof: Rewrite equation 9,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 42: rd(mult(X5, rd(X2, X5)), rd(X2, X5)) = mult(rd(X5, X5), X5).
% 9.02/9.26 Proof: A critical pair between equations 35 and 32.
% 9.02/9.26
% 9.02/9.26 44: ld(ld(X5, X1), mult(ld(X5, X1), X5)) = mult(rd(X5, X5), X5).
% 9.02/9.26 Proof: A critical pair between equations 37 and 29.
% 9.02/9.26
% 9.02/9.26 49: mult(rd(X5, X5), rd(mult(X5, X7), X7)) = ld(X5, mult(X5, mult(X5, rd(X7, X7)))).
% 9.02/9.26 Proof: A critical pair between equations 35 and 36.
% 9.02/9.26
% 9.02/9.26 51: mult(rd(X4, X4), rd(mult(X4, X5), X5)) = rd(mult(X4, X5), rd(mult(X5, X5), X5)).
% 9.02/9.26 Proof: A critical pair between equations 35 and 32.
% 9.02/9.26
% 9.02/9.26 52: mult(rd(X4, X4), mult(rd(X4, X5), X5)) = mult(rd(X4, X5), X5).
% 9.02/9.26 Proof: Rewrite equation 51,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [32,3].
% 9.02/9.26
% 9.02/9.26 53: mult(rd(X5, X7), X7) = mult(X5, mult(X5, ld(X5, rd(X7, X7)))).
% 9.02/9.26 Proof: Rewrite equation 49,
% 9.02/9.26 lhs with equations [3,52]
% 9.02/9.26 rhs with equations [2,2].
% 9.02/9.26
% 9.02/9.26 55: mult(ld(X5, X1), ld(ld(X5, X1), X5)) = mult(rd(X5, X5), X5).
% 9.02/9.26 Proof: Rewrite equation 44,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 56: mult(rd(X5, rd(X2, X5)), rd(X2, X5)) = mult(rd(X5, X5), X5).
% 9.02/9.26 Proof: Rewrite equation 42,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 57: mult(rd(X0, X0), X0) = X0.
% 9.02/9.26 Proof: Rewrite equation 32,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 58: mult(rd(mult(X0, X1), X3), X3) = mult(X0, mult(rd(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 31,
% 9.02/9.26 lhs with equations [35,3,52]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 59: mult(X0, ld(X0, rd(X1, X1))) = mult(rd(rd(X0, X0), X1), X1).
% 9.02/9.26 Proof: Rewrite equation 30,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 60: mult(mult(X0, ld(X0, mult(X2, X3))), rd(mult(X2, X3), mult(X2, X3))) = mult(mult(X0, ld(X0, X2)), X3).
% 9.02/9.26 Proof: Rewrite equation 39,
% 9.02/9.26 lhs with equations [38,2]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 61: mult(mult(X0, ld(X0, X4)), rd(X4, X4)) = mult(mult(rd(rd(X0, X0), X4), X4), X4).
% 9.02/9.26 Proof: Rewrite equation 38,
% 9.02/9.26 lhs with equations [2]
% 9.02/9.26 rhs with equations [37,2,59].
% 9.02/9.26
% 9.02/9.26 62: mult(mult(rd(rd(X0, X0), X4), X4), X4) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 9.02/9.26 Proof: Rewrite equation 37,
% 9.02/9.26 lhs with equations [2,59]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 63: mult(rd(X4, X3), X3) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 35,
% 9.02/9.26 lhs with equations [3,52]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 65: mult(X4, mult(rd(rd(X4, X4), X3), X3)) = mult(rd(X4, X3), X3).
% 9.02/9.26 Proof: Rewrite equation 36,
% 9.02/9.26 lhs with equations [2,2,59]
% 9.02/9.26 rhs with equations [3,63].
% 9.02/9.26
% 9.02/9.26 66: rd(X6, X7) = mult(rd(rd(X6, X7), X7), X7).
% 9.02/9.26 Proof: A critical pair between equations 57 and 63.
% 9.02/9.26
% 9.02/9.26 71: mult(rd(X6, X6), X6) = mult(rd(X6, X6), ld(ld(X6, X6), X6)).
% 9.02/9.26 Proof: A critical pair between equations 55 and 28.
% 9.02/9.26
% 9.02/9.26 74: mult(rd(X2, X2), ld(rd(X2, X2), X2)) = ld(rd(X2, X2), X2).
% 9.02/9.26 Proof: A critical pair between equations 2 and 57.
% 9.02/9.26
% 9.02/9.26 77: mult(rd(X6, X6), X6) = mult(ld(X6, mult(X6, X7)), ld(mult(X6, ld(X6, X7)), X6)).
% 9.02/9.26 Proof: A critical pair between equations 55 and 2.
% 9.02/9.26
% 9.02/9.26 78: mult(ld(X6, X6), X6) = ld(ld(X6, mult(X6, X7)), mult(ld(X6, mult(X6, X7)), X6)).
% 9.02/9.26 Proof: Rewrite equation 77,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [2,2].
% 9.02/9.26
% 9.02/9.26 80: ld(ld(X2, X2), mult(ld(X2, X2), X2)) = ld(ld(X2, X2), X2).
% 9.02/9.26 Proof: Rewrite equation 74,
% 9.02/9.26 lhs with equations [28,28,2]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 83: mult(ld(X6, X6), X6) = ld(ld(X6, X6), X6).
