TSTP Solution File: GRP557-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 10:56:15 EDT 2022
% Result : Unsatisfiable 2.80s 2.95s
% Output : Proof 2.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n025.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 : Tue Jun 14 00:40:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.80/2.95 % SZS status Unsatisfiable
% 2.80/2.95 % SZS output start Proof
% 2.80/2.95 The input problem is unsatisfiable because
% 2.80/2.95
% 2.80/2.95 [1] the following set of Horn clauses is unsatisfiable:
% 2.80/2.95
% 2.80/2.95 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B
% 2.80/2.95 multiply(A, B) = divide(A, inverse(B))
% 2.80/2.95 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 2.80/2.95
% 2.80/2.95 This holds because
% 2.80/2.95
% 2.80/2.95 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.80/2.95
% 2.80/2.95 E:
% 2.80/2.95 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B
% 2.80/2.95 f1(multiply(inverse(a1), a1)) = true__
% 2.80/2.95 f1(multiply(inverse(b1), b1)) = false__
% 2.80/2.95 multiply(A, B) = divide(A, inverse(B))
% 2.80/2.95 G:
% 2.80/2.95 true__ = false__
% 2.80/2.95
% 2.80/2.95 This holds because
% 2.80/2.95
% 2.80/2.95 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.80/2.95
% 2.80/2.95 multiply(Y0, divide(Y1, multiply(Y0, Y1))) = inverse(g1)
% 2.80/2.95 divide(A, inverse(B)) -> multiply(A, B)
% 2.80/2.95 divide(A, inverse(divide(divide(B, C), divide(A, C)))) -> B
% 2.80/2.95 divide(X1, X1) -> g1
% 2.80/2.95 divide(Y0, g1) -> Y0
% 2.80/2.95 divide(Y0, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(Y1, X2))))))) -> Y1
% 2.80/2.95 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, Y3)))))) -> Y3
% 2.80/2.95 divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y0, Y3)))))) -> Y1
% 2.80/2.95 divide(Y0, inverse(divide(divide(Y1, inverse(divide(Y2, Y0))), Y2))) -> Y1
% 2.80/2.95 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))) -> Y1
% 2.80/2.95 divide(Y0, inverse(inverse(inverse(divide(X1, X1))))) -> Y0
% 2.80/2.95 divide(Y0, inverse(inverse(inverse(inverse(divide(X1, X1)))))) -> Y0
% 2.80/2.95 divide(inverse(divide(divide(X1, X2), divide(Y1, X2))), inverse(X1)) -> Y1
% 2.80/2.95 f1(divide(inverse(a1), inverse(a1))) -> true__
% 2.80/2.95 f1(g1) -> false__
% 2.80/2.95 f1(g1) -> true__
% 2.80/2.95 f1(multiply(inverse(a1), a1)) -> true__
% 2.80/2.95 f1(multiply(inverse(b1), b1)) -> false__
% 2.80/2.95 g2 -> inverse(g1)
% 2.80/2.95 inverse(divide(divide(X1, X1), Y1)) -> Y1
% 2.80/2.95 inverse(divide(g1, Y1)) -> Y1
% 2.80/2.95 inverse(g1) -> g1
% 2.80/2.95 inverse(inverse(g1)) -> g1
% 2.80/2.95 multiply(Y0, divide(X1, Y0)) -> X1
% 2.80/2.95 multiply(Y0, divide(Y1, multiply(Y0, Y1))) -> g1
% 2.80/2.95 multiply(Y0, g1) -> Y0
% 2.80/2.95 multiply(Y0, inverse(divide(X1, X1))) -> Y0
% 2.80/2.95 multiply(Y0, multiply(false__, divide(false__, multiply(false__, false__)))) -> Y0
% 2.80/2.95 multiply(Y0, multiply(inverse(X1), X1)) -> Y0
% 2.80/2.95 multiply(false__, divide(false__, multiply(false__, false__))) -> g1
% 2.80/2.95 multiply(g1, Y1) -> Y1
% 2.80/2.95 multiply(inverse(X1), multiply(Y1, X1)) -> Y1
% 2.80/2.95 multiply(inverse(Y1), Y1) -> g1
% 2.80/2.95 multiply(inverse(divide(X1, X1)), Y1) -> Y1
% 2.80/2.95 multiply(inverse(divide(X1, Y1)), X1) -> Y1
% 2.80/2.95 multiply(inverse(inverse(divide(X1, X1))), Y1) -> Y1
% 2.80/2.95 multiply(multiply(false__, divide(false__, multiply(false__, false__))), Y1) -> Y1
% 2.80/2.95 true__ -> false__
% 2.80/2.95 with the LPO induced by
% 2.80/2.95 a1 > b1 > g2 > inverse > divide > multiply > g1 > f1 > true__ > false__
% 2.80/2.95
% 2.80/2.95 % SZS output end Proof
% 2.80/2.95
%------------------------------------------------------------------------------