TSTP Solution File: GRP608-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP608-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n011.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 01:15:30 EDT 2023
% Result : Unsatisfiable 9.57s 9.83s
% Output : CNFRefutation 9.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP608-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.08/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:59:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 9.57/9.83 % SZS status Unsatisfiable
% 9.57/9.83 % SZS output start Proof
% 9.57/9.83 original problem:
% 9.57/9.83 axioms:
% 9.57/9.83 double_divide(inverse(double_divide(A, inverse(double_divide(inverse(B), double_divide(A, C))))), C) = B
% 9.57/9.83 multiply(A, B) = inverse(double_divide(B, A))
% 9.57/9.83 goal:
% 9.57/9.83 multiply(a(), b()) != multiply(b(), a())
% 9.57/9.83 To show the unsatisfiability of the original goal,
% 9.57/9.83 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 9.57/9.83 Here is an equational proof:
% 9.57/9.83 0: double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(X1), double_divide(X0, X2))))), X2) = X1.
% 9.57/9.83 Proof: Axiom.
% 9.57/9.83
% 9.57/9.83 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 9.57/9.83 Proof: Axiom.
% 9.57/9.83
% 9.57/9.83 2: double_divide(X3, inverse(double_divide(inverse(X4), double_divide(X3, double_divide(X0, X2))))) = double_divide(inverse(double_divide(X0, inverse(X4))), X2).
% 9.57/9.83 Proof: A critical pair between equations 0 and 0.
% 9.57/9.83
% 9.57/9.83 3: X1 = double_divide(inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(X4), double_divide(X3, X5))))), inverse(double_divide(inverse(X1), X4)))), X5).
% 9.57/9.83 Proof: A critical pair between equations 0 and 0.
% 9.57/9.83
% 9.57/9.83 4: X1 = double_divide(multiply(multiply(X4, inverse(X1)), multiply(multiply(double_divide(X3, X5), inverse(X4)), X3)), X5).
% 9.57/9.83 Proof: Rewrite equation 3,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1,1].
% 9.57/9.83
% 9.57/9.83 5: double_divide(multiply(multiply(double_divide(X0, X2), inverse(X1)), X0), X2) = X1.
% 9.57/9.83 Proof: Rewrite equation 0,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 6: double_divide(X3, multiply(double_divide(X3, double_divide(X0, X2)), inverse(X4))) = double_divide(multiply(inverse(X4), X0), X2).
% 9.57/9.83 Proof: Rewrite equation 2,
% 9.57/9.83 lhs with equations [1]
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 8: double_divide(X3, X4) = double_divide(multiply(multiply(double_divide(X0, X2), multiply(X4, X3)), X0), X2).
% 9.57/9.83 Proof: A critical pair between equations 5 and 1.
% 9.57/9.83
% 9.57/9.83 9: multiply(X7, multiply(inverse(X5), X6)) = inverse(double_divide(X8, multiply(double_divide(X8, double_divide(X6, X7)), inverse(X5)))).
% 9.57/9.83 Proof: A critical pair between equations 1 and 6.
% 9.57/9.83
% 9.57/9.83 10: multiply(multiply(double_divide(X5, double_divide(X6, X7)), inverse(X8)), X5) = inverse(double_divide(multiply(inverse(X8), X6), X7)).
% 9.57/9.83 Proof: A critical pair between equations 1 and 6.
% 9.57/9.83
% 9.57/9.83 11: multiply(X9, multiply(multiply(X6, inverse(X7)), multiply(multiply(double_divide(X8, X9), inverse(X6)), X8))) = inverse(X7).
% 9.57/9.83 Proof: A critical pair between equations 1 and 4.
% 9.57/9.83
% 9.57/9.83 14: X1 = double_divide(multiply(multiply(double_divide(X6, X7), inverse(X1)), multiply(multiply(double_divide(X3, X5), multiply(X7, X6)), X3)), X5).