% 9.02/9.26 Proof: Rewrite equation 71,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [28,2,80].
% 9.02/9.26
% 9.02/9.26 88: rd(X6, X7) = rd(rd(mult(X6, X7), X7), X7).
% 9.02/9.26 Proof: Rewrite equation 66,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [3,3].
% 9.02/9.26
% 9.02/9.26 89: mult(X4, rd(mult(ld(X4, X4), X3), X3)) = rd(mult(X4, X3), X3).
% 9.02/9.26 Proof: Rewrite equation 65,
% 9.02/9.26 lhs with equations [28,3]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 90: rd(mult(X4, X3), X3) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 63,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 91: mult(ld(X0, mult(X0, X4)), ld(X4, X4)) = mult(ld(X0, X0), ld(ld(X4, X4), X4)).
% 9.02/9.26 Proof: Rewrite equation 61,
% 9.02/9.26 lhs with equations [2,28]
% 9.02/9.26 rhs with equations [28,3,58,28,83].
% 9.02/9.26
% 9.02/9.26 92: mult(ld(X0, X0), ld(ld(mult(X2, X3), mult(X2, X3)), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 9.02/9.26 Proof: Rewrite equation 60,
% 9.02/9.26 lhs with equations [2,28,91]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 93: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(ld(X0, X0), X1), X1).
% 9.02/9.26 Proof: Rewrite equation 59,
% 9.02/9.26 lhs with equations [28,2]
% 9.02/9.26 rhs with equations [28,3].
% 9.02/9.26
% 9.02/9.26 94: rd(mult(mult(X0, X1), X3), X3) = mult(X0, rd(mult(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 58,
% 9.02/9.26 lhs with equations [3]
% 9.02/9.26 rhs with equations [3].
% 9.02/9.26
% 9.02/9.26 95: ld(X0, mult(X0, mult(X0, ld(X1, X1)))) = rd(mult(X0, X1), X1).
% 9.02/9.26 Proof: Rewrite equation 3,
% 9.02/9.26 lhs with equations [53,28,2,2]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 96: ld(ld(X0, X0), X0) = X0.
% 9.02/9.26 Proof: Rewrite equation 57,
% 9.02/9.26 lhs with equations [28,83]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 97: ld(X0, mult(X0, X0)) = X0.
% 9.02/9.26 Proof: Rewrite equation 33,
% 9.02/9.26 lhs with equations [28,2]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 98: rd(mult(X5, X5), X5) = X5.
% 9.02/9.26 Proof: Rewrite equation 56,
% 9.02/9.26 lhs with equations [53,28,2,2,95,90]
% 9.02/9.26 rhs with equations [28,83,96].
% 9.02/9.26
% 9.02/9.26 100: mult(rd(X5, X7), X7) = rd(mult(X5, X7), X7).
% 9.02/9.26 Proof: Rewrite equation 53,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28,2,2,95].
% 9.02/9.26
% 9.02/9.26 103: mult(ld(X0, X0), X4) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 9.02/9.26 Proof: Rewrite equation 62,
% 9.02/9.26 lhs with equations [28,100,93,92,83,96,83,96,83,96,96]
% 9.02/9.26 rhs with equations [2].
% 9.02/9.26
% 9.02/9.26 105: mult(ld(X0, X0), ld(X0, X1)) = ld(X0, X1).
% 9.02/9.26 Proof: A critical pair between equations 103 and 97.
% 9.02/9.26
% 9.02/9.26 108: mult(ld(X5, X5), X4) = ld(X5, mult(ld(X5, mult(X5, X5)), X4)).
% 9.02/9.26 Proof: A critical pair between equations 103 and 97.
% 9.02/9.26
% 9.02/9.26 109: rd(X8, rd(X9, X10)) = rd(rd(mult(X8, X10), X10), rd(X9, X10)).
% 9.02/9.26 Proof: A critical pair between equations 88 and 90.
% 9.02/9.26
% 9.02/9.26 112: rd(mult(X4, ld(X4, X4)), ld(X4, X4)) = mult(X4, ld(X4, X4)).
% 9.02/9.26 Proof: A critical pair between equations 89 and 98.
% 9.02/9.26
% 9.02/9.26 114: rd(mult(X4, X5), X5) = rd(mult(X4, ld(X5, X5)), rd(X5, X5)).
% 9.02/9.26 Proof: A critical pair between equations 90 and 28.
% 9.02/9.26
% 9.02/9.26 118: mult(rd(X4, X5), X5) = mult(rd(X4, rd(X5, X5)), rd(X5, X5)).
% 9.02/9.26 Proof: Rewrite equation 114,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [28,100].
% 9.02/9.26
% 9.02/9.26 119: mult(rd(X4, X4), X4) = mult(X4, rd(X4, X4)).
% 9.02/9.26 Proof: Rewrite equation 112,
% 9.02/9.26 lhs with equations [28,28,100,118]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 122: rd(X8, rd(X9, X10)) = rd(mult(rd(X8, X10), X10), rd(X9, X10)).
% 9.02/9.26 Proof: Rewrite equation 109,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 123: mult(rd(X5, X5), X4) = mult(X5, ld(X5, X4)).
% 9.02/9.26 Proof: Rewrite equation 108,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [97,2].
