TSTP Solution File: GRP437-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP437-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n029.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 01:15:00 EDT 2023
% Result : Unsatisfiable 113.18s 113.55s
% Output : CNFRefutation 113.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP437-1 : TPTP v8.1.2. Released v2.6.0.
% 0.03/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 23:17:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 113.18/113.55 % SZS status Unsatisfiable
% 113.18/113.55 % SZS output start Proof
% 113.18/113.55 original problem:
% 113.18/113.55 axioms:
% 113.18/113.55 multiply(A, inverse(multiply(B, multiply(C, multiply(multiply(inverse(C), inverse(multiply(D, B))), A))))) = D
% 113.18/113.55 goal:
% 113.18/113.55 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 113.18/113.55 To show the unsatisfiability of the original goal,
% 113.18/113.55 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 113.18/113.55 Here is an equational proof:
% 113.18/113.55 0: multiply(X0, inverse(multiply(X1, multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(X3, X1))), X0))))) = X3.
% 113.18/113.55 Proof: Axiom.
% 113.18/113.55
% 113.18/113.55 1: X5 = multiply(X0, inverse(multiply(multiply(X6, multiply(multiply(inverse(X6), inverse(multiply(X7, X5))), inverse(X2))), multiply(X2, multiply(X7, X0))))).
% 113.18/113.55 Proof: A critical pair between equations 0 and 0.
% 113.18/113.55
% 113.18/113.55 3: X3 = multiply(inverse(multiply(X5, multiply(X6, multiply(multiply(inverse(X6), inverse(multiply(X7, X5))), multiply(inverse(X2), inverse(multiply(X3, X1))))))), inverse(multiply(X1, multiply(X2, X7)))).
% 113.18/113.55 Proof: A critical pair between equations 0 and 0.
% 113.18/113.55
% 113.18/113.55 4: multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(X11, X9))), inverse(X6))) = multiply(X0, inverse(multiply(multiply(X6, multiply(X11, inverse(X2))), multiply(X2, multiply(X9, X0))))).
% 113.18/113.55 Proof: A critical pair between equations 1 and 0.
% 113.18/113.55
% 113.18/113.55 6: multiply(X12, multiply(X10, inverse(X6))) = multiply(X0, inverse(multiply(multiply(X6, multiply(X11, inverse(X2))), multiply(X2, multiply(multiply(X9, multiply(multiply(inverse(X9), inverse(multiply(X10, X11))), inverse(X12))), X0))))).
% 113.18/113.55 Proof: A critical pair between equations 1 and 1.
% 113.18/113.55
% 113.18/113.55 10: inverse(multiply(X9, multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(X11, X9))), X8)))) = multiply(X0, inverse(multiply(multiply(X6, multiply(multiply(inverse(X6), inverse(X11)), inverse(X2))), multiply(X2, multiply(X8, X0))))).
% 113.18/113.55 Proof: A critical pair between equations 1 and 0.
% 113.18/113.55
% 113.18/113.55 11: multiply(X11, X10) = multiply(X0, inverse(multiply(multiply(multiply(X8, multiply(X9, multiply(multiply(inverse(X9), inverse(multiply(X10, X8))), multiply(inverse(X11), inverse(multiply(X12, X13)))))), multiply(X12, inverse(X2))), multiply(X2, multiply(X13, X0))))).
% 113.18/113.55 Proof: A critical pair between equations 1 and 3.
% 113.18/113.55
% 113.18/113.55 14: multiply(X9, multiply(multiply(inverse(X9), inverse(multiply(X10, X11))), inverse(X12))) = multiply(inverse(multiply(X5, multiply(X6, multiply(multiply(inverse(X6), inverse(multiply(X7, X5))), X11)))), inverse(multiply(multiply(X12, multiply(X10, inverse(X2))), multiply(X2, X7)))).
% 113.18/113.55 Proof: A critical pair between equations 3 and 1.
% 113.18/113.55
% 113.18/113.55 16: multiply(X11, X10) = multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(X12, X13))), inverse(multiply(X8, multiply(X9, multiply(multiply(inverse(X9), inverse(multiply(X10, X8))), multiply(inverse(X11), inverse(multiply(X12, X13))))))))).
% 113.18/113.55 Proof: Rewrite equation 11,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [4].
% 113.18/113.55
% 113.18/113.55 18: multiply(X12, multiply(X10, inverse(X6))) = multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(X11, multiply(X9, multiply(multiply(inverse(X9), inverse(multiply(X10, X11))), inverse(X12)))))), inverse(X6))).