% 9.57/9.83 Proof: A critical pair between equations 4 and 1.
% 9.57/9.83
% 9.57/9.83 15: double_divide(X6, X7) = double_divide(multiply(multiply(X4, multiply(X7, X6)), multiply(multiply(double_divide(X3, X5), inverse(X4)), X3)), X5).
% 9.57/9.83 Proof: A critical pair between equations 4 and 1.
% 9.57/9.83
% 9.57/9.83 17: double_divide(multiply(inverse(X4), X0), X2) = double_divide(multiply(multiply(double_divide(X5, double_divide(X0, X2)), inverse(X7)), X5), multiply(X7, inverse(X4))).
% 9.57/9.83 Proof: A critical pair between equations 6 and 5.
% 9.57/9.83
% 9.57/9.83 18: X1 = double_divide(multiply(multiply(X4, inverse(X1)), multiply(multiply(X8, inverse(X4)), multiply(multiply(double_divide(X6, X7), inverse(X8)), X6))), X7).
% 9.57/9.83 Proof: A critical pair between equations 4 and 5.
% 9.57/9.83
% 9.57/9.83 19: X1 = double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X6, inverse(double_divide(inverse(X8), double_divide(X6, X7))))), inverse(double_divide(inverse(X4), X8)))), inverse(double_divide(inverse(X1), X4)))), X7).
% 9.57/9.83 Proof: Rewrite equation 18,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1,1,1,1].
% 9.57/9.83
% 9.57/9.83 20: double_divide(X6, X7) = double_divide(inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(X4), double_divide(X3, X5))))), inverse(double_divide(inverse(double_divide(X6, X7)), X4)))), X5).
% 9.57/9.83 Proof: Rewrite equation 15,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1,1,1].
% 9.57/9.83
% 9.57/9.83 21: X1 = double_divide(inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(X6, X7)), double_divide(X3, X5))))), inverse(double_divide(inverse(X1), double_divide(X6, X7))))), X5).
% 9.57/9.83 Proof: Rewrite equation 14,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1,1,1].
% 9.57/9.83
% 9.57/9.83 22: inverse(double_divide(inverse(double_divide(inverse(double_divide(X8, inverse(double_divide(inverse(X6), double_divide(X8, X9))))), inverse(double_divide(inverse(X7), X6)))), X9)) = inverse(X7).
% 9.57/9.83 Proof: Rewrite equation 11,
% 9.57/9.83 lhs with equations [1,1,1,1,1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 23: inverse(double_divide(X5, inverse(double_divide(inverse(X8), double_divide(X5, double_divide(X6, X7)))))) = inverse(double_divide(inverse(double_divide(X6, inverse(X8))), X7)).
% 9.57/9.83 Proof: Rewrite equation 10,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 24: double_divide(X3, X4) = double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(X3, X4)), double_divide(X0, X2))))), X2).
% 9.57/9.83 Proof: Rewrite equation 8,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1].
% 9.57/9.83
% 9.57/9.83 26: double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(X1), double_divide(X0, X2))))), X2) = X1.
% 9.57/9.83 Proof: Rewrite equation 5,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 27: X1 = double_divide(inverse(double_divide(X5, inverse(double_divide(inverse(double_divide(inverse(X4), double_divide(X3, X5))), double_divide(X5, double_divide(X3, inverse(double_divide(inverse(X1), X4)))))))), X5).
% 9.57/9.83 Proof: Rewrite equation 4,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1,1,23].
% 9.57/9.83
% 9.57/9.83 28: double_divide(inverse(double_divide(X0, inverse(X4))), X2) = double_divide(inverse(double_divide(X5, inverse(double_divide(inverse(X7), double_divide(X5, double_divide(X0, X2)))))), inverse(double_divide(inverse(X4), X7))).
% 9.57/9.83 Proof: Rewrite equation 17,
% 9.57/9.83 lhs with equations [1]
% 9.57/9.83 rhs with equations [1,1,1].
