TSTP Solution File: GRP604-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP604-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n004.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 01:15:29 EDT 2023
% Result : Unsatisfiable 18.81s 19.12s
% Output : CNFRefutation 18.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP604-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.08/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:41:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 18.81/19.12 % SZS status Unsatisfiable
% 18.81/19.12 % SZS output start Proof
% 18.81/19.12 original problem:
% 18.81/19.12 axioms:
% 18.81/19.12 inverse(double_divide(inverse(double_divide(A, inverse(double_divide(B, double_divide(A, C))))), C)) = B
% 18.81/19.12 multiply(A, B) = inverse(double_divide(B, A))
% 18.81/19.12 goal:
% 18.81/19.12 multiply(a(), b()) != multiply(b(), a())
% 18.81/19.12 To show the unsatisfiability of the original goal,
% 18.81/19.12 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 18.81/19.12 Here is an equational proof:
% 18.81/19.12 0: inverse(double_divide(inverse(double_divide(X0, inverse(double_divide(X1, double_divide(X0, X2))))), X2)) = X1.
% 18.81/19.12 Proof: Axiom.
% 18.81/19.12
% 18.81/19.12 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 18.81/19.12 Proof: Axiom.
% 18.81/19.12
% 18.81/19.12 2: inverse(double_divide(X3, inverse(double_divide(X4, double_divide(X3, double_divide(X0, X2)))))) = inverse(double_divide(inverse(double_divide(X0, X4)), X2)).
% 18.81/19.12 Proof: A critical pair between equations 0 and 0.
% 18.81/19.12
% 18.81/19.12 3: multiply(X2, multiply(multiply(double_divide(X0, X2), X1), X0)) = X1.
% 18.81/19.12 Proof: Rewrite equation 0,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 4: multiply(multiply(double_divide(X3, double_divide(X0, X2)), X4), X3) = multiply(X2, multiply(X4, X0)).
% 18.81/19.12 Proof: Rewrite equation 2,
% 18.81/19.12 lhs with equations [1,1]
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 5: X8 = multiply(double_divide(X6, X7), multiply(X7, multiply(X8, X6))).
% 18.81/19.12 Proof: A critical pair between equations 3 and 4.
% 18.81/19.12
% 18.81/19.12 6: X8 = inverse(double_divide(inverse(double_divide(inverse(double_divide(X6, X8)), X7)), double_divide(X6, X7))).
% 18.81/19.12 Proof: Rewrite equation 5,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 7: inverse(double_divide(X3, inverse(double_divide(X4, double_divide(X3, double_divide(X0, X2)))))) = inverse(double_divide(inverse(double_divide(X0, X4)), X2)).
% 18.81/19.12 Proof: Rewrite equation 4,
% 18.81/19.12 lhs with equations [1,1]
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 8: inverse(double_divide(inverse(double_divide(X0, inverse(double_divide(X1, double_divide(X0, X2))))), X2)) = X1.
% 18.81/19.12 Proof: Rewrite equation 3,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 9: X11 = inverse(double_divide(X10, double_divide(inverse(double_divide(X9, X10)), double_divide(X9, X11)))).
% 18.81/19.12 Proof: A critical pair between equations 6 and 6.
% 18.81/19.12
% 18.81/19.12 10: inverse(double_divide(X3, inverse(double_divide(X11, double_divide(X3, double_divide(inverse(double_divide(X9, X10)), double_divide(X9, X11))))))) = X10.
% 18.81/19.12 Proof: A critical pair between equations 7 and 6.
% 18.81/19.12
% 18.81/19.12 12: double_divide(X9, X11) = inverse(double_divide(inverse(double_divide(X10, X7)), double_divide(inverse(double_divide(inverse(double_divide(X9, X10)), X11)), X7))).
% 18.81/19.12 Proof: A critical pair between equations 6 and 6.
% 18.81/19.12
% 18.81/19.12 13: X11 = inverse(double_divide(inverse(double_divide(X10, X7)), double_divide(inverse(double_divide(X9, inverse(double_divide(X10, double_divide(X9, X11))))), X7))).