% 9.02/9.26
% 9.02/9.26 124: mult(rd(X0, X0), ld(X0, X1)) = ld(X0, X1).
% 9.02/9.26 Proof: Rewrite equation 105,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 129: mult(X5, rd(X5, X5)) = X5.
% 9.02/9.26 Proof: Rewrite equation 98,
% 9.02/9.26 lhs with equations [100,119]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 130: ld(rd(X0, X0), X0) = X0.
% 9.02/9.26 Proof: Rewrite equation 96,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 131: mult(rd(X0, X0), X1) = ld(X0, mult(X0, X1)).
% 9.02/9.26 Proof: Rewrite equation 2,
% 9.02/9.26 lhs with equations [123]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 132: mult(rd(X0, X0), mult(X0, rd(X1, X1))) = mult(rd(X0, X1), X1).
% 9.02/9.26 Proof: Rewrite equation 95,
% 9.02/9.26 lhs with equations [28,131]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 133: mult(rd(mult(X0, X1), X3), X3) = mult(X0, mult(rd(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 94,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 134: mult(rd(X0, X0), rd(X1, X1)) = mult(rd(rd(X0, X0), X1), X1).
% 9.02/9.26 Proof: Rewrite equation 93,
% 9.02/9.26 lhs with equations [28,131]
% 9.02/9.26 rhs with equations [28,100].
% 9.02/9.26
% 9.02/9.26 135: mult(rd(X4, X3), X3) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 90,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 136: mult(X4, mult(rd(rd(X4, X4), X3), X3)) = mult(rd(X4, X3), X3).
% 9.02/9.26 Proof: Rewrite equation 89,
% 9.02/9.26 lhs with equations [28,100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 139: X6 = mult(rd(mult(rd(X6, X6), X7), mult(rd(X6, X6), X7)), X6).
% 9.02/9.26 Proof: Rewrite equation 78,
% 9.02/9.26 lhs with equations [28,119,129]
% 9.02/9.26 rhs with equations [131,131,131].
% 9.02/9.26
% 9.02/9.26 140: mult(rd(X0, X0), X4) = mult(rd(ld(X0, X1), ld(X0, X1)), X4).
% 9.02/9.26 Proof: Rewrite equation 103,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [131].
% 9.02/9.26
% 9.02/9.26 142: mult(rd(X0, X0), mult(X2, X3)) = mult(mult(rd(X0, X0), X2), X3).
% 9.02/9.26 Proof: Rewrite equation 92,
% 9.02/9.26 lhs with equations [28,28,130]
% 9.02/9.26 rhs with equations [131].
% 9.02/9.26
% 9.02/9.26 150: mult(rd(X6, X6), mult(X6, X7)) = mult(X6, mult(rd(X6, X6), X7)).
% 9.02/9.26 Proof: A critical pair between equations 123 and 131.
% 9.02/9.26
% 9.02/9.26 152: ld(X2, mult(X2, X3)) = mult(rd(X2, X2), mult(rd(X2, X2), X3)).
% 9.02/9.26 Proof: A critical pair between equations 124 and 131.
% 9.02/9.26
% 9.02/9.26 157: ld(X2, mult(X2, X3)) = mult(ld(X2, X2), mult(ld(X2, X2), X3)).
% 9.02/9.26 Proof: Rewrite equation 152,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28,28].
% 9.02/9.26
% 9.02/9.26 159: mult(ld(X6, X6), mult(X6, X7)) = mult(X6, mult(ld(X6, X6), X7)).
% 9.02/9.26 Proof: Rewrite equation 150,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 165: mult(ld(X0, X0), mult(X2, X3)) = mult(mult(ld(X0, X0), X2), X3).
% 9.02/9.26 Proof: Rewrite equation 142,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 166: mult(ld(X0, X0), X4) = mult(ld(ld(X0, X1), ld(X0, X1)), X4).
% 9.02/9.26 Proof: Rewrite equation 140,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 167: X6 = mult(ld(mult(ld(X6, X6), X7), mult(ld(X6, X6), X7)), X6).
% 9.02/9.26 Proof: Rewrite equation 139,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28,28,28].
% 9.02/9.26
% 9.02/9.26 170: mult(X4, rd(mult(ld(X4, X4), X3), X3)) = rd(mult(X4, X3), X3).
% 9.02/9.26 Proof: Rewrite equation 136,
% 9.02/9.26 lhs with equations [28,100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 171: rd(mult(X4, X3), X3) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 135,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 172: rd(mult(mult(X0, X1), X3), X3) = mult(X0, rd(mult(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 133,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 173: mult(ld(X0, X0), X1) = ld(X0, mult(X0, X1)).
% 9.02/9.26 Proof: Rewrite equation 131,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 174: mult(X5, ld(X5, X5)) = X5.
% 9.02/9.26 Proof: Rewrite equation 129,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 178: ld(X0, mult(X0, ld(X0, X1))) = ld(X0, X1).
% 9.02/9.26 Proof: Rewrite equation 124,
% 9.02/9.26 lhs with equations [28,173]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 179: ld(X5, mult(X5, X4)) = mult(X5, ld(X5, X4)).
% 9.02/9.26 Proof: Rewrite equation 123,
% 9.02/9.26 lhs with equations [28,173]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 180: rd(X8, rd(X9, X10)) = rd(rd(mult(X8, X10), X10), rd(X9, X10)).
