TSTP Solution File: BOO009-2 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : BOO009-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 23:46:19 EDT 2022
% Result : Unsatisfiable 5.27s 5.28s
% Output : Proof 5.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO009-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n027.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 16:06:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.27/5.28 % SZS status Unsatisfiable
% 5.27/5.28 % SZS output start Proof
% 5.27/5.28 The input problem is unsatisfiable because
% 5.27/5.28
% 5.27/5.28 [1] the following set of Horn clauses is unsatisfiable:
% 5.27/5.28
% 5.27/5.28 add(X, Y) = add(Y, X)
% 5.27/5.28 multiply(X, Y) = multiply(Y, X)
% 5.27/5.28 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 5.27/5.28 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 5.27/5.28 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 5.27/5.28 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 5.27/5.28 add(X, inverse(X)) = multiplicative_identity
% 5.27/5.28 add(inverse(X), X) = multiplicative_identity
% 5.27/5.28 multiply(X, inverse(X)) = additive_identity
% 5.27/5.28 multiply(inverse(X), X) = additive_identity
% 5.27/5.28 multiply(X, multiplicative_identity) = X
% 5.27/5.28 multiply(multiplicative_identity, X) = X
% 5.27/5.28 add(X, additive_identity) = X
% 5.27/5.28 add(additive_identity, X) = X
% 5.27/5.28 multiply(a, add(a, b)) = a ==> \bottom
% 5.27/5.28
% 5.27/5.28 This holds because
% 5.27/5.28
% 5.27/5.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.27/5.28
% 5.27/5.28 E:
% 5.27/5.28 add(X, Y) = add(Y, X)
% 5.27/5.28 add(X, additive_identity) = X
% 5.27/5.28 add(X, inverse(X)) = multiplicative_identity
% 5.27/5.28 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 5.27/5.28 add(additive_identity, X) = X
% 5.27/5.28 add(inverse(X), X) = multiplicative_identity
% 5.27/5.28 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 5.27/5.28 f1(a) = false__
% 5.27/5.28 f1(multiply(a, add(a, b))) = true__
% 5.27/5.28 multiply(X, Y) = multiply(Y, X)
% 5.27/5.28 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 5.27/5.28 multiply(X, inverse(X)) = additive_identity
% 5.27/5.28 multiply(X, multiplicative_identity) = X
% 5.27/5.28 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 5.27/5.28 multiply(inverse(X), X) = additive_identity
% 5.27/5.28 multiply(multiplicative_identity, X) = X
% 5.27/5.28 G:
% 5.27/5.28 true__ = false__
% 5.27/5.28
% 5.27/5.28 This holds because
% 5.27/5.28
% 5.27/5.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.27/5.28
% 5.27/5.28 add(X, Y) = add(Y, X)
% 5.27/5.28 multiply(X, Y) = multiply(Y, X)
% 5.27/5.28 add(X, inverse(X)) -> multiplicative_identity
% 5.27/5.28 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z))
% 5.27/5.28 add(Y0, Y0) -> Y0
% 5.27/5.28 add(Y0, add(Y0, X1)) -> add(Y0, X1)
% 5.27/5.28 add(Y0, inverse(multiplicative_identity)) -> Y0
% 5.27/5.28 add(Y0, multiplicative_identity) -> multiplicative_identity
% 5.27/5.28 add(Y1, add(Y0, multiply(Y0, Y1))) -> add(Y0, Y1)
% 5.27/5.28 add(add(Y0, Y0), add(Y1, multiply(Y1, Y0))) -> add(Y0, Y1)
% 5.27/5.28 add(add(Y1, Y1), add(Y0, multiply(Y0, Y1))) -> add(Y0, Y1)
% 5.27/5.28 add(inverse(X), X) -> multiplicative_identity
% 5.27/5.28 add(inverse(multiplicative_identity), Y0) -> Y0
% 5.27/5.28 add(multiplicative_identity, Y1) -> multiplicative_identity
% 5.27/5.28 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z))
% 5.27/5.28 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 5.27/5.28 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 5.27/5.28 add(multiply(Y0, Y1), multiply(Y0, additive_identity)) -> multiply(Y0, Y1)
% 5.27/5.28 add(multiply(Y0, Y1), multiply(Y0, inverse(Y1))) -> Y0
% 5.27/5.28 add(multiply(Y0, Y1), multiply(Y1, inverse(Y0))) -> Y1
% 5.27/5.28 add(multiply(Y0, Y2), multiply(additive_identity, Y2)) -> multiply(Y0, Y2)
% 5.27/5.28 add(multiply(Y0, Y2), multiply(inverse(Y0), Y2)) -> Y2
% 5.27/5.28 add(multiply(Y0, additive_identity), multiply(Y0, Y2)) -> multiply(Y0, Y2)
% 5.27/5.28 add(multiply(additive_identity, Y2), multiply(Y1, Y2)) -> multiply(Y1, Y2)
% 5.27/5.28 additive_identity -> inverse(multiplicative_identity)
% 5.27/5.28 f1(a) -> false__
% 5.27/5.28 f1(multiply(a, add(a, b))) -> true__
% 5.27/5.28 inverse(inverse(Y0)) -> Y0
% 5.27/5.28 multiply(X, inverse(X)) -> inverse(multiplicative_identity)
% 5.27/5.28 multiply(X, multiplicative_identity) -> X
% 5.27/5.28 multiply(Y0, add(Y0, Y2)) -> Y0
% 5.27/5.28 multiply(Y0, add(Y1, Y0)) -> Y0
% 5.27/5.28 multiply(Y0, additive_identity) -> inverse(multiplicative_identity)
% 5.27/5.28 multiply(Y0, inverse(multiplicative_identity)) -> inverse(multiplicative_identity)
% 5.27/5.28 multiply(Y1, Y1) -> Y1
% 5.27/5.28 multiply(Y1, add(inverse(X0), Y1)) -> Y1
% 5.27/5.28 multiply(additive_identity, Y1) -> inverse(multiplicative_identity)
% 5.27/5.28 multiply(inverse(X), X) -> inverse(multiplicative_identity)
% 5.27/5.28 multiply(inverse(multiplicative_identity), Y0) -> inverse(multiplicative_identity)
% 5.27/5.28 multiply(multiplicative_identity, X) -> X
% 5.27/5.28 multiply(multiply(Y1, add(Y2, Y1)), multiply(Y2, add(Y1, Y2))) -> multiply(Y1, Y2)
% 5.27/5.28 true__ -> false__
% 5.27/5.28 with the LPO induced by
% 5.27/5.28 b > add > multiply > additive_identity > multiplicative_identity > inverse > a > f1 > true__ > false__
% 5.27/5.28
% 5.27/5.28 % SZS output end Proof
% 5.27/5.28
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