% 113.18/113.55 Proof: Rewrite equation 6,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [4].
% 113.18/113.55
% 113.18/113.55 19: inverse(multiply(X9, multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(multiply(X14, X15), X9))), X14)))) = X15.
% 113.18/113.55 Proof: A critical pair between equations 10 and 1.
% 113.18/113.55
% 113.18/113.55 20: multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(multiply(inverse(X13), inverse(multiply(X14, X15))), X14))), inverse(X13))) = X15.
% 113.18/113.55 Proof: A critical pair between equations 4 and 1.
% 113.18/113.55
% 113.18/113.55 21: X14 = multiply(X15, multiply(X16, inverse(multiply(multiply(X17, multiply(multiply(inverse(X17), inverse(X14)), inverse(X18))), multiply(X18, multiply(X15, X16)))))).
% 113.18/113.55 Proof: A critical pair between equations 0 and 10.
% 113.18/113.55
% 113.18/113.55 23: multiply(X9, multiply(multiply(inverse(X9), inverse(multiply(X10, multiply(inverse(X16), inverse(multiply(X17, multiply(X12, multiply(X10, inverse(X16))))))))), inverse(X12))) = X17.
% 113.18/113.55 Proof: A critical pair between equations 14 and 3.
% 113.18/113.55
% 113.18/113.55 25: multiply(X15, multiply(multiply(inverse(X15), inverse(multiply(X13, X14))), inverse(X16))) = multiply(X0, inverse(multiply(multiply(X16, multiply(X13, inverse(X17))), multiply(X17, multiply(X14, X0))))).
% 113.18/113.55 Proof: A critical pair between equations 1 and 18.
% 113.18/113.55
% 113.18/113.55 29: inverse(multiply(X9, multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(X11, X9))), multiply(inverse(X14), inverse(multiply(X15, multiply(X6, multiply(multiply(inverse(X6), inverse(X11)), inverse(X14)))))))))) = X15.
% 113.18/113.55 Proof: A critical pair between equations 10 and 0.
% 113.18/113.55
% 113.18/113.55 30: multiply(X10, multiply(multiply(inverse(X10), inverse(multiply(multiply(inverse(X13), inverse(X14)), X16))), inverse(X13))) = inverse(multiply(X17, multiply(X18, multiply(multiply(inverse(X18), inverse(multiply(X14, X17))), X16)))).
% 113.18/113.55 Proof: A critical pair between equations 4 and 10.
% 113.18/113.55
% 113.18/113.55 31: X14 = multiply(X15, multiply(X15, multiply(multiply(inverse(X15), inverse(multiply(multiply(inverse(X17), inverse(X14)), X15))), inverse(X17)))).
% 113.18/113.55 Proof: Rewrite equation 21,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [25].
% 113.18/113.55
% 113.18/113.55 32: X20 = multiply(X20, inverse(multiply(multiply(X21, multiply(multiply(inverse(X21), inverse(X18)), inverse(X19))), multiply(X19, X18)))).
% 113.18/113.55 Proof: A critical pair between equations 3 and 29.
% 113.18/113.55
% 113.18/113.55 33: X14 = multiply(multiply(inverse(X20), inverse(multiply(X21, multiply(X22, multiply(multiply(inverse(X22), inverse(X14)), inverse(X20)))))), X21).
% 113.18/113.55 Proof: A critical pair between equations 31 and 23.
% 113.18/113.55
% 113.18/113.55 34: X15 = inverse(multiply(multiply(inverse(X20), inverse(multiply(X21, multiply(X22, multiply(multiply(inverse(X22), X15), inverse(X20)))))), X21)).
% 113.18/113.55 Proof: A critical pair between equations 19 and 23.
% 113.18/113.55
% 113.18/113.55 36: X19 = multiply(inverse(X22), inverse(multiply(multiply(inverse(X20), inverse(multiply(X21, multiply(X22, multiply(X19, inverse(X20)))))), X21))).
% 113.18/113.55 Proof: A critical pair between equations 0 and 23.
% 113.18/113.55
% 113.18/113.55 37: X15 = inverse(multiply(multiply(X18, multiply(multiply(inverse(X18), inverse(multiply(X19, multiply(X14, X15)))), inverse(X10))), multiply(X10, multiply(X19, X14)))).
