TSTP Solution File: GRP476-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP476-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n015.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 01:15:06 EDT 2023
% Result : Unsatisfiable 32.95s 33.23s
% Output : CNFRefutation 32.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP476-1 : TPTP v8.1.2. Released v2.6.0.
% 0.13/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n015.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 22:49:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 32.95/33.23 % SZS status Unsatisfiable
% 32.95/33.23 % SZS output start Proof
% 32.95/33.23 original problem:
% 32.95/33.23 axioms:
% 32.95/33.23 divide(inverse(divide(divide(divide(A, B), C), divide(D, C))), divide(B, A)) = D
% 32.95/33.23 multiply(A, B) = divide(A, inverse(B))
% 32.95/33.23 goal:
% 32.95/33.23 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 32.95/33.23 To show the unsatisfiability of the original goal,
% 32.95/33.23 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 32.95/33.23 Here is an equational proof:
% 32.95/33.23 0: divide(inverse(divide(divide(divide(X0, X1), X2), divide(X3, X2))), divide(X1, X0)) = X3.
% 32.95/33.23 Proof: Axiom.
% 32.95/33.23
% 32.95/33.23 1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 32.95/33.23 Proof: Axiom.
% 32.95/33.23
% 32.95/33.23 2: X3 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X2), divide(X3, X2))), X7).
% 32.95/33.23 Proof: A critical pair between equations 0 and 0.
% 32.95/33.23
% 32.95/33.23 3: inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))) = divide(inverse(divide(divide(divide(X0, X1), divide(X5, X4)), X7)), divide(X1, X0)).
% 32.95/33.23 Proof: A critical pair between equations 0 and 0.
% 32.95/33.23
% 32.95/33.23 4: X3 = divide(inverse(divide(divide(X7, X2), divide(X3, X2))), divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))))).
% 32.95/33.23 Proof: A critical pair between equations 0 and 0.
% 32.95/33.23
% 32.95/33.23 5: inverse(divide(divide(divide(X4, X5), X6), divide(divide(X11, divide(X5, X4)), X6))) = X11.
% 32.95/33.23 Proof: A critical pair between equations 3 and 0.
% 32.95/33.23
% 32.95/33.23 9: X11 = divide(divide(inverse(divide(divide(divide(X12, X13), divide(inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))), divide(X5, X4))), X11)), divide(X13, X12)), X7).
% 32.95/33.23 Proof: A critical pair between equations 2 and 3.
% 32.95/33.23
% 32.95/33.23 18: X11 = divide(divide(inverse(divide(divide(divide(X12, X13), X7), X11)), divide(X13, X12)), X7).
% 32.95/33.23 Proof: Rewrite equation 9,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [0].
% 32.95/33.23
% 32.95/33.23 19: X3 = divide(inverse(divide(divide(multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6))), X2), divide(X3, X2))), X7).
% 32.95/33.23 Proof: Rewrite equation 2,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 20: X3 = divide(inverse(divide(divide(X7, X2), divide(X3, X2))), multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6)))).
% 32.95/33.23 Proof: Rewrite equation 4,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 38: X3 = divide(inverse(divide(divide(X7, X2), divide(X3, X2))), divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))))).
% 32.95/33.23 Proof: Rewrite equation 20,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 39: X3 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X2), divide(X3, X2))), X7).
% 32.95/33.23 Proof: Rewrite equation 19,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 46: X3 = divide(inverse(divide(X17, divide(X3, X16))), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))).
% 32.95/33.23 Proof: A critical pair between equations 0 and 18.
% 32.95/33.23
% 32.95/33.23 48: X11 = inverse(divide(X17, divide(divide(X11, divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))), X16))).
% 32.95/33.23 Proof: A critical pair between equations 5 and 18.
% 32.95/33.23
% 32.95/33.23 50: divide(X15, divide(X13, X12)) = divide(X15, divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(divide(X12, X13), X6))))).
