TSTP Solution File: RNG007-4 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:36:07 EDT 2022
% Result : Unsatisfiable 0.90s 1.06s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.10 % Command : moca.sh %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Mon May 30 04:56:27 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.90/1.06 % SZS status Unsatisfiable
% 0.90/1.06 % SZS output start Proof
% 0.90/1.06 The input problem is unsatisfiable because
% 0.90/1.06
% 0.90/1.06 [1] the following set of Horn clauses is unsatisfiable:
% 0.90/1.06
% 0.90/1.06 add(additive_identity, X) = X
% 0.90/1.06 add(additive_inverse(X), X) = additive_identity
% 0.90/1.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.90/1.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.90/1.06 additive_inverse(additive_identity) = additive_identity
% 0.90/1.06 additive_inverse(additive_inverse(X)) = X
% 0.90/1.06 multiply(X, additive_identity) = additive_identity
% 0.90/1.06 multiply(additive_identity, X) = additive_identity
% 0.90/1.06 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y))
% 0.90/1.06 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 0.90/1.06 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 0.90/1.06 add(add(X, Y), Z) = add(X, add(Y, Z))
% 0.90/1.06 add(X, Y) = add(Y, X)
% 0.90/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.90/1.06 multiply(X, X) = X
% 0.90/1.06 add(a, a) = additive_identity ==> \bottom
% 0.90/1.06
% 0.90/1.06 This holds because
% 0.90/1.06
% 0.90/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.90/1.06
% 0.90/1.06 E:
% 0.90/1.06 add(X, Y) = add(Y, X)
% 0.90/1.06 add(add(X, Y), Z) = add(X, add(Y, Z))
% 0.90/1.06 add(additive_identity, X) = X
% 0.90/1.06 add(additive_inverse(X), X) = additive_identity
% 0.90/1.06 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y))
% 0.90/1.06 additive_inverse(additive_identity) = additive_identity
% 0.90/1.06 additive_inverse(additive_inverse(X)) = X
% 0.90/1.06 f1(add(a, a)) = true__
% 0.90/1.06 f1(additive_identity) = false__
% 0.90/1.06 multiply(X, X) = X
% 0.90/1.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.90/1.06 multiply(X, additive_identity) = additive_identity
% 0.90/1.06 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 0.90/1.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.90/1.06 multiply(additive_identity, X) = additive_identity
% 0.90/1.06 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 0.90/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.90/1.06 G:
% 0.90/1.06 true__ = false__
% 0.90/1.06
% 0.90/1.06 This holds because
% 0.90/1.06
% 0.90/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.90/1.06
% 0.90/1.06 add(X, Y) = add(Y, X)
% 0.90/1.06 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2))
% 0.90/1.06 add(Y1, multiply(Y0, Y1)) = multiply(add(Y0, Y1), Y1)
% 0.90/1.06 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2))
% 0.90/1.06 add(Y2, multiply(Y2, Y1)) = multiply(Y2, add(Y1, Y2))
% 0.90/1.06 multiply(X0, additive_inverse(Y1)) = multiply(additive_inverse(X0), Y1)
% 0.90/1.06 add(X0, additive_inverse(X0)) -> additive_identity
% 0.90/1.06 add(X0, additive_inverse(add(X1, add(X0, additive_inverse(X1))))) -> additive_identity
% 0.90/1.06 add(Y0, Y0) -> additive_identity
% 0.90/1.06 add(Y0, add(Y1, Y0)) -> Y1
% 0.90/1.06 add(Y0, add(Y1, add(Y0, Y1))) -> additive_identity
% 0.90/1.06 add(Y0, add(Y1, add(Y0, add(Y1, X1)))) -> X1
% 0.90/1.06 add(Y1, add(Y1, Y2)) -> Y2
% 0.90/1.06 add(Y1, additive_identity) -> Y1
% 0.90/1.06 add(Y1, multiply(Y1, Y2)) -> multiply(Y1, add(Y1, Y2))
% 0.90/1.06 add(Y1, multiply(Y2, Y1)) -> multiply(add(Y1, Y2), Y1)
% 0.90/1.06 add(add(X, Y), Z) -> add(X, add(Y, Z))
% 0.90/1.06 add(additive_identity, X) -> X
% 0.90/1.06 add(additive_inverse(X), X) -> additive_identity
% 0.90/1.06 add(additive_inverse(X), additive_inverse(Y)) -> additive_inverse(add(X, Y))
% 0.90/1.06 add(additive_inverse(Y0), X0) -> additive_inverse(add(Y0, additive_inverse(X0)))
% 0.90/1.06 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 0.90/1.06 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 0.90/1.06 additive_inverse(Y1) -> Y1
% 0.90/1.06 additive_inverse(add(Y0, additive_identity)) -> additive_inverse(Y0)
% 0.90/1.06 additive_inverse(add(additive_inverse(X0), Y1)) -> add(X0, additive_inverse(Y1))
% 0.90/1.06 additive_inverse(additive_identity) -> additive_identity
% 0.90/1.06 additive_inverse(additive_inverse(X)) -> X
% 0.90/1.06 additive_inverse(multiply(X, Y)) -> multiply(X, additive_inverse(Y))
% 0.90/1.06 additive_inverse(multiply(X, Y)) -> multiply(additive_inverse(X), Y)
% 0.90/1.06 f1(add(a, a)) -> true__
% 0.90/1.06 f1(additive_identity) -> false__
% 0.90/1.06 multiply(X, X) -> X
% 0.90/1.06 multiply(X, additive_identity) -> additive_identity
% 0.90/1.06 multiply(Y0, add(Y0, add(X1, Y0))) -> multiply(Y0, X1)
% 0.90/1.06 multiply(Y0, multiply(Y1, multiply(Y0, Y1))) -> multiply(Y0, Y1)
% 0.90/1.06 multiply(Y1, additive_inverse(Y1)) -> additive_inverse(Y1)
% 0.90/1.06 multiply(Y1, multiply(Y1, Y2)) -> multiply(Y1, Y2)
% 0.90/1.06 multiply(add(Y0, add(X1, Y0)), Y0) -> multiply(X1, Y0)
% 0.90/1.06 multiply(additive_identity, X) -> additive_identity
% 0.90/1.06 multiply(additive_inverse(X0), X0) -> X0
% 0.90/1.06 multiply(additive_inverse(X0), additive_inverse(X1)) -> multiply(X0, X1)
% 0.90/1.06 multiply(additive_inverse(Y1), Y1) -> additive_inverse(Y1)
% 0.90/1.06 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.90/1.06 true__ -> false__
% 0.90/1.06 with the LPO induced by
% 0.90/1.06 a > f1 > add > additive_inverse > multiply > additive_identity > true__ > false__
% 0.90/1.06
% 0.90/1.06 % SZS output end Proof
% 0.90/1.06
%------------------------------------------------------------------------------