% 9.57/9.83
% 9.57/9.83 32: inverse(double_divide(X5, inverse(double_divide(inverse(X5), double_divide(X5, double_divide(X6, X7)))))) = inverse(double_divide(X8, inverse(double_divide(inverse(X5), double_divide(X8, double_divide(X6, X7)))))).
% 9.57/9.83 Proof: Rewrite equation 9,
% 9.57/9.83 lhs with equations [1,1,23]
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 34: X1 = double_divide(inverse(X13), inverse(double_divide(inverse(X1), X13))).
% 9.57/9.83 Proof: A critical pair between equations 19 and 21.
% 9.57/9.83
% 9.57/9.83 35: inverse(X7) = inverse(double_divide(inverse(X11), inverse(double_divide(inverse(X7), X11)))).
% 9.57/9.83 Proof: A critical pair between equations 22 and 26.
% 9.57/9.83
% 9.57/9.83 37: double_divide(X6, X7) = double_divide(inverse(X9), inverse(double_divide(inverse(double_divide(X6, X7)), X9))).
% 9.57/9.83 Proof: A critical pair between equations 20 and 26.
% 9.57/9.83
% 9.57/9.83 38: X12 = double_divide(inverse(double_divide(inverse(double_divide(X10, inverse(X12))), X11)), double_divide(X10, X11)).
% 9.57/9.83 Proof: A critical pair between equations 21 and 28.
% 9.57/9.83
% 9.57/9.83 39: double_divide(inverse(X7), double_divide(X8, double_divide(X8, inverse(double_divide(inverse(X9), X7))))) = X9.
% 9.57/9.83 Proof: A critical pair between equations 24 and 27.
% 9.57/9.83
% 9.57/9.83 41: inverse(X7) = inverse(double_divide(inverse(double_divide(X11, X12)), inverse(double_divide(inverse(X7), double_divide(X11, X12))))).
% 9.57/9.83 Proof: A critical pair between equations 22 and 24.
% 9.57/9.83
% 9.57/9.83 42: X1 = double_divide(inverse(double_divide(inverse(X10), inverse(double_divide(inverse(X1), X4)))), inverse(double_divide(inverse(X4), X10))).
% 9.57/9.83 Proof: A critical pair between equations 19 and 26.
% 9.57/9.83
% 9.57/9.83 44: double_divide(X6, X7) = double_divide(inverse(double_divide(inverse(double_divide(X10, inverse(double_divide(X6, X7)))), X11)), double_divide(X10, X11)).
% 9.57/9.83 Proof: A critical pair between equations 20 and 28.
% 9.57/9.83
% 9.57/9.83 47: double_divide(X6, X7) = double_divide(multiply(X11, multiply(multiply(X7, X6), X10)), double_divide(X10, X11)).
% 9.57/9.83 Proof: Rewrite equation 44,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1].
% 9.57/9.83
% 9.57/9.83 49: X1 = double_divide(multiply(multiply(X4, inverse(X1)), inverse(X10)), multiply(X10, inverse(X4))).
% 9.57/9.83 Proof: Rewrite equation 42,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1].
% 9.57/9.83
% 9.57/9.83 50: inverse(X7) = multiply(multiply(double_divide(X11, X12), inverse(X7)), multiply(X12, X11)).
% 9.57/9.83 Proof: Rewrite equation 41,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,1].
% 9.57/9.83
% 9.57/9.83 52: double_divide(inverse(X7), double_divide(X8, double_divide(X8, multiply(X7, inverse(X9))))) = X9.
% 9.57/9.83 Proof: Rewrite equation 39,
% 9.57/9.83 lhs with equations [1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 53: X12 = double_divide(multiply(X11, multiply(inverse(X12), X10)), double_divide(X10, X11)).
