TSTP Solution File: GRP451-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP451-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n032.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 10:55:32 EDT 2022
% Result : Unsatisfiable 0.46s 0.63s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP451-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.11 % Command : moca.sh %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jun 13 22:31:27 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.46/0.63 % SZS status Unsatisfiable
% 0.46/0.63 % SZS output start Proof
% 0.46/0.63 The input problem is unsatisfiable because
% 0.46/0.63
% 0.46/0.63 [1] the following set of Horn clauses is unsatisfiable:
% 0.46/0.63
% 0.46/0.63 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(divide(A, A), A), C)))), C) = B
% 0.46/0.63 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.46/0.63 inverse(A) = divide(divide(B, B), A)
% 0.46/0.63 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 0.46/0.63
% 0.46/0.63 This holds because
% 0.46/0.63
% 0.46/0.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.46/0.63
% 0.46/0.63 E:
% 0.46/0.63 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(divide(A, A), A), C)))), C) = B
% 0.46/0.63 f1(multiply(inverse(a1), a1)) = true__
% 0.46/0.63 f1(multiply(inverse(b1), b1)) = false__
% 0.46/0.63 inverse(A) = divide(divide(B, B), A)
% 0.46/0.63 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.46/0.63 G:
% 0.46/0.63 true__ = false__
% 0.46/0.63
% 0.46/0.63 This holds because
% 0.46/0.63
% 0.46/0.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.46/0.63
% 0.46/0.63 divide(X0, X0) = divide(Y0, Y0)
% 0.46/0.63 divide(X0, X0) = inverse(divide(Y0, Y0))
% 0.46/0.63 divide(false__, false__) = divide(X0, X0)
% 0.46/0.63 divide(false__, false__) = inverse(inverse(inverse(divide(Y0, Y0))))
% 0.46/0.63 divide(inverse(divide(Y0, inverse(divide(inverse(Y0), Y2)))), Y2) = divide(X0, X0)
% 0.46/0.63 divide(inverse(inverse(inverse(inverse(Y1)))), Y1) = divide(Y2, Y2)
% 0.46/0.63 inverse(divide(X0, X0)) = divide(false__, false__)
% 0.46/0.63 inverse(divide(X0, X0)) = inverse(divide(Y0, Y0))
% 0.46/0.63 inverse(inverse(divide(X0, X0))) = divide(false__, false__)
% 0.46/0.63 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.46/0.63 divide(Y0, divide(inverse(inverse(divide(X0, X0))), Y2)) -> divide(Y0, inverse(Y2))
% 0.46/0.63 divide(divide(B, B), A) -> inverse(A)
% 0.46/0.63 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(divide(A, A), A), C)))), C) -> B
% 0.46/0.63 divide(divide(inverse(divide(X0, X0)), inverse(divide(Y1, divide(inverse(divide(X0, X0)), Y2)))), Y2) -> Y1
% 0.46/0.63 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1)
% 0.46/0.63 divide(inverse(divide(Y0, divide(Y1, divide(inverse(Y0), Y2)))), Y2) -> Y1
% 0.46/0.63 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1)
% 0.46/0.63 divide(inverse(inverse(divide(Y0, divide(inverse(inverse(divide(X0, X0))), Y2)))), Y2) -> Y0
% 0.46/0.63 divide(inverse(inverse(divide(Y1, divide(inverse(divide(X0, X0)), Y2)))), Y2) -> Y1
% 0.46/0.63 divide(inverse(inverse(inverse(divide(X0, X0)))), Y1) -> inverse(Y1)
% 0.46/0.63 f1(divide(X0, X0)) -> false__
% 0.46/0.63 f1(divide(X0, X0)) -> true__
% 0.46/0.63 f1(divide(false__, false__)) -> false__
% 0.46/0.63 f1(divide(false__, false__)) -> true__
% 0.46/0.63 f1(divide(inverse(a1), inverse(a1))) -> true__
% 0.46/0.63 f1(divide(inverse(b1), inverse(b1))) -> false__
% 0.46/0.63 f1(inverse(divide(X1, X1))) -> false__
% 0.46/0.63 f1(inverse(divide(X1, X1))) -> true__
% 0.46/0.63 f1(inverse(inverse(divide(X0, X0)))) -> false__
% 0.46/0.63 f1(inverse(inverse(divide(X0, X0)))) -> true__
% 0.46/0.63 f1(multiply(inverse(a1), a1)) -> true__
% 0.46/0.63 f1(multiply(inverse(b1), b1)) -> false__
% 0.46/0.63 true__ -> false__
% 0.46/0.63 with the LPO induced by
% 0.46/0.63 a1 > b1 > f1 > multiply > divide > inverse > true__ > false__
% 0.46/0.63
% 0.46/0.63 % SZS output end Proof
% 0.46/0.63
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