% 113.18/113.55 Proof: A critical pair between equations 19 and 0.
% 113.18/113.55
% 113.18/113.55 38: multiply(inverse(X20), inverse(multiply(X21, multiply(X22, multiply(X19, inverse(X20)))))) = multiply(X0, inverse(multiply(X21, multiply(X22, multiply(X19, X0))))).
% 113.18/113.55 Proof: A critical pair between equations 1 and 23.
% 113.18/113.55
% 113.18/113.55 40: multiply(multiply(inverse(X17), inverse(multiply(X18, X19))), inverse(X20)) = inverse(multiply(multiply(X20, multiply(X18, inverse(X10))), multiply(X10, multiply(X19, X17)))).
% 113.18/113.55 Proof: A critical pair between equations 19 and 1.
% 113.18/113.55
% 113.18/113.55 41: multiply(X19, X18) = multiply(X18, multiply(multiply(inverse(X18), inverse(multiply(X20, multiply(X21, multiply(multiply(inverse(X21), inverse(X18)), inverse(X19)))))), X20)).
% 113.18/113.55 Proof: A critical pair between equations 16 and 29.
% 113.18/113.55
% 113.18/113.55 44: X15 = multiply(multiply(inverse(X14), inverse(multiply(multiply(inverse(X18), inverse(multiply(X19, multiply(X14, X15)))), X19))), inverse(X18)).
% 113.18/113.55 Proof: Rewrite equation 37,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [40].
% 113.18/113.55
% 113.18/113.55 51: X26 = multiply(inverse(X25), inverse(multiply(multiply(X27, inverse(multiply(X24, multiply(X25, multiply(X26, X27))))), X24))).
% 113.18/113.55 Proof: A critical pair between equations 36 and 38.
% 113.18/113.55
% 113.18/113.55 52: X15 = inverse(multiply(multiply(X27, inverse(multiply(X24, multiply(X25, multiply(multiply(inverse(X25), X15), X27))))), X24)).
% 113.18/113.55 Proof: A critical pair between equations 34 and 38.
% 113.18/113.55
% 113.18/113.55 53: X14 = multiply(multiply(X27, inverse(multiply(X24, multiply(X25, multiply(multiply(inverse(X25), inverse(X14)), X27))))), X24).
% 113.18/113.55 Proof: A critical pair between equations 33 and 38.
% 113.18/113.55
% 113.18/113.55 54: X20 = multiply(X20, inverse(multiply(X25, multiply(X23, multiply(multiply(inverse(X23), inverse(multiply(X24, X25))), X24))))).
% 113.18/113.55 Proof: A critical pair between equations 32 and 20.
% 113.18/113.55
% 113.18/113.55 56: multiply(X25, multiply(multiply(inverse(X25), X26), inverse(X23))) = multiply(X10, multiply(multiply(inverse(X10), X26), inverse(X23))).
% 113.18/113.55 Proof: A critical pair between equations 20 and 34.
% 113.18/113.55
% 113.18/113.55 57: X20 = multiply(X20, multiply(multiply(inverse(X26), inverse(multiply(multiply(inverse(X22), inverse(multiply(X25, X26))), X25))), inverse(X22))).
% 113.18/113.55 Proof: A critical pair between equations 32 and 40.
% 113.18/113.55
% 113.18/113.55 58: multiply(multiply(inverse(X23), inverse(X24)), inverse(X25)) = inverse(multiply(multiply(X25, X24), multiply(X10, multiply(inverse(X10), X23)))).
% 113.18/113.55 Proof: A critical pair between equations 19 and 32.
% 113.18/113.55
% 113.18/113.55 60: multiply(X25, multiply(multiply(inverse(X25), inverse(X26)), inverse(X23))) = multiply(X10, multiply(multiply(inverse(X10), inverse(X26)), inverse(X23))).
% 113.18/113.55 Proof: A critical pair between equations 20 and 33.
% 113.18/113.55
% 113.18/113.55 63: multiply(X12, multiply(inverse(X12), inverse(X6))) = multiply(inverse(X12), multiply(inverse(inverse(X12)), inverse(X6))).
% 113.18/113.55 Proof: A critical pair between equations 18 and 54.
% 113.18/113.55
% 113.18/113.55 64: X20 = multiply(X20, multiply(multiply(inverse(multiply(X30, multiply(multiply(inverse(X30), X31), inverse(X22)))), X31), inverse(X22))).
% 113.18/113.55 Proof: A critical pair between equations 57 and 52.
