TSTP Solution File: GRP473-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP473-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% 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 01:15:05 EDT 2023
% Result : Unsatisfiable 34.07s 34.35s
% Output : CNFRefutation 34.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP473-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 22:23:25 EDT 2023
% 0.13/0.33 % CPUTime :
% 34.07/34.35 % SZS status Unsatisfiable
% 34.07/34.35 % SZS output start Proof
% 34.07/34.35 original problem:
% 34.07/34.35 axioms:
% 34.07/34.35 divide(divide(inverse(divide(A, B)), divide(divide(C, D), A)), divide(D, C)) = B
% 34.07/34.35 multiply(A, B) = divide(A, inverse(B))
% 34.07/34.35 goal:
% 34.07/34.35 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 34.07/34.35 To show the unsatisfiability of the original goal,
% 34.07/34.35 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 34.07/34.35 Here is an equational proof:
% 34.07/34.35 0: divide(divide(inverse(divide(X0, X1)), divide(divide(X2, X3), X0)), divide(X3, X2)) = X1.
% 34.07/34.35 Proof: Axiom.
% 34.07/34.35
% 34.07/34.35 1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 34.07/34.35 Proof: Axiom.
% 34.07/34.35
% 34.07/34.35 2: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), X5), divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5)))).
% 34.07/34.35 Proof: A critical pair between equations 0 and 0.
% 34.07/34.35
% 34.07/34.35 3: X1 = divide(divide(inverse(divide(X0, X1)), divide(divide(divide(X7, X6), divide(inverse(divide(X4, X5)), divide(divide(X6, X7), X4))), X0)), X5).
% 34.07/34.35 Proof: A critical pair between equations 0 and 0.
% 34.07/34.35
% 34.07/34.35 4: X1 = divide(divide(inverse(divide(X0, X1)), divide(X5, X0)), divide(divide(X7, X6), divide(inverse(divide(X4, X5)), divide(divide(X6, X7), X4)))).
% 34.07/34.35 Proof: A critical pair between equations 0 and 0.
% 34.07/34.35
% 34.07/34.35 5: divide(X7, X6) = divide(divide(inverse(X5), divide(divide(X2, X3), divide(inverse(divide(X4, X5)), divide(divide(X6, X7), X4)))), divide(X3, X2)).
% 34.07/34.35 Proof: A critical pair between equations 0 and 0.
% 34.07/34.35
% 34.07/34.35 6: divide(X7, X6) = divide(divide(inverse(X5), X9), divide(divide(divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5))), X8), inverse(divide(X8, X9)))).
% 34.07/34.35 Proof: A critical pair between equations 5 and 0.
% 34.07/34.35
% 34.07/34.35 11: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), divide(X11, X10)), divide(divide(divide(X6, X7), divide(inverse(divide(X8, X9)), divide(divide(X10, X11), X8))), inverse(X9))).
% 34.07/34.35 Proof: A critical pair between equations 2 and 0.
% 34.07/34.35
% 34.07/34.35 16: divide(divide(divide(X9, X8), X12), inverse(divide(X12, X11))) = divide(divide(inverse(X10), X5), divide(divide(divide(X11, inverse(divide(divide(X8, X9), X10))), X4), inverse(divide(X4, X5)))).
% 34.07/34.35 Proof: A critical pair between equations 2 and 2.
% 34.07/34.35
% 34.07/34.35 21: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), divide(X11, X10)), multiply(divide(divide(X6, X7), divide(inverse(divide(X8, X9)), divide(divide(X10, X11), X8))), X9)).
% 34.07/34.35 Proof: Rewrite equation 11,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 25: divide(X7, X6) = divide(divide(inverse(X5), X9), multiply(divide(multiply(divide(divide(X6, X7), X4), divide(X4, X5)), X8), divide(X8, X9))).
% 34.07/34.35 Proof: Rewrite equation 6,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 26: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), X5), multiply(divide(divide(X6, X7), X4), divide(X4, X5))).
% 34.07/34.35 Proof: Rewrite equation 2,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 27: multiply(divide(divide(X9, X8), X12), divide(X12, X11)) = divide(divide(inverse(X10), X5), multiply(divide(multiply(X11, divide(divide(X8, X9), X10)), X4), divide(X4, X5))).
