TSTP Solution File: GRP431-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP431-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n010.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 01:14:59 EDT 2023
% Result : Unsatisfiable 20.89s 21.12s
% Output : CNFRefutation 20.89s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP431-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 22:33:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.89/21.12 % SZS status Unsatisfiable
% 20.89/21.12 % SZS output start Proof
% 20.89/21.12 original problem:
% 20.89/21.12 axioms:
% 20.89/21.12 multiply(A, inverse(multiply(B, multiply(multiply(multiply(C, inverse(C)), inverse(multiply(D, B))), A)))) = D
% 20.89/21.12 goal:
% 20.89/21.12 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 20.89/21.12 To show the unsatisfiability of the original goal,
% 20.89/21.12 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 20.89/21.12 Here is an equational proof:
% 20.89/21.12 0: multiply(X0, inverse(multiply(X1, multiply(multiply(multiply(X2, inverse(X2)), inverse(multiply(X3, X1))), X0)))) = X3.
% 20.89/21.12 Proof: Axiom.
% 20.89/21.12
% 20.89/21.12 1: X5 = multiply(X0, inverse(multiply(multiply(multiply(multiply(X6, inverse(X6)), inverse(multiply(X7, X5))), multiply(X2, inverse(X2))), multiply(X7, X0)))).
% 20.89/21.12 Proof: A critical pair between equations 0 and 0.
% 20.89/21.12
% 20.89/21.12 2: X4 = multiply(X0, inverse(multiply(inverse(multiply(X5, multiply(multiply(multiply(X6, inverse(X6)), inverse(multiply(X7, X5))), X4))), multiply(multiply(multiply(X2, inverse(X2)), inverse(X7)), X0)))).
% 20.89/21.12 Proof: A critical pair between equations 0 and 0.
% 20.89/21.12
% 20.89/21.12 3: X3 = multiply(inverse(multiply(X5, multiply(multiply(multiply(X6, inverse(X6)), inverse(multiply(X7, X5))), multiply(multiply(X2, inverse(X2)), inverse(multiply(X3, X1)))))), inverse(multiply(X1, X7))).
% 20.89/21.12 Proof: A critical pair between equations 0 and 0.
% 20.89/21.12
% 20.89/21.12 4: multiply(multiply(multiply(X10, inverse(X10)), inverse(multiply(X11, X9))), multiply(X6, inverse(X6))) = multiply(X0, inverse(multiply(multiply(X11, multiply(X2, inverse(X2))), multiply(X9, X0)))).
% 20.89/21.12 Proof: A critical pair between equations 1 and 0.
% 20.89/21.12
% 20.89/21.12 6: X9 = multiply(inverse(multiply(X5, multiply(multiply(multiply(X6, inverse(X6)), inverse(multiply(X7, X5))), X11))), inverse(multiply(multiply(multiply(multiply(X10, inverse(X10)), inverse(multiply(X11, X9))), multiply(X2, inverse(X2))), X7))).
% 20.89/21.12 Proof: A critical pair between equations 3 and 0.
% 20.89/21.12
% 20.89/21.12 9: inverse(multiply(X9, multiply(multiply(multiply(X10, inverse(X10)), inverse(multiply(X11, X9))), X8))) = multiply(X0, inverse(multiply(multiply(multiply(multiply(X6, inverse(X6)), inverse(X11)), multiply(X2, inverse(X2))), multiply(X8, X0)))).
% 20.89/21.12 Proof: A critical pair between equations 1 and 0.
% 20.89/21.12
% 20.89/21.12 11: multiply(multiply(multiply(X9, inverse(X9)), inverse(multiply(X10, X11))), multiply(X12, inverse(X12))) = multiply(inverse(multiply(X5, multiply(multiply(multiply(X6, inverse(X6)), inverse(multiply(X7, X5))), X11))), inverse(multiply(multiply(X10, multiply(X2, inverse(X2))), X7))).
% 20.89/21.12 Proof: A critical pair between equations 3 and 1.
% 20.89/21.12
% 20.89/21.12 18: X14 = multiply(X15, multiply(X16, inverse(multiply(multiply(multiply(multiply(X17, inverse(X17)), inverse(X14)), multiply(X18, inverse(X18))), multiply(X15, X16))))).
% 20.89/21.12 Proof: A critical pair between equations 0 and 9.
% 20.89/21.12
% 20.89/21.12 20: multiply(multiply(multiply(X9, inverse(X9)), inverse(multiply(multiply(multiply(X17, inverse(X17)), inverse(multiply(X16, X18))), X16))), multiply(X12, inverse(X12))) = X18.
% 20.89/21.12 Proof: A critical pair between equations 11 and 6.
% 20.89/21.12
% 20.89/21.12 21: X2 = multiply(inverse(multiply(X14, multiply(X16, inverse(multiply(multiply(X13, multiply(X17, inverse(X17))), multiply(X14, X16)))))), inverse(multiply(inverse(X2), X13))).