% 113.18/113.55
% 113.18/113.55 66: multiply(X19, multiply(inverse(X19), X27)) = multiply(multiply(inverse(X19), X27), multiply(inverse(multiply(inverse(X19), X27)), X27)).
% 113.18/113.55 Proof: A critical pair between equations 41 and 54.
% 113.18/113.55
% 113.18/113.55 67: X20 = multiply(X20, multiply(X30, multiply(multiply(inverse(X30), inverse(multiply(multiply(inverse(X31), inverse(X29)), X29))), inverse(X31)))).
% 113.18/113.55 Proof: A critical pair between equations 54 and 30.
% 113.18/113.55
% 113.18/113.55 68: X20 = multiply(X20, inverse(multiply(multiply(inverse(X28), inverse(multiply(X29, multiply(X30, multiply(inverse(X30), inverse(X28)))))), X29))).
% 113.18/113.55 Proof: A critical pair between equations 54 and 23.
% 113.18/113.55
% 113.18/113.55 72: multiply(X29, inverse(multiply(X30, multiply(X28, multiply(X31, X29))))) = multiply(X0, inverse(multiply(X30, multiply(X28, multiply(X31, X0))))).
% 113.18/113.55 Proof: A critical pair between equations 0 and 51.
% 113.18/113.55
% 113.18/113.55 75: multiply(X34, multiply(inverse(X34), inverse(X32))) = multiply(X10, multiply(inverse(X10), inverse(X32))).
% 113.18/113.55 Proof: A critical pair between equations 20 and 68.
% 113.18/113.55
% 113.18/113.55 76: multiply(multiply(inverse(X34), inverse(X35)), X35) = multiply(multiply(inverse(X34), inverse(X32)), X32).
% 113.18/113.55 Proof: A critical pair between equations 53 and 67.
% 113.18/113.55
% 113.18/113.55 77: X20 = multiply(X20, multiply(inverse(multiply(X34, multiply(inverse(X34), inverse(X32)))), inverse(X32))).
% 113.18/113.55 Proof: A critical pair between equations 57 and 68.
% 113.18/113.55
% 113.18/113.55 79: X20 = multiply(X20, inverse(multiply(multiply(X36, inverse(multiply(X33, multiply(X34, multiply(inverse(X34), X36))))), X33))).
% 113.18/113.55 Proof: A critical pair between equations 68 and 72.
% 113.18/113.55
% 113.18/113.55 85: multiply(X30, multiply(multiply(inverse(X30), inverse(X33)), inverse(X34))) = multiply(X35, multiply(multiply(inverse(X35), inverse(X33)), inverse(X34))).
% 113.18/113.55 Proof: A critical pair between equations 64 and 60.
% 113.18/113.55
% 113.18/113.55 88: multiply(X12, multiply(inverse(X12), inverse(X36))) = multiply(X37, multiply(inverse(X37), inverse(X36))).
% 113.18/113.55 Proof: A critical pair between equations 63 and 75.
% 113.18/113.55
% 113.18/113.55 89: X37 = multiply(multiply(X37, inverse(multiply(X24, multiply(X36, multiply(multiply(inverse(X36), inverse(X38)), X38))))), X24).
% 113.18/113.55 Proof: A critical pair between equations 53 and 76.
% 113.18/113.55
% 113.18/113.55 90: X3 = multiply(multiply(X3, X1), inverse(multiply(X1, multiply(X36, multiply(multiply(inverse(X36), inverse(X38)), X38))))).
% 113.18/113.55 Proof: A critical pair between equations 0 and 76.
% 113.18/113.55
% 113.18/113.55 92: X20 = multiply(X20, inverse(multiply(multiply(X36, multiply(multiply(inverse(X36), inverse(X38)), X38)), multiply(X19, inverse(X19))))).
% 113.18/113.55 Proof: A critical pair between equations 32 and 76.
% 113.18/113.55
% 113.18/113.55 94: multiply(X30, multiply(multiply(inverse(X30), inverse(inverse(X34))), inverse(X34))) = multiply(X36, multiply(multiply(inverse(X36), inverse(X38)), X38)).
% 113.18/113.55 Proof: A critical pair between equations 85 and 76.
% 113.18/113.55
% 113.18/113.55 98: X20 = multiply(X20, multiply(multiply(inverse(multiply(X36, multiply(multiply(inverse(X36), inverse(X38)), X38))), inverse(inverse(X22))), inverse(X22))).