% 34.07/34.35 Proof: Rewrite equation 16,
% 34.07/34.35 lhs with equations [1]
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 34: multiply(divide(divide(X9, X8), X12), divide(X12, divide(divide(X15, X16), divide(X8, X9)))) = divide(X16, X15).
% 34.07/34.35 Proof: A critical pair between equations 27 and 25.
% 34.07/34.35
% 34.07/34.35 47: divide(divide(divide(X9, X8), X12), inverse(divide(X12, divide(divide(X15, X16), divide(X8, X9))))) = divide(X16, X15).
% 34.07/34.35 Proof: Rewrite equation 34,
% 34.07/34.35 lhs with equations [1]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 48: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), X5), divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5)))).
% 34.07/34.35 Proof: Rewrite equation 26,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 49: divide(X7, X6) = divide(divide(inverse(X5), X9), divide(divide(divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5))), X8), inverse(divide(X8, X9)))).
% 34.07/34.35 Proof: Rewrite equation 25,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 53: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), divide(X11, X10)), divide(divide(divide(X6, X7), divide(inverse(divide(X8, X9)), divide(divide(X10, X11), X8))), inverse(X9))).
% 34.07/34.35 Proof: Rewrite equation 21,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 62: divide(X16, X15) = divide(X18, inverse(divide(divide(X20, X19), divide(divide(X15, X16), divide(divide(divide(X19, X20), X17), inverse(divide(X17, X18))))))).
% 34.07/34.35 Proof: A critical pair between equations 47 and 0.
% 34.07/34.35
% 34.07/34.35 63: X1 = divide(divide(inverse(divide(inverse(divide(X19, divide(divide(X20, X21), divide(X18, X17)))), X1)), divide(X21, X20)), divide(X19, divide(X17, X18))).
% 34.07/34.35 Proof: A critical pair between equations 0 and 47.
% 34.07/34.35
% 34.07/34.35 65: divide(X21, X20) = divide(divide(divide(divide(divide(X21, X20), X22), inverse(divide(X22, X19))), divide(inverse(divide(X17, X18)), divide(X19, X17))), inverse(X18)).
% 34.07/34.35 Proof: A critical pair between equations 47 and 4.
% 34.07/34.35
% 34.07/34.35 75: divide(X21, X20) = multiply(divide(multiply(divide(divide(X21, X20), X22), divide(X22, X19)), divide(inverse(divide(X17, X18)), divide(X19, X17))), X18).
% 34.07/34.35 Proof: Rewrite equation 65,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 76: divide(X16, X15) = multiply(X18, divide(divide(X20, X19), divide(divide(X15, X16), multiply(divide(divide(X19, X20), X17), divide(X17, X18))))).
% 34.07/34.35 Proof: Rewrite equation 62,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 81: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), divide(X11, X10)), multiply(divide(divide(X6, X7), divide(inverse(divide(X8, X9)), divide(divide(X10, X11), X8))), X9)).
% 34.07/34.35 Proof: Rewrite equation 53,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 85: divide(X7, X6) = divide(divide(inverse(X5), X9), multiply(divide(multiply(divide(divide(X6, X7), X4), divide(X4, X5)), X8), divide(X8, X9))).
% 34.07/34.35 Proof: Rewrite equation 49,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 86: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), X5), multiply(divide(divide(X6, X7), X4), divide(X4, X5))).
% 34.07/34.35 Proof: Rewrite equation 48,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 122: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), X5), divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5)))).
% 34.07/34.35 Proof: Rewrite equation 86,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 123: divide(X7, X6) = divide(divide(inverse(X5), X9), divide(divide(divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5))), X8), inverse(divide(X8, X9)))).
% 34.07/34.35 Proof: Rewrite equation 85,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 127: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), divide(X11, X10)), divide(divide(divide(X6, X7), divide(inverse(divide(X8, X9)), divide(divide(X10, X11), X8))), inverse(X9))).
% 34.07/34.35 Proof: Rewrite equation 81,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 132: divide(X16, X15) = divide(X18, inverse(divide(divide(X20, X19), divide(divide(X15, X16), divide(divide(divide(X19, X20), X17), inverse(divide(X17, X18))))))).
% 34.07/34.35 Proof: Rewrite equation 76,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 133: divide(X21, X20) = divide(divide(divide(divide(divide(X21, X20), X22), inverse(divide(X22, X19))), divide(inverse(divide(X17, X18)), divide(X19, X17))), inverse(X18)).