% 18.81/19.12 Proof: A critical pair between equations 6 and 8.
% 18.81/19.12
% 18.81/19.12 17: inverse(double_divide(X10, double_divide(X9, double_divide(X11, X12)))) = inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X11, X10)), X12)), X7)), double_divide(X9, X7))).
% 18.81/19.12 Proof: A critical pair between equations 6 and 7.
% 18.81/19.12
% 18.81/19.12 18: X8 = inverse(double_divide(inverse(double_divide(inverse(double_divide(X11, X10)), X12)), double_divide(X6, inverse(double_divide(X10, double_divide(inverse(double_divide(X6, X8)), double_divide(X11, X12))))))).
% 18.81/19.12 Proof: A critical pair between equations 6 and 7.
% 18.81/19.12
% 18.81/19.12 23: X8 = multiply(double_divide(X6, multiply(double_divide(multiply(X8, X6), double_divide(X11, X12)), X10)), multiply(X12, multiply(X10, X11))).
% 18.81/19.12 Proof: Rewrite equation 18,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1,1].
% 18.81/19.12
% 18.81/19.12 27: X11 = multiply(double_divide(multiply(multiply(double_divide(X9, X11), X10), X9), X7), multiply(X7, X10)).
% 18.81/19.12 Proof: Rewrite equation 13,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1].
% 18.81/19.12
% 18.81/19.12 28: double_divide(X9, X11) = multiply(double_divide(multiply(X11, multiply(X10, X9)), X7), multiply(X7, X10)).
% 18.81/19.12 Proof: Rewrite equation 12,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1].
% 18.81/19.12
% 18.81/19.12 30: multiply(multiply(double_divide(X3, double_divide(multiply(X10, X9), double_divide(X9, X11))), X11), X3) = X10.
% 18.81/19.12 Proof: Rewrite equation 10,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 31: X11 = multiply(double_divide(multiply(X10, X9), double_divide(X9, X11)), X10).
% 18.81/19.12 Proof: Rewrite equation 9,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 32: multiply(X2, multiply(multiply(double_divide(X0, X2), X1), X0)) = X1.
% 18.81/19.12 Proof: Rewrite equation 8,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 33: X8 = multiply(double_divide(X6, X7), multiply(X7, multiply(X8, X6))).
% 18.81/19.12 Proof: Rewrite equation 6,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 34: multiply(double_divide(X9, double_divide(X11, X12)), X10) = multiply(double_divide(X9, X7), multiply(X7, multiply(X12, multiply(X10, X11)))).
% 18.81/19.12 Proof: Rewrite equation 17,
% 18.81/19.12 lhs with equations [1]
% 18.81/19.12 rhs with equations [1,1,1,1].
% 18.81/19.12
% 18.81/19.12 36: X11 = double_divide(X14, multiply(double_divide(multiply(X13, X14), X11), X13)).
% 18.81/19.12 Proof: A critical pair between equations 27 and 28.
% 18.81/19.12
% 18.81/19.12 37: double_divide(multiply(X13, X14), double_divide(X14, X15)) = multiply(double_divide(X13, X7), multiply(X7, X15)).
% 18.81/19.12 Proof: A critical pair between equations 27 and 30.
% 18.81/19.12
% 18.81/19.12 40: X11 = multiply(double_divide(X14, double_divide(multiply(X13, multiply(X14, X12)), X11)), double_divide(X12, X13)).
% 18.81/19.12 Proof: A critical pair between equations 31 and 33.
% 18.81/19.12
% 18.81/19.12 43: multiply(double_divide(multiply(multiply(double_divide(X13, X14), multiply(X12, multiply(X10, X11))), X13), double_divide(X11, X12)), X10) = X14.
% 18.81/19.12 Proof: A critical pair between equations 34 and 27.