% 9.02/9.26 Proof: Rewrite equation 122,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 183: rd(mult(X4, X5), X5) = rd(mult(X4, ld(X5, X5)), ld(X5, X5)).
% 9.02/9.26 Proof: Rewrite equation 118,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [28,28,100].
% 9.02/9.26
% 9.02/9.26 185: ld(X0, mult(X0, ld(X1, X1))) = rd(ld(X0, mult(X0, X1)), X1).
% 9.02/9.26 Proof: Rewrite equation 134,
% 9.02/9.26 lhs with equations [28,28,173]
% 9.02/9.26 rhs with equations [28,100,173].
% 9.02/9.26
% 9.02/9.26 187: ld(X0, mult(X0, mult(X0, ld(X1, X1)))) = rd(mult(X0, X1), X1).
% 9.02/9.26 Proof: Rewrite equation 132,
% 9.02/9.26 lhs with equations [28,28,173]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 188: X7 = ld(X7, mult(X7, X7)).
% 9.02/9.26 Proof: A critical pair between equations 174 and 179.
% 9.02/9.26
% 9.02/9.26 197: rd(mult(X6, X6), X6) = rd(X6, ld(X6, X6)).
% 9.02/9.26 Proof: A critical pair between equations 183 and 174.
% 9.02/9.26
% 9.02/9.26 198: rd(mult(X6, X6), X6) = ld(X6, mult(X6, X6)).
% 9.02/9.26 Proof: A critical pair between equations 187 and 174.
% 9.02/9.26
% 9.02/9.26 201: mult(rd(X6, X6), X6) = X6.
% 9.02/9.26 Proof: Rewrite equation 198,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [188].
% 9.02/9.26
% 9.02/9.26 202: X6 = rd(X6, rd(X6, X6)).
% 9.02/9.26 Proof: Rewrite equation 197,
% 9.02/9.26 lhs with equations [100,201]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 209: mult(X0, mult(X0, ld(X0, rd(X1, X1)))) = mult(rd(X0, X1), X1).
% 9.02/9.26 Proof: Rewrite equation 187,
% 9.02/9.26 lhs with equations [28,179,179]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 211: mult(X0, ld(X0, rd(X1, X1))) = rd(mult(X0, ld(X0, X1)), X1).
% 9.02/9.26 Proof: Rewrite equation 185,
% 9.02/9.26 lhs with equations [28,179]
% 9.02/9.26 rhs with equations [179].
% 9.02/9.26
% 9.02/9.26 216: rd(X8, rd(X9, X10)) = rd(mult(rd(X8, X10), X10), rd(X9, X10)).
% 9.02/9.26 Proof: Rewrite equation 180,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 217: mult(rd(X5, X5), X4) = mult(X5, ld(X5, X4)).
% 9.02/9.26 Proof: Rewrite equation 179,
% 9.02/9.26 lhs with equations [173,28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 218: ld(X0, mult(rd(X0, X0), X1)) = ld(X0, X1).
% 9.02/9.26 Proof: Rewrite equation 178,
% 9.02/9.26 lhs with equations [217]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 222: mult(rd(X0, X0), X1) = mult(rd(X0, X0), mult(rd(X0, X0), X1)).
% 9.02/9.26 Proof: Rewrite equation 173,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [157,28,28].
% 9.02/9.26
% 9.02/9.26 223: mult(rd(mult(X0, X1), X3), X3) = mult(X0, mult(rd(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 172,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 224: mult(rd(X4, X3), X3) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 171,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 225: mult(X4, mult(rd(rd(X4, X4), X3), X3)) = mult(rd(X4, X3), X3).
% 9.02/9.26 Proof: Rewrite equation 170,
% 9.02/9.26 lhs with equations [28,100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 228: X6 = mult(rd(mult(rd(X6, X6), X7), mult(rd(X6, X6), X7)), X6).
% 9.02/9.26 Proof: Rewrite equation 167,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28,28,28].
% 9.02/9.26
% 9.02/9.26 229: mult(rd(X0, X0), X4) = mult(rd(ld(X0, X1), ld(X0, X1)), X4).
% 9.02/9.26 Proof: Rewrite equation 166,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 230: mult(rd(X0, X0), mult(X2, X3)) = mult(mult(rd(X0, X0), X2), X3).
% 9.02/9.26 Proof: Rewrite equation 165,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 233: mult(rd(X6, X6), mult(X6, X7)) = mult(X6, mult(rd(X6, X6), X7)).
% 9.02/9.26 Proof: Rewrite equation 159,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 234: ld(X2, mult(X2, X3)) = mult(rd(X2, X2), X3).
% 9.02/9.26 Proof: Rewrite equation 157,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28,28,222].
% 9.02/9.26
% 9.02/9.26 236: ld(X7, X8) = mult(rd(X7, X7), ld(X7, X8)).
% 9.02/9.26 Proof: A critical pair between equations 201 and 229.
% 9.02/9.26
% 9.02/9.26 237: mult(rd(X7, X7), mult(X7, X3)) = mult(X7, X3).
% 9.02/9.26 Proof: A critical pair between equations 230 and 201.
% 9.02/9.26
% 9.02/9.26 243: ld(ld(X5, X6), X7) = ld(ld(X5, X6), mult(rd(X5, X5), X7)).
% 9.02/9.26 Proof: A critical pair between equations 218 and 229.