% 32.95/33.23 Proof: A critical pair between equations 38 and 5.
% 32.95/33.23
% 32.95/33.23 55: X3 = divide(inverse(divide(divide(X17, X2), divide(X3, X2))), divide(X16, divide(inverse(divide(divide(divide(X14, X15), X16), X17)), divide(X15, X14)))).
% 32.95/33.23 Proof: A critical pair between equations 0 and 18.
% 32.95/33.23
% 32.95/33.23 57: X11 = inverse(divide(divide(X17, X6), divide(divide(X11, divide(X16, divide(inverse(divide(divide(divide(X14, X15), X16), X17)), divide(X15, X14)))), X6))).
% 32.95/33.23 Proof: A critical pair between equations 5 and 18.
% 32.95/33.23
% 32.95/33.23 60: divide(X15, divide(X13, X12)) = divide(X15, multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(divide(X12, X13), X6)))).
% 32.95/33.23 Proof: Rewrite equation 50,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 62: X11 = inverse(divide(X17, divide(divide(X11, multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))), X16))).
% 32.95/33.23 Proof: Rewrite equation 48,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 63: X3 = divide(inverse(divide(X17, divide(X3, X16))), multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))).
% 32.95/33.23 Proof: Rewrite equation 46,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 64: X3 = divide(inverse(divide(divide(multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6))), X2), divide(X3, X2))), X7).
% 32.95/33.23 Proof: Rewrite equation 39,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 71: inverse(divide(divide(X18, X19), divide(X20, X19))) = inverse(divide(divide(X18, X6), divide(X20, X6))).
% 32.95/33.23 Proof: A critical pair between equations 57 and 55.
% 32.95/33.23
% 32.95/33.23 84: X3 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X2), divide(X3, X2))), X7).
% 32.95/33.23 Proof: Rewrite equation 64,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 85: X3 = divide(inverse(divide(X17, divide(X3, X16))), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))).
% 32.95/33.23 Proof: Rewrite equation 63,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 86: X11 = inverse(divide(X17, divide(divide(X11, divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))), X16))).
% 32.95/33.23 Proof: Rewrite equation 62,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 88: divide(X15, divide(X13, X12)) = divide(X15, divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(divide(X12, X13), X6))))).
% 32.95/33.23 Proof: Rewrite equation 60,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 97: inverse(divide(divide(inverse(divide(divide(divide(X21, X22), divide(X20, divide(X22, X21))), X24)), X19), divide(X20, X19))) = inverse(X24).
% 32.95/33.23 Proof: A critical pair between equations 71 and 18.
% 32.95/33.23
% 32.95/33.23 102: X17 = inverse(divide(divide(divide(X4, X5), inverse(divide(divide(divide(divide(X5, X4), X17), X19), divide(divide(X20, X21), X19)))), divide(X21, X20))).
% 32.95/33.23 Proof: A critical pair between equations 5 and 88.
% 32.95/33.23
% 32.95/33.23 110: X17 = inverse(divide(multiply(divide(X4, X5), divide(divide(divide(divide(X5, X4), X17), X19), divide(divide(X20, X21), X19))), divide(X21, X20))).
% 32.95/33.23 Proof: Rewrite equation 102,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 115: X11 = inverse(divide(X17, divide(divide(X11, multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))), X16))).
% 32.95/33.23 Proof: Rewrite equation 86,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 116: X3 = divide(inverse(divide(X17, divide(X3, X16))), multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))).
% 32.95/33.23 Proof: Rewrite equation 85,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 117: X3 = divide(inverse(divide(divide(multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6))), X2), divide(X3, X2))), X7).
% 32.95/33.23 Proof: Rewrite equation 84,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 137: X3 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X2), divide(X3, X2))), X7).
% 32.95/33.23 Proof: Rewrite equation 117,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 138: X3 = divide(inverse(divide(X17, divide(X3, X16))), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))).