% 34.07/34.35 Proof: Rewrite equation 75,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 157: X1 = divide(divide(inverse(divide(divide(inverse(divide(X25, divide(X10, X11))), divide(divide(X23, X24), X25)), X1)), divide(X11, X10)), divide(X23, X24)).
% 34.07/34.35 Proof: A critical pair between equations 127 and 133.
% 34.07/34.35
% 34.07/34.35 162: divide(X16, X15) = multiply(X18, divide(divide(X20, X19), divide(divide(X15, X16), multiply(divide(divide(X19, X20), X17), divide(X17, X18))))).
% 34.07/34.35 Proof: Rewrite equation 132,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 167: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), divide(X11, X10)), multiply(divide(divide(X6, X7), divide(inverse(divide(X8, X9)), divide(divide(X10, X11), X8))), X9)).
% 34.07/34.35 Proof: Rewrite equation 127,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 171: divide(X7, X6) = divide(divide(inverse(X5), X9), multiply(divide(multiply(divide(divide(X6, X7), X4), divide(X4, X5)), X8), divide(X8, X9))).
% 34.07/34.35 Proof: Rewrite equation 123,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 172: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), X5), multiply(divide(divide(X6, X7), X4), divide(X4, X5))).
% 34.07/34.35 Proof: Rewrite equation 122,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 200: divide(X29, X28) = divide(divide(inverse(divide(X10, X11)), divide(X11, X10)), divide(X28, X29)).
% 34.07/34.35 Proof: A critical pair between equations 157 and 0.
% 34.07/34.35
% 34.07/34.35 220: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), X5), divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5)))).
% 34.07/34.35 Proof: Rewrite equation 172,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 221: divide(X7, X6) = divide(divide(inverse(X5), X9), divide(divide(divide(divide(divide(X6, X7), X4), inverse(divide(X4, X5))), X8), inverse(divide(X8, X9)))).
% 34.07/34.35 Proof: Rewrite equation 171,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 225: X1 = divide(divide(inverse(divide(divide(X7, X6), X1)), divide(X11, X10)), divide(divide(divide(X6, X7), divide(inverse(divide(X8, X9)), divide(divide(X10, X11), X8))), inverse(X9))).
% 34.07/34.35 Proof: Rewrite equation 167,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1].
% 34.07/34.35
% 34.07/34.35 230: divide(X16, X15) = divide(X18, inverse(divide(divide(X20, X19), divide(divide(X15, X16), divide(divide(divide(X19, X20), X17), inverse(divide(X17, X18))))))).
% 34.07/34.35 Proof: Rewrite equation 162,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [1,1].
% 34.07/34.35
% 34.07/34.35 261: divide(inverse(divide(X34, divide(X32, divide(X30, X31)))), divide(divide(X31, X30), X34)) = X32.
% 34.07/34.35 Proof: A critical pair between equations 200 and 220.
% 34.07/34.35
% 34.07/34.35 266: divide(X29, X28) = divide(divide(X32, X33), divide(inverse(divide(X34, divide(X28, X29))), divide(divide(X33, X32), X34))).
% 34.07/34.35 Proof: A critical pair between equations 200 and 3.
% 34.07/34.35
% 34.07/34.35 269: divide(inverse(X36), divide(divide(X31, X30), divide(inverse(divide(X35, X36)), divide(divide(divide(X30, X31), X33), X35)))) = X33.
% 34.07/34.35 Proof: A critical pair between equations 200 and 225.
% 34.07/34.35
% 34.07/34.35 271: X1 = divide(divide(inverse(divide(divide(X32, X33), X1)), divide(X33, X32)), divide(divide(X31, X30), inverse(divide(X30, X31)))).
% 34.07/34.35 Proof: A critical pair between equations 0 and 200.
% 34.07/34.35
% 34.07/34.35 273: divide(divide(X38, X37), X35) = divide(divide(inverse(divide(X20, X21)), divide(X21, X20)), divide(X35, divide(X38, X37))).
% 34.07/34.35 Proof: A critical pair between equations 63 and 261.
% 34.07/34.35
% 34.07/34.35 276: divide(divide(divide(divide(X11, X10), inverse(divide(X10, X11))), X37), inverse(divide(X37, divide(X38, X39)))) = divide(X39, X38).
% 34.07/34.35 Proof: A critical pair between equations 200 and 266.