% 9.57/9.83 Proof: Rewrite equation 38,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 54: double_divide(X6, X7) = double_divide(inverse(X9), multiply(X9, multiply(X7, X6))).
% 9.57/9.83 Proof: Rewrite equation 37,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 56: inverse(X7) = multiply(multiply(X11, inverse(X7)), inverse(X11)).
% 9.57/9.83 Proof: Rewrite equation 35,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 57: X1 = double_divide(inverse(X13), multiply(X13, inverse(X1))).
% 9.57/9.83 Proof: Rewrite equation 34,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 59: double_divide(multiply(multiply(double_divide(X0, X2), inverse(X1)), X0), X2) = X1.
% 9.57/9.83 Proof: Rewrite equation 26,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 66: multiply(multiply(double_divide(X5, double_divide(X6, X7)), inverse(X5)), X5) = multiply(multiply(double_divide(X8, double_divide(X6, X7)), inverse(X5)), X8).
% 9.57/9.83 Proof: Rewrite equation 32,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 71: multiply(multiply(double_divide(X5, double_divide(X6, X7)), inverse(X8)), X5) = multiply(X7, multiply(inverse(X8), X6)).
% 9.57/9.83 Proof: Rewrite equation 23,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 72: X13 = double_divide(inverse(X13), multiply(X12, inverse(X12))).
% 9.57/9.83 Proof: A critical pair between equations 49 and 56.
% 9.57/9.83
% 9.57/9.83 73: X15 = double_divide(inverse(X14), double_divide(inverse(X14), X15)).
% 9.57/9.83 Proof: A critical pair between equations 52 and 57.
% 9.57/9.83
% 9.57/9.83 74: X14 = double_divide(inverse(multiply(X14, inverse(X15))), inverse(X15)).
% 9.57/9.83 Proof: A critical pair between equations 57 and 56.
% 9.57/9.83
% 9.57/9.83 80: multiply(X4, multiply(multiply(double_divide(X3, X4), inverse(X5)), X3)) = inverse(X5).
% 9.57/9.83 Proof: A critical pair between equations 1 and 59.
% 9.57/9.83
% 9.57/9.83 81: double_divide(X13, X14) = double_divide(inverse(multiply(double_divide(X13, X14), inverse(X15))), inverse(X15)).
% 9.57/9.83 Proof: A critical pair between equations 54 and 50.
% 9.57/9.83
% 9.57/9.83 83: double_divide(inverse(X13), X12) = double_divide(multiply(X11, inverse(X13)), double_divide(inverse(X12), X11)).
% 9.57/9.83 Proof: A critical pair between equations 47 and 56.
% 9.57/9.83
% 9.57/9.83 84: double_divide(inverse(X13), X12) = double_divide(inverse(double_divide(inverse(X13), X11)), double_divide(inverse(X12), X11)).
% 9.57/9.83 Proof: Rewrite equation 83,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 85: double_divide(X13, X14) = double_divide(inverse(inverse(double_divide(inverse(X15), double_divide(X13, X14)))), inverse(X15)).
% 9.57/9.83 Proof: Rewrite equation 81,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 86: inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(X5), double_divide(X3, X4))))), X4)) = inverse(X5).
% 9.57/9.83 Proof: Rewrite equation 80,
% 9.57/9.83 lhs with equations [1,1,1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 89: X14 = double_divide(inverse(inverse(double_divide(inverse(X15), X14))), inverse(X15)).
% 9.57/9.83 Proof: Rewrite equation 74,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 90: X13 = double_divide(inverse(X13), inverse(double_divide(inverse(X12), X12))).
% 9.57/9.83 Proof: Rewrite equation 72,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 91: inverse(double_divide(X5, inverse(double_divide(inverse(X8), double_divide(X5, double_divide(X6, X7)))))) = inverse(double_divide(inverse(double_divide(X6, inverse(X8))), X7)).