% 32.95/33.23 Proof: Rewrite equation 116,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 139: X11 = inverse(divide(X17, divide(divide(X11, divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))), X16))).
% 32.95/33.23 Proof: Rewrite equation 115,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 144: X17 = inverse(divide(divide(divide(X4, X5), inverse(divide(divide(divide(divide(X5, X4), X17), X19), divide(divide(X20, X21), X19)))), divide(X21, X20))).
% 32.95/33.23 Proof: Rewrite equation 110,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [1].
% 32.95/33.23
% 32.95/33.23 154: inverse(divide(divide(X28, divide(X26, X25)), divide(X20, divide(X26, X25)))) = inverse(divide(divide(X28, X19), divide(X20, X19))).
% 32.95/33.23 Proof: A critical pair between equations 97 and 5.
% 32.95/33.23
% 32.95/33.23 155: divide(X27, X26) = divide(divide(X24, divide(X23, X22)), inverse(divide(divide(divide(divide(X23, X22), X24), X25), divide(divide(X26, X27), X25)))).
% 32.95/33.23 Proof: A critical pair between equations 18 and 144.
% 32.95/33.23
% 32.95/33.23 160: inverse(divide(divide(divide(inverse(divide(divide(divide(X21, X22), X23), X24)), divide(X22, X21)), X19), divide(X20, X19))) = inverse(divide(X24, divide(X20, X23))).
% 32.95/33.23 Proof: A critical pair between equations 71 and 18.
% 32.95/33.23
% 32.95/33.23 165: inverse(divide(divide(X29, X6), divide(X31, X6))) = inverse(divide(divide(X29, divide(X32, X33)), divide(X31, divide(X32, X33)))).
% 32.95/33.23 Proof: A critical pair between equations 71 and 154.
% 32.95/33.23
% 32.95/33.23 174: X19 = divide(inverse(X21), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X18), inverse(divide(divide(divide(X18, X19), X20), divide(X21, X20))))))).
% 32.95/33.23 Proof: A critical pair between equations 138 and 0.
% 32.95/33.23
% 32.95/33.23 180: divide(X14, X15) = divide(inverse(divide(X32, X33)), divide(divide(X15, X14), inverse(divide(X33, X32)))).
% 32.95/33.23 Proof: A critical pair between equations 174 and 155.
% 32.95/33.23
% 32.95/33.23 190: inverse(divide(divide(X34, divide(X32, X33)), divide(X36, divide(X32, X33)))) = inverse(divide(divide(X34, divide(X37, X38)), divide(X36, divide(X37, X38)))).
% 32.95/33.23 Proof: A critical pair between equations 165 and 154.
% 32.95/33.23
% 32.95/33.23 195: inverse(divide(divide(X39, divide(X37, X38)), divide(X42, divide(X37, X38)))) = inverse(divide(divide(X39, X43), divide(X42, X43))).
% 32.95/33.23 Proof: A critical pair between equations 190 and 154.
% 32.95/33.23
% 32.95/33.23 199: divide(divide(X35, X34), inverse(divide(divide(divide(X34, X35), inverse(divide(X33, X32))), X37))) = divide(inverse(divide(X32, X33)), X37).
% 32.95/33.23 Proof: A critical pair between equations 180 and 18.
% 32.95/33.23
% 32.95/33.23 202: X36 = inverse(divide(divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), inverse(divide(X35, X34))), inverse(divide(X34, X35))))), X36)).
% 32.95/33.23 Proof: A critical pair between equations 139 and 180.
% 32.95/33.23
% 32.95/33.23 207: X36 = inverse(divide(divide(inverse(divide(X34, X35)), inverse(divide(X34, X35))), X36)).
% 32.95/33.23 Proof: Rewrite equation 202,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [199].
% 32.95/33.23
% 32.95/33.23 209: inverse(divide(divide(X44, X43), divide(X47, X43))) = inverse(divide(divide(X44, X48), divide(X47, X48))).
