TSTP Solution File: BOO011-2 by Moca---0.1
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% File : Moca---0.1
% Problem : BOO011-2 : 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 23:46:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO011-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n019.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 22:43:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 The input problem is unsatisfiable because
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% 0.20/0.40 [1] the following set of Horn clauses is unsatisfiable:
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% 0.20/0.40 add(X, Y) = add(Y, X)
% 0.20/0.40 multiply(X, Y) = multiply(Y, X)
% 0.20/0.40 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 0.20/0.40 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 0.20/0.40 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.20/0.40 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.20/0.40 add(X, inverse(X)) = multiplicative_identity
% 0.20/0.40 add(inverse(X), X) = multiplicative_identity
% 0.20/0.40 multiply(X, inverse(X)) = additive_identity
% 0.20/0.40 multiply(inverse(X), X) = additive_identity
% 0.20/0.40 multiply(X, multiplicative_identity) = X
% 0.20/0.40 multiply(multiplicative_identity, X) = X
% 0.20/0.40 add(X, additive_identity) = X
% 0.20/0.40 add(additive_identity, X) = X
% 0.20/0.40 inverse(additive_identity) = multiplicative_identity ==> \bottom
% 0.20/0.40
% 0.20/0.40 This holds because
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% 0.20/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.20/0.40 E:
% 0.20/0.40 add(X, Y) = add(Y, X)
% 0.20/0.40 add(X, additive_identity) = X
% 0.20/0.40 add(X, inverse(X)) = multiplicative_identity
% 0.20/0.40 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 0.20/0.40 add(additive_identity, X) = X
% 0.20/0.40 add(inverse(X), X) = multiplicative_identity
% 0.20/0.40 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 0.20/0.40 f1(inverse(additive_identity)) = true__
% 0.20/0.40 f1(multiplicative_identity) = false__
% 0.20/0.40 multiply(X, Y) = multiply(Y, X)
% 0.20/0.40 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.20/0.40 multiply(X, inverse(X)) = additive_identity
% 0.20/0.40 multiply(X, multiplicative_identity) = X
% 0.20/0.40 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.20/0.40 multiply(inverse(X), X) = additive_identity
% 0.20/0.40 multiply(multiplicative_identity, X) = X
% 0.20/0.40 G:
% 0.20/0.40 true__ = false__
% 0.20/0.40
% 0.20/0.40 This holds because
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% 0.20/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
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% 0.20/0.40 add(X, Y) = add(Y, X)
% 0.20/0.40 multiply(X, Y) = multiply(Y, X)
% 0.20/0.40 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2))
% 0.20/0.40 add(X, additive_identity) -> X
% 0.20/0.40 add(X, inverse(X)) -> multiplicative_identity
% 0.20/0.40 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z))
% 0.20/0.40 add(Y0, multiplicative_identity) -> multiplicative_identity
% 0.20/0.40 add(additive_identity, X) -> X
% 0.20/0.40 add(inverse(X), X) -> multiplicative_identity
% 0.20/0.40 add(multiplicative_identity, inverse(Y0)) -> multiplicative_identity
% 0.20/0.40 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z))
% 0.20/0.40 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 0.20/0.40 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 0.20/0.40 f1(inverse(additive_identity)) -> true__
% 0.20/0.40 f1(multiplicative_identity) -> false__
% 0.20/0.40 inverse(additive_identity) -> multiplicative_identity
% 0.20/0.40 inverse(multiplicative_identity) -> additive_identity
% 0.20/0.40 multiply(X, inverse(X)) -> additive_identity
% 0.20/0.40 multiply(X, multiplicative_identity) -> X
% 0.20/0.40 multiply(Y0, add(Y0, Y0)) -> Y0
% 0.20/0.40 multiply(Y0, add(Y0, multiplicative_identity)) -> Y0
% 0.20/0.40 multiply(Y1, add(multiplicative_identity, Y1)) -> Y1
% 0.20/0.40 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1)
% 0.20/0.40 multiply(add(Y0, Y2), add(multiplicative_identity, Y2)) -> add(Y0, Y2)
% 0.20/0.40 multiply(add(Y0, multiplicative_identity), add(Y0, Y2)) -> add(Y0, Y2)
% 0.20/0.40 multiply(add(multiplicative_identity, Y2), add(Y1, Y2)) -> add(Y1, Y2)
% 0.20/0.40 multiply(additive_identity, add(multiplicative_identity, Y1)) -> multiply(additive_identity, Y1)
% 0.20/0.40 multiply(inverse(X), X) -> additive_identity
% 0.20/0.40 multiply(multiplicative_identity, X) -> X
% 0.20/0.40 true__ -> false__
% 0.20/0.40 with the LPO induced by
% 0.20/0.40 f1 > inverse > additive_identity > multiplicative_identity > add > multiply > true__ > false__
% 0.20/0.40
% 0.20/0.40 % SZS output end Proof
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