% 9.57/9.83 Proof: Rewrite equation 71,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 97: double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(X1), double_divide(X0, X2))))), X2) = X1.
% 9.57/9.83 Proof: Rewrite equation 59,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 99: X1 = double_divide(inverse(X13), inverse(double_divide(inverse(X1), X13))).
% 9.57/9.83 Proof: Rewrite equation 57,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 100: X12 = double_divide(inverse(double_divide(inverse(double_divide(X10, inverse(X12))), X11)), double_divide(X10, X11)).
% 9.57/9.83 Proof: Rewrite equation 53,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 110: inverse(double_divide(X5, inverse(double_divide(inverse(X5), double_divide(X5, double_divide(X6, X7)))))) = inverse(double_divide(X8, inverse(double_divide(inverse(X5), double_divide(X8, double_divide(X6, X7)))))).
% 9.57/9.83 Proof: Rewrite equation 66,
% 9.57/9.83 lhs with equations [1,1]
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 113: double_divide(inverse(double_divide(inverse(X12), inverse(X15))), X12) = X15.
% 9.57/9.83 Proof: A critical pair between equations 84 and 100.
% 9.57/9.83
% 9.57/9.83 114: X14 = inverse(double_divide(inverse(double_divide(inverse(X17), X17)), X14)).
% 9.57/9.83 Proof: A critical pair between equations 89 and 90.
% 9.57/9.83
% 9.57/9.83 116: inverse(double_divide(inverse(X17), X16)) = double_divide(inverse(X16), X17).
% 9.57/9.83 Proof: A critical pair between equations 73 and 99.
% 9.57/9.83
% 9.57/9.83 117: X16 = double_divide(inverse(double_divide(inverse(X16), inverse(X17))), X17).
% 9.57/9.83 Proof: A critical pair between equations 97 and 73.
% 9.57/9.83
% 9.57/9.83 119: double_divide(inverse(X16), X17) = double_divide(inverse(inverse(X17)), inverse(X16)).
% 9.57/9.83 Proof: A critical pair between equations 85 and 73.
% 9.57/9.83
% 9.57/9.83 123: inverse(X16) = inverse(double_divide(inverse(double_divide(inverse(X16), inverse(X17))), X17)).
% 9.57/9.83 Proof: A critical pair between equations 86 and 73.
% 9.57/9.83
% 9.57/9.83 124: inverse(X16) = multiply(X17, multiply(inverse(X17), inverse(X16))).
% 9.57/9.83 Proof: Rewrite equation 123,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 129: X16 = double_divide(multiply(inverse(X17), inverse(X16)), X17).
% 9.57/9.83 Proof: Rewrite equation 117,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1].
% 9.57/9.83
% 9.57/9.83 130: X14 = multiply(X14, multiply(X17, inverse(X17))).
% 9.57/9.83 Proof: Rewrite equation 114,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 131: double_divide(multiply(inverse(X15), inverse(X12)), X12) = X15.
% 9.57/9.83 Proof: Rewrite equation 113,
% 9.57/9.83 lhs with equations [1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 135: X12 = double_divide(multiply(X11, multiply(inverse(X12), X10)), double_divide(X10, X11)).
% 9.57/9.83 Proof: Rewrite equation 100,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 148: multiply(X16, inverse(X17)) = double_divide(inverse(X16), X17).
% 9.57/9.83 Proof: Rewrite equation 116,
% 9.57/9.83 lhs with equations [1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 151: multiply(inverse(multiply(X5, multiply(double_divide(X6, X7), X5))), X5) = multiply(inverse(multiply(X5, multiply(double_divide(X6, X7), X8))), X8).
% 9.57/9.83 Proof: Rewrite equation 110,
% 9.57/9.83 lhs with equations [148,1,1]
% 9.57/9.83 rhs with equations [148,1,1].
% 9.57/9.83
% 9.57/9.83 158: multiply(inverse(multiply(X8, multiply(double_divide(X6, X7), X5))), X5) = multiply(X7, multiply(inverse(X8), X6)).
