TSTP Solution File: GRP533-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP533-1 : TPTP v8.1.0. Released v2.6.0.
% 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 10:56:05 EDT 2022
% Result : Unsatisfiable 0.45s 0.67s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP533-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 04:25:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.45/0.67 % SZS status Unsatisfiable
% 0.45/0.67 % SZS output start Proof
% 0.45/0.67 The input problem is unsatisfiable because
% 0.45/0.67
% 0.45/0.67 [1] the following set of Horn clauses is unsatisfiable:
% 0.45/0.67
% 0.45/0.67 divide(divide(A, divide(divide(A, B), C)), B) = C
% 0.45/0.67 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.45/0.67 inverse(A) = divide(divide(B, B), A)
% 0.45/0.67 identity = divide(A, A)
% 0.45/0.67 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 0.45/0.67
% 0.45/0.67 This holds because
% 0.45/0.67
% 0.45/0.67 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.45/0.67
% 0.45/0.67 E:
% 0.45/0.67 divide(divide(A, divide(divide(A, B), C)), B) = C
% 0.45/0.67 f1(multiply(inverse(a1), a1)) = true__
% 0.45/0.67 f1(multiply(inverse(b1), b1)) = false__
% 0.45/0.67 identity = divide(A, A)
% 0.45/0.67 inverse(A) = divide(divide(B, B), A)
% 0.45/0.67 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.45/0.67 G:
% 0.45/0.67 true__ = false__
% 0.45/0.67
% 0.45/0.67 This holds because
% 0.45/0.67
% 0.45/0.67 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.45/0.67
% 0.45/0.67 inverse(A) = divide(divide(B, B), A)
% 0.45/0.67 divide(A, A) -> identity
% 0.45/0.67 divide(A, divide(divide(C, C), B)) -> multiply(A, B)
% 0.45/0.67 divide(Y0, divide(identity, Y2)) -> multiply(Y0, Y2)
% 0.45/0.67 divide(Y0, identity) -> multiply(Y0, identity)
% 0.45/0.67 divide(Y0, multiply(Y0, identity)) -> identity
% 0.45/0.67 divide(divide(A, divide(divide(A, B), C)), B) -> C
% 0.45/0.67 divide(divide(Y0, identity), Y1) -> divide(Y0, Y1)
% 0.45/0.67 divide(divide(Y0, multiply(divide(Y0, Y1), identity)), Y1) -> identity
% 0.45/0.67 divide(divide(Y1, divide(identity, Y2)), Y1) -> Y2
% 0.45/0.67 divide(multiply(Y0, identity), Y1) -> divide(Y0, Y1)
% 0.45/0.67 f1(identity) -> false__
% 0.45/0.67 f1(identity) -> true__
% 0.45/0.67 f1(multiply(divide(identity, a1), a1)) -> true__
% 0.45/0.67 f1(multiply(divide(identity, b1), b1)) -> false__
% 0.45/0.67 f1(multiply(inverse(a1), a1)) -> true__
% 0.45/0.67 f1(multiply(inverse(b1), b1)) -> false__
% 0.45/0.67 multiply(X1, divide(identity, X1)) -> identity
% 0.45/0.67 multiply(Y1, identity) -> Y1
% 0.45/0.67 multiply(divide(Y0, divide(Y0, Y2)), identity) -> Y2
% 0.45/0.67 multiply(divide(Y0, divide(multiply(Y0, identity), Y2)), identity) -> Y2
% 0.45/0.67 multiply(divide(identity, Y2), Y2) -> identity
% 0.45/0.67 multiply(identity, Y1) -> Y1
% 0.45/0.67 multiply(identity, identity) -> identity
% 0.45/0.67 multiply(multiply(Y0, identity), identity) -> multiply(Y0, identity)
% 0.45/0.67 multiply(multiply(identity, identity), identity) -> identity
% 0.45/0.67 true__ -> false__
% 0.45/0.67 with the LPO induced by
% 0.45/0.67 a1 > b1 > f1 > inverse > divide > identity > multiply > true__ > false__
% 0.45/0.67
% 0.45/0.67 % SZS output end Proof
% 0.45/0.67
%------------------------------------------------------------------------------