TSTP Solution File: GRP606-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP606-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n019.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 9.20s 9.47s
% Output : CNFRefutation 9.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP606-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 02:26:43 EDT 2023
% 0.16/0.34 % CPUTime :
% 9.20/9.47 % SZS status Unsatisfiable
% 9.20/9.47 % SZS output start Proof
% 9.20/9.47 original problem:
% 9.20/9.47 axioms:
% 9.20/9.47 double_divide(inverse(double_divide(A, inverse(double_divide(inverse(B), double_divide(A, C))))), C) = B
% 9.20/9.47 multiply(A, B) = inverse(double_divide(B, A))
% 9.20/9.47 goal:
% 9.20/9.47 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 9.20/9.47 To show the unsatisfiability of the original goal,
% 9.20/9.47 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 9.20/9.47 Here is an equational proof:
% 9.20/9.47 0: double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(X1), double_divide(X0, X2))))), X2) = X1.
% 9.20/9.47 Proof: Axiom.
% 9.20/9.47
% 9.20/9.47 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 9.20/9.47 Proof: Axiom.
% 9.20/9.47
% 9.20/9.47 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).
% 9.20/9.47 Proof: A critical pair between equations 0 and 0.
% 9.20/9.47
% 9.20/9.47 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).
% 9.20/9.47 Proof: A critical pair between equations 0 and 0.
% 9.20/9.47
% 9.20/9.47 4: X1 = double_divide(multiply(multiply(X4, inverse(X1)), multiply(multiply(double_divide(X3, X5), inverse(X4)), X3)), X5).
% 9.20/9.47 Proof: Rewrite equation 3,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1,1].
% 9.20/9.47
% 9.20/9.47 5: double_divide(multiply(multiply(double_divide(X0, X2), inverse(X1)), X0), X2) = X1.
% 9.20/9.47 Proof: Rewrite equation 0,
% 9.20/9.47 lhs with equations [1,1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 6: double_divide(X3, multiply(double_divide(X3, double_divide(X0, X2)), inverse(X4))) = double_divide(multiply(inverse(X4), X0), X2).
% 9.20/9.47 Proof: Rewrite equation 2,
% 9.20/9.47 lhs with equations [1]
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 8: double_divide(X3, X4) = double_divide(multiply(multiply(double_divide(X0, X2), multiply(X4, X3)), X0), X2).
% 9.20/9.47 Proof: A critical pair between equations 5 and 1.
% 9.20/9.47
% 9.20/9.47 10: multiply(multiply(double_divide(X5, double_divide(X6, X7)), inverse(X8)), X5) = inverse(double_divide(multiply(inverse(X8), X6), X7)).
% 9.20/9.47 Proof: A critical pair between equations 1 and 6.
% 9.20/9.47
% 9.20/9.47 11: multiply(X9, multiply(multiply(X6, inverse(X7)), multiply(multiply(double_divide(X8, X9), inverse(X6)), X8))) = inverse(X7).
% 9.20/9.47 Proof: A critical pair between equations 1 and 4.
% 9.20/9.47
% 9.20/9.47 14: X1 = double_divide(multiply(multiply(double_divide(X6, X7), inverse(X1)), multiply(multiply(double_divide(X3, X5), multiply(X7, X6)), X3)), X5).
% 9.20/9.47 Proof: A critical pair between equations 4 and 1.
% 9.20/9.47
% 9.20/9.47 15: double_divide(X6, X7) = double_divide(multiply(multiply(X4, multiply(X7, X6)), multiply(multiply(double_divide(X3, X5), inverse(X4)), X3)), X5).
% 9.20/9.47 Proof: A critical pair between equations 4 and 1.
% 9.20/9.47
% 9.20/9.47 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))).
% 9.20/9.47 Proof: A critical pair between equations 6 and 5.
% 9.20/9.47
% 9.20/9.47 18: X1 = double_divide(multiply(multiply(X4, inverse(X1)), multiply(multiply(X8, inverse(X4)), multiply(multiply(double_divide(X6, X7), inverse(X8)), X6))), X7).
% 9.20/9.47 Proof: A critical pair between equations 4 and 5.
% 9.20/9.47
% 9.20/9.47 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).
% 9.20/9.47 Proof: Rewrite equation 18,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1,1,1,1].
% 9.20/9.47
% 9.20/9.47 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).
% 9.20/9.47 Proof: Rewrite equation 15,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1,1,1].
% 9.20/9.47
% 9.20/9.47 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).
