TSTP Solution File: GRP553-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP553-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n006.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 10:56:13 EDT 2022
% Result : Unsatisfiable 5.21s 5.32s
% Output : Proof 5.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP553-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : moca.sh %s
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jun 13 23:05:26 EDT 2022
% 0.13/0.32 % CPUTime :
% 5.21/5.32 % SZS status Unsatisfiable
% 5.21/5.32 % SZS output start Proof
% 5.21/5.32 The input problem is unsatisfiable because
% 5.21/5.32
% 5.21/5.32 [1] the following set of Horn clauses is unsatisfiable:
% 5.21/5.32
% 5.21/5.32 divide(divide(A, inverse(divide(B, divide(A, C)))), C) = B
% 5.21/5.32 multiply(A, B) = divide(A, inverse(B))
% 5.21/5.32 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 5.21/5.32
% 5.21/5.32 This holds because
% 5.21/5.32
% 5.21/5.32 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.21/5.32
% 5.21/5.32 E:
% 5.21/5.32 divide(divide(A, inverse(divide(B, divide(A, C)))), C) = B
% 5.21/5.32 f1(multiply(inverse(a1), a1)) = true__
% 5.21/5.32 f1(multiply(inverse(b1), b1)) = false__
% 5.21/5.32 multiply(A, B) = divide(A, inverse(B))
% 5.21/5.32 G:
% 5.21/5.32 true__ = false__
% 5.21/5.32
% 5.21/5.32 This holds because
% 5.21/5.32
% 5.21/5.32 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.21/5.32
% 5.21/5.32 divide(X1, divide(Y2, divide(inverse(X1), inverse(Y0)))) = divide(Y0, Y2)
% 5.21/5.32 divide(X1, divide(Y2, inverse(X0))) = divide(divide(inverse(X0), inverse(X1)), Y2)
% 5.21/5.32 divide(X1, divide(Y2, inverse(X0))) = divide(inverse(divide(X0, X1)), Y2)
% 5.21/5.32 divide(X1, divide(Y2, inverse(divide(X1, Y0)))) = divide(Y0, Y2)
% 5.21/5.32 divide(Y0, Y0) = divide(Y2, Y2)
% 5.21/5.32 divide(Y0, inverse(divide(Y1, divide(Y0, X1)))) = divide(divide(divide(X0, inverse(divide(X1, divide(X0, Y3)))), inverse(Y1)), Y3)
% 5.21/5.32 divide(divide(X0, X2), inverse(X1)) = divide(divide(X0, inverse(X1)), X2)
% 5.21/5.32 divide(divide(X1, X1), divide(Y2, Y1)) = divide(Y1, Y2)
% 5.21/5.32 divide(divide(X2, X1), divide(inverse(X0), inverse(X2))) = divide(X0, X1)
% 5.21/5.32 divide(divide(X2, X1), inverse(divide(X0, X2))) = divide(X0, X1)
% 5.21/5.32 divide(divide(Y0, inverse(X0)), X1) = divide(Y0, divide(inverse(X0), inverse(X1)))
% 5.21/5.32 divide(divide(Y0, inverse(X0)), X1) = divide(Y0, inverse(divide(X0, X1)))
% 5.21/5.32 divide(divide(divide(X2, inverse(X1)), inverse(Y1)), X3) = divide(divide(Y2, inverse(Y1)), inverse(divide(X1, divide(Y2, divide(X2, X3)))))
% 5.21/5.32 divide(divide(divide(Y2, inverse(X1)), Y3), inverse(divide(Y1, X1))) = divide(divide(Y2, inverse(Y1)), Y3)
% 5.21/5.32 divide(X0, inverse(divide(X1, divide(X0, Y0)))) -> divide(Y0, inverse(X1))
% 5.21/5.32 divide(X0, inverse(divide(X1, divide(X0, divide(Y0, Y2))))) -> divide(divide(Y0, inverse(X1)), Y2)
% 5.21/5.32 divide(X1, divide(X1, Y1)) -> Y1
% 5.21/5.32 divide(X1, divide(Y0, inverse(divide(X1, divide(Y0, inverse(Y1)))))) -> Y1
% 5.21/5.32 divide(Y0, divide(X1, X1)) -> Y0
