TSTP Solution File: GRP554-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP554-1 : 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 01:15:20 EDT 2023
% Result : Unsatisfiable 1.06s 1.43s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP554-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % 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 20:57:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.06/1.43 % SZS status Unsatisfiable
% 1.06/1.43 % SZS output start Proof
% 1.06/1.43 original problem:
% 1.06/1.43 axioms:
% 1.06/1.43 divide(divide(A, inverse(divide(B, divide(A, C)))), C) = B
% 1.06/1.43 multiply(A, B) = divide(A, inverse(B))
% 1.06/1.43 goal:
% 1.06/1.43 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 1.06/1.43 To show the unsatisfiability of the original goal,
% 1.06/1.43 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.06/1.43 Here is an equational proof:
% 1.06/1.43 0: divide(divide(X0, inverse(divide(X1, divide(X0, X2)))), X2) = X1.
% 1.06/1.43 Proof: Axiom.
% 1.06/1.43
% 1.06/1.43 1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.06/1.43 Proof: Axiom.
% 1.06/1.43
% 1.06/1.43 2: X1 = divide(divide(divide(X3, inverse(divide(X4, divide(X3, X5)))), inverse(divide(X1, X4))), X5).
% 1.06/1.43 Proof: A critical pair between equations 0 and 0.
% 1.06/1.43
% 1.06/1.43 3: divide(X3, inverse(divide(X4, divide(X3, divide(X0, X2))))) = divide(divide(X0, inverse(X4)), X2).
% 1.06/1.43 Proof: A critical pair between equations 0 and 0.
% 1.06/1.43
% 1.06/1.43 4: X1 = divide(multiply(multiply(X3, divide(X4, divide(X3, X5))), divide(X1, X4)), X5).
% 1.06/1.43 Proof: Rewrite equation 2,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1,1].
% 1.06/1.43
% 1.06/1.43 5: divide(multiply(X0, divide(X1, divide(X0, X2))), X2) = X1.
% 1.06/1.43 Proof: Rewrite equation 0,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 6: multiply(X3, divide(X4, divide(X3, divide(X0, X2)))) = divide(multiply(X0, X4), X2).
% 1.06/1.43 Proof: Rewrite equation 3,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 7: X6 = divide(divide(multiply(X7, X6), X8), divide(X7, X8)).
% 1.06/1.43 Proof: A critical pair between equations 5 and 6.
% 1.06/1.43
% 1.06/1.43 9: X1 = divide(multiply(X3, divide(X1, multiply(X3, X4))), inverse(X4)).
% 1.06/1.43 Proof: A critical pair between equations 5 and 1.
% 1.06/1.43
% 1.06/1.43 14: X6 = divide(multiply(multiply(X3, divide(inverse(X7), divide(X3, X5))), multiply(X6, X7)), X5).
% 1.06/1.43 Proof: A critical pair between equations 4 and 1.
% 1.06/1.43
% 1.06/1.43 16: X1 = multiply(multiply(multiply(X3, divide(X4, divide(X3, inverse(X7)))), divide(X1, X4)), X7).
% 1.06/1.43 Proof: A critical pair between equations 4 and 1.
% 1.06/1.43
% 1.06/1.43 18: divide(multiply(multiply(X5, divide(X6, divide(X5, X7))), X4), X7) = multiply(X3, divide(X4, divide(X3, X6))).
% 1.06/1.43 Proof: A critical pair between equations 6 and 5.
% 1.06/1.43
% 1.06/1.43 20: X1 = divide(divide(divide(X3, inverse(divide(X4, divide(X3, inverse(X7))))), inverse(divide(X1, X4))), inverse(X7)).
% 1.06/1.43 Proof: Rewrite equation 16,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1,1,1].
% 1.06/1.43
% 1.06/1.43 21: X6 = divide(divide(divide(X3, inverse(divide(inverse(X7), divide(X3, X5)))), inverse(divide(X6, inverse(X7)))), X5).
% 1.06/1.43 Proof: Rewrite equation 14,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1,1,1].
% 1.06/1.43
% 1.06/1.43 24: X1 = divide(divide(X3, inverse(divide(X1, divide(X3, inverse(X4))))), inverse(X4)).
% 1.06/1.43 Proof: Rewrite equation 9,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1,1].
% 1.06/1.43
% 1.06/1.43 25: X6 = divide(divide(divide(X7, inverse(X6)), X8), divide(X7, X8)).
% 1.06/1.43 Proof: Rewrite equation 7,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 26: divide(divide(X0, inverse(divide(X1, divide(X0, X2)))), X2) = X1.