% 32.95/33.23 Proof: A critical pair between equations 195 and 165.
% 32.95/33.23
% 32.95/33.23 217: X36 = inverse(divide(divide(X39, inverse(divide(divide(inverse(divide(X37, X38)), inverse(divide(X37, X38))), X39))), X36)).
% 32.95/33.23 Proof: A critical pair between equations 207 and 207.
% 32.95/33.23
% 32.95/33.23 221: X36 = inverse(divide(divide(X39, X39), X36)).
% 32.95/33.23 Proof: Rewrite equation 217,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [207].
% 32.95/33.23
% 32.95/33.23 227: inverse(divide(divide(X49, X43), divide(X47, X43))) = divide(X47, X49).
% 32.95/33.23 Proof: A critical pair between equations 209 and 221.
% 32.95/33.23
% 32.95/33.23 233: divide(X14, X15) = divide(X41, divide(divide(X15, X14), inverse(divide(X41, divide(X40, X40))))).
% 32.95/33.23 Proof: A critical pair between equations 180 and 221.
% 32.95/33.23
% 32.95/33.23 242: X3 = divide(divide(X3, divide(divide(X5, X4), divide(X7, divide(X4, X5)))), X7).
% 32.95/33.23 Proof: Rewrite equation 137,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [227,227].
% 32.95/33.23
% 32.95/33.23 245: X11 = divide(divide(X11, divide(X16, divide(inverse(divide(divide(divide(X14, X15), X16), X17)), divide(X15, X14)))), X17).
% 32.95/33.23 Proof: Rewrite equation 57,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [227].
% 32.95/33.23
% 32.95/33.23 246: X17 = inverse(divide(divide(divide(X4, X5), divide(divide(X20, X21), divide(divide(X5, X4), X17))), divide(X21, X20))).
% 32.95/33.23 Proof: Rewrite equation 144,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [227].
% 32.95/33.23
% 32.95/33.23 260: divide(X20, divide(inverse(divide(divide(divide(X21, X22), X23), X24)), divide(X22, X21))) = inverse(divide(X24, divide(X20, X23))).
% 32.95/33.23 Proof: Rewrite equation 160,
% 32.95/33.23 lhs with equations [227]
% 32.95/33.23 rhs with equations [].
% 32.95/33.23
% 32.95/33.23 261: divide(X5, X4) = inverse(divide(X4, X5)).
% 32.95/33.23 Proof: A critical pair between equations 246 and 242.
% 32.95/33.23
% 32.95/33.23 267: X11 = divide(divide(X11, inverse(divide(X29, divide(X28, X28)))), X29).
% 32.95/33.23 Proof: A critical pair between equations 245 and 260.
% 32.95/33.23
% 32.95/33.23 274: X11 = divide(divide(X11, divide(divide(X28, X28), X29)), X29).
% 32.95/33.23 Proof: Rewrite equation 267,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [261].
% 32.95/33.23
% 32.95/33.23 280: X36 = divide(X36, divide(X39, X39)).
% 32.95/33.23 Proof: Rewrite equation 221,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [261].
% 32.95/33.23
% 32.95/33.23 295: divide(X14, X15) = divide(X41, divide(divide(X15, X14), inverse(X41))).
% 32.95/33.23 Proof: Rewrite equation 233,
% 32.95/33.23 lhs with equations []
% 32.95/33.23 rhs with equations [280].
% 32.95/33.23
% 32.95/33.23 308: X42 = divide(divide(X44, X44), inverse(X42)).
% 32.95/33.23 Proof: A critical pair between equations 274 and 295.
% 32.95/33.23
% 32.95/33.23 322: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 32.95/33.23 Proof: Rewrite lhs with equations [1,1,308]
% 32.95/33.23 rhs with equations [].
% 32.95/33.23
% 32.95/33.23 % SZS output end Proof
%------------------------------------------------------------------------------