% 9.57/9.83 Proof: Rewrite equation 91,
% 9.57/9.83 lhs with equations [148,1,1]
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 159: inverse(inverse(X18)) = X18.
% 9.57/9.83 Proof: A critical pair between equations 124 and 130.
% 9.57/9.83
% 9.57/9.83 164: X12 = double_divide(X18, double_divide(inverse(inverse(X12)), X18)).
% 9.57/9.83 Proof: A critical pair between equations 135 and 130.
% 9.57/9.83
% 9.57/9.83 171: X12 = double_divide(X18, double_divide(X12, X18)).
% 9.57/9.83 Proof: Rewrite equation 164,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [159].
% 9.57/9.83
% 9.57/9.83 173: inverse(double_divide(X5, inverse(double_divide(inverse(X8), double_divide(X5, double_divide(X6, X7)))))) = double_divide(inverse(X7), double_divide(X6, inverse(X8))).
% 9.57/9.83 Proof: Rewrite equation 158,
% 9.57/9.83 lhs with equations [1,148,1]
% 9.57/9.83 rhs with equations [1,148].
% 9.57/9.83
% 9.57/9.83 174: inverse(double_divide(inverse(X17), X16)) = double_divide(inverse(X16), X17).
% 9.57/9.83 Proof: Rewrite equation 148,
% 9.57/9.83 lhs with equations [1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 183: X12 = double_divide(double_divide(inverse(X11), double_divide(X10, inverse(X12))), double_divide(X10, X11)).
% 9.57/9.83 Proof: Rewrite equation 135,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1,174].
% 9.57/9.83
% 9.57/9.83 187: double_divide(double_divide(X15, X12), X12) = X15.
% 9.57/9.83 Proof: Rewrite equation 131,
% 9.57/9.83 lhs with equations [1,174,159]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 189: X16 = double_divide(double_divide(X17, X16), X17).
% 9.57/9.83 Proof: Rewrite equation 129,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,174,159].
% 9.57/9.83
% 9.57/9.83 200: double_divide(X5, double_divide(X6, X7)) = inverse(double_divide(X8, double_divide(inverse(double_divide(X8, double_divide(X6, X7))), X5))).
% 9.57/9.83 Proof: Rewrite equation 151,
% 9.57/9.83 lhs with equations [1,1,174,174,1,171,159]
% 9.57/9.83 rhs with equations [1,1,174,174,1].
% 9.57/9.83
% 9.57/9.83 203: double_divide(inverse(X16), X17) = double_divide(X17, inverse(X16)).
% 9.57/9.83 Proof: Rewrite equation 119,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [159].
% 9.57/9.83
% 9.57/9.83 205: X11 = double_divide(X20, double_divide(X20, X11)).
% 9.57/9.83 Proof: A critical pair between equations 183 and 171.
% 9.57/9.83
% 9.57/9.83 211: double_divide(X17, inverse(inverse(X19))) = double_divide(X19, X17).
% 9.57/9.83 Proof: A critical pair between equations 203 and 159.
% 9.57/9.83
% 9.57/9.83 217: X16 = double_divide(X17, inverse(multiply(X16, X17))).
% 9.57/9.83 Proof: Rewrite equation 189,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [211,1].
% 9.57/9.83
% 9.57/9.83 218: double_divide(X12, inverse(multiply(X12, X15))) = X15.
% 9.57/9.83 Proof: Rewrite equation 187,
% 9.57/9.83 lhs with equations [211,1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 231: double_divide(X5, double_divide(X6, X7)) = multiply(double_divide(multiply(double_divide(X6, X7), X8), X5), X8).
% 9.57/9.83 Proof: Rewrite equation 200,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [1,1].
% 9.57/9.83
% 9.57/9.83 232: multiply(X16, inverse(X17)) = double_divide(inverse(X16), X17).