% 20.89/21.12 Proof: A critical pair between equations 3 and 4.
% 20.89/21.12
% 20.89/21.12 31: X20 = multiply(multiply(multiply(X9, inverse(X9)), inverse(inverse(X20))), multiply(X12, inverse(X12))).
% 20.89/21.12 Proof: A critical pair between equations 20 and 20.
% 20.89/21.12
% 20.89/21.12 33: X2 = multiply(inverse(X22), inverse(multiply(inverse(X2), multiply(multiply(X21, inverse(X21)), inverse(X22))))).
% 20.89/21.12 Proof: A critical pair between equations 21 and 18.
% 20.89/21.12
% 20.89/21.12 37: multiply(multiply(multiply(X20, inverse(X20)), inverse(multiply(X21, X22))), X21) = multiply(X15, multiply(X16, inverse(multiply(X22, multiply(X15, X16))))).
% 20.89/21.12 Proof: A critical pair between equations 18 and 20.
% 20.89/21.12
% 20.89/21.12 40: multiply(X15, multiply(X16, inverse(multiply(X24, multiply(X15, X16))))) = inverse(X24).
% 20.89/21.12 Proof: A critical pair between equations 37 and 20.
% 20.89/21.12
% 20.89/21.12 43: X24 = multiply(X24, inverse(multiply(X25, multiply(X26, multiply(X27, inverse(multiply(X25, multiply(X26, X27)))))))).
% 20.89/21.12 Proof: A critical pair between equations 0 and 37.
% 20.89/21.12
% 20.89/21.12 44: multiply(X24, multiply(multiply(multiply(X25, inverse(X25)), inverse(multiply(multiply(X28, inverse(X28)), X24))), X27)) = X27.
% 20.89/21.12 Proof: A critical pair between equations 33 and 2.
% 20.89/21.12
% 20.89/21.12 45: multiply(multiply(multiply(X20, inverse(X20)), inverse(multiply(X21, inverse(X24)))), X21) = multiply(multiply(X25, inverse(X25)), X24).
% 20.89/21.12 Proof: A critical pair between equations 37 and 33.
% 20.89/21.12
% 20.89/21.12 52: X24 = multiply(X24, inverse(multiply(X25, inverse(X25)))).
% 20.89/21.12 Proof: Rewrite equation 43,
% 20.89/21.12 lhs with equations []
% 20.89/21.12 rhs with equations [40].
% 20.89/21.12
% 20.89/21.12 53: X2 = multiply(inverse(inverse(multiply(X13, multiply(X17, inverse(X17))))), inverse(multiply(inverse(X2), X13))).
% 20.89/21.12 Proof: Rewrite equation 21,
% 20.89/21.12 lhs with equations []
% 20.89/21.12 rhs with equations [40].
% 20.89/21.12
% 20.89/21.12 55: X14 = inverse(multiply(multiply(multiply(X17, inverse(X17)), inverse(X14)), multiply(X18, inverse(X18)))).
% 20.89/21.12 Proof: Rewrite equation 18,
% 20.89/21.12 lhs with equations []
% 20.89/21.12 rhs with equations [40].
% 20.89/21.12
% 20.89/21.12 61: multiply(multiply(multiply(X20, inverse(X20)), inverse(multiply(X21, X22))), X21) = inverse(X22).
% 20.89/21.12 Proof: Rewrite equation 37,
% 20.89/21.12 lhs with equations []
% 20.89/21.12 rhs with equations [40].
% 20.89/21.12
% 20.89/21.12 62: multiply(X33, inverse(X33)) = multiply(X31, inverse(X31)).
% 20.89/21.12 Proof: A critical pair between equations 44 and 20.
% 20.89/21.12
% 20.89/21.12 63: multiply(multiply(X25, inverse(X25)), X24) = inverse(inverse(X24)).
% 20.89/21.12 Proof: A critical pair between equations 45 and 20.
% 20.89/21.12
% 20.89/21.12 65: inverse(X22) = multiply(inverse(inverse(inverse(multiply(X21, X22)))), X21).
% 20.89/21.12 Proof: A critical pair between equations 61 and 61.
% 20.89/21.12
% 20.89/21.12 67: inverse(inverse(multiply(inverse(inverse(X28)), multiply(X27, inverse(X27))))) = X28.
% 20.89/21.12 Proof: A critical pair between equations 52 and 53.
% 20.89/21.12
% 20.89/21.12 69: X14 = inverse(multiply(inverse(inverse(inverse(X14))), multiply(X18, inverse(X18)))).
% 20.89/21.12 Proof: A critical pair between equations 55 and 61.