% 113.18/113.55 Proof: A critical pair between equations 64 and 76.
% 113.18/113.55
% 113.18/113.55 101: multiply(X19, inverse(X19)) = multiply(inverse(X19), inverse(inverse(X19))).
% 113.18/113.55 Proof: A critical pair between equations 41 and 89.
% 113.18/113.55
% 113.18/113.55 102: multiply(X19, multiply(inverse(X19), inverse(X39))) = multiply(X40, multiply(inverse(X40), inverse(X39))).
% 113.18/113.55 Proof: A critical pair between equations 66 and 88.
% 113.18/113.55
% 113.18/113.55 103: multiply(multiply(inverse(X41), inverse(X42)), X42) = multiply(multiply(inverse(X41), inverse(inverse(X18))), inverse(X18)).
% 113.18/113.55 Proof: A critical pair between equations 44 and 89.
% 113.18/113.55
% 113.18/113.55 104: multiply(X36, multiply(multiply(inverse(X36), inverse(X38)), X38)) = multiply(X39, multiply(multiply(inverse(X39), inverse(X41)), X41)).
% 113.18/113.55 Proof: A critical pair between equations 94 and 76.
% 113.18/113.55
% 113.18/113.55 106: multiply(multiply(inverse(X40), inverse(X41)), X41) = inverse(multiply(multiply(X42, inverse(X42)), multiply(X10, multiply(inverse(X10), X40)))).
% 113.18/113.55 Proof: A critical pair between equations 19 and 92.
% 113.18/113.55
% 113.18/113.55 110: multiply(X25, multiply(multiply(inverse(X25), inverse(inverse(X40))), inverse(X40))) = multiply(X41, multiply(multiply(inverse(X41), inverse(X42)), X42)).
% 113.18/113.55 Proof: A critical pair between equations 56 and 94.
% 113.18/113.55
% 113.18/113.55 111: multiply(X25, multiply(multiply(inverse(X25), inverse(inverse(X42))), inverse(X42))) = multiply(X40, multiply(multiply(inverse(X40), inverse(X41)), X41)).
% 113.18/113.55 Proof: A critical pair between equations 56 and 98.
% 113.18/113.55
% 113.18/113.55 113: multiply(X25, multiply(multiply(inverse(X25), inverse(X42)), X42)) = multiply(X40, multiply(multiply(inverse(X40), inverse(X41)), X41)).
% 113.18/113.55 Proof: Rewrite equation 111,
% 113.18/113.55 lhs with equations [103]
% 113.18/113.55 rhs with equations [].
% 113.18/113.55
% 113.18/113.55 114: multiply(multiply(inverse(X40), inverse(X41)), X41) = multiply(multiply(inverse(X40), inverse(X42)), X42).
% 113.18/113.55 Proof: Rewrite equation 106,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [58,103].
% 113.18/113.55
% 113.18/113.55 115: multiply(multiply(inverse(X43), inverse(X41)), X41) = multiply(multiply(X43, inverse(X43)), inverse(X43)).
% 113.18/113.55 Proof: A critical pair between equations 114 and 101.
% 113.18/113.55
% 113.18/113.55 117: X20 = multiply(X20, multiply(inverse(multiply(X35, multiply(X35, inverse(X35)))), inverse(inverse(X35)))).
% 113.18/113.55 Proof: A critical pair between equations 77 and 101.
% 113.18/113.55
% 113.18/113.55 122: X37 = multiply(multiply(X37, inverse(multiply(X24, multiply(X39, multiply(multiply(X39, inverse(X39)), inverse(X39)))))), X24).
% 113.18/113.55 Proof: A critical pair between equations 89 and 101.
% 113.18/113.55
% 113.18/113.55 123: X3 = multiply(multiply(X3, X1), inverse(multiply(X1, multiply(X39, multiply(multiply(X39, inverse(X39)), inverse(X39)))))).
% 113.18/113.55 Proof: A critical pair between equations 90 and 101.
% 113.18/113.55
% 113.18/113.55 125: multiply(X41, multiply(multiply(inverse(X41), inverse(X42)), X42)) = multiply(X45, multiply(multiply(inverse(X45), inverse(X46)), X46)).
% 113.18/113.55 Proof: A critical pair between equations 110 and 113.
% 113.18/113.55
% 113.18/113.55 126: multiply(X36, multiply(multiply(inverse(X36), inverse(X38)), X38)) = multiply(X42, multiply(multiply(X42, inverse(X42)), inverse(X42))).