% 34.07/34.35
% 34.07/34.35 281: X37 = divide(inverse(divide(divide(X30, X31), X37)), divide(divide(X31, X30), divide(inverse(divide(X35, X36)), divide(X36, X35)))).
% 34.07/34.35 Proof: A critical pair between equations 261 and 200.
% 34.07/34.35
% 34.07/34.35 282: inverse(divide(X37, divide(X38, X39))) = divide(inverse(divide(X39, X38)), divide(divide(X37, divide(X36, X35)), divide(X35, X36))).
% 34.07/34.35 Proof: A critical pair between equations 261 and 266.
% 34.07/34.35
% 34.07/34.35 286: X37 = divide(inverse(divide(divide(X39, X38), X37)), divide(X38, X39)).
% 34.07/34.35 Proof: A critical pair between equations 281 and 266.
% 34.07/34.35
% 34.07/34.35 287: X40 = divide(X40, divide(inverse(divide(X41, X42)), divide(X42, X41))).
% 34.07/34.35 Proof: A critical pair between equations 0 and 281.
% 34.07/34.35
% 34.07/34.35 288: inverse(divide(X41, X42)) = divide(inverse(X40), divide(divide(X41, X42), X40)).
% 34.07/34.35 Proof: A critical pair between equations 269 and 281.
% 34.07/34.35
% 34.07/34.35 289: divide(X29, X28) = divide(divide(divide(X42, X41), inverse(divide(X41, X42))), divide(X28, X29)).
% 34.07/34.35 Proof: A critical pair between equations 200 and 281.
% 34.07/34.35
% 34.07/34.35 290: X31 = divide(inverse(divide(X4, divide(X31, divide(X7, X6)))), divide(divide(X6, X7), X4)).
% 34.07/34.35 Proof: A critical pair between equations 220 and 200.
% 34.07/34.35
% 34.07/34.35 291: divide(X7, X6) = divide(divide(inverse(divide(X6, X7)), divide(X43, X44)), divide(X44, X43)).
% 34.07/34.35 Proof: A critical pair between equations 221 and 276.
% 34.07/34.35
% 34.07/34.35 293: inverse(divide(X41, divide(X42, divide(divide(divide(X44, X43), inverse(divide(X43, X44))), X41)))) = X42.
% 34.07/34.35 Proof: A critical pair between equations 282 and 281.
% 34.07/34.35
% 34.07/34.35 299: X1 = divide(X1, divide(divide(X31, X30), inverse(divide(X30, X31)))).
% 34.07/34.35 Proof: Rewrite equation 271,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [286].
% 34.07/34.35
% 34.07/34.35 302: X42 = inverse(divide(divide(X47, X48), divide(X42, divide(X48, X47)))).
% 34.07/34.35 Proof: A critical pair between equations 293 and 289.
% 34.07/34.35
% 34.07/34.35 307: X37 = inverse(divide(divide(inverse(divide(X42, X41)), divide(X41, X42)), X37)).
% 34.07/34.35 Proof: A critical pair between equations 286 and 299.
% 34.07/34.35
% 34.07/34.35 311: divide(divide(X46, divide(X47, X48)), X45) = divide(X46, divide(X45, divide(X48, X47))).
% 34.07/34.35 Proof: A critical pair between equations 291 and 290.
% 34.07/34.35
% 34.07/34.35 312: inverse(divide(X37, divide(X42, divide(divide(X35, X36), divide(X37, divide(X36, X35)))))) = X42.
% 34.07/34.35 Proof: A critical pair between equations 282 and 286.
% 34.07/34.35
% 34.07/34.35 316: divide(inverse(divide(X0, X1)), divide(divide(X3, X2), divide(X0, divide(X2, X3)))) = X1.
% 34.07/34.35 Proof: Rewrite equation 0,
% 34.07/34.35 lhs with equations [311]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 324: inverse(divide(X45, X46)) = divide(X46, X45).
% 34.07/34.35 Proof: A critical pair between equations 288 and 316.
% 34.07/34.35
% 34.07/34.35 325: X51 = divide(X51, divide(divide(X49, X50), divide(X49, X50))).
% 34.07/34.35 Proof: A critical pair between equations 290 and 302.
% 34.07/34.35
% 34.07/34.35 329: divide(X45, divide(X46, X47)) = inverse(divide(divide(X46, X47), X45)).