% 9.02/9.26
% 9.02/9.26 251: ld(ld(X5, X6), X7) = ld(ld(X5, X6), mult(ld(X5, X5), X7)).
% 9.02/9.26 Proof: Rewrite equation 243,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 254: mult(ld(X7, X7), mult(X7, X3)) = mult(X7, X3).
% 9.02/9.26 Proof: Rewrite equation 237,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 255: ld(X7, X8) = mult(ld(X7, X7), ld(X7, X8)).
% 9.02/9.26 Proof: Rewrite equation 236,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 257: ld(X2, mult(X2, X3)) = mult(ld(X2, X2), X3).
% 9.02/9.26 Proof: Rewrite equation 234,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 258: ld(X6, mult(X6, mult(X6, X7))) = mult(X6, ld(X6, mult(X6, X7))).
% 9.02/9.26 Proof: Rewrite equation 233,
% 9.02/9.26 lhs with equations [28,257]
% 9.02/9.26 rhs with equations [28,257].
% 9.02/9.26
% 9.02/9.26 261: ld(X0, mult(X0, mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 9.02/9.26 Proof: Rewrite equation 230,
% 9.02/9.26 lhs with equations [28,257]
% 9.02/9.26 rhs with equations [28,257].
% 9.02/9.26
% 9.02/9.26 262: ld(X0, mult(X0, X4)) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 9.02/9.26 Proof: Rewrite equation 229,
% 9.02/9.26 lhs with equations [28,257]
% 9.02/9.26 rhs with equations [28,257].
% 9.02/9.26
% 9.02/9.26 263: X6 = ld(ld(X6, mult(X6, X7)), ld(X6, mult(X6, mult(X7, X6)))).
% 9.02/9.26 Proof: Rewrite equation 228,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28,257,28,257,28,257,261].
% 9.02/9.26
% 9.02/9.26 266: mult(X4, rd(ld(X4, mult(X4, X3)), X3)) = rd(mult(X4, X3), X3).
% 9.02/9.26 Proof: Rewrite equation 225,
% 9.02/9.26 lhs with equations [28,100,257]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 267: rd(mult(X4, X3), X3) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 9.02/9.26 Proof: Rewrite equation 224,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 268: rd(mult(mult(X0, X1), X3), X3) = mult(X0, rd(mult(X1, X3), X3)).
% 9.02/9.26 Proof: Rewrite equation 223,
% 9.02/9.26 lhs with equations [100]
% 9.02/9.26 rhs with equations [100].
% 9.02/9.26
% 9.02/9.26 270: mult(X5, mult(X5, ld(X5, ld(X7, X7)))) = rd(mult(X5, X7), X7).
% 9.02/9.26 Proof: Rewrite equation 100,
% 9.02/9.26 lhs with equations [209,28]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 275: ld(X5, mult(X5, X4)) = mult(X5, ld(X5, X4)).
% 9.02/9.26 Proof: Rewrite equation 217,
% 9.02/9.26 lhs with equations [28,257]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 276: rd(X8, rd(X9, X10)) = rd(ld(X8, mult(X8, mult(X8, ld(X10, X10)))), rd(X9, X10)).
% 9.02/9.26 Proof: Rewrite equation 216,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [209,28,275,275].
% 9.02/9.26
% 9.02/9.26 281: ld(X0, mult(X0, ld(X1, X1))) = rd(ld(X0, mult(X0, X1)), X1).
% 9.02/9.26 Proof: Rewrite equation 211,
% 9.02/9.26 lhs with equations [28,275]
% 9.02/9.26 rhs with equations [275].
% 9.02/9.26
% 9.02/9.26 283: rd(mult(X0, X1), X1) = mult(rd(X0, X1), X1).
% 9.02/9.26 Proof: Rewrite equation 209,
% 9.02/9.26 lhs with equations [28,275,281,266]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 286: X6 = rd(X6, ld(X6, X6)).
% 9.02/9.26 Proof: Rewrite equation 202,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [28].
% 9.02/9.26
% 9.02/9.26 288: ld(ld(X9, X9), X10) = ld(X9, mult(X9, X10)).
% 9.02/9.26 Proof: A critical pair between equations 251 and 262.
% 9.02/9.26
% 9.02/9.26 289: mult(X8, X3) = ld(X8, mult(X8, mult(X8, X3))).
% 9.02/9.26 Proof: A critical pair between equations 254 and 257.
% 9.02/9.26
% 9.02/9.26 297: ld(ld(X8, X6), X9) = ld(ld(X8, X6), ld(X8, mult(X8, X9))).
% 9.02/9.26 Proof: A critical pair between equations 251 and 257.
% 9.02/9.26
% 9.02/9.26 302: ld(ld(X8, X6), X9) = ld(ld(X8, X6), ld(ld(X8, X8), X9)).
% 9.02/9.26 Proof: Rewrite equation 297,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [288].
% 9.02/9.26
% 9.02/9.26 305: mult(X8, X3) = ld(ld(X8, X8), mult(X8, X3)).
% 9.02/9.26 Proof: Rewrite equation 289,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [288].
% 9.02/9.26
% 9.02/9.26 311: rd(X8, rd(X9, X10)) = rd(mult(X8, ld(X10, X10)), rd(X9, X10)).
% 9.02/9.26 Proof: Rewrite equation 276,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [288,305].