% 113.18/113.55 Proof: A critical pair between equations 104 and 101.
% 113.18/113.55
% 113.18/113.55 130: multiply(X36, multiply(multiply(X36, inverse(X36)), inverse(X36))) = multiply(X42, multiply(multiply(X42, inverse(X42)), inverse(X42))).
% 113.18/113.55 Proof: Rewrite equation 126,
% 113.18/113.55 lhs with equations [115]
% 113.18/113.55 rhs with equations [].
% 113.18/113.55
% 113.18/113.55 131: multiply(X41, multiply(multiply(X41, inverse(X41)), inverse(X41))) = multiply(X45, multiply(multiply(X45, inverse(X45)), inverse(X45))).
% 113.18/113.55 Proof: Rewrite equation 125,
% 113.18/113.55 lhs with equations [115]
% 113.18/113.55 rhs with equations [115].
% 113.18/113.55
% 113.18/113.55 133: multiply(X30, multiply(multiply(X30, inverse(X30)), inverse(X30))) = multiply(X36, multiply(multiply(X36, inverse(X36)), inverse(X36))).
% 113.18/113.55 Proof: Rewrite equation 94,
% 113.18/113.55 lhs with equations [115]
% 113.18/113.55 rhs with equations [115].
% 113.18/113.55
% 113.18/113.55 138: X20 = multiply(X20, inverse(multiply(multiply(X22, multiply(multiply(X22, inverse(X22)), inverse(X19))), multiply(X19, inverse(X22))))).
% 113.18/113.55 Proof: A critical pair between equations 32 and 101.
% 113.18/113.55
% 113.18/113.55 145: multiply(X41, multiply(multiply(X41, inverse(X41)), inverse(X41))) = multiply(inverse(X46), multiply(multiply(X46, inverse(X46)), inverse(inverse(X46)))).
% 113.18/113.55 Proof: A critical pair between equations 131 and 101.
% 113.18/113.55
% 113.18/113.55 147: multiply(X30, multiply(multiply(X30, inverse(X30)), inverse(X30))) = multiply(inverse(X37), multiply(multiply(X37, inverse(X37)), inverse(inverse(X37)))).
% 113.18/113.55 Proof: A critical pair between equations 133 and 101.
% 113.18/113.55
% 113.18/113.55 148: multiply(X25, multiply(multiply(inverse(X25), inverse(inverse(X23))), inverse(X23))) = multiply(X44, multiply(multiply(X44, inverse(X44)), inverse(X44))).
% 113.18/113.55 Proof: A critical pair between equations 56 and 115.
% 113.18/113.55
% 113.18/113.55 149: multiply(X25, multiply(multiply(X25, inverse(X25)), inverse(X25))) = multiply(X44, multiply(multiply(X44, inverse(X44)), inverse(X44))).
% 113.18/113.55 Proof: Rewrite equation 148,
% 113.18/113.55 lhs with equations [115]
% 113.18/113.55 rhs with equations [].
% 113.18/113.55
% 113.18/113.55 151: multiply(X44, multiply(multiply(X44, inverse(X44)), inverse(X44))) = multiply(inverse(X48), multiply(multiply(X48, inverse(X48)), inverse(inverse(X48)))).
% 113.18/113.55 Proof: A critical pair between equations 149 and 145.
% 113.18/113.55
% 113.18/113.55 157: multiply(X45, multiply(multiply(X45, inverse(X45)), inverse(X45))) = multiply(inverse(X47), multiply(multiply(X47, inverse(X47)), inverse(inverse(X47)))).
% 113.18/113.55 Proof: A critical pair between equations 131 and 147.
% 113.18/113.55
% 113.18/113.55 159: X20 = multiply(X20, inverse(multiply(multiply(inverse(X23), multiply(multiply(X23, inverse(X23)), inverse(X19))), multiply(X19, inverse(inverse(X23)))))).
% 113.18/113.55 Proof: A critical pair between equations 138 and 101.
% 113.18/113.55
% 113.18/113.55 166: X3 = multiply(multiply(X3, X1), inverse(multiply(X1, multiply(inverse(X49), multiply(multiply(X49, inverse(X49)), inverse(inverse(X49))))))).
% 113.18/113.55 Proof: A critical pair between equations 123 and 157.
