TSTP Solution File: GRP710-11 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n028.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 : 600s
% DateTime : Sat Jul 16 10:58:04 EDT 2022
% Result : Unsatisfiable 9.30s 9.41s
% Output : Proof 9.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n028.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 10:32:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.30/9.41 % SZS status Unsatisfiable
% 9.30/9.41 % SZS output start Proof
% 9.30/9.41 The input problem is unsatisfiable because
% 9.30/9.41
% 9.30/9.41 [1] the following set of Horn clauses is unsatisfiable:
% 9.30/9.41
% 9.30/9.41 mult(A, unit) = A
% 9.30/9.41 mult(unit, A) = A
% 9.30/9.41 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 9.30/9.41 mult(A, i(A)) = unit
% 9.30/9.41 mult(i(A), A) = unit
% 9.30/9.41 mult(X5, x4) = x3 ==> \bottom
% 9.30/9.41
% 9.30/9.41 This holds because
% 9.30/9.41
% 9.30/9.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.30/9.41
% 9.30/9.41 E:
% 9.30/9.41 f1(mult(X5, x4)) = true__
% 9.30/9.41 f1(x3) = false__
% 9.30/9.41 mult(A, i(A)) = unit
% 9.30/9.41 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 9.30/9.41 mult(A, unit) = A
% 9.30/9.41 mult(i(A), A) = unit
% 9.30/9.41 mult(unit, A) = A
% 9.30/9.41 G:
% 9.30/9.41 true__ = false__
% 9.30/9.41
% 9.30/9.41 This holds because
% 9.30/9.41
% 9.30/9.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.30/9.41
% 9.30/9.41
% 9.30/9.41 f1(Y0) -> true__
% 9.30/9.41 f1(i(mult(X0, mult(X0, mult(X0, mult(X0, x4)))))) -> true__
% 9.30/9.41 f1(i(mult(Y1, mult(Y1, i(x4))))) -> true__
% 9.30/9.41 f1(i(mult(Y1, mult(Y1, x4)))) -> true__
% 9.30/9.41 f1(i(mult(i(mult(x4, x4)), x4))) -> true__
% 9.30/9.41 f1(i(mult(i(x4), i(x4)))) -> true__
% 9.30/9.41 f1(i(mult(i(x4), mult(i(x4), i(x4))))) -> true__
% 9.30/9.41 f1(i(mult(mult(X0, x4), mult(X0, mult(x4, x4))))) -> true__
% 9.30/9.41 f1(i(mult(x4, mult(x4, mult(x4, x4))))) -> true__
% 9.30/9.41 f1(i(mult(x4, x4))) -> true__
% 9.30/9.41 f1(i(x4)) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, i(x4)))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, i(x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, x4))))))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(Y1, mult(Y1, x4))))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(i(x4), i(x4))))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, x4))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(Y1, mult(Y1, i(x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(Y1, mult(Y1, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(Y1, mult(Y1, x4))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(i(mult(x4, x4)), x4)))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(i(x4), i(x4))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(x4, mult(x4, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, mult(x4, x4)))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X0, x4))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, i(x4))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, mult(X1, x4))))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, mult(x4, x4))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, x4)))) -> true__
% 9.30/9.41 f1(mult(X0, mult(i(x4), i(x4)))) -> true__
