TSTP Solution File: GRP470-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP470-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n002.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 01:15:05 EDT 2023
% Result : Unsatisfiable 69.36s 69.78s
% Output : CNFRefutation 69.36s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP470-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n002.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 20:02:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 69.36/69.78 % SZS status Unsatisfiable
% 69.36/69.78 % SZS output start Proof
% 69.36/69.78 original problem:
% 69.36/69.78 axioms:
% 69.36/69.78 divide(inverse(divide(A, divide(B, divide(C, D)))), divide(divide(D, C), A)) = B
% 69.36/69.78 multiply(A, B) = divide(A, inverse(B))
% 69.36/69.78 goal:
% 69.36/69.78 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 69.36/69.78 To show the unsatisfiability of the original goal,
% 69.36/69.78 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 69.36/69.78 Here is an equational proof:
% 69.36/69.78 0: divide(inverse(divide(X0, divide(X1, divide(X2, X3)))), divide(divide(X3, X2), X0)) = X1.
% 69.36/69.78 Proof: Axiom.
% 69.36/69.78
% 69.36/69.78 1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 69.36/69.78 Proof: Axiom.
% 69.36/69.78
% 69.36/69.78 2: inverse(divide(X4, divide(X5, divide(X6, X7)))) = divide(inverse(divide(X0, X5)), divide(divide(X4, divide(X7, X6)), X0)).
% 69.36/69.78 Proof: A critical pair between equations 0 and 0.
% 69.36/69.78
% 69.36/69.78 3: divide(X7, X6) = divide(inverse(X5), divide(divide(X3, X2), inverse(divide(divide(X2, X3), divide(X5, divide(X6, X7)))))).
% 69.36/69.78 Proof: A critical pair between equations 0 and 0.
% 69.36/69.78
% 69.36/69.78 4: X1 = divide(inverse(divide(X0, divide(X1, divide(divide(divide(X7, X6), X4), inverse(divide(X4, divide(X5, divide(X6, X7)))))))), divide(X5, X0)).
% 69.36/69.78 Proof: A critical pair between equations 0 and 0.
% 69.36/69.78
% 69.36/69.78 6: X1 = divide(divide(inverse(divide(X0, X1)), divide(divide(X0, X5), X0)), divide(X5, X0)).
% 69.36/69.78 Proof: Rewrite equation 4,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [2,0].
% 69.36/69.78
% 69.36/69.78 11: divide(inverse(divide(X0, divide(inverse(divide(X8, X9)), divide(divide(X8, X10), X8)))), divide(divide(X4, divide(X8, X10)), X0)) = inverse(divide(X4, X9)).
% 69.36/69.78 Proof: A critical pair between equations 2 and 6.
% 69.36/69.78
% 69.36/69.78 14: divide(X9, divide(X10, X11)) = divide(divide(divide(inverse(divide(X12, X9)), divide(divide(X8, divide(X11, X10)), X12)), divide(divide(X8, X5), X8)), divide(X5, X8)).
% 69.36/69.78 Proof: A critical pair between equations 6 and 2.
% 69.36/69.78
% 69.36/69.78 19: divide(divide(inverse(divide(X0, inverse(divide(X8, X9)))), divide(divide(X0, divide(X8, divide(X8, X10))), X0)), divide(divide(X4, divide(X8, X10)), X0)) = inverse(divide(X4, X9)).
% 69.36/69.78 Proof: Rewrite equation 11,
% 69.36/69.78 lhs with equations [2]
% 69.36/69.78 rhs with equations [].
% 69.36/69.78
% 69.36/69.78 23: divide(inverse(divide(X14, X15)), divide(divide(X14, X16), X14)) = divide(inverse(divide(X17, X15)), divide(divide(X14, X16), X17)).
% 69.36/69.78 Proof: A critical pair between equations 14 and 19.
% 69.36/69.78
% 69.36/69.78 41: divide(X7, X6) = divide(inverse(X5), multiply(divide(X3, X2), divide(divide(X2, X3), divide(X5, divide(X6, X7))))).
% 69.36/69.78 Proof: Rewrite equation 3,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [1].
% 69.36/69.78
% 69.36/69.78 43: X19 = divide(divide(inverse(divide(X21, X19)), divide(divide(X18, X20), X21)), divide(X20, X18)).
% 69.36/69.78 Proof: A critical pair between equations 6 and 23.
% 69.36/69.78
% 69.36/69.78 44: X9 = divide(inverse(divide(X10, divide(X9, divide(X12, X11)))), divide(divide(X11, X12), X10)).
% 69.36/69.78 Proof: A critical pair between equations 6 and 2.
% 69.36/69.78
% 69.36/69.78 61: divide(X7, X6) = divide(inverse(X5), divide(divide(X3, X2), inverse(divide(divide(X2, X3), divide(X5, divide(X6, X7)))))).
% 69.36/69.78 Proof: Rewrite equation 41,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [1].
% 69.36/69.78
% 69.36/69.78 71: X25 = divide(inverse(X23), divide(divide(X11, X12), divide(inverse(divide(X22, X23)), divide(divide(divide(X12, X11), X25), X22)))).