% 1.06/1.43 Proof: Rewrite equation 5,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 27: X1 = divide(divide(divide(X3, inverse(divide(X4, divide(X3, X5)))), inverse(divide(X1, X4))), X5).
% 1.06/1.43 Proof: Rewrite equation 4,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1,1].
% 1.06/1.43
% 1.06/1.43 28: divide(divide(divide(X5, inverse(divide(X6, divide(X5, X7)))), inverse(X4)), X7) = divide(X3, inverse(divide(X4, divide(X3, X6)))).
% 1.06/1.43 Proof: Rewrite equation 18,
% 1.06/1.43 lhs with equations [1,1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 31: divide(X3, inverse(divide(X4, divide(X3, divide(X0, X2))))) = divide(divide(X0, inverse(X4)), X2).
% 1.06/1.43 Proof: Rewrite equation 6,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 32: X1 = divide(X9, inverse(divide(X1, X9))).
% 1.06/1.43 Proof: A critical pair between equations 20 and 24.
% 1.06/1.43
% 1.06/1.43 33: X6 = divide(inverse(X7), inverse(divide(X6, inverse(X7)))).
% 1.06/1.43 Proof: A critical pair between equations 21 and 24.
% 1.06/1.43
% 1.06/1.43 34: divide(X3, inverse(divide(divide(X11, X9), divide(X3, X9)))) = X11.
% 1.06/1.43 Proof: A critical pair between equations 28 and 20.
% 1.06/1.43
% 1.06/1.43 35: divide(X10, divide(X9, divide(X9, inverse(divide(X12, X10))))) = X12.
% 1.06/1.43 Proof: A critical pair between equations 25 and 27.
% 1.06/1.43
% 1.06/1.43 36: divide(X3, inverse(divide(X10, divide(X3, X9)))) = divide(X9, inverse(X10)).
% 1.06/1.43 Proof: A critical pair between equations 28 and 24.
% 1.06/1.43
% 1.06/1.43 50: divide(X10, divide(X9, multiply(X9, divide(X12, X10)))) = X12.
% 1.06/1.43 Proof: Rewrite equation 35,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 51: multiply(X3, divide(divide(X11, X9), divide(X3, X9))) = X11.
% 1.06/1.43 Proof: Rewrite equation 34,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 52: X6 = multiply(inverse(X7), multiply(X6, X7)).
% 1.06/1.43 Proof: Rewrite equation 33,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1,1].
% 1.06/1.43
% 1.06/1.43 53: X1 = multiply(X9, divide(X1, X9)).
% 1.06/1.43 Proof: Rewrite equation 32,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 55: divide(multiply(X0, divide(X1, divide(X0, X2))), X2) = X1.
% 1.06/1.43 Proof: Rewrite equation 26,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 56: X6 = divide(divide(multiply(X7, X6), X8), divide(X7, X8)).
% 1.06/1.43 Proof: Rewrite equation 25,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 62: multiply(X3, divide(X10, divide(X3, X9))) = multiply(X9, X10).
% 1.06/1.43 Proof: Rewrite equation 36,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 63: multiply(divide(X0, X2), X4) = divide(multiply(X0, X4), X2).
% 1.06/1.43 Proof: Rewrite equation 31,
% 1.06/1.43 lhs with equations [1,62]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 64: multiply(multiply(divide(X7, X7), X4), X6) = multiply(X6, X4).
% 1.06/1.43 Proof: Rewrite equation 28,
% 1.06/1.43 lhs with equations [1,62,63,1,63,63]
% 1.06/1.43 rhs with equations [1,62].
% 1.06/1.43
% 1.06/1.43 65: X14 = divide(X13, divide(X13, X14)).
% 1.06/1.43 Proof: A critical pair between equations 50 and 53.
% 1.06/1.43
% 1.06/1.43 66: X12 = divide(multiply(X13, X12), X13).
% 1.06/1.43 Proof: A critical pair between equations 55 and 62.
% 1.06/1.43
% 1.06/1.43 67: X10 = multiply(inverse(divide(X11, X10)), X11).
% 1.06/1.43 Proof: A critical pair between equations 52 and 53.
% 1.06/1.43
% 1.06/1.43 71: multiply(X6, divide(X11, divide(X7, X7))) = multiply(X11, X6).
% 1.06/1.43 Proof: A critical pair between equations 64 and 53.
% 1.06/1.43
% 1.06/1.43 81: X10 = divide(inverse(divide(X11, X10)), inverse(X11)).