% 9.20/9.47 Proof: Rewrite equation 14,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1,1,1].
% 9.20/9.47
% 9.20/9.47 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).
% 9.20/9.47 Proof: Rewrite equation 11,
% 9.20/9.47 lhs with equations [1,1,1,1,1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 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)).
% 9.20/9.47 Proof: Rewrite equation 10,
% 9.20/9.47 lhs with equations [1,1]
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 24: double_divide(X3, X4) = double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(X3, X4)), double_divide(X0, X2))))), X2).
% 9.20/9.47 Proof: Rewrite equation 8,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1].
% 9.20/9.47
% 9.20/9.47 26: double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(X1), double_divide(X0, X2))))), X2) = X1.
% 9.20/9.47 Proof: Rewrite equation 5,
% 9.20/9.47 lhs with equations [1,1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 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).
% 9.20/9.47 Proof: Rewrite equation 4,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1,1,23].
% 9.20/9.47
% 9.20/9.47 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))).
% 9.20/9.47 Proof: Rewrite equation 17,
% 9.20/9.47 lhs with equations [1]
% 9.20/9.47 rhs with equations [1,1,1].
% 9.20/9.47
% 9.20/9.47 34: X1 = double_divide(inverse(X13), inverse(double_divide(inverse(X1), X13))).
% 9.20/9.47 Proof: A critical pair between equations 19 and 21.
% 9.20/9.47
% 9.20/9.47 35: inverse(X7) = inverse(double_divide(inverse(X11), inverse(double_divide(inverse(X7), X11)))).
% 9.20/9.47 Proof: A critical pair between equations 22 and 26.
% 9.20/9.47
% 9.20/9.47 37: double_divide(X6, X7) = double_divide(inverse(X9), inverse(double_divide(inverse(double_divide(X6, X7)), X9))).
% 9.20/9.47 Proof: A critical pair between equations 20 and 26.
% 9.20/9.47
% 9.20/9.47 38: X12 = double_divide(inverse(double_divide(inverse(double_divide(X10, inverse(X12))), X11)), double_divide(X10, X11)).
% 9.20/9.47 Proof: A critical pair between equations 21 and 28.
% 9.20/9.47
% 9.20/9.47 39: double_divide(inverse(X7), double_divide(X8, double_divide(X8, inverse(double_divide(inverse(X9), X7))))) = X9.
% 9.20/9.47 Proof: A critical pair between equations 24 and 27.
% 9.20/9.47
% 9.20/9.47 41: inverse(X7) = inverse(double_divide(inverse(double_divide(X11, X12)), inverse(double_divide(inverse(X7), double_divide(X11, X12))))).
% 9.20/9.47 Proof: A critical pair between equations 22 and 24.
% 9.20/9.47
% 9.20/9.47 42: X1 = double_divide(inverse(double_divide(inverse(X10), inverse(double_divide(inverse(X1), X4)))), inverse(double_divide(inverse(X4), X10))).
% 9.20/9.47 Proof: A critical pair between equations 19 and 26.
% 9.20/9.47
% 9.20/9.47 49: X1 = double_divide(multiply(multiply(X4, inverse(X1)), inverse(X10)), multiply(X10, inverse(X4))).
% 9.20/9.47 Proof: Rewrite equation 42,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1].
% 9.20/9.47
% 9.20/9.47 50: inverse(X7) = multiply(multiply(double_divide(X11, X12), inverse(X7)), multiply(X12, X11)).
% 9.20/9.47 Proof: Rewrite equation 41,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,1].
% 9.20/9.47
% 9.20/9.47 52: double_divide(inverse(X7), double_divide(X8, double_divide(X8, multiply(X7, inverse(X9))))) = X9.
% 9.20/9.47 Proof: Rewrite equation 39,
% 9.20/9.47 lhs with equations [1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 53: X12 = double_divide(multiply(X11, multiply(inverse(X12), X10)), double_divide(X10, X11)).
% 9.20/9.47 Proof: Rewrite equation 38,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1].
% 9.20/9.47
% 9.20/9.47 54: double_divide(X6, X7) = double_divide(inverse(X9), multiply(X9, multiply(X7, X6))).
% 9.20/9.47 Proof: Rewrite equation 37,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1].
% 9.20/9.47
% 9.20/9.47 56: inverse(X7) = multiply(multiply(X11, inverse(X7)), inverse(X11)).
% 9.20/9.47 Proof: Rewrite equation 35,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1].
% 9.20/9.47
% 9.20/9.47 57: X1 = double_divide(inverse(X13), multiply(X13, inverse(X1))).
