TSTP Solution File: BOO013-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n017.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 : Thu Jul 14 23:46:25 EDT 2022
% Result : Unsatisfiable 8.97s 8.88s
% Output : Proof 8.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n017.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 : Wed Jun 1 14:34:57 EDT 2022
% 0.20/0.34 % CPUTime :
% 8.97/8.88 % SZS status Unsatisfiable
% 8.97/8.88 % SZS output start Proof
% 8.97/8.88 The input problem is unsatisfiable because
% 8.97/8.88
% 8.97/8.88 [1] the following set of Horn clauses is unsatisfiable:
% 8.97/8.88
% 8.97/8.88 add(X, Y) = add(Y, X)
% 8.97/8.88 multiply(X, Y) = multiply(Y, X)
% 8.97/8.88 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 8.97/8.88 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 8.97/8.88 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 8.97/8.88 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 8.97/8.88 add(X, inverse(X)) = multiplicative_identity
% 8.97/8.88 add(inverse(X), X) = multiplicative_identity
% 8.97/8.88 multiply(X, inverse(X)) = additive_identity
% 8.97/8.88 multiply(inverse(X), X) = additive_identity
% 8.97/8.88 multiply(X, multiplicative_identity) = X
% 8.97/8.88 multiply(multiplicative_identity, X) = X
% 8.97/8.88 add(X, additive_identity) = X
% 8.97/8.88 add(additive_identity, X) = X
% 8.97/8.88 add(a, b) = multiplicative_identity
% 8.97/8.88 add(a, c) = multiplicative_identity
% 8.97/8.88 multiply(a, b) = additive_identity
% 8.97/8.88 multiply(a, c) = additive_identity
% 8.97/8.88 b = c ==> \bottom
% 8.97/8.88
% 8.97/8.88 This holds because
% 8.97/8.88
% 8.97/8.88 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.97/8.88
% 8.97/8.88 E:
% 8.97/8.88 add(X, Y) = add(Y, X)
% 8.97/8.88 add(X, additive_identity) = X
% 8.97/8.88 add(X, inverse(X)) = multiplicative_identity
% 8.97/8.88 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 8.97/8.88 add(a, b) = multiplicative_identity
% 8.97/8.88 add(a, c) = multiplicative_identity
% 8.97/8.88 add(additive_identity, X) = X
% 8.97/8.88 add(inverse(X), X) = multiplicative_identity
% 8.97/8.88 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 8.97/8.88 f1(b) = true__
% 8.97/8.88 f1(c) = false__
% 8.97/8.88 multiply(X, Y) = multiply(Y, X)
% 8.97/8.88 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 8.97/8.88 multiply(X, inverse(X)) = additive_identity
% 8.97/8.88 multiply(X, multiplicative_identity) = X
% 8.97/8.88 multiply(a, b) = additive_identity
% 8.97/8.88 multiply(a, c) = additive_identity
% 8.97/8.88 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 8.97/8.88 multiply(inverse(X), X) = additive_identity
% 8.97/8.88 multiply(multiplicative_identity, X) = X
% 8.97/8.88 G:
% 8.97/8.88 true__ = false__
% 8.97/8.88
% 8.97/8.88 This holds because
% 8.97/8.88
% 8.97/8.88 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.97/8.88
% 8.97/8.88 add(X, Y) = add(Y, X)
% 8.97/8.88 multiply(X, Y) = multiply(Y, X)
% 8.97/8.88 add(X, additive_identity) -> X
% 8.97/8.88 add(X, inverse(X)) -> add(a, c)
% 8.97/8.88 add(Y0, multiply(a, b)) -> Y0
% 8.97/8.88 add(Y0, multiply(a, c)) -> Y0
% 8.97/8.88 add(a, a) -> a
% 8.97/8.88 add(additive_identity, X) -> X
% 8.97/8.88 add(b, inverse(a)) -> inverse(a)
% 8.97/8.88 add(c, b) -> c
% 8.97/8.88 add(c, c) -> c
% 8.97/8.88 add(c, inverse(a)) -> inverse(a)
% 8.97/8.88 add(inverse(X), X) -> add(a, c)
% 8.97/8.88 add(multiply(Y0, a), multiply(Y0, c)) -> Y0
% 8.97/8.88 add(multiply(a, Y0), multiply(c, Y0)) -> Y0
% 8.97/8.88 add(multiply(a, b), Y0) -> Y0
% 8.97/8.88 add(multiply(a, b), multiply(a, multiply(a, b))) -> multiply(a, c)
% 8.97/8.88 add(multiply(a, c), Y0) -> Y0
% 8.97/8.88 additive_identity -> multiply(a, c)
% 8.97/8.88 b -> c
% 8.97/8.88 f1(b) -> true__
% 8.97/8.88 f1(c) -> false__
% 8.97/8.88 inverse(add(a, c)) -> multiply(a, c)
% 8.97/8.88 inverse(multiply(a, c)) -> add(a, c)
% 8.97/8.88 multiplicative_identity -> add(a, c)
% 8.97/8.88 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z))
% 8.97/8.88 multiply(X, inverse(X)) -> multiply(a, c)
% 8.97/8.88 multiply(a, multiply(a, c)) -> multiply(a, c)
% 8.97/8.88 multiply(add(X, Y), Z) -> add(multiply(X, Z), multiply(Y, Z))
% 8.97/8.88 multiply(add(X, Y), add(X, Z)) -> add(X, multiply(Y, Z))
% 8.97/8.88 multiply(add(X, Z), add(Y, Z)) -> add(multiply(X, Y), Z)
% 8.97/8.88 multiply(add(Y0, Y2), add(add(a, b), Y2)) -> add(Y0, Y2)
% 8.97/8.88 multiply(add(Y0, Y2), add(add(a, c), Y2)) -> add(Y0, Y2)
% 8.97/8.88 multiply(add(Y0, a), add(Y0, b)) -> Y0
% 8.97/8.88 multiply(add(Y0, a), add(Y0, c)) -> Y0
% 8.97/8.88 multiply(add(Y0, a), add(b, Y0)) -> Y0
% 8.97/8.88 multiply(add(Y0, a), add(c, Y0)) -> Y0
% 8.97/8.88 multiply(add(a, Y0), add(Y0, b)) -> Y0
% 8.97/8.88 multiply(add(a, Y0), add(Y0, c)) -> Y0
% 8.97/8.88 multiply(add(a, Y0), add(b, Y0)) -> Y0
% 8.97/8.88 multiply(add(a, Y0), add(c, Y0)) -> Y0
% 8.97/8.88 multiply(add(a, Y0), multiply(add(Y0, Y0), add(Y0, b))) -> Y0
% 8.97/8.88 multiply(add(a, Y0), multiply(add(Y0, Y0), add(Y0, c))) -> Y0
% 8.97/8.88 multiply(b, b) -> c
% 8.97/8.88 multiply(c, c) -> c
% 8.97/8.88 multiply(inverse(X), X) -> multiply(a, c)
% 8.97/8.88 multiply(multiply(add(Y0, b), add(Y0, Y0)), add(a, Y0)) -> Y0
% 8.97/8.88 multiply(multiply(add(Y0, c), add(Y0, Y0)), add(a, Y0)) -> Y0
% 8.97/8.88 true__ -> false__
% 8.97/8.88 with the LPO induced by
% 8.97/8.88 f1 > inverse > additive_identity > multiplicative_identity > b > c > multiply > add > a > true__ > false__
% 8.97/8.88
% 8.97/8.88 % SZS output end Proof
% 8.97/8.88
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