% 5.21/5.32 divide(Y0, divide(divide(inverse(X0), inverse(X1)), inverse(Y0))) -> divide(X0, X1)
% 5.21/5.32 divide(Y0, divide(false__, false__)) -> Y0
% 5.21/5.32 divide(Y0, divide(inverse(Y1), inverse(Y0))) -> Y1
% 5.21/5.32 divide(Y1, divide(Y1, inverse(X1))) -> inverse(X1)
% 5.21/5.32 divide(Y1, divide(divide(divide(inverse(X0), inverse(X1)), inverse(X0)), X1)) -> Y1
% 5.21/5.32 divide(Y1, inverse(divide(Y3, Y1))) -> Y3
% 5.21/5.32 divide(divide(A, inverse(divide(B, divide(A, C)))), C) -> B
% 5.21/5.32 divide(divide(X0, X1), divide(inverse(Y1), divide(inverse(X0), inverse(X1)))) -> Y1
% 5.21/5.32 divide(divide(X1, X1), inverse(Y1)) -> Y1
% 5.21/5.32 divide(divide(X1, Y2), divide(Y0, Y2)) -> divide(X1, Y0)
% 5.21/5.32 divide(divide(X1, inverse(Y1)), X1) -> Y1
% 5.21/5.32 divide(divide(Y0, X1), inverse(divide(X1, Y2))) -> divide(Y0, Y2)
% 5.21/5.32 divide(divide(Y0, Y0), divide(inverse(X0), inverse(X1))) -> divide(X0, X1)
% 5.21/5.32 divide(divide(Y0, Y1), divide(X1, X1)) -> divide(Y0, Y1)
% 5.21/5.32 divide(divide(Y0, divide(inverse(X1), inverse(Y2))), X1) -> divide(Y0, Y2)
% 5.21/5.32 divide(divide(Y0, inverse(divide(Y1, X1))), inverse(divide(X1, Y0))) -> Y1
% 5.21/5.32 divide(divide(Y0, inverse(divide(Y1, divide(divide(X2, inverse(X1)), X3)))), inverse(divide(X1, divide(Y0, divide(X2, X3))))) -> Y1
% 5.21/5.32 divide(divide(Y2, Y2), divide(divide(X1, X1), Y0)) -> Y0
% 5.21/5.32 divide(divide(Y2, Y2), divide(divide(false__, false__), Y0)) -> Y0
% 5.21/5.32 divide(divide(divide(X0, inverse(divide(X1, divide(X0, Y2)))), inverse(divide(Y1, X1))), Y2) -> Y1
% 5.21/5.32 divide(divide(divide(X2, inverse(Y1)), X3), divide(X2, X3)) -> Y1
% 5.21/5.32 divide(divide(divide(Y0, inverse(Y1)), inverse(divide(X1, Y0))), X1) -> Y1
% 5.21/5.32 divide(divide(divide(divide(X0, inverse(divide(X1, divide(X0, Y2)))), inverse(divide(Y1, X1))), inverse(divide(Y3, Y1))), Y2) -> Y3
% 5.21/5.32 divide(divide(false__, false__), divide(Y0, divide(Y0, divide(inverse(X0), inverse(X1))))) -> divide(X0, X1)
% 5.21/5.32 divide(divide(inverse(X0), inverse(X0)), inverse(Y1)) -> Y1
% 5.21/5.32 divide(divide(inverse(X0), inverse(X2)), divide(inverse(X0), inverse(X1))) -> divide(X2, X1)
% 5.21/5.32 divide(divide(inverse(Y0), inverse(Y1)), inverse(Y0)) -> Y1
% 5.21/5.32 divide(inverse(X1), inverse(inverse(divide(X0, X1)))) -> inverse(X0)
% 5.21/5.32 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1
% 5.21/5.32 f1(divide(X1, X1)) -> false__
% 5.21/5.32 f1(divide(X1, X1)) -> true__
% 5.21/5.32 f1(divide(inverse(a1), inverse(a1))) -> true__
% 5.21/5.32 f1(divide(inverse(b1), inverse(b1))) -> false__
% 5.21/5.32 f1(multiply(inverse(a1), a1)) -> true__
% 5.21/5.32 f1(multiply(inverse(b1), b1)) -> false__
% 5.21/5.32 inverse(divide(X1, Y0)) -> divide(inverse(X1), inverse(Y0))
% 5.21/5.32 multiply(A, B) -> divide(A, inverse(B))
% 5.21/5.32 true__ -> false__
% 5.21/5.32 with the LPO induced by
% 5.21/5.32 a1 > b1 > f1 > multiply > inverse > divide > true__ > false__
% 5.21/5.32
% 5.21/5.32 % SZS output end Proof
% 5.21/5.32
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