% 9.20/9.47 Proof: Rewrite equation 34,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 59: double_divide(multiply(multiply(double_divide(X0, X2), inverse(X1)), X0), X2) = X1.
% 9.20/9.47 Proof: Rewrite equation 26,
% 9.20/9.47 lhs with equations [1,1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 72: X13 = double_divide(inverse(X13), multiply(X12, inverse(X12))).
% 9.20/9.47 Proof: A critical pair between equations 49 and 56.
% 9.20/9.47
% 9.20/9.47 73: X15 = double_divide(inverse(X14), double_divide(inverse(X14), X15)).
% 9.20/9.47 Proof: A critical pair between equations 52 and 57.
% 9.20/9.47
% 9.20/9.47 74: X14 = double_divide(inverse(multiply(X14, inverse(X15))), inverse(X15)).
% 9.20/9.47 Proof: A critical pair between equations 57 and 56.
% 9.20/9.47
% 9.20/9.47 80: multiply(X4, multiply(multiply(double_divide(X3, X4), inverse(X5)), X3)) = inverse(X5).
% 9.20/9.47 Proof: A critical pair between equations 1 and 59.
% 9.20/9.47
% 9.20/9.47 81: double_divide(X13, X14) = double_divide(inverse(multiply(double_divide(X13, X14), inverse(X15))), inverse(X15)).
% 9.20/9.47 Proof: A critical pair between equations 54 and 50.
% 9.20/9.47
% 9.20/9.47 85: double_divide(X13, X14) = double_divide(inverse(inverse(double_divide(inverse(X15), double_divide(X13, X14)))), inverse(X15)).
% 9.20/9.47 Proof: Rewrite equation 81,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 86: inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(X5), double_divide(X3, X4))))), X4)) = inverse(X5).
% 9.20/9.47 Proof: Rewrite equation 80,
% 9.20/9.47 lhs with equations [1,1,1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 89: X14 = double_divide(inverse(inverse(double_divide(inverse(X15), X14))), inverse(X15)).
% 9.20/9.47 Proof: Rewrite equation 74,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 90: X13 = double_divide(inverse(X13), inverse(double_divide(inverse(X12), X12))).
% 9.20/9.47 Proof: Rewrite equation 72,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 97: double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(X1), double_divide(X0, X2))))), X2) = X1.
% 9.20/9.47 Proof: Rewrite equation 59,
% 9.20/9.47 lhs with equations [1,1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 99: X1 = double_divide(inverse(X13), inverse(double_divide(inverse(X1), X13))).
% 9.20/9.47 Proof: Rewrite equation 57,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 100: X12 = double_divide(inverse(double_divide(inverse(double_divide(X10, inverse(X12))), X11)), double_divide(X10, X11)).
% 9.20/9.47 Proof: Rewrite equation 53,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1].
% 9.20/9.47
% 9.20/9.47 114: X14 = inverse(double_divide(inverse(double_divide(inverse(X17), X17)), X14)).
% 9.20/9.47 Proof: A critical pair between equations 89 and 90.
% 9.20/9.47
% 9.20/9.47 116: inverse(double_divide(inverse(X17), X16)) = double_divide(inverse(X16), X17).
% 9.20/9.47 Proof: A critical pair between equations 73 and 99.
% 9.20/9.47
% 9.20/9.47 117: X16 = double_divide(inverse(double_divide(inverse(X16), inverse(X17))), X17).
% 9.20/9.47 Proof: A critical pair between equations 97 and 73.
% 9.20/9.47
% 9.20/9.47 119: double_divide(inverse(X16), X17) = double_divide(inverse(inverse(X17)), inverse(X16)).
% 9.20/9.47 Proof: A critical pair between equations 85 and 73.
% 9.20/9.47
% 9.20/9.47 123: inverse(X16) = inverse(double_divide(inverse(double_divide(inverse(X16), inverse(X17))), X17)).
% 9.20/9.47 Proof: A critical pair between equations 86 and 73.
% 9.20/9.47
% 9.20/9.47 124: inverse(X16) = multiply(X17, multiply(inverse(X17), inverse(X16))).
% 9.20/9.47 Proof: Rewrite equation 123,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1].
% 9.20/9.47
% 9.20/9.47 129: X16 = double_divide(multiply(inverse(X17), inverse(X16)), X17).
% 9.20/9.47 Proof: Rewrite equation 117,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1].