% 113.18/113.55
% 113.18/113.55 170: multiply(X42, multiply(multiply(X42, inverse(X42)), inverse(X42))) = multiply(inverse(X50), multiply(multiply(X50, inverse(X50)), inverse(inverse(X50)))).
% 113.18/113.55 Proof: A critical pair between equations 130 and 151.
% 113.18/113.55
% 113.18/113.55 172: multiply(X25, multiply(multiply(inverse(X25), inverse(inverse(X23))), inverse(X23))) = multiply(X44, multiply(multiply(X44, inverse(X44)), inverse(X44))).
% 113.18/113.55 Proof: A critical pair between equations 56 and 115.
% 113.18/113.55
% 113.18/113.55 173: X20 = multiply(X20, inverse(multiply(inverse(X37), multiply(multiply(X37, inverse(X37)), inverse(inverse(multiply(X37, multiply(X37, inverse(X37))))))))).
% 113.18/113.55 Proof: A critical pair between equations 159 and 117.
% 113.18/113.55
% 113.18/113.55 178: multiply(X25, multiply(multiply(X25, inverse(X25)), inverse(X25))) = multiply(X44, multiply(multiply(X44, inverse(X44)), inverse(X44))).
% 113.18/113.55 Proof: Rewrite equation 172,
% 113.18/113.55 lhs with equations [115]
% 113.18/113.55 rhs with equations [].
% 113.18/113.55
% 113.18/113.55 183: multiply(X25, multiply(multiply(X25, inverse(X25)), inverse(X25))) = multiply(inverse(X52), multiply(multiply(X52, inverse(X52)), inverse(inverse(X52)))).
% 113.18/113.55 Proof: A critical pair between equations 178 and 170.
% 113.18/113.55
% 113.18/113.55 188: multiply(X42, multiply(multiply(X42, inverse(X42)), inverse(X42))) = multiply(X10, multiply(multiply(inverse(X10), inverse(inverse(X13))), inverse(X13))).
% 113.18/113.55 Proof: A critical pair between equations 20 and 122.
% 113.18/113.55
% 113.18/113.55 191: multiply(X19, multiply(inverse(X19), inverse(multiply(multiply(X42, inverse(multiply(X43, multiply(X41, multiply(X44, X42))))), X43)))) = multiply(X41, X44).
% 113.18/113.55 Proof: A critical pair between equations 102 and 51.
% 113.18/113.55
% 113.18/113.55 195: multiply(X42, multiply(multiply(X42, inverse(X42)), inverse(X42))) = multiply(X10, multiply(multiply(X10, inverse(X10)), inverse(X10))).
% 113.18/113.55 Proof: Rewrite equation 188,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [115].
% 113.18/113.55
% 113.18/113.55 199: multiply(X48, inverse(X48)) = multiply(X19, inverse(X19)).
% 113.18/113.55 Proof: A critical pair between equations 191 and 79.
% 113.18/113.55
% 113.18/113.55 210: inverse(X20) = multiply(X0, inverse(multiply(inverse(inverse(X20)), multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(X20, inverse(X20)))), X0))))).
% 113.18/113.55 Proof: A critical pair between equations 0 and 101.
% 113.18/113.55
% 113.18/113.55 214: multiply(X29, inverse(X29)) = multiply(inverse(X29), inverse(inverse(X29))).
% 113.18/113.55 Proof: A critical pair between equations 53 and 210.
% 113.18/113.55
% 113.18/113.55 218: multiply(X48, inverse(X48)) = multiply(X51, multiply(multiply(X51, inverse(X51)), inverse(X51))).
% 113.18/113.55 Proof: A critical pair between equations 199 and 123.
% 113.18/113.55
% 113.18/113.55 219: multiply(X39, multiply(multiply(X39, inverse(X39)), inverse(X39))) = multiply(X50, inverse(X50)).
% 113.18/113.55 Proof: A critical pair between equations 123 and 199.
% 113.18/113.55
% 113.18/113.55 225: multiply(X48, inverse(X48)) = multiply(inverse(X52), multiply(multiply(X52, inverse(X52)), inverse(inverse(X52)))).
% 113.18/113.55 Proof: A critical pair between equations 199 and 166.
% 113.18/113.55
% 113.18/113.55 231: X37 = multiply(multiply(X37, inverse(multiply(X24, multiply(X52, inverse(X52))))), X24).
% 113.18/113.55 Proof: A critical pair between equations 122 and 219.
% 113.18/113.55
% 113.18/113.55 234: multiply(X42, multiply(multiply(X42, inverse(X42)), inverse(X42))) = multiply(X52, inverse(X52)).