% 9.57/9.83 Proof: Rewrite equation 174,
% 9.57/9.83 lhs with equations [1]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 233: multiply(inverse(multiply(X8, multiply(double_divide(X6, X7), X5))), X5) = multiply(X7, multiply(inverse(X8), X6)).
% 9.57/9.83 Proof: Rewrite equation 173,
% 9.57/9.83 lhs with equations [232,1,1]
% 9.57/9.83 rhs with equations [232,1].
% 9.57/9.83
% 9.57/9.83 234: multiply(X16, inverse(X17)) = double_divide(X17, inverse(X16)).
% 9.57/9.83 Proof: Rewrite equation 203,
% 9.57/9.83 lhs with equations [232]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 246: inverse(multiply(X22, X21)) = double_divide(X21, X22).
% 9.57/9.83 Proof: A critical pair between equations 205 and 217.
% 9.57/9.83
% 9.57/9.83 248: X16 = multiply(multiply(X16, X18), inverse(X18)).
% 9.57/9.83 Proof: A critical pair between equations 217 and 234.
% 9.57/9.83
% 9.57/9.83 249: X15 = multiply(multiply(X18, X15), inverse(X18)).
% 9.57/9.83 Proof: A critical pair between equations 218 and 234.
% 9.57/9.83
% 9.57/9.83 265: multiply(X16, inverse(X17)) = inverse(multiply(inverse(X16), X17)).
% 9.57/9.83 Proof: Rewrite equation 234,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [246].
% 9.57/9.83
% 9.57/9.83 266: multiply(inverse(multiply(X8, multiply(inverse(multiply(X7, X6)), X5))), X5) = multiply(X7, multiply(inverse(X8), X6)).
% 9.57/9.83 Proof: Rewrite equation 233,
% 9.57/9.83 lhs with equations [246]
% 9.57/9.83 rhs with equations [].
% 9.57/9.83
% 9.57/9.83 267: multiply(X16, inverse(X17)) = inverse(multiply(X17, inverse(X16))).
% 9.57/9.83 Proof: Rewrite equation 232,
% 9.57/9.83 lhs with equations []
% 9.57/9.83 rhs with equations [246].
% 9.57/9.83
% 9.57/9.83 283: multiply(multiply(X7, X6), inverse(X5)) = multiply(X7, multiply(inverse(X5), X6)).
% 9.57/9.83 Proof: Rewrite equation 231,
% 9.57/9.83 lhs with equations [246,246,265]
% 9.57/9.83 rhs with equations [246,246,266].
% 9.57/9.83
% 9.57/9.83 291: multiply(X19, multiply(inverse(X19), X20)) = X20.
% 9.57/9.83 Proof: A critical pair between equations 283 and 249.
% 9.57/9.83
% 9.57/9.83 294: X16 = multiply(multiply(X16, inverse(X19)), X19).
% 9.57/9.83 Proof: A critical pair between equations 248 and 159.
% 9.57/9.83
% 9.57/9.83 298: multiply(X19, inverse(multiply(X19, X20))) = inverse(X20).
% 9.57/9.83 Proof: A critical pair between equations 267 and 249.
% 9.57/9.83
% 9.57/9.83 308: X21 = multiply(inverse(X22), multiply(X21, X22)).
% 9.57/9.83 Proof: A critical pair between equations 294 and 298.
% 9.57/9.83
% 9.57/9.83 323: multiply(X24, X23) = multiply(X23, X24).
% 9.57/9.83 Proof: A critical pair between equations 291 and 308.
% 9.57/9.83
% 9.57/9.83 352: multiply(a(), b()) = multiply(b(), a()).
% 9.57/9.83 Proof: Rewrite lhs with equations []
% 9.57/9.83 rhs with equations [323].
% 9.57/9.83
% 9.57/9.83 % SZS output end Proof
%------------------------------------------------------------------------------