% 1.06/1.43 Proof: Rewrite equation 67,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 82: X12 = divide(divide(X13, inverse(X12)), X13).
% 1.06/1.43 Proof: Rewrite equation 66,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 83: divide(divide(X0, X2), inverse(X4)) = divide(divide(X0, inverse(X4)), X2).
% 1.06/1.43 Proof: Rewrite equation 63,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 88: X6 = divide(divide(divide(X7, inverse(X6)), X8), divide(X7, X8)).
% 1.06/1.43 Proof: Rewrite equation 56,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 91: X1 = divide(X9, inverse(divide(X1, X9))).
% 1.06/1.43 Proof: Rewrite equation 53,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 92: divide(X3, inverse(divide(divide(X11, X9), divide(X3, X9)))) = X11.
% 1.06/1.43 Proof: Rewrite equation 51,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 98: divide(X6, inverse(divide(X11, divide(X7, X7)))) = divide(X11, inverse(X6)).
% 1.06/1.43 Proof: Rewrite equation 71,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 99: divide(X3, inverse(divide(X10, divide(X3, X9)))) = divide(X9, inverse(X10)).
% 1.06/1.43 Proof: Rewrite equation 62,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 103: X15 = divide(X15, divide(X14, X14)).
% 1.06/1.43 Proof: A critical pair between equations 88 and 82.
% 1.06/1.43
% 1.06/1.43 104: divide(divide(X14, X14), inverse(X15)) = X15.
% 1.06/1.43 Proof: A critical pair between equations 83 and 82.
% 1.06/1.43
% 1.06/1.43 106: divide(divide(X13, X14), inverse(X14)) = X13.
% 1.06/1.43 Proof: A critical pair between equations 98 and 92.
% 1.06/1.43
% 1.06/1.43 108: inverse(divide(X16, X15)) = divide(X15, X16).
% 1.06/1.43 Proof: A critical pair between equations 65 and 91.
% 1.06/1.43
% 1.06/1.43 109: divide(X13, inverse(X14)) = divide(X14, inverse(X13)).
% 1.06/1.43 Proof: A critical pair between equations 98 and 99.
% 1.06/1.43
% 1.06/1.43 113: inverse(X15) = divide(inverse(divide(X15, X16)), X16).
% 1.06/1.43 Proof: A critical pair between equations 65 and 81.
% 1.06/1.43
% 1.06/1.43 114: inverse(X15) = divide(divide(X16, X15), X16).
% 1.06/1.43 Proof: Rewrite equation 113,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [108].
% 1.06/1.43
% 1.06/1.43 117: multiply(divide(X13, X14), X14) = X13.
% 1.06/1.43 Proof: Rewrite equation 106,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 119: multiply(divide(X14, X14), X15) = X15.
% 1.06/1.43 Proof: Rewrite equation 104,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 138: multiply(X13, X14) = multiply(X14, X13).
% 1.06/1.43 Proof: Rewrite equation 109,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 142: multiply(divide(X0, X2), X4) = divide(multiply(X0, X4), X2).
% 1.06/1.43 Proof: Rewrite equation 83,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 145: inverse(X15) = divide(divide(X18, X18), X15).
% 1.06/1.43 Proof: A critical pair between equations 114 and 103.
% 1.06/1.43
% 1.06/1.43 150: divide(X17, X18) = multiply(inverse(X18), X17).
% 1.06/1.43 Proof: A critical pair between equations 117 and 114.
% 1.06/1.43
% 1.06/1.43 154: X15 = multiply(multiply(inverse(X17), X17), X15).
% 1.06/1.43 Proof: A critical pair between equations 119 and 1.
% 1.06/1.43
% 1.06/1.43 155: X15 = inverse(inverse(X15)).
% 1.06/1.43 Proof: Rewrite equation 154,
% 1.06/1.43 lhs with equations []
% 1.06/1.43 rhs with equations [150,142,1,114].
% 1.06/1.43
% 1.06/1.43 182: divide(X13, inverse(X14)) = divide(X14, inverse(X13)).
% 1.06/1.43 Proof: Rewrite equation 138,
% 1.06/1.43 lhs with equations [1]
% 1.06/1.43 rhs with equations [1].
% 1.06/1.43
% 1.06/1.43 183: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 1.06/1.43 Proof: Rewrite lhs with equations [1,182,155,1,145,155]
% 1.06/1.43 rhs with equations [].
% 1.06/1.43
% 1.06/1.43 % SZS output end Proof
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