TSTP Solution File: BOO012-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n032.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 23:46:23 EDT 2022
% Result : Unsatisfiable 5.40s 5.50s
% Output : Proof 5.40s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.09 % Command : moca.sh %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Wed Jun 1 15:37:59 EDT 2022
% 0.09/0.28 % CPUTime :
% 5.40/5.50 % SZS status Unsatisfiable
% 5.40/5.50 % SZS output start Proof
% 5.40/5.50 The input problem is unsatisfiable because
% 5.40/5.50
% 5.40/5.50 [1] the following set of Horn clauses is unsatisfiable:
% 5.40/5.50
% 5.40/5.50 add(X, Y) = add(Y, X)
% 5.40/5.50 multiply(X, Y) = multiply(Y, X)
% 5.40/5.50 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 5.40/5.50 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 5.40/5.50 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 5.40/5.50 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 5.40/5.50 add(X, inverse(X)) = multiplicative_identity
% 5.40/5.50 add(inverse(X), X) = multiplicative_identity
% 5.40/5.50 multiply(X, inverse(X)) = additive_identity
% 5.40/5.50 multiply(inverse(X), X) = additive_identity
% 5.40/5.50 multiply(X, multiplicative_identity) = X
% 5.40/5.50 multiply(multiplicative_identity, X) = X
% 5.40/5.50 add(X, additive_identity) = X
% 5.40/5.50 add(additive_identity, X) = X
% 5.40/5.50 inverse(inverse(x)) = x ==> \bottom
% 5.40/5.50
% 5.40/5.50 This holds because
% 5.40/5.50
% 5.40/5.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.40/5.50
% 5.40/5.50 E:
% 5.40/5.50 add(X, Y) = add(Y, X)
% 5.40/5.50 add(X, additive_identity) = X
% 5.40/5.50 add(X, inverse(X)) = multiplicative_identity
% 5.40/5.50 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 5.40/5.50 add(additive_identity, X) = X
% 5.40/5.50 add(inverse(X), X) = multiplicative_identity
% 5.40/5.50 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 5.40/5.50 f1(inverse(inverse(x))) = true__
% 5.40/5.50 f1(x) = false__
% 5.40/5.50 multiply(X, Y) = multiply(Y, X)
% 5.40/5.50 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 5.40/5.50 multiply(X, inverse(X)) = additive_identity
% 5.40/5.50 multiply(X, multiplicative_identity) = X
% 5.40/5.50 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 5.40/5.50 multiply(inverse(X), X) = additive_identity
% 5.40/5.50 multiply(multiplicative_identity, X) = X
% 5.40/5.50 G:
% 5.40/5.50 true__ = false__
% 5.40/5.50
% 5.40/5.50 This holds because
% 5.40/5.50
% 5.40/5.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.40/5.50
% 5.40/5.50 add(X, Y) = add(Y, X)
% 5.40/5.50 multiply(X, Y) = multiply(Y, X)
% 5.40/5.50 multiply(Y1, multiply(add(Y0, Y1), add(Y0, Y2))) = multiply(add(Y0, Y2), Y1)
% 5.40/5.50 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2))
% 5.40/5.50 multiply(inverse(Y0), add(Y0, Y1)) = multiply(Y1, inverse(Y0))
% 5.40/5.50 multiply(inverse(Y1), add(Y0, Y1)) = multiply(Y0, inverse(Y1))
% 5.40/5.50 add(X, additive_identity) -> X
% 5.40/5.50 add(X, inverse(X)) -> multiplicative_identity
% 5.40/5.50 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z))
% 5.40/5.50 add(Y0, Y0) -> Y0
% 5.40/5.50 add(Y0, inverse(inverse(Y0))) -> Y0
% 5.40/5.50 add(Y0, inverse(inverse(Y0))) -> inverse(inverse(Y0))
% 5.40/5.50 add(Y0, multiplicative_identity) -> multiplicative_identity
% 5.40/5.50 add(additive_identity, X) -> X
% 5.40/5.50 add(inverse(X), X) -> multiplicative_identity
% 5.40/5.50 add(multiplicative_identity, Y1) -> multiplicative_identity
