TSTP Solution File: BOO005-4 by Moca---0.1
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% File : Moca---0.1
% Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 23:46:15 EDT 2022
% Result : Unsatisfiable 0.74s 0.90s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 1 21:57:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.74/0.90 % SZS status Unsatisfiable
% 0.74/0.90 % SZS output start Proof
% 0.74/0.90 The input problem is unsatisfiable because
% 0.74/0.90
% 0.74/0.90 [1] the following set of Horn clauses is unsatisfiable:
% 0.74/0.90
% 0.74/0.90 add(X, Y) = add(Y, X)
% 0.74/0.90 multiply(X, Y) = multiply(Y, X)
% 0.74/0.90 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 0.74/0.90 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.74/0.90 add(X, additive_identity) = X
% 0.74/0.90 multiply(X, multiplicative_identity) = X
% 0.74/0.90 add(X, inverse(X)) = multiplicative_identity
% 0.74/0.90 multiply(X, inverse(X)) = additive_identity
% 0.74/0.90 add(a, multiplicative_identity) = multiplicative_identity ==> \bottom
% 0.74/0.90
% 0.74/0.90 This holds because
% 0.74/0.90
% 0.74/0.90 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.74/0.90
% 0.74/0.90 E:
% 0.74/0.90 add(X, Y) = add(Y, X)
% 0.74/0.90 add(X, additive_identity) = X
% 0.74/0.90 add(X, inverse(X)) = multiplicative_identity
% 0.74/0.90 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 0.74/0.90 f1(add(a, multiplicative_identity)) = true__
% 0.74/0.90 f1(multiplicative_identity) = false__
% 0.74/0.90 multiply(X, Y) = multiply(Y, X)
% 0.74/0.90 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.74/0.90 multiply(X, inverse(X)) = additive_identity
% 0.74/0.91 multiply(X, multiplicative_identity) = X
% 0.74/0.91 G:
% 0.74/0.91 true__ = false__
% 0.74/0.91
% 0.74/0.91 This holds because
% 0.74/0.91
% 0.74/0.91 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.74/0.91
% 0.74/0.91 add(X, Y) = add(Y, X)
% 0.74/0.91 multiply(X, Y) = multiply(Y, X)
% 0.74/0.91 multiply(Y0, add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2))
% 0.74/0.91 multiply(add(Y0, Y0), add(Y0, Y1)) = multiply(Y0, add(Y1, multiplicative_identity))
% 0.74/0.91 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2))
% 0.74/0.91 multiply(add(multiplicative_identity, Y0), additive_identity) = multiply(additive_identity, Y0)
% 0.74/0.91 add(X, additive_identity) -> X
% 0.74/0.91 add(X, inverse(X)) -> multiplicative_identity
% 0.74/0.91 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z))
% 0.74/0.91 add(Y0, inverse(inverse(Y0))) -> Y0
% 0.74/0.91 add(Y0, multiplicative_identity) -> multiplicative_identity
% 0.74/0.91 add(Y1, Y1) -> Y1
% 0.74/0.91 add(additive_identity, Y0) -> Y0
% 0.74/0.91 add(multiplicative_identity, Y0) -> multiplicative_identity
% 0.74/0.91 add(multiplicative_identity, multiplicative_identity) -> multiplicative_identity
% 0.74/0.91 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 0.74/0.91 f1(add(a, multiplicative_identity)) -> true__
% 0.74/0.91 f1(add(multiplicative_identity, a)) -> true__
% 0.74/0.91 f1(multiplicative_identity) -> false__
% 0.74/0.91 inverse(additive_identity) -> multiplicative_identity
% 0.74/0.91 inverse(multiplicative_identity) -> additive_identity
% 0.74/0.91 multiply(X, inverse(X)) -> additive_identity
% 0.74/0.91 multiply(X, multiplicative_identity) -> X
% 0.74/0.91 multiply(Y0, Y0) -> Y0
% 0.74/0.91 multiply(Y0, add(Y0, Y0)) -> Y0
% 0.74/0.91 multiply(Y0, add(Y0, Y1)) -> Y0
% 0.74/0.91 multiply(Y0, add(Y0, inverse(additive_identity))) -> Y0
% 0.74/0.91 multiply(Y0, add(Y0, multiplicative_identity)) -> Y0
% 0.74/0.91 multiply(Y0, add(multiplicative_identity, Y0)) -> Y0
% 0.74/0.91 multiply(Y0, add(multiplicative_identity, inverse(Y0))) -> add(Y0, Y0)
% 0.74/0.91 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0
% 0.74/0.91 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1)
% 0.74/0.91 multiply(additive_identity, Y0) -> additive_identity
% 0.74/0.91 multiply(additive_identity, add(Y1, multiplicative_identity)) -> multiply(additive_identity, Y1)
% 0.74/0.91 multiply(additive_identity, add(multiplicative_identity, Y1)) -> multiply(additive_identity, Y1)
% 0.74/0.91 multiply(additive_identity, additive_identity) -> additive_identity
% 0.74/0.91 multiply(multiplicative_identity, Y0) -> Y0
% 0.74/0.91 true__ -> false__
% 0.74/0.91 with the LPO induced by
% 0.74/0.91 a > f1 > inverse > additive_identity > add > multiply > multiplicative_identity > true__ > false__
% 0.74/0.91
% 0.74/0.91 % SZS output end Proof
% 0.74/0.91
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