% 9.02/9.26
% 9.02/9.26 312: ld(ld(X5, X5), X4) = mult(X5, ld(X5, X4)).
% 9.02/9.26 Proof: Rewrite equation 275,
% 9.02/9.26 lhs with equations [288]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 316: mult(X5, ld(ld(X5, X5), ld(X7, X7))) = rd(mult(X5, X7), X7).
% 9.02/9.26 Proof: Rewrite equation 270,
% 9.02/9.26 lhs with equations [312]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 317: X6 = ld(ld(ld(X6, X6), X7), ld(ld(X6, X6), mult(X7, X6))).
% 9.02/9.26 Proof: Rewrite equation 263,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [288,288].
% 9.02/9.26
% 9.02/9.26 318: ld(ld(X0, X0), X4) = ld(ld(ld(X0, X1), ld(X0, X1)), X4).
% 9.02/9.26 Proof: Rewrite equation 262,
% 9.02/9.26 lhs with equations [288]
% 9.02/9.26 rhs with equations [288].
% 9.02/9.26
% 9.02/9.26 319: ld(ld(X0, X0), mult(X2, X3)) = mult(ld(ld(X0, X0), X2), X3).
% 9.02/9.26 Proof: Rewrite equation 261,
% 9.02/9.26 lhs with equations [288]
% 9.02/9.26 rhs with equations [288].
% 9.02/9.26
% 9.02/9.26 320: mult(X6, X7) = mult(X6, ld(ld(X6, X6), X7)).
% 9.02/9.26 Proof: Rewrite equation 258,
% 9.02/9.26 lhs with equations [288,305]
% 9.02/9.26 rhs with equations [288].
% 9.02/9.26
% 9.02/9.26 321: ld(ld(X2, X2), X3) = mult(ld(X2, X2), X3).
% 9.02/9.26 Proof: Rewrite equation 257,
% 9.02/9.26 lhs with equations [288]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 322: ld(X7, X8) = ld(ld(X7, X7), ld(X7, X8)).
% 9.02/9.26 Proof: Rewrite equation 255,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [321].
% 9.02/9.26
% 9.02/9.26 323: rd(mult(X8, X7), X7) = mult(X8, ld(X7, X7)).
% 9.02/9.26 Proof: A critical pair between equations 316 and 320.
% 9.02/9.26
% 9.02/9.26 326: rd(X8, rd(X11, X11)) = rd(mult(X8, ld(X11, X11)), ld(X11, X11)).
% 9.02/9.26 Proof: A critical pair between equations 311 and 28.
% 9.02/9.26
% 9.02/9.26 328: rd(mult(X4, X5), X5) = rd(mult(X4, ld(X5, X5)), rd(X5, X5)).
% 9.02/9.26 Proof: A critical pair between equations 267 and 28.
% 9.02/9.26
% 9.02/9.26 331: X9 = ld(mult(X9, X10), ld(ld(X9, X9), mult(mult(X9, X10), X9))).
% 9.02/9.26 Proof: A critical pair between equations 317 and 305.
% 9.02/9.26
% 9.02/9.26 332: ld(ld(X9, X9), mult(mult(X9, X10), X3)) = mult(mult(X9, X10), X3).
% 9.02/9.26 Proof: A critical pair between equations 319 and 305.
% 9.02/9.26
% 9.02/9.26 334: ld(ld(X11, mult(X11, X12)), X9) = ld(ld(ld(X11, X11), X12), ld(ld(X11, X11), X9)).
% 9.02/9.26 Proof: A critical pair between equations 302 and 288.
% 9.02/9.26
% 9.02/9.26 335: ld(ld(ld(X11, X11), X12), X9) = ld(ld(ld(X11, X11), X12), ld(ld(X11, X11), X9)).
% 9.02/9.26 Proof: Rewrite equation 334,
% 9.02/9.26 lhs with equations [288]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 336: X9 = ld(ld(mult(X9, X10), mult(X9, X10)), X9).
% 9.02/9.26 Proof: Rewrite equation 331,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [332,288].
% 9.02/9.26
% 9.02/9.26 337: rd(mult(X4, X5), X5) = rd(rd(mult(X4, X5), X5), ld(X5, X5)).
% 9.02/9.26 Proof: Rewrite equation 328,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [323,28].
% 9.02/9.26
% 9.02/9.26 338: rd(X8, ld(X11, X11)) = rd(mult(X8, X11), X11).
% 9.02/9.26 Proof: Rewrite equation 326,
% 9.02/9.26 lhs with equations [28]
% 9.02/9.26 rhs with equations [323,337].
% 9.02/9.26
% 9.02/9.26 339: rd(X8, ld(X7, X7)) = mult(X8, ld(X7, X7)).
% 9.02/9.26 Proof: Rewrite equation 323,
% 9.02/9.26 lhs with equations [338]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 342: X6 = ld(ld(ld(X6, X6), X7), mult(X7, X6)).
% 9.02/9.26 Proof: Rewrite equation 317,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [335].
% 9.02/9.26
% 9.02/9.26 345: rd(X4, ld(X3, X3)) = rd(X4, ld(rd(X2, X3), rd(X2, X3))).
% 9.02/9.26 Proof: Rewrite equation 267,
% 9.02/9.26 lhs with equations [338]
% 9.02/9.26 rhs with equations [338].
