TSTP Solution File: GRP551-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 10:56:12 EDT 2022
% Result : Unsatisfiable 15.26s 15.28s
% Output : Proof 15.26s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : moca.sh %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 19:20:09 EDT 2022
% 0.14/0.36 % CPUTime :
% 15.26/15.28 % SZS status Unsatisfiable
% 15.26/15.28 % SZS output start Proof
% 15.26/15.28 The input problem is unsatisfiable because
% 15.26/15.28
% 15.26/15.28 [1] the following set of Horn clauses is unsatisfiable:
% 15.26/15.28
% 15.26/15.28 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) = C
% 15.26/15.28 multiply(A, B) = divide(A, divide(identity, B))
% 15.26/15.28 inverse(A) = divide(identity, A)
% 15.26/15.28 identity = divide(A, A)
% 15.26/15.28 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom
% 15.26/15.28
% 15.26/15.28 This holds because
% 15.26/15.28
% 15.26/15.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 15.26/15.28
% 15.26/15.28 E:
% 15.26/15.28 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) = C
% 15.26/15.28 f1(multiply(a3, multiply(b3, c3))) = false__
% 15.26/15.28 f1(multiply(multiply(a3, b3), c3)) = true__
% 15.26/15.28 identity = divide(A, A)
% 15.26/15.28 inverse(A) = divide(identity, A)
% 15.26/15.28 multiply(A, B) = divide(A, divide(identity, B))
% 15.26/15.28 G:
% 15.26/15.28 true__ = false__
% 15.26/15.28
% 15.26/15.28 This holds because
% 15.26/15.28
% 15.26/15.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 15.26/15.28
% 15.26/15.28 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0))
% 15.26/15.28 divide(X0, inverse(Y1)) = divide(Y1, inverse(inverse(inverse(X0))))
% 15.26/15.28 divide(X1, inverse(Y1)) = divide(Y1, inverse(divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, X1))))))))
% 15.26/15.28 divide(Y0, X1) = inverse(divide(X0, inverse(divide(X1, divide(X0, inverse(Y0))))))
% 15.26/15.28 divide(divide(X1, X0), inverse(Y1)) = divide(Y1, divide(X0, X1))
% 15.26/15.28 divide(divide(Y0, Y1), divide(X1, X0)) = divide(divide(X0, X1), divide(Y1, Y0))
% 15.26/15.28 divide(inverse(Y0), X0) = divide(inverse(X0), Y0)
% 15.26/15.28 divide(inverse(Y0), X0) = divide(inverse(inverse(inverse(X0))), Y0)
% 15.26/15.28 divide(inverse(Y0), inverse(Y1)) = divide(Y1, Y0)
% 15.26/15.28 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(X1, divide(X0, Y1))
% 15.26/15.28 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(Y1, divide(X0, X1))
% 15.26/15.28 inverse(divide(X1, Y0)) = divide(Y0, X1)
% 15.26/15.28 inverse(divide(Y0, inverse(X1))) = divide(X0, divide(X1, inverse(divide(X0, inverse(Y0)))))
% 15.26/15.28 inverse(divide(Y0, inverse(X1))) = inverse(divide(X0, inverse(divide(X1, divide(X0, Y0)))))
% 15.26/15.28 inverse(divide(Y0, inverse(divide(X1, X0)))) = divide(divide(X0, X1), Y0)
% 15.26/15.28 inverse(divide(Y0, inverse(divide(X1, Y1)))) = divide(divide(Y1, Y0), X1)
% 15.26/15.28 inverse(divide(Y0, inverse(divide(X1, Y1)))) = inverse(divide(X1, divide(Y1, Y0)))
% 15.26/15.28 inverse(divide(divide(X2, X0), X1)) = divide(X0, inverse(divide(X1, X2)))
% 15.26/15.28 inverse(divide(divide(X2, X1), X0)) = divide(X0, inverse(divide(X1, X2)))
% 15.26/15.28 divide(A, A) -> identity
% 15.26/15.28 divide(X0, divide(X0, Y1)) -> Y1
% 15.26/15.28 divide(X0, divide(X1, divide(divide(X1, X0), X2))) -> inverse(X2)
% 15.26/15.28 divide(X0, divide(inverse(Y1), inverse(X0))) -> Y1
% 15.26/15.28 divide(X0, divide(inverse(Y1), inverse(divide(divide(Y1, inverse(X0)), Y2)))) -> Y2
% 15.26/15.28 divide(X0, inverse(divide(Y1, divide(divide(Y1, inverse(X0)), Y2)))) -> Y2
% 15.26/15.28 divide(X0, inverse(divide(inverse(X0), Y1))) -> inverse(Y1)
% 15.26/15.28 divide(X2, divide(X1, divide(divide(X1, X0), X2))) -> inverse(X0)
% 15.26/15.28 divide(Y0, divide(X0, inverse(Y0))) -> inverse(X0)
