TSTP Solution File: RNG008-3 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 20:36:08 EDT 2022
% Result : Unsatisfiable 25.76s 25.71s
% Output : Proof 25.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n026.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 : Mon May 30 18:56:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 25.76/25.71 % SZS status Unsatisfiable
% 25.76/25.71 % SZS output start Proof
% 25.76/25.71 The input problem is unsatisfiable because
% 25.76/25.71
% 25.76/25.71 [1] the following set of Horn clauses is unsatisfiable:
% 25.76/25.71
% 25.76/25.71 add(additive_identity, X) = X
% 25.76/25.71 add(additive_inverse(X), X) = additive_identity
% 25.76/25.71 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 25.76/25.71 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 25.76/25.71 additive_inverse(additive_identity) = additive_identity
% 25.76/25.71 additive_inverse(additive_inverse(X)) = X
% 25.76/25.71 multiply(X, additive_identity) = additive_identity
% 25.76/25.71 multiply(additive_identity, X) = additive_identity
% 25.76/25.71 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y))
% 25.76/25.71 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 25.76/25.71 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 25.76/25.71 add(add(X, Y), Z) = add(X, add(Y, Z))
% 25.76/25.71 add(X, Y) = add(Y, X)
% 25.76/25.71 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 25.76/25.71 add(X, additive_identity) = X
% 25.76/25.71 add(X, additive_inverse(X)) = additive_identity
% 25.76/25.71 multiply(X, X) = X
% 25.76/25.71 multiply(a, b) = c
% 25.76/25.71 multiply(b, a) = c ==> \bottom
% 25.76/25.71
% 25.76/25.71 This holds because
% 25.76/25.71
% 25.76/25.71 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 25.76/25.71
% 25.76/25.71 E:
% 25.76/25.71 add(X, Y) = add(Y, X)
% 25.76/25.71 add(X, additive_identity) = X
% 25.76/25.71 add(X, additive_inverse(X)) = additive_identity
% 25.76/25.71 add(add(X, Y), Z) = add(X, add(Y, Z))
% 25.76/25.71 add(additive_identity, X) = X
% 25.76/25.71 add(additive_inverse(X), X) = additive_identity
% 25.76/25.71 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y))
% 25.76/25.71 additive_inverse(additive_identity) = additive_identity
% 25.76/25.71 additive_inverse(additive_inverse(X)) = X
% 25.76/25.71 f1(c) = false__
% 25.76/25.71 f1(multiply(b, a)) = true__
% 25.76/25.71 multiply(X, X) = X
% 25.76/25.71 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 25.76/25.71 multiply(X, additive_identity) = additive_identity
% 25.76/25.71 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 25.76/25.71 multiply(a, b) = c
% 25.76/25.71 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 25.76/25.71 multiply(additive_identity, X) = additive_identity
% 25.76/25.71 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 25.76/25.71 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 25.76/25.71 G:
% 25.76/25.71 true__ = false__
% 25.76/25.71
% 25.76/25.71 This holds because
% 25.76/25.71
% 25.76/25.71 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 25.76/25.71
% 25.76/25.71 add(X, Y) = add(Y, X)
% 25.76/25.71 add(Y0, multiply(Y1, add(Y1, X1))) = add(Y1, add(Y0, multiply(Y1, X1)))
% 25.76/25.71 add(Y0, multiply(Y1, add(Y1, X1))) = add(Y1, add(multiply(Y1, X1), Y0))
% 25.76/25.71 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2))
% 25.76/25.71 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2))
% 25.76/25.71 multiply(X0, X1) = multiply(X1, X0)
% 25.76/25.71 multiply(Y1, multiply(Y0, Y2)) = multiply(Y0, multiply(Y1, Y2))
% 25.76/25.71 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y1, Y2))
% 25.76/25.71 multiply(add(Y1, Y0), Y1) = multiply(add(Y0, Y1), Y1)
% 25.76/25.71 add(X, additive_identity) -> X
% 25.76/25.71 add(X, additive_inverse(X)) -> additive_identity
% 25.76/25.71 add(X0, X0) -> g1
% 25.76/25.71 add(X0, add(X0, Y0)) -> Y0
% 25.76/25.71 add(Y0, add(X1, add(Y0, Y2))) -> add(X1, Y2)
% 25.76/25.71 add(Y0, add(Y1, Y0)) -> Y1
% 25.76/25.71 add(Y0, add(Y1, add(X1, add(Y0, Y1)))) -> X1
% 25.76/25.71 add(Y0, g1) -> Y0
% 25.76/25.71 add(Y1, multiply(Y1, Y2)) -> multiply(Y1, add(Y1, Y2))
% 25.76/25.71 add(Y1, multiply(Y2, Y1)) -> multiply(add(Y1, Y2), Y1)
% 25.76/25.71 add(add(X, Y), Z) -> add(X, add(Y, Z))
% 25.76/25.71 add(additive_identity, X) -> X
% 25.76/25.71 add(additive_inverse(X), X) -> additive_identity
% 25.76/25.71 add(g1, Y0) -> Y0
% 25.76/25.71 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 25.76/25.71 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 25.76/25.71 add(multiply(X0, X1), add(Y0, multiply(X1, X0))) -> Y0
% 25.76/25.71 add(multiply(X0, X1), add(multiply(X1, X0), Y0)) -> Y0
% 25.76/25.71 add(multiply(X0, multiply(X1, Y1)), multiply(Y1, multiply(X0, X1))) -> g1
% 25.76/25.71 add(multiply(Y0, X1), multiply(X1, Y0)) -> g1
% 25.76/25.71 additive_inverse(X0) -> X0
% 25.76/25.71 c -> multiply(a, b)
% 25.76/25.71 f1(multiply(a, b)) -> false__
% 25.76/25.71 f1(multiply(b, a)) -> true__
% 25.76/25.71 g1 -> additive_identity
% 25.76/25.71 multiply(X, X) -> X
% 25.76/25.71 multiply(X, additive_identity) -> additive_identity
% 25.76/25.71 multiply(Y0, add(Y0, multiply(X1, multiply(Y0, add(Y0, X1))))) -> Y0
% 25.76/25.71 multiply(Y0, g1) -> g1
% 25.76/25.71 multiply(Y0, multiply(X0, multiply(X1, Y0))) -> multiply(Y0, multiply(X0, X1))
% 25.76/25.71 multiply(Y0, multiply(X1, add(X1, Y0))) -> g1
% 25.76/25.71 multiply(Y0, multiply(X1, add(Y0, X1))) -> g1
% 25.76/25.71 multiply(Y0, multiply(X1, multiply(Y0, Y2))) -> multiply(Y0, multiply(X1, Y2))
% 25.76/25.71 multiply(Y1, multiply(X1, Y1)) -> multiply(Y1, X1)
% 25.76/25.71 multiply(Y1, multiply(Y1, Y2)) -> multiply(Y1, Y2)
% 25.76/25.71 multiply(add(X1, Y0), X1) -> multiply(X1, add(X1, Y0))
% 25.76/25.71 multiply(additive_identity, X) -> additive_identity
% 25.76/25.71 multiply(g1, Y0) -> g1
% 25.76/25.71 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 25.76/25.71 true__ -> false__
% 25.76/25.71 with the LPO induced by
% 25.76/25.71 c > a > b > add > multiply > g1 > f1 > additive_identity > additive_inverse > true__ > false__
% 25.76/25.71
% 25.76/25.71 % SZS output end Proof
% 25.76/25.71
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