% 9.02/9.26
% 9.02/9.26 346: rd(mult(X0, X1), ld(X3, X3)) = mult(X0, rd(X1, ld(X3, X3))).
% 9.02/9.26 Proof: Rewrite equation 268,
% 9.02/9.26 lhs with equations [338]
% 9.02/9.26 rhs with equations [338].
% 9.02/9.26
% 9.02/9.26 351: rd(X0, ld(X1, X1)) = mult(rd(X0, X1), X1).
% 9.02/9.26 Proof: Rewrite equation 283,
% 9.02/9.26 lhs with equations [338]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 353: rd(mult(X0, X7), ld(X7, X7)) = mult(X0, X7).
% 9.02/9.26 Proof: A critical pair between equations 346 and 286.
% 9.02/9.26
% 9.02/9.26 360: rd(ld(X9, X9), ld(X7, X7)) = ld(ld(X9, X9), ld(X7, X7)).
% 9.02/9.26 Proof: A critical pair between equations 339 and 321.
% 9.02/9.26
% 9.02/9.26 372: ld(ld(X11, X11), ld(X12, X12)) = ld(X11, rd(X11, ld(X12, X12))).
% 9.02/9.26 Proof: A critical pair between equations 288 and 339.
% 9.02/9.26
% 9.02/9.26 373: rd(mult(X12, X13), ld(X13, X13)) = mult(rd(X12, ld(X13, X13)), X13).
% 9.02/9.26 Proof: A critical pair between equations 351 and 338.
% 9.02/9.26
% 9.02/9.26 375: rd(mult(X0, mult(X8, X9)), ld(X9, X9)) = mult(X0, mult(X8, X9)).
% 9.02/9.26 Proof: A critical pair between equations 346 and 353.
% 9.02/9.26
% 9.02/9.26 378: ld(X8, X9) = ld(ld(ld(X8, X8), X10), mult(X10, ld(X8, X9))).
% 9.02/9.26 Proof: A critical pair between equations 342 and 318.
% 9.02/9.26
% 9.02/9.26 379: X9 = ld(ld(ld(X9, X9), ld(X8, X8)), ld(ld(X8, X8), X9)).
% 9.02/9.26 Proof: A critical pair between equations 342 and 321.
% 9.02/9.26
% 9.02/9.26 382: mult(X12, X13) = mult(rd(X12, ld(X13, X13)), X13).
% 9.02/9.26 Proof: Rewrite equation 373,
% 9.02/9.26 lhs with equations [353]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 391: mult(X14, rd(X15, X16)) = mult(rd(X14, ld(X16, X16)), rd(X15, X16)).
% 9.02/9.26 Proof: A critical pair between equations 382 and 345.
% 9.02/9.26
% 9.02/9.26 477: ld(X10, X11) = ld(ld(ld(X10, X10), ld(X8, X8)), ld(ld(X8, X8), ld(X10, X11))).
% 9.02/9.26 Proof: A critical pair between equations 379 and 318.
% 9.02/9.26
% 9.02/9.26 483: ld(ld(X11, X12), X9) = ld(ld(ld(X11, X11), X13), mult(X13, ld(ld(X11, X12), X9))).
% 9.02/9.26 Proof: A critical pair between equations 378 and 318.
% 9.02/9.26
% 9.02/9.26 487: ld(ld(X14, X12), X9) = ld(mult(X14, X15), mult(mult(X14, X15), ld(ld(X14, X12), X9))).
% 9.02/9.26 Proof: A critical pair between equations 483 and 305.
% 9.02/9.26
% 9.02/9.26 492: mult(X14, rd(X15, ld(X18, X18))) = mult(rd(X14, ld(X18, X18)), rd(X15, ld(X18, X18))).
% 9.02/9.26 Proof: A critical pair between equations 391 and 322.
% 9.02/9.26
% 9.02/9.26 499: rd(mult(X14, X15), ld(X18, X18)) = rd(mult(rd(X14, ld(X18, X18)), X15), ld(X18, X18)).
% 9.02/9.26 Proof: Rewrite equation 492,
% 9.02/9.26 lhs with equations [346]
% 9.02/9.26 rhs with equations [346].
% 9.02/9.26
% 9.02/9.26 502: ld(ld(X14, X12), X9) = ld(ld(mult(X14, X15), mult(X14, X15)), ld(ld(X14, X12), X9)).
% 9.02/9.26 Proof: Rewrite equation 487,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [288].
% 9.02/9.26
% 9.02/9.26 509: rd(mult(X14, mult(X20, X21)), ld(X21, X21)) = mult(rd(X14, ld(X21, X21)), mult(X20, X21)).
% 9.02/9.26 Proof: A critical pair between equations 499 and 375.
% 9.02/9.26
% 9.02/9.26 517: mult(X14, mult(X20, X21)) = mult(rd(X14, ld(X21, X21)), mult(X20, X21)).
% 9.02/9.26 Proof: Rewrite equation 509,
% 9.02/9.26 lhs with equations [375]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 518: mult(ld(X22, X22), mult(X20, X23)) = mult(ld(ld(X22, X22), ld(X23, X23)), mult(X20, X23)).
% 9.02/9.26 Proof: A critical pair between equations 517 and 360.
% 9.02/9.26
% 9.02/9.26 532: ld(ld(X22, X22), mult(X20, X23)) = ld(ld(X22, X22), ld(ld(X23, X23), mult(X20, X23))).