% 15.26/15.28 divide(Y0, inverse(divide(Y1, Y0))) -> Y1
% 15.26/15.28 divide(Y1, identity) -> inverse(inverse(Y1))
% 15.26/15.28 divide(divide(X1, X0), divide(Y1, divide(X0, X1))) -> inverse(Y1)
% 15.26/15.28 divide(divide(X1, X0), inverse(divide(Y1, inverse(divide(X0, X1))))) -> Y1
% 15.26/15.28 divide(divide(X1, Y1), divide(divide(X1, Y2), Y1)) -> Y2
% 15.26/15.28 divide(divide(Y1, Y0), X1) -> inverse(divide(Y0, divide(Y1, X1)))
% 15.26/15.28 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) -> C
% 15.26/15.28 divide(identity, A) -> inverse(A)
% 15.26/15.28 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1)
% 15.26/15.28 divide(inverse(Y0), X1) -> inverse(divide(Y0, inverse(X1)))
% 15.26/15.28 divide(inverse(Y0), divide(X0, Y0)) -> inverse(X0)
% 15.26/15.28 divide(inverse(Y0), divide(divide(divide(Y1, Y0), Y2), Y1)) -> Y2
% 15.26/15.28 divide(inverse(Y0), divide(divide(inverse(Y0), Y2), identity)) -> Y2
% 15.26/15.28 divide(inverse(Y0), divide(inverse(Y2), Y0)) -> Y2
% 15.26/15.28 divide(inverse(Y0), identity) -> inverse(Y0)
% 15.26/15.28 divide(inverse(Y0), inverse(X1)) -> inverse(divide(Y0, X1))
% 15.26/15.28 divide(inverse(inverse(X1)), inverse(inverse(X0))) -> divide(X1, X0)
% 15.26/15.28 divide(inverse(inverse(Y1)), identity) -> Y1
% 15.26/15.28 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__
% 15.26/15.28 f1(divide(b3, inverse(divide(a3, inverse(c3))))) -> true__
% 15.26/15.28 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__
% 15.26/15.28 f1(multiply(a3, multiply(b3, c3))) -> false__
% 15.26/15.28 f1(multiply(multiply(a3, b3), c3)) -> true__
% 15.26/15.28 inverse(divide(X0, divide(X1, divide(Y1, divide(X0, X1))))) -> inverse(Y1)
% 15.26/15.28 inverse(divide(X0, divide(X1, inverse(divide(Y1, inverse(divide(X0, X1))))))) -> Y1
% 15.26/15.28 inverse(divide(X0, divide(Y1, divide(divide(Y1, X0), Y2)))) -> Y2
% 15.26/15.28 inverse(divide(X0, inverse(divide(inverse(X0), Y1)))) -> Y1
% 15.26/15.28 inverse(divide(X1, divide(divide(X1, X0), X2))) -> inverse(divide(X0, inverse(X2)))
% 15.26/15.28 inverse(divide(Y0, inverse(divide(X0, Y0)))) -> inverse(X0)
% 15.26/15.28 inverse(divide(Y0, inverse(divide(divide(X1, X0), Y0)))) -> divide(X0, X1)
% 15.26/15.28 inverse(divide(divide(Y1, X1), divide(Y1, divide(X1, Y2)))) -> Y2
% 15.26/15.28 inverse(divide(divide(Y1, X1), inverse(divide(divide(X1, Y2), Y1)))) -> Y2
% 15.26/15.28 inverse(divide(divide(divide(Y1, identity), Y2), Y1)) -> Y2
% 15.26/15.28 inverse(divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, X1))))))) -> inverse(X1)
% 15.26/15.28 inverse(divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, inverse(Y1)))))))) -> Y1
% 15.26/15.28 inverse(divide(false__, inverse(divide(X1, divide(false__, divide(Y1, X1)))))) -> inverse(Y1)
% 15.26/15.28 inverse(divide(false__, inverse(divide(X1, divide(false__, inverse(divide(Y1, inverse(X1)))))))) -> Y1
% 15.26/15.28 inverse(divide(inverse(X0), inverse(divide(X0, Y1)))) -> Y1
% 15.26/15.28 inverse(divide(inverse(Y0), inverse(X1))) -> divide(Y0, X1)
% 15.26/15.28 inverse(divide(inverse(Y0), inverse(divide(X1, inverse(Y0))))) -> inverse(X1)
% 15.26/15.28 inverse(divide(inverse(Y0), inverse(divide(inverse(inverse(Y0)), Y1)))) -> Y1
% 15.26/15.28 inverse(divide(inverse(Y1), identity)) -> Y1
% 15.26/15.28 inverse(identity) -> identity
% 15.26/15.28 inverse(inverse(Y0)) -> Y0
% 15.26/15.28 inverse(inverse(inverse(Y0))) -> inverse(Y0)
% 15.26/15.28 inverse(inverse(inverse(inverse(Y1)))) -> Y1
% 15.26/15.28 multiply(A, B) -> divide(A, divide(identity, B))
% 15.26/15.28 true__ -> false__
% 15.26/15.28 with the LPO induced by
% 15.26/15.28 c3 > b3 > a3 > f1 > multiply > divide > identity > inverse > true__ > false__
% 15.26/15.28
% 15.26/15.28 % SZS output end Proof
% 15.26/15.28
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