% 69.36/69.78 Proof: A critical pair between equations 44 and 43.
% 69.36/69.78
% 69.36/69.78 72: X19 = divide(divide(inverse(divide(divide(X25, X24), X19)), X23), divide(divide(divide(X24, X25), X22), inverse(divide(X22, X23)))).
% 69.36/69.78 Proof: A critical pair between equations 43 and 43.
% 69.36/69.78
% 69.36/69.78 74: divide(X7, X6) = divide(inverse(X25), divide(divide(divide(divide(divide(X6, X7), X25), X22), inverse(divide(X22, X23))), inverse(X23))).
% 69.36/69.78 Proof: A critical pair between equations 61 and 43.
% 69.36/69.78
% 69.36/69.78 75: divide(divide(X14, divide(divide(X11, X10), X16)), divide(X10, X11)) = divide(divide(X14, divide(divide(X16, X5), X16)), divide(X5, X16)).
% 69.36/69.78 Proof: A critical pair between equations 14 and 44.
% 69.36/69.78
% 69.36/69.78 76: divide(X7, X6) = divide(inverse(X25), multiply(multiply(divide(divide(divide(X6, X7), X25), X22), divide(X22, X23)), X23)).
% 69.36/69.78 Proof: Rewrite equation 74,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [1,1].
% 69.36/69.78
% 69.36/69.78 77: X19 = divide(divide(inverse(divide(divide(X25, X24), X19)), X23), multiply(divide(divide(X24, X25), X22), divide(X22, X23))).
% 69.36/69.78 Proof: Rewrite equation 72,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [1].
% 69.36/69.78
% 69.36/69.78 111: X19 = divide(divide(inverse(divide(divide(X25, X24), X19)), X23), divide(divide(divide(X24, X25), X22), inverse(divide(X22, X23)))).
% 69.36/69.78 Proof: Rewrite equation 77,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [1].
% 69.36/69.78
% 69.36/69.78 112: divide(X7, X6) = divide(inverse(X25), divide(divide(divide(divide(divide(X6, X7), X25), X22), inverse(divide(X22, X23))), inverse(X23))).
% 69.36/69.78 Proof: Rewrite equation 76,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [1,1].
% 69.36/69.78
% 69.36/69.78 129: inverse(divide(X29, X30)) = divide(inverse(X23), divide(divide(X29, divide(divide(X27, X28), divide(inverse(X30), X23))), divide(X28, X27))).
% 69.36/69.78 Proof: A critical pair between equations 71 and 112.
% 69.36/69.78
% 69.36/69.78 143: inverse(divide(inverse(divide(divide(inverse(X30), X23), X32)), X30)) = divide(inverse(X23), X32).
% 69.36/69.78 Proof: A critical pair between equations 129 and 43.
% 69.36/69.78
% 69.36/69.78 145: X19 = divide(inverse(divide(X32, X35)), divide(divide(divide(X33, X34), divide(inverse(X35), divide(divide(X34, X33), X19))), X32)).
% 69.36/69.78 Proof: A critical pair between equations 43 and 129.
% 69.36/69.78
% 69.36/69.78 146: inverse(divide(inverse(X31), divide(X34, X31))) = divide(inverse(divide(divide(divide(X33, X32), X35), X34)), divide(X35, divide(X33, X32))).
% 69.36/69.78 Proof: A critical pair between equations 129 and 71.
% 69.36/69.78
% 69.36/69.78 156: X37 = divide(X40, divide(divide(inverse(X37), divide(divide(X39, X38), X40)), divide(X38, X39))).
% 69.36/69.78 Proof: A critical pair between equations 43 and 145.
% 69.36/69.78
% 69.36/69.78 157: divide(inverse(divide(divide(X35, X36), X33)), divide(X36, X35)) = inverse(divide(inverse(X34), divide(X33, X34))).
% 69.36/69.78 Proof: A critical pair between equations 143 and 43.
% 69.36/69.78
% 69.36/69.78 158: X33 = divide(divide(divide(inverse(X34), X35), divide(divide(X18, X20), inverse(divide(divide(inverse(X33), X34), X35)))), divide(X20, X18)).
% 69.36/69.78 Proof: A critical pair between equations 43 and 143.
% 69.36/69.78
% 69.36/69.78 159: divide(inverse(X36), divide(divide(divide(X34, X33), X37), inverse(divide(X37, X36)))) = inverse(divide(inverse(X35), divide(divide(X33, X34), X35))).
% 69.36/69.78 Proof: A critical pair between equations 143 and 111.
% 69.36/69.78
% 69.36/69.78 169: inverse(divide(inverse(X34), divide(X40, X34))) = inverse(divide(inverse(X41), divide(X40, X41))).
% 69.36/69.78 Proof: A critical pair between equations 157 and 146.
% 69.36/69.78
% 69.36/69.78 171: X37 = divide(divide(X44, X43), divide(X42, divide(divide(divide(X43, X44), inverse(X37)), inverse(X42)))).