% 9.02/9.26 Proof: Rewrite equation 518,
% 9.02/9.26 lhs with equations [321]
% 9.02/9.26 rhs with equations [319,321].
% 9.02/9.26
% 9.02/9.26 604: ld(ld(mult(X13, X14), mult(X13, X14)), ld(X14, X14)) = ld(mult(X13, X14), mult(X13, X14)).
% 9.02/9.26 Proof: A critical pair between equations 372 and 353.
% 9.02/9.26
% 9.02/9.26 607: ld(mult(X16, ld(X16, X18)), mult(X16, ld(X16, X18))) = ld(ld(X16, X18), ld(X16, X18)).
% 9.02/9.26 Proof: A critical pair between equations 604 and 502.
% 9.02/9.26
% 9.02/9.26 619: ld(ld(ld(X16, X16), X18), X18) = ld(ld(X16, X18), ld(X16, X18)).
% 9.02/9.26 Proof: Rewrite equation 607,
% 9.02/9.26 lhs with equations [312,312,335]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 629: ld(ld(mult(X19, X20), X19), ld(mult(X19, X20), X19)) = ld(X19, X19).
% 9.02/9.26 Proof: A critical pair between equations 619 and 336.
% 9.02/9.26
% 9.02/9.26 645: ld(ld(mult(X21, X22), mult(X21, X22)), X4) = ld(ld(X21, X21), X4).
% 9.02/9.26 Proof: A critical pair between equations 318 and 629.
% 9.02/9.26
% 9.02/9.26 658: ld(ld(X13, X13), ld(X14, X14)) = ld(mult(X13, X14), mult(X13, X14)).
% 9.02/9.26 Proof: Rewrite equation 604,
% 9.02/9.26 lhs with equations [645]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 659: ld(ld(X23, X23), X4) = ld(ld(ld(X23, X23), ld(X24, X24)), X4).
% 9.02/9.26 Proof: A critical pair between equations 645 and 658.
% 9.02/9.26
% 9.02/9.26 673: ld(X10, X11) = ld(ld(X10, X10), ld(ld(X8, X8), ld(X10, X11))).
% 9.02/9.26 Proof: Rewrite equation 477,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [659].
% 9.02/9.26
% 9.02/9.26 698: mult(X12, ld(ld(X13, X13), ld(X12, X14))) = mult(X12, ld(X12, X14)).
% 9.02/9.26 Proof: A critical pair between equations 320 and 673.
% 9.02/9.26
% 9.02/9.26 700: X12 = ld(ld(X12, X14), mult(ld(ld(X13, X13), ld(X12, X14)), X12)).
% 9.02/9.26 Proof: A critical pair between equations 342 and 673.
% 9.02/9.26
% 9.02/9.26 706: X12 = ld(ld(X12, X14), ld(ld(X13, X13), mult(ld(X12, X14), X12))).
% 9.02/9.26 Proof: Rewrite equation 700,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [319].
% 9.02/9.26
% 9.02/9.26 708: mult(X12, ld(ld(X13, X13), ld(X12, X14))) = ld(ld(X12, X12), X14).
% 9.02/9.26 Proof: Rewrite equation 698,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [312].
% 9.02/9.26
% 9.02/9.26 717: X15 = ld(ld(ld(X15, X15), X16), ld(ld(X13, X13), mult(ld(X15, mult(X15, X16)), X15))).
% 9.02/9.26 Proof: A critical pair between equations 706 and 288.
% 9.02/9.26
% 9.02/9.26 718: ld(ld(X15, X15), mult(X15, X16)) = mult(X15, ld(ld(X13, X13), ld(ld(X15, X15), X16))).
% 9.02/9.26 Proof: A critical pair between equations 708 and 288.
% 9.02/9.26
% 9.02/9.26 725: mult(X15, X16) = mult(X15, ld(ld(X13, X13), ld(ld(X15, X15), X16))).
% 9.02/9.26 Proof: Rewrite equation 718,
% 9.02/9.26 lhs with equations [305]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 726: X15 = ld(ld(ld(X15, X15), X16), ld(ld(X13, X13), mult(X16, X15))).
% 9.02/9.26 Proof: Rewrite equation 717,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [288,319,532].
% 9.02/9.26
% 9.02/9.26 733: X25 = ld(ld(X25, X25), ld(ld(X13, X13), mult(ld(X26, X26), X25))).
% 9.02/9.26 Proof: A critical pair between equations 726 and 659.
% 9.02/9.26
% 9.02/9.26 741: X25 = ld(ld(X25, X25), ld(ld(X13, X13), ld(ld(X26, X26), X25))).
% 9.02/9.26 Proof: Rewrite equation 733,
% 9.02/9.26 lhs with equations []
% 9.02/9.26 rhs with equations [321].
% 9.02/9.26
% 9.02/9.26 746: mult(X28, ld(ld(X29, X29), X27)) = mult(X28, X27).
% 9.02/9.26 Proof: A critical pair between equations 725 and 741.
% 9.02/9.26
% 9.02/9.26 758: mult(x3(), ld(x4(), mult(x4(), x5()))) = mult(x3(), x5()).
% 9.02/9.26 Proof: Rewrite lhs with equations [288,746]
% 9.02/9.26 rhs with equations [].
% 9.02/9.26
% 9.02/9.26 % SZS output end Proof
%------------------------------------------------------------------------------