% 18.81/19.12
% 18.81/19.12 46: multiply(double_divide(X9, double_divide(multiply(X15, X13), double_divide(X13, X14))), X14) = multiply(double_divide(X9, X7), multiply(X7, X15)).
% 18.81/19.12 Proof: A critical pair between equations 34 and 33.
% 18.81/19.12
% 18.81/19.12 50: inverse(double_divide(X10, double_divide(inverse(double_divide(X13, inverse(double_divide(inverse(double_divide(inverse(double_divide(X11, X10)), X12)), double_divide(X13, X14))))), double_divide(X11, X12)))) = X14.
% 18.81/19.12 Proof: Rewrite equation 43,
% 18.81/19.12 lhs with equations [1,1,1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 53: X11 = inverse(double_divide(double_divide(X12, X13), double_divide(X14, double_divide(inverse(double_divide(inverse(double_divide(X12, X14)), X13)), X11)))).
% 18.81/19.12 Proof: Rewrite equation 40,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 56: X11 = double_divide(X14, inverse(double_divide(X13, double_divide(inverse(double_divide(X14, X13)), X11)))).
% 18.81/19.12 Proof: Rewrite equation 36,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 58: X8 = inverse(double_divide(inverse(double_divide(inverse(double_divide(X6, X8)), X7)), double_divide(X6, X7))).
% 18.81/19.12 Proof: Rewrite equation 33,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 59: inverse(double_divide(inverse(double_divide(X0, inverse(double_divide(X1, double_divide(X0, X2))))), X2)) = X1.
% 18.81/19.12 Proof: Rewrite equation 32,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 60: X11 = inverse(double_divide(X10, double_divide(inverse(double_divide(X9, X10)), double_divide(X9, X11)))).
% 18.81/19.12 Proof: Rewrite equation 31,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 61: inverse(double_divide(X3, inverse(double_divide(X11, double_divide(X3, double_divide(inverse(double_divide(X9, X10)), double_divide(X9, X11))))))) = X10.
% 18.81/19.12 Proof: Rewrite equation 30,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 63: double_divide(X9, X11) = inverse(double_divide(inverse(double_divide(X10, X7)), double_divide(inverse(double_divide(inverse(double_divide(X9, X10)), X11)), X7))).
% 18.81/19.12 Proof: Rewrite equation 28,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1].
% 18.81/19.12
% 18.81/19.12 64: X11 = inverse(double_divide(inverse(double_divide(X10, X7)), double_divide(inverse(double_divide(X9, inverse(double_divide(X10, double_divide(X9, X11))))), X7))).
% 18.81/19.12 Proof: Rewrite equation 27,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1].
% 18.81/19.12
% 18.81/19.12 68: X8 = inverse(double_divide(inverse(double_divide(inverse(double_divide(X11, X10)), X12)), double_divide(X6, inverse(double_divide(X10, double_divide(inverse(double_divide(X6, X8)), double_divide(X11, X12))))))).
% 18.81/19.12 Proof: Rewrite equation 23,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1,1].
% 18.81/19.12
% 18.81/19.12 71: inverse(double_divide(X14, double_divide(X9, double_divide(inverse(double_divide(X13, X15)), double_divide(X13, X14))))) = inverse(double_divide(inverse(double_divide(X15, X7)), double_divide(X9, X7))).
% 18.81/19.12 Proof: Rewrite equation 46,
% 18.81/19.12 lhs with equations [1,1]
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 73: double_divide(inverse(double_divide(X14, X13)), double_divide(X14, X15)) = inverse(double_divide(inverse(double_divide(X15, X7)), double_divide(X13, X7))).
% 18.81/19.12 Proof: Rewrite equation 37,
% 18.81/19.12 lhs with equations [1]
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 75: double_divide(inverse(double_divide(X14, X16)), double_divide(X14, inverse(double_divide(X16, X17)))) = X17.
% 18.81/19.12 Proof: A critical pair between equations 73 and 58.