% 34.07/34.35 Proof: A critical pair between equations 307 and 273.
% 34.07/34.35
% 34.07/34.35 334: inverse(divide(divide(X43, divide(X36, X35)), divide(X35, X36))) = inverse(X43).
% 34.07/34.35 Proof: A critical pair between equations 312 and 287.
% 34.07/34.35
% 34.07/34.35 336: divide(divide(X35, X36), divide(X43, divide(X36, X35))) = inverse(X43).
% 34.07/34.35 Proof: Rewrite equation 334,
% 34.07/34.35 lhs with equations [329]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 339: divide(X42, divide(X41, X41)) = X42.
% 34.07/34.35 Proof: Rewrite equation 293,
% 34.07/34.35 lhs with equations [324,324,311,325]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 349: divide(X16, X15) = divide(X18, divide(divide(X15, X16), divide(divide(X20, X19), divide(divide(X18, X17), divide(divide(X19, X20), X17))))).
% 34.07/34.35 Proof: Rewrite equation 230,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [324,324,311].
% 34.07/34.35
% 34.07/34.35 362: X1 = divide(divide(divide(X1, X0), divide(X5, X0)), divide(divide(X7, X6), divide(divide(X5, X4), divide(divide(X6, X7), X4)))).
% 34.07/34.35 Proof: Rewrite equation 4,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [324,324].
% 34.07/34.35
% 34.07/34.35 365: divide(divide(divide(divide(X11, X10), divide(X11, X10)), X37), divide(divide(X38, X39), X37)) = divide(X39, X38).
% 34.07/34.35 Proof: Rewrite equation 276,
% 34.07/34.35 lhs with equations [324,324]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 371: divide(X29, X28) = divide(divide(divide(X42, X41), divide(X42, X41)), divide(X28, X29)).
% 34.07/34.35 Proof: Rewrite equation 289,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [324].
% 34.07/34.35
% 34.07/34.35 410: inverse(X44) = divide(divide(X45, X45), X44).
% 34.07/34.35 Proof: A critical pair between equations 336 and 339.
% 34.07/34.35
% 34.07/34.35 417: divide(divide(X23, X22), divide(X21, X22)) = divide(X23, X21).
% 34.07/34.35 Proof: A critical pair between equations 349 and 362.
% 34.07/34.35
% 34.07/34.35 418: inverse(X46) = divide(divide(divide(X44, X45), divide(X44, X45)), X46).
% 34.07/34.35 Proof: A critical pair between equations 336 and 371.
% 34.07/34.35
% 34.07/34.35 419: inverse(X43) = divide(divide(divide(X45, X45), X44), divide(X43, X44)).
% 34.07/34.35 Proof: A critical pair between equations 336 and 339.
% 34.07/34.35
% 34.07/34.35 422: divide(divide(X11, X11), divide(X38, X39)) = divide(X39, X38).
% 34.07/34.35 Proof: Rewrite equation 365,
% 34.07/34.35 lhs with equations [417,417]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 434: inverse(X43) = divide(divide(X45, X45), X43).
% 34.07/34.35 Proof: Rewrite equation 419,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [417].
% 34.07/34.35
% 34.07/34.35 435: inverse(X46) = divide(divide(X44, X44), X46).
% 34.07/34.35 Proof: Rewrite equation 418,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [417].
% 34.07/34.35
% 34.07/34.35 439: divide(divide(X44, X44), X44) = divide(divide(X45, X45), X44).
% 34.07/34.35 Proof: Rewrite equation 410,
% 34.07/34.35 lhs with equations [435]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 461: inverse(X47) = divide(divide(X47, X47), X47).
% 34.07/34.35 Proof: A critical pair between equations 434 and 439.
% 34.07/34.35
% 34.07/34.35 474: multiply(X0, X1) = divide(X0, divide(divide(X1, X1), X1)).
% 34.07/34.35 Proof: Rewrite equation 1,
% 34.07/34.35 lhs with equations []
% 34.07/34.35 rhs with equations [461].
% 34.07/34.35
% 34.07/34.35 489: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 34.07/34.35 Proof: Rewrite lhs with equations [461,474,417,417,474,422,339]
% 34.07/34.35 rhs with equations [].
% 34.07/34.35
% 34.07/34.35 % SZS output end Proof
%------------------------------------------------------------------------------