% 9.30/9.41 f1(mult(X0, mult(i(x4), mult(i(x4), mult(i(x4), i(x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(mult(Y1, mult(Y1, i(x4))), mult(Y1, mult(Y1, i(x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(mult(Y1, mult(Y1, mult(x4, x4))), mult(Y1, mult(Y1, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(mult(Y1, mult(Y1, x4)), mult(Y1, mult(Y1, x4))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(mult(i(mult(x4, x4)), x4), mult(i(mult(x4, x4)), x4)))) -> true__
% 9.30/9.41 f1(mult(X0, mult(x4, mult(x4, mult(x4, mult(x4, mult(x4, mult(x4, mult(x4, x4))))))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(x4, mult(x4, mult(x4, x4))))) -> true__
% 9.30/9.41 f1(mult(X0, mult(x4, x4))) -> true__
% 9.30/9.41 f1(mult(X5, x4)) -> true__
% 9.30/9.41 f1(mult(Y0, i(mult(x4, x4)))) -> true__
% 9.30/9.41 f1(mult(Y0, i(x4))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(X0, mult(X0, mult(X0, mult(X0, i(x4))))))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(X0, mult(X0, mult(X0, mult(X0, x4)))))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(Y0, mult(X0, mult(X0, mult(X0, mult(X0, x4))))))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(Y0, mult(mult(X0, x4), mult(X0, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(i(mult(x4, x4)), x4))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(i(x4), mult(i(x4), i(x4))))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(mult(X0, i(x4)), mult(X0, mult(i(x4), i(x4)))))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(mult(X0, mult(x4, x4)), mult(X0, mult(x4, mult(x4, mult(x4, x4))))))) -> true__
% 9.30/9.41 f1(mult(Y0, mult(mult(X0, x4), mult(X0, mult(x4, x4))))) -> true__
% 9.30/9.41 f1(mult(i(mult(x4, x4)), mult(i(mult(x4, x4)), i(mult(x4, x4))))) -> true__
% 9.30/9.41 f1(mult(i(x4), i(x4))) -> true__
% 9.30/9.41 f1(mult(i(x4), mult(i(x4), i(x4)))) -> true__
% 9.30/9.41 f1(mult(mult(X0, i(x4)), mult(X0, mult(i(x4), i(x4))))) -> true__
% 9.30/9.41 f1(mult(mult(X0, mult(X0, x4)), mult(X0, mult(X0, mult(x4, x4))))) -> true__
% 9.30/9.41 f1(mult(mult(X0, mult(Y1, mult(Y1, x4))), mult(X0, mult(mult(Y1, mult(Y1, x4)), mult(Y1, mult(Y1, x4)))))) -> true__
% 9.30/9.41 f1(mult(mult(X0, mult(i(x4), i(x4))), mult(X0, mult(i(x4), mult(i(x4), mult(i(x4), i(x4))))))) -> true__
% 9.30/9.41 f1(mult(mult(X0, mult(x4, x4)), mult(X0, mult(x4, mult(x4, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(mult(X0, mult(x4, x4)), mult(mult(X0, x4), mult(x4, x4)))) -> true__
% 9.30/9.41 f1(mult(mult(X0, x4), mult(X0, mult(x4, x4)))) -> true__
% 9.30/9.41 f1(mult(mult(X0, x4), mult(mult(X0, x4), mult(mult(X0, x4), mult(X0, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(mult(mult(X0, x4), mult(x4, x4)), mult(X0, mult(x4, mult(x4, mult(x4, x4)))))) -> true__
% 9.30/9.41 f1(mult(x4, mult(x4, mult(x4, x4)))) -> true__
% 9.30/9.41 f1(unit) -> true__
% 9.30/9.41 f1(x3) -> false__
% 9.30/9.41 f1(x4) -> true__
% 9.30/9.41 i(i(X0)) -> X0
% 9.30/9.41 i(unit) -> unit
% 9.30/9.41 mult(A, i(A)) -> unit
% 9.30/9.41 mult(A, unit) -> A
% 9.30/9.41 mult(X0, mult(X0, mult(X0, i(mult(X0, mult(X0, X0)))))) -> unit
% 9.30/9.41 mult(X0, mult(X0, mult(i(mult(X0, X0)), mult(X0, mult(X0, Y1))))) -> mult(X0, mult(X0, Y1))
% 9.30/9.41 mult(X0, mult(i(X0), mult(X0, X1))) -> mult(X0, X1)
% 9.30/9.41 mult(Y0, i(mult(Y0, Y0))) -> i(Y0)
% 9.30/9.41 mult(Y0, mult(Y0, i(mult(Y0, mult(Y0, mult(Y0, Y0)))))) -> i(mult(Y0, Y0))