% 18.81/19.12
% 18.81/19.12 76: X18 = inverse(double_divide(X17, inverse(double_divide(inverse(double_divide(X18, X19)), double_divide(X17, X19))))).
% 18.81/19.12 Proof: A critical pair between equations 60 and 73.
% 18.81/19.12
% 18.81/19.12 77: X11 = double_divide(X15, inverse(double_divide(double_divide(inverse(double_divide(X16, X15)), double_divide(X16, X17)), double_divide(X17, X11)))).
% 18.81/19.12 Proof: A critical pair between equations 56 and 60.
% 18.81/19.12
% 18.81/19.12 78: double_divide(inverse(double_divide(X14, inverse(double_divide(inverse(double_divide(X18, X16)), X19)))), double_divide(X14, X16)) = double_divide(X18, X19).
% 18.81/19.12 Proof: A critical pair between equations 73 and 63.
% 18.81/19.12
% 18.81/19.12 79: double_divide(inverse(double_divide(X14, inverse(double_divide(X18, inverse(double_divide(X16, double_divide(X18, X19))))))), double_divide(X14, X16)) = X19.
% 18.81/19.12 Proof: A critical pair between equations 73 and 64.
% 18.81/19.12
% 18.81/19.12 82: double_divide(inverse(double_divide(X12, X17)), double_divide(X12, X19)) = inverse(double_divide(inverse(double_divide(X19, X20)), double_divide(X17, X20))).
% 18.81/19.12 Proof: A critical pair between equations 53 and 71.
% 18.81/19.12
% 18.81/19.12 92: double_divide(multiply(multiply(multiply(double_divide(X18, X19), X16), X18), X14), double_divide(X14, X16)) = X19.
% 18.81/19.12 Proof: Rewrite equation 79,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 93: double_divide(multiply(multiply(X19, multiply(X16, X18)), X14), double_divide(X14, X16)) = double_divide(X18, X19).
% 18.81/19.12 Proof: Rewrite equation 78,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 94: X11 = double_divide(X15, multiply(double_divide(X17, X11), double_divide(multiply(X15, X16), double_divide(X16, X17)))).
% 18.81/19.12 Proof: Rewrite equation 77,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 95: X18 = multiply(multiply(double_divide(X17, X19), multiply(X19, X18)), X17).
% 18.81/19.12 Proof: Rewrite equation 76,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 96: double_divide(multiply(X16, X14), double_divide(X14, multiply(X17, X16))) = X17.
% 18.81/19.12 Proof: Rewrite equation 75,
% 18.81/19.12 lhs with equations [1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 99: X8 = multiply(double_divide(X6, multiply(double_divide(multiply(X8, X6), double_divide(X11, X12)), X10)), multiply(X12, multiply(X10, X11))).
% 18.81/19.12 Proof: Rewrite equation 68,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1,1].
% 18.81/19.12
% 18.81/19.12 105: multiply(multiply(double_divide(X3, double_divide(multiply(X10, X9), double_divide(X9, X11))), X11), X3) = X10.
% 18.81/19.12 Proof: Rewrite equation 61,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 107: multiply(X2, multiply(multiply(double_divide(X0, X2), X1), X0)) = X1.
% 18.81/19.12 Proof: Rewrite equation 59,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 108: X8 = multiply(double_divide(X6, X7), multiply(X7, multiply(X8, X6))).
% 18.81/19.12 Proof: Rewrite equation 58,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 115: multiply(double_divide(multiply(multiply(double_divide(X13, X14), multiply(X12, multiply(X10, X11))), X13), double_divide(X11, X12)), X10) = X14.
% 18.81/19.12 Proof: Rewrite equation 50,
% 18.81/19.12 lhs with equations [1,1,1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 118: double_divide(multiply(X17, X12), double_divide(X12, X19)) = multiply(double_divide(X17, X20), multiply(X20, X19)).
% 18.81/19.12 Proof: Rewrite equation 82,
% 18.81/19.12 lhs with equations [1]
% 18.81/19.12 rhs with equations [1,1].