% 113.18/113.55 Proof: A critical pair between equations 195 and 219.
% 113.18/113.55
% 113.18/113.55 235: multiply(X10, multiply(multiply(X10, inverse(X10)), inverse(X10))) = multiply(X53, inverse(X53)).
% 113.18/113.55 Proof: A critical pair between equations 195 and 218.
% 113.18/113.55
% 113.18/113.55 236: multiply(X25, multiply(multiply(X25, inverse(X25)), inverse(X25))) = multiply(X54, inverse(X54)).
% 113.18/113.55 Proof: A critical pair between equations 183 and 225.
% 113.18/113.55
% 113.18/113.55 237: multiply(X19, inverse(X19)) = multiply(X52, multiply(multiply(X52, inverse(X52)), inverse(X52))).
% 113.18/113.55 Proof: A critical pair between equations 199 and 219.
% 113.18/113.55
% 113.18/113.55 239: multiply(X29, inverse(X29)) = multiply(X53, multiply(multiply(X53, inverse(X53)), inverse(X53))).
% 113.18/113.55 Proof: A critical pair between equations 214 and 218.
% 113.18/113.55
% 113.18/113.55 240: multiply(X29, inverse(X29)) = multiply(X53, inverse(X53)).
% 113.18/113.55 Proof: Rewrite equation 239,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [235].
% 113.18/113.55
% 113.18/113.55 241: multiply(X19, inverse(X19)) = multiply(X52, inverse(X52)).
% 113.18/113.55 Proof: Rewrite equation 237,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [234].
% 113.18/113.55
% 113.18/113.55 245: inverse(X55) = multiply(multiply(inverse(X55), inverse(inverse(X18))), inverse(X18)).
% 113.18/113.55 Proof: A critical pair between equations 44 and 231.
% 113.18/113.55
% 113.18/113.55 246: multiply(X24, multiply(X52, inverse(X52))) = multiply(multiply(X55, inverse(X55)), X24).
% 113.18/113.55 Proof: A critical pair between equations 231 and 240.
% 113.18/113.55
% 113.18/113.55 247: X53 = multiply(X53, multiply(X54, multiply(multiply(X54, inverse(X54)), inverse(X54)))).
% 113.18/113.55 Proof: A critical pair between equations 231 and 138.
% 113.18/113.55
% 113.18/113.55 255: X53 = multiply(X53, multiply(X54, inverse(X54))).
% 113.18/113.55 Proof: Rewrite equation 247,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [236].
% 113.18/113.55
% 113.18/113.55 256: inverse(X55) = multiply(multiply(X55, inverse(X55)), inverse(X55)).
% 113.18/113.55 Proof: Rewrite equation 245,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [115].
% 113.18/113.55
% 113.18/113.55 257: X3 = multiply(multiply(X3, X1), inverse(X1)).
% 113.18/113.55 Proof: Rewrite equation 123,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [256,255].
% 113.18/113.55
% 113.18/113.55 264: X20 = multiply(X20, inverse(multiply(inverse(X37), X37))).
% 113.18/113.55 Proof: Rewrite equation 173,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [255,257].
% 113.18/113.55
% 113.18/113.55 272: X24 = multiply(multiply(X55, inverse(X55)), X24).
% 113.18/113.55 Proof: Rewrite equation 246,
% 113.18/113.55 lhs with equations [255]
% 113.18/113.55 rhs with equations [].
% 113.18/113.55
% 113.18/113.55 273: multiply(X48, inverse(X48)) = multiply(X52, inverse(X52)).
% 113.18/113.55 Proof: Rewrite equation 225,
% 113.18/113.55 lhs with equations []
% 113.18/113.55 rhs with equations [272,241].
% 113.18/113.55
% 113.18/113.55 326: multiply(X52, inverse(X52)) = multiply(inverse(X54), X54).
% 113.18/113.55 Proof: A critical pair between equations 273 and 264.
% 113.18/113.55
% 113.18/113.55 352: X24 = multiply(multiply(inverse(X57), X57), X24).
% 113.18/113.55 Proof: A critical pair between equations 272 and 326.
% 113.18/113.55
% 113.18/113.55 385: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 113.18/113.55 Proof: Rewrite lhs with equations [352]
% 113.18/113.55 rhs with equations [].
% 113.18/113.55
% 113.18/113.55 % SZS output end Proof
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