% 69.36/69.78 Proof: A critical pair between equations 156 and 156.
% 69.36/69.78
% 69.36/69.78 172: X19 = divide(X42, divide(divide(divide(X43, X44), inverse(divide(divide(X44, X43), X19))), inverse(X42))).
% 69.36/69.78 Proof: A critical pair between equations 43 and 156.
% 69.36/69.78
% 69.36/69.78 180: X39 = divide(inverse(divide(inverse(X40), divide(X39, X40))), divide(divide(divide(X38, X37), X22), inverse(divide(X22, divide(X38, X37))))).
% 69.36/69.78 Proof: A critical pair between equations 111 and 157.
% 69.36/69.78
% 69.36/69.78 184: inverse(divide(inverse(X35), divide(divide(divide(X42, X41), inverse(X41)), X35))) = X42.
% 69.36/69.78 Proof: A critical pair between equations 159 and 180.
% 69.36/69.78
% 69.36/69.78 185: divide(X48, inverse(X45)) = divide(divide(X48, divide(divide(X46, X47), X45)), divide(X47, X46)).
% 69.36/69.78 Proof: A critical pair between equations 171 and 112.
% 69.36/69.78
% 69.36/69.78 188: inverse(divide(inverse(X41), divide(X43, X41))) = divide(inverse(divide(divide(X44, X45), X43)), divide(X45, X44)).
% 69.36/69.78 Proof: A critical pair between equations 169 and 157.
% 69.36/69.78
% 69.36/69.78 189: X37 = divide(inverse(inverse(X37)), divide(X48, divide(inverse(divide(divide(X47, X46), X48)), divide(X46, X47)))).
% 69.36/69.78 Proof: A critical pair between equations 156 and 172.
% 69.36/69.78
% 69.36/69.78 199: X19 = divide(inverse(divide(X21, X19)), inverse(X21)).
% 69.36/69.78 Proof: Rewrite equation 43,
% 69.36/69.78 lhs with equations []
% 69.36/69.78 rhs with equations [185].
% 69.36/69.78
% 69.36/69.78 203: inverse(X22) = divide(inverse(X23), inverse(inverse(divide(X22, X23)))).
% 69.36/69.78 Proof: A critical pair between equations 199 and 199.
% 69.36/69.78
% 69.36/69.78 204: divide(divide(divide(X44, X45), inverse(X45)), X43) = divide(X44, inverse(inverse(X43))).
% 69.36/69.78 Proof: A critical pair between equations 199 and 184.
% 69.36/69.78
% 69.36/69.78 207: X37 = divide(inverse(inverse(X37)), divide(X51, inverse(divide(inverse(X52), divide(X51, X52))))).
% 69.36/69.78 Proof: A critical pair between equations 189 and 188.
% 69.36/69.78
% 69.36/69.78 211: divide(X49, inverse(X52)) = divide(divide(X49, divide(divide(X52, X53), X52)), divide(X53, X52)).
% 69.36/69.78 Proof: A critical pair between equations 185 and 75.
% 69.36/69.78
% 69.36/69.78 218: X46 = inverse(divide(inverse(X48), divide(X46, inverse(inverse(X48))))).
% 69.36/69.78 Proof: A critical pair between equations 184 and 204.
% 69.36/69.78
% 69.36/69.78 219: inverse(inverse(divide(X24, X25))) = divide(inverse(inverse(X24)), inverse(inverse(X25))).
% 69.36/69.78 Proof: A critical pair between equations 203 and 199.
% 69.36/69.78
% 69.36/69.78 221: X37 = divide(inverse(inverse(X37)), divide(divide(divide(X54, X55), inverse(X55)), X54)).
% 69.36/69.78 Proof: A critical pair between equations 207 and 184.
% 69.36/69.78
% 69.36/69.78 225: divide(divide(inverse(X54), X55), inverse(inverse(divide(divide(inverse(X58), X54), X55)))) = X58.
% 69.36/69.78 Proof: A critical pair between equations 211 and 158.
% 69.36/69.78
% 69.36/69.78 230: divide(divide(inverse(X54), X55), divide(divide(inverse(inverse(inverse(X58))), inverse(inverse(X54))), inverse(inverse(X55)))) = X58.
% 69.36/69.78 Proof: Rewrite equation 225,
% 69.36/69.78 lhs with equations [219,219]
% 69.36/69.78 rhs with equations [].
% 69.36/69.78
% 69.36/69.78 234: divide(divide(inverse(inverse(inverse(X56))), X58), inverse(X58)) = inverse(X56).
% 69.36/69.78 Proof: A critical pair between equations 218 and 221.
% 69.36/69.78
% 69.36/69.78 257: X59 = divide(divide(inverse(X54), inverse(X54)), inverse(X59)).
% 69.36/69.78 Proof: A critical pair between equations 230 and 234.
% 69.36/69.78
% 69.36/69.78 290: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 69.36/69.78 Proof: Rewrite lhs with equations [1,1,257]
% 69.36/69.78 rhs with equations [].
% 69.36/69.78
% 69.36/69.78 % SZS output end Proof
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