% 20.89/21.12
% 20.89/21.12 70: X20 = multiply(inverse(inverse(inverse(inverse(X20)))), multiply(X12, inverse(X12))).
% 20.89/21.12 Proof: A critical pair between equations 31 and 61.
% 20.89/21.12
% 20.89/21.12 90: multiply(X24, multiply(inverse(inverse(inverse(inverse(inverse(X24))))), X27)) = X27.
% 20.89/21.12 Proof: Rewrite equation 44,
% 20.89/21.12 lhs with equations [63,63]
% 20.89/21.12 rhs with equations [].
% 20.89/21.12
% 20.89/21.12 99: multiply(X29, inverse(X29)) = multiply(X24, inverse(X24)).
% 20.89/21.12 Proof: A critical pair between equations 90 and 70.
% 20.89/21.12
% 20.89/21.12 101: X2 = multiply(X29, inverse(multiply(inverse(X2), inverse(inverse(X29))))).
% 20.89/21.12 Proof: A critical pair between equations 53 and 67.
% 20.89/21.12
% 20.89/21.12 105: inverse(multiply(X30, inverse(X30))) = multiply(inverse(X29), inverse(inverse(X29))).
% 20.89/21.12 Proof: A critical pair between equations 65 and 67.
% 20.89/21.12
% 20.89/21.12 106: inverse(inverse(inverse(multiply(X25, inverse(X25))))) = multiply(X35, inverse(X35)).
% 20.89/21.12 Proof: A critical pair between equations 63 and 62.
% 20.89/21.12
% 20.89/21.12 107: inverse(inverse(inverse(multiply(X27, inverse(X27))))) = multiply(X25, inverse(X25)).
% 20.89/21.12 Proof: A critical pair between equations 63 and 52.
% 20.89/21.12
% 20.89/21.12 108: inverse(inverse(inverse(inverse(X25)))) = multiply(X26, multiply(inverse(X26), X25)).
% 20.89/21.12 Proof: A critical pair between equations 40 and 69.
% 20.89/21.12
% 20.89/21.12 111: multiply(X25, inverse(X25)) = multiply(X35, inverse(X35)).
% 20.89/21.12 Proof: Rewrite equation 106,
% 20.89/21.12 lhs with equations [107]
% 20.89/21.12 rhs with equations [].
% 20.89/21.12
% 20.89/21.12 112: inverse(multiply(X30, inverse(X30))) = multiply(X29, inverse(X29)).
% 20.89/21.12 Proof: Rewrite equation 105,
% 20.89/21.12 lhs with equations []
% 20.89/21.12 rhs with equations [99].
% 20.89/21.12
% 20.89/21.12 115: X2 = multiply(X2, multiply(X32, inverse(X32))).
% 20.89/21.12 Proof: A critical pair between equations 101 and 112.
% 20.89/21.12
% 20.89/21.12 127: X20 = inverse(inverse(inverse(inverse(X20)))).
% 20.89/21.12 Proof: Rewrite equation 70,
% 20.89/21.12 lhs with equations []
% 20.89/21.12 rhs with equations [115].
% 20.89/21.12
% 20.89/21.12 143: X25 = multiply(X26, multiply(inverse(X26), X25)).
% 20.89/21.12 Proof: Rewrite equation 108,
% 20.89/21.12 lhs with equations [127]
% 20.89/21.12 rhs with equations [].
% 20.89/21.12
% 20.89/21.12 152: X33 = inverse(inverse(X33)).
% 20.89/21.12 Proof: A critical pair between equations 115 and 143.
% 20.89/21.12
% 20.89/21.12 163: X27 = multiply(inverse(inverse(multiply(X27, X28))), inverse(X28)).
% 20.89/21.12 Proof: A critical pair between equations 143 and 65.
% 20.89/21.12
% 20.89/21.12 164: X27 = multiply(multiply(X27, X28), inverse(X28)).
% 20.89/21.12 Proof: Rewrite equation 163,
% 20.89/21.12 lhs with equations []
% 20.89/21.12 rhs with equations [152].
% 20.89/21.12
% 20.89/21.12 191: X27 = multiply(multiply(X27, inverse(X34)), X34).
% 20.89/21.12 Proof: A critical pair between equations 164 and 152.
% 20.89/21.12
% 20.89/21.12 198: multiply(X35, inverse(X35)) = multiply(inverse(X36), X36).
% 20.89/21.12 Proof: A critical pair between equations 111 and 152.
% 20.89/21.12
% 20.89/21.12 205: X37 = multiply(multiply(inverse(X38), X38), X37).
% 20.89/21.12 Proof: A critical pair between equations 191 and 198.
% 20.89/21.12
% 20.89/21.12 221: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 20.89/21.12 Proof: Rewrite lhs with equations [205]
% 20.89/21.12 rhs with equations [].
% 20.89/21.12
% 20.89/21.12 % SZS output end Proof
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