% 18.81/19.12
% 18.81/19.12 125: multiply(double_divide(X19, multiply(X20, X18)), multiply(X18, X19)) = inverse(X20).
% 18.81/19.12 Proof: A critical pair between equations 1 and 96.
% 18.81/19.12
% 18.81/19.12 131: double_divide(multiply(X21, X22), double_divide(X22, X23)) = double_divide(multiply(X21, X14), double_divide(X14, X23)).
% 18.81/19.12 Proof: A critical pair between equations 92 and 105.
% 18.81/19.12
% 18.81/19.12 132: X11 = double_divide(X21, multiply(double_divide(X23, X11), multiply(double_divide(X21, X24), multiply(X24, X23)))).
% 18.81/19.12 Proof: A critical pair between equations 94 and 118.
% 18.81/19.12
% 18.81/19.12 140: X11 = double_divide(X21, inverse(double_divide(inverse(double_divide(inverse(double_divide(X23, X24)), double_divide(X21, X24))), double_divide(X23, X11)))).
% 18.81/19.12 Proof: Rewrite equation 132,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 144: inverse(double_divide(inverse(double_divide(X19, X18)), double_divide(X19, inverse(double_divide(X18, X20))))) = inverse(X20).
% 18.81/19.12 Proof: Rewrite equation 125,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 148: inverse(double_divide(X10, double_divide(inverse(double_divide(X13, inverse(double_divide(inverse(double_divide(inverse(double_divide(X11, X10)), X12)), double_divide(X13, X14))))), double_divide(X11, X12)))) = X14.
% 18.81/19.12 Proof: Rewrite equation 115,
% 18.81/19.12 lhs with equations [1,1,1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 155: X8 = inverse(double_divide(inverse(double_divide(inverse(double_divide(X6, X8)), X7)), double_divide(X6, X7))).
% 18.81/19.12 Proof: Rewrite equation 108,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 156: inverse(double_divide(inverse(double_divide(X0, inverse(double_divide(X1, double_divide(X0, X2))))), X2)) = X1.
% 18.81/19.12 Proof: Rewrite equation 107,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 163: X8 = inverse(double_divide(inverse(double_divide(inverse(double_divide(X11, X10)), X12)), double_divide(X6, inverse(double_divide(X10, double_divide(inverse(double_divide(X6, X8)), double_divide(X11, X12))))))).
% 18.81/19.12 Proof: Rewrite equation 99,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1,1,1].
% 18.81/19.12
% 18.81/19.12 167: X18 = inverse(double_divide(X17, inverse(double_divide(inverse(double_divide(X18, X19)), double_divide(X17, X19))))).
% 18.81/19.12 Proof: Rewrite equation 95,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 169: double_divide(inverse(double_divide(X14, inverse(double_divide(inverse(double_divide(X18, X16)), X19)))), double_divide(X14, X16)) = double_divide(X18, X19).
% 18.81/19.12 Proof: Rewrite equation 93,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 176: double_divide(inverse(double_divide(X22, X21)), double_divide(X22, X23)) = double_divide(inverse(double_divide(X14, X21)), double_divide(X14, X23)).
% 18.81/19.12 Proof: Rewrite equation 131,
% 18.81/19.12 lhs with equations [1]
% 18.81/19.12 rhs with equations [1].
% 18.81/19.12
% 18.81/19.12 184: X28 = inverse(double_divide(X27, double_divide(inverse(X28), double_divide(X26, double_divide(X26, X27))))).
% 18.81/19.12 Proof: A critical pair between equations 148 and 140.
% 18.81/19.12
% 18.81/19.12 185: inverse(double_divide(X21, X22)) = inverse(double_divide(X21, double_divide(X20, double_divide(X20, X22)))).
% 18.81/19.12 Proof: A critical pair between equations 156 and 169.
% 18.81/19.12
% 18.81/19.12 186: inverse(double_divide(inverse(double_divide(inverse(double_divide(X21, X22)), X25)), double_divide(X21, X22))) = X25.