% 5.40/5.50 add(multiplicative_identity, inverse(Y0)) -> multiplicative_identity
% 5.40/5.50 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z))
% 5.40/5.50 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 5.40/5.50 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 5.40/5.50 f1(inverse(inverse(x))) -> true__
% 5.40/5.50 f1(x) -> false__
% 5.40/5.50 inverse(additive_identity) -> multiplicative_identity
% 5.40/5.50 inverse(inverse(Y0)) -> Y0
% 5.40/5.50 inverse(multiplicative_identity) -> additive_identity
% 5.40/5.50 multiply(X, inverse(X)) -> additive_identity
% 5.40/5.50 multiply(X, multiplicative_identity) -> X
% 5.40/5.50 multiply(Y0, Y0) -> Y0
% 5.40/5.50 multiply(Y0, add(Y0, Y0)) -> Y0
% 5.40/5.50 multiply(Y0, add(Y0, Y1)) -> Y0
% 5.40/5.50 multiply(Y0, add(Y0, multiplicative_identity)) -> Y0
% 5.40/5.50 multiply(Y0, add(Y1, Y0)) -> Y0
% 5.40/5.50 multiply(Y0, add(Y1, inverse(Y0))) -> multiply(Y0, Y1)
% 5.40/5.50 multiply(Y0, add(inverse(Y0), Y2)) -> multiply(Y0, Y2)
% 5.40/5.50 multiply(Y0, inverse(inverse(Y0))) -> Y0
% 5.40/5.50 multiply(Y0, inverse(inverse(inverse(Y0)))) -> additive_identity
% 5.40/5.50 multiply(Y0, multiply(add(Y1, Y0), add(Y1, Y2))) -> multiply(Y0, add(Y1, Y2))
% 5.40/5.50 multiply(Y0, multiply(add(Y1, Y2), add(Y1, Y0))) -> multiply(Y0, add(Y1, Y2))
% 5.40/5.50 multiply(Y1, add(multiplicative_identity, Y1)) -> Y1
% 5.40/5.50 multiply(Y1, additive_identity) -> additive_identity
% 5.40/5.50 multiply(Y1, inverse(inverse(Y1))) -> inverse(inverse(Y1))
% 5.40/5.50 multiply(Y1, multiply(add(Y0, Y2), add(Y0, Y1))) -> multiply(add(Y0, Y2), Y1)
% 5.40/5.50 multiply(add(Y0, Y0), add(Y0, Y2)) -> Y0
% 5.40/5.50 multiply(add(Y0, Y0), add(Y1, Y0)) -> Y0
% 5.40/5.50 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0
% 5.40/5.50 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1)
% 5.40/5.50 multiply(add(Y0, Y1), add(Y1, Y1)) -> Y1
% 5.40/5.50 multiply(add(Y0, Y1), add(Y1, inverse(Y0))) -> Y1
% 5.40/5.50 multiply(add(Y0, Y2), add(inverse(Y0), Y2)) -> Y2
% 5.40/5.50 multiply(add(Y0, Y2), add(multiplicative_identity, Y2)) -> add(Y0, Y2)
% 5.40/5.50 multiply(add(Y0, Y2), inverse(Y0)) -> multiply(Y2, inverse(Y0))
% 5.40/5.50 multiply(add(Y0, Y2), inverse(Y2)) -> multiply(Y0, inverse(Y2))
% 5.40/5.50 multiply(add(Y0, inverse(multiply(Y0, Y1))), add(Y1, inverse(multiply(Y0, Y1)))) -> multiplicative_identity
% 5.40/5.50 multiply(add(Y0, multiplicative_identity), add(Y0, Y2)) -> add(Y0, Y2)
% 5.40/5.50 multiply(add(Y1, Y2), add(Y1, Y1)) -> Y1
% 5.40/5.50 multiply(add(multiplicative_identity, Y2), add(Y1, Y2)) -> add(Y1, Y2)
% 5.40/5.50 multiply(additive_identity, Y0) -> additive_identity
% 5.40/5.50 multiply(additive_identity, add(multiplicative_identity, Y1)) -> multiply(additive_identity, Y1)
% 5.40/5.50 multiply(additive_identity, additive_identity) -> additive_identity
% 5.40/5.50 multiply(inverse(X), X) -> additive_identity
% 5.40/5.50 multiply(inverse(X0), add(X0, Y1)) -> multiply(inverse(X0), Y1)
% 5.40/5.50 multiply(inverse(X0), add(Y1, X0)) -> multiply(inverse(X0), Y1)
% 5.40/5.50 multiply(inverse(Y0), inverse(inverse(inverse(Y0)))) -> inverse(inverse(inverse(Y0)))
% 5.40/5.50 multiply(multiplicative_identity, X) -> X
% 5.40/5.50 true__ -> false__
% 5.40/5.50 with the LPO induced by
% 5.40/5.50 x > f1 > inverse > additive_identity > multiplicative_identity > add > multiply > true__ > false__
% 5.40/5.50
% 5.40/5.50 % SZS output end Proof
% 5.40/5.50
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