% 9.20/9.47
% 9.20/9.47 130: X14 = multiply(X14, multiply(X17, inverse(X17))).
% 9.20/9.47 Proof: Rewrite equation 114,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1].
% 9.20/9.47
% 9.20/9.47 135: X12 = double_divide(multiply(X11, multiply(inverse(X12), X10)), double_divide(X10, X11)).
% 9.20/9.47 Proof: Rewrite equation 100,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1].
% 9.20/9.47
% 9.20/9.47 148: multiply(X16, inverse(X17)) = double_divide(inverse(X16), X17).
% 9.20/9.47 Proof: Rewrite equation 116,
% 9.20/9.47 lhs with equations [1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 159: inverse(inverse(X18)) = X18.
% 9.20/9.47 Proof: A critical pair between equations 124 and 130.
% 9.20/9.47
% 9.20/9.47 164: X12 = double_divide(X18, double_divide(inverse(inverse(X12)), X18)).
% 9.20/9.47 Proof: A critical pair between equations 135 and 130.
% 9.20/9.47
% 9.20/9.47 171: X12 = double_divide(X18, double_divide(X12, X18)).
% 9.20/9.47 Proof: Rewrite equation 164,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [159].
% 9.20/9.47
% 9.20/9.47 174: inverse(double_divide(inverse(X17), X16)) = double_divide(inverse(X16), X17).
% 9.20/9.47 Proof: Rewrite equation 148,
% 9.20/9.47 lhs with equations [1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 183: X12 = double_divide(double_divide(inverse(X11), double_divide(X10, inverse(X12))), double_divide(X10, X11)).
% 9.20/9.47 Proof: Rewrite equation 135,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,1,174].
% 9.20/9.47
% 9.20/9.47 189: X16 = double_divide(double_divide(X17, X16), X17).
% 9.20/9.47 Proof: Rewrite equation 129,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [1,174,159].
% 9.20/9.47
% 9.20/9.47 203: double_divide(inverse(X16), X17) = double_divide(X17, inverse(X16)).
% 9.20/9.47 Proof: Rewrite equation 119,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [159].
% 9.20/9.47
% 9.20/9.47 205: X11 = double_divide(X20, double_divide(X20, X11)).
% 9.20/9.47 Proof: A critical pair between equations 183 and 171.
% 9.20/9.47
% 9.20/9.47 211: double_divide(X17, inverse(inverse(X19))) = double_divide(X19, X17).
% 9.20/9.47 Proof: A critical pair between equations 203 and 159.
% 9.20/9.47
% 9.20/9.47 217: X16 = double_divide(X17, inverse(multiply(X16, X17))).
% 9.20/9.47 Proof: Rewrite equation 189,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [211,1].
% 9.20/9.47
% 9.20/9.47 232: multiply(X16, inverse(X17)) = double_divide(inverse(X16), X17).
% 9.20/9.47 Proof: Rewrite equation 174,
% 9.20/9.47 lhs with equations [1]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 234: multiply(X16, inverse(X17)) = double_divide(X17, inverse(X16)).
% 9.20/9.47 Proof: Rewrite equation 203,
% 9.20/9.47 lhs with equations [232]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 246: inverse(multiply(X22, X21)) = double_divide(X21, X22).
% 9.20/9.47 Proof: A critical pair between equations 205 and 217.
% 9.20/9.47
% 9.20/9.47 248: X16 = multiply(multiply(X16, X18), inverse(X18)).
% 9.20/9.47 Proof: A critical pair between equations 217 and 234.
% 9.20/9.47
% 9.20/9.47 265: multiply(X16, inverse(X17)) = inverse(multiply(inverse(X16), X17)).
% 9.20/9.47 Proof: Rewrite equation 234,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [246].
% 9.20/9.47
% 9.20/9.47 274: X12 = multiply(multiply(X11, X10), multiply(multiply(X12, inverse(X10)), inverse(X11))).
% 9.20/9.47 Proof: Rewrite equation 183,
% 9.20/9.47 lhs with equations []
% 9.20/9.47 rhs with equations [246,265,246,246,246,265,159].
% 9.20/9.47
% 9.20/9.47 295: X19 = multiply(multiply(inverse(X10), X10), X19).
% 9.20/9.47 Proof: A critical pair between equations 274 and 248.
% 9.20/9.47
% 9.20/9.47 306: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 9.20/9.47 Proof: Rewrite lhs with equations [295]
% 9.20/9.47 rhs with equations [].
% 9.20/9.47
% 9.20/9.47 % SZS output end Proof
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