% 18.81/19.12 Proof: A critical pair between equations 144 and 163.
% 18.81/19.12
% 18.81/19.12 187: X22 = inverse(double_divide(inverse(X23), double_divide(X21, double_divide(X21, inverse(double_divide(X22, X23)))))).
% 18.81/19.12 Proof: A critical pair between equations 155 and 144.
% 18.81/19.12
% 18.81/19.12 189: X24 = inverse(double_divide(X24, inverse(double_divide(inverse(double_divide(X27, X26)), double_divide(X27, X26))))).
% 18.81/19.12 Proof: A critical pair between equations 167 and 176.
% 18.81/19.12
% 18.81/19.12 201: X24 = multiply(multiply(double_divide(X27, X26), multiply(X26, X27)), X24).
% 18.81/19.12 Proof: Rewrite equation 189,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,1,1].
% 18.81/19.12
% 18.81/19.12 202: X22 = multiply(multiply(X23, X22), inverse(X23)).
% 18.81/19.12 Proof: Rewrite equation 187,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1,185,1].
% 18.81/19.12
% 18.81/19.12 203: multiply(double_divide(X21, X22), multiply(X25, multiply(X22, X21))) = X25.
% 18.81/19.12 Proof: Rewrite equation 186,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 204: multiply(X22, X21) = multiply(double_divide(X20, double_divide(X20, X22)), X21).
% 18.81/19.12 Proof: Rewrite equation 185,
% 18.81/19.12 lhs with equations [1]
% 18.81/19.12 rhs with equations [1].
% 18.81/19.12
% 18.81/19.12 205: X28 = multiply(double_divide(inverse(X28), double_divide(X26, double_divide(X26, X27))), X27).
% 18.81/19.12 Proof: Rewrite equation 184,
% 18.81/19.12 lhs with equations []
% 18.81/19.12 rhs with equations [1].
% 18.81/19.12
% 18.81/19.12 223: multiply(X2, multiply(multiply(double_divide(X0, X2), X1), X0)) = X1.
% 18.81/19.12 Proof: Rewrite equation 156,
% 18.81/19.12 lhs with equations [1,1,1]
% 18.81/19.12 rhs with equations [].
% 18.81/19.12
% 18.81/19.12 255: multiply(double_divide(inverse(X29), X31), X31) = X29.
% 18.81/19.12 Proof: A critical pair between equations 204 and 205.
% 18.81/19.12
% 18.81/19.12 260: X24 = multiply(multiply(X29, multiply(double_divide(X28, X29), X28)), X24).
% 18.81/19.12 Proof: A critical pair between equations 201 and 204.
% 18.81/19.12
% 18.81/19.12 263: X25 = multiply(X27, multiply(X25, multiply(double_divide(X26, X27), X26))).
% 18.81/19.12 Proof: A critical pair between equations 203 and 204.
% 18.81/19.12
% 18.81/19.12 267: X25 = multiply(inverse(X32), multiply(X25, X32)).
% 18.81/19.12 Proof: A critical pair between equations 263 and 255.
% 18.81/19.12
% 18.81/19.12 270: inverse(X30) = multiply(double_divide(X28, X30), X28).
% 18.81/19.12 Proof: A critical pair between equations 260 and 202.
% 18.81/19.12
% 18.81/19.12 288: X31 = multiply(X32, multiply(inverse(X32), X31)).
% 18.81/19.12 Proof: A critical pair between equations 223 and 270.
% 18.81/19.12
% 18.81/19.12 344: multiply(X34, X33) = multiply(X33, X34).
% 18.81/19.12 Proof: A critical pair between equations 288 and 267.
% 18.81/19.12
% 18.81/19.12 393: multiply(a(), b()) = multiply(b(), a()).
% 18.81/19.12 Proof: Rewrite lhs with equations []
% 18.81/19.12 rhs with equations [344].
% 18.81/19.12
% 18.81/19.12 % SZS output end Proof
%------------------------------------------------------------------------------