% 9.30/9.41 mult(Y0, mult(Y0, mult(Y0, mult(Y0, i(mult(Y0, mult(Y0, mult(Y0, Y0)))))))) -> unit
% 9.30/9.41 mult(Y0, mult(Y0, mult(i(mult(Y0, Y0)), i(mult(Y0, Y0))))) -> i(mult(Y0, Y0))
% 9.30/9.41 mult(Y0, mult(Y1, mult(Y1, i(mult(Y0, mult(Y1, mult(Y1, mult(Y0, mult(Y1, Y1))))))))) -> i(mult(Y0, mult(Y1, Y1)))
% 9.30/9.41 mult(Y0, mult(Y1, mult(Y1, i(mult(mult(Y0, Y1), Y1))))) -> unit
% 9.30/9.41 mult(Y0, mult(i(Y0), i(Y0))) -> i(Y0)
% 9.30/9.41 mult(Y0, mult(i(Y0), mult(i(Y0), Y2))) -> mult(i(Y0), Y2)
% 9.30/9.41 mult(Y0, mult(i(mult(Y0, Y0)), i(mult(Y0, Y0)))) -> mult(i(Y0), i(mult(Y0, Y0)))
% 9.30/9.41 mult(Y0, mult(i(mult(Y0, Y0)), mult(i(mult(Y0, Y0)), i(mult(i(Y0), i(mult(Y0, Y0))))))) -> unit
% 9.30/9.41 mult(Y0, mult(mult(Y0, i(mult(Y0, Y0))), mult(Y0, i(mult(Y0, Y0))))) -> mult(Y0, i(mult(Y0, Y0)))
% 9.30/9.41 mult(Y0, mult(mult(i(Y0), mult(Y0, X1)), mult(i(Y0), mult(Y0, X1)))) -> mult(mult(Y0, X1), mult(i(Y0), mult(Y0, X1)))
% 9.30/9.41 mult(Y1, mult(Y1, i(mult(Y1, Y1)))) -> unit
% 9.30/9.41 mult(i(A), A) -> unit
% 9.30/9.41 mult(i(X0), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, mult(X0, X0))
% 9.30/9.41 mult(i(X0), mult(X0, mult(X0, mult(X0, mult(X0, i(mult(X0, mult(X0, X0)))))))) -> unit
% 9.30/9.41 mult(i(X0), mult(X0, mult(i(X0), Y1))) -> mult(i(X0), Y1)
% 9.30/9.41 mult(i(X0), mult(mult(X0, mult(X0, X1)), mult(X0, mult(X0, X1)))) -> mult(mult(X0, X1), mult(X0, mult(X0, X1)))
% 9.30/9.41 mult(i(Y1), mult(Y1, Y1)) -> Y1
% 9.30/9.41 mult(i(Y1), mult(Y1, mult(Y1, Y2))) -> mult(Y1, Y2)
% 9.30/9.41 mult(i(mult(X0, X0)), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, X0)
% 9.30/9.41 mult(i(mult(X0, X0)), mult(X0, mult(X0, mult(X0, mult(X0, Y1))))) -> mult(X0, mult(X0, Y1))
% 9.30/9.41 mult(i(mult(X0, Y1)), mult(mult(X0, Y1), mult(X0, mult(Y1, Y1)))) -> mult(X0, mult(Y1, Y1))
% 9.30/9.41 mult(i(mult(X0, mult(X1, X1))), mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, X1)))))) -> mult(X0, mult(X1, X1))
% 9.30/9.41 mult(mult(X0, Y1), mult(i(mult(X0, Y1)), mult(X0, mult(Y1, Y1)))) -> mult(X0, mult(Y1, Y1))
% 9.30/9.41 mult(mult(X0, mult(X0, X0)), Y2) -> mult(X0, mult(X0, mult(X0, Y2)))
% 9.30/9.41 mult(mult(X0, mult(X0, Y1)), Y1) -> mult(X0, mult(X0, mult(Y1, Y1)))
% 9.30/9.41 mult(mult(X0, mult(X0, mult(X0, X0))), Y1) -> mult(X0, mult(X0, mult(X0, mult(X0, Y1))))
% 9.30/9.41 mult(mult(X0, mult(Y1, Y1)), Y1) -> mult(mult(X0, Y1), mult(Y1, Y1))
% 9.30/9.41 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1))
% 9.30/9.41 mult(mult(Y1, Y1), Y2) -> mult(Y1, mult(Y1, Y2))
% 9.30/9.41 mult(mult(i(Y0), i(mult(Y0, Y0))), Y2) -> mult(Y0, mult(i(mult(Y0, Y0)), mult(i(mult(Y0, Y0)), Y2)))
% 9.30/9.41 mult(mult(i(mult(X0, X0)), X0), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, mult(X0, X0))
% 9.30/9.41 mult(mult(i(mult(X0, mult(X0, mult(X0, X0)))), mult(X0, X0)), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, X0)
% 9.30/9.41 mult(mult(i(mult(Y1, Y1)), Y1), mult(Y1, Y1)) -> Y1
% 9.30/9.41 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C)))
% 9.30/9.41 mult(unit, A) -> A
% 9.30/9.41 true__ -> false__
% 9.30/9.41 with the LPO induced by
% 9.30/9.41 x4 > x3 > f1 > i > unit > mult > true__ > false__
% 9.30/9.41
% 9.30/9.41 % SZS output end Proof
% 9.30/9.41
%------------------------------------------------------------------------------