TSTP Solution File: BOO013-4 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n023.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 8.83s 8.78s
% Output : Proof 8.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 16:22:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 8.83/8.78 % SZS status Unsatisfiable
% 8.83/8.78 % SZS output start Proof
% 8.83/8.78 The input problem is unsatisfiable because
% 8.83/8.78
% 8.83/8.78 [1] the following set of Horn clauses is unsatisfiable:
% 8.83/8.78
% 8.83/8.78 add(X, Y) = add(Y, X)
% 8.83/8.78 multiply(X, Y) = multiply(Y, X)
% 8.83/8.78 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 8.83/8.78 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 8.83/8.78 add(X, additive_identity) = X
% 8.83/8.78 multiply(X, multiplicative_identity) = X
% 8.83/8.78 add(X, inverse(X)) = multiplicative_identity
% 8.83/8.78 multiply(X, inverse(X)) = additive_identity
% 8.83/8.78 add(a, b) = multiplicative_identity
% 8.83/8.78 multiply(a, b) = additive_identity
% 8.83/8.78 b = inverse(a) ==> \bottom
% 8.83/8.78
% 8.83/8.78 This holds because
% 8.83/8.78
% 8.83/8.78 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.83/8.78
% 8.83/8.78 E:
% 8.83/8.78 add(X, Y) = add(Y, X)
% 8.83/8.78 add(X, additive_identity) = X
% 8.83/8.78 add(X, inverse(X)) = multiplicative_identity
% 8.83/8.78 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 8.83/8.78 add(a, b) = multiplicative_identity
% 8.83/8.78 f1(b) = true__
% 8.83/8.78 f1(inverse(a)) = false__
% 8.83/8.78 multiply(X, Y) = multiply(Y, X)
% 8.83/8.78 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 8.83/8.78 multiply(X, inverse(X)) = additive_identity
% 8.83/8.78 multiply(X, multiplicative_identity) = X
% 8.83/8.78 multiply(a, b) = additive_identity
% 8.83/8.78 G:
% 8.83/8.78 true__ = false__
% 8.83/8.78
% 8.83/8.78 This holds because
% 8.83/8.78
% 8.83/8.78 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.83/8.78
% 8.83/8.78 add(X, Y) = add(Y, X)
% 8.83/8.78 multiply(X, Y) = multiply(Y, X)
% 8.83/8.78 multiply(Y0, add(Y0, Y1)) = multiply(Y0, add(Y1, add(b, a)))
% 8.83/8.78 multiply(Y0, add(Y0, Y2)) = multiply(Y0, add(add(b, a), Y2))
% 8.83/8.78 multiply(Y0, add(Y1, Y0)) = multiply(Y0, add(Y1, add(b, a)))
% 8.83/8.78 multiply(Y0, add(Y1, Y0)) = multiply(Y0, add(add(b, a), Y1))
% 8.83/8.78 multiply(add(Y0, Y0), add(Y0, Y1)) = multiply(Y0, add(Y1, add(b, a)))
% 8.83/8.78 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(add(b, a), Y2))
% 8.83/8.78 multiply(add(add(b, a), Y1), Y0) = multiply(Y0, add(Y0, Y1))
% 8.83/8.78 add(X, additive_identity) -> X
% 8.83/8.78 add(X, inverse(X)) -> multiplicative_identity
% 8.83/8.78 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z))
% 8.83/8.78 add(Y0, add(b, a)) -> add(b, a)
% 8.83/8.78 add(Y0, inverse(inverse(Y0))) -> Y0
% 8.83/8.78 add(Y1, Y1) -> Y1
% 8.83/8.78 add(a, inverse(b)) -> inverse(b)
% 8.83/8.78 add(b, inverse(a)) -> inverse(a)
% 8.83/8.78 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 8.83/8.78 add(multiply(b, a), Y0) -> Y0
% 8.83/8.78 additive_identity -> multiply(a, b)
% 8.83/8.78 f1(b) -> true__
% 8.83/8.78 f1(inverse(a)) -> false__
% 8.83/8.78 inverse(a) -> b
% 8.83/8.78 inverse(add(b, a)) -> multiply(b, a)
% 8.83/8.78 inverse(b) -> a
% 8.83/8.78 inverse(inverse(Y1)) -> Y1
% 8.83/8.78 inverse(multiply(b, a)) -> add(b, a)
% 8.83/8.78 multiplicative_identity -> add(a, b)
% 8.83/8.78 multiply(X, inverse(X)) -> additive_identity
% 8.83/8.78 multiply(X, multiplicative_identity) -> X
% 8.83/8.78 multiply(Y0, Y0) -> Y0
% 8.83/8.78 multiply(Y0, add(Y0, Y0)) -> Y0
% 8.83/8.78 multiply(Y0, add(Y0, add(b, a))) -> Y0
% 8.83/8.78 multiply(Y0, add(add(b, a), Y0)) -> Y0
% 8.83/8.78 multiply(Y0, add(add(b, a), inverse(Y0))) -> Y0
% 8.83/8.78 multiply(Y0, add(b, a)) -> Y0
% 8.83/8.78 multiply(Y0, multiply(multiply(b, a), Y0)) -> multiply(Y0, multiply(b, a))
% 8.83/8.78 multiply(Y1, multiply(multiply(b, a), Y1)) -> multiply(multiply(b, a), Y1)
% 8.83/8.78 multiply(a, add(b, add(b, a))) -> a
% 8.83/8.78 multiply(a, add(b, b)) -> multiply(b, a)
% 8.83/8.78 multiply(a, add(b, inverse(inverse(a)))) -> inverse(inverse(a))
% 8.83/8.78 multiply(add(Y0, Y1), add(Y0, add(b, a))) -> add(Y0, Y1)
% 8.83/8.78 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0
% 8.83/8.78 multiply(add(Y0, Y1), add(inverse(Y0), Y1)) -> Y1
% 8.83/8.78 multiply(add(Y0, Y1), add(inverse(Y1), Y0)) -> Y0
% 8.83/8.78 multiply(add(Y0, a), add(b, Y0)) -> Y0
% 8.83/8.78 multiply(add(Y0, b), add(Y0, a)) -> Y0
% 8.83/8.78 multiply(add(Y0, b), add(a, Y0)) -> Y0
% 8.83/8.78 multiply(add(Y1, Y0), add(Y0, inverse(Y1))) -> Y0
% 8.83/8.78 multiply(add(Y1, add(b, a)), inverse(Y1)) -> inverse(Y1)
% 8.83/8.78 multiply(add(a, Y0), add(Y0, b)) -> Y0
% 8.83/8.78 multiply(add(add(b, a), Y0), inverse(Y0)) -> inverse(Y0)
% 8.83/8.78 multiply(add(b, Y0), add(Y0, a)) -> Y0
% 8.83/8.78 multiply(add(b, Y0), add(a, Y0)) -> Y0
% 8.83/8.78 multiply(add(b, a), Y0) -> Y0
% 8.83/8.78 multiply(add(inverse(Y1), Y0), add(Y0, Y1)) -> Y0
% 8.83/8.78 multiply(multiply(Y1, add(Y1, Y2)), multiply(Y2, add(Y2, Y1))) -> multiply(Y1, Y2)
% 8.83/8.78 multiply(multiply(a, add(b, b)), Y1) -> multiply(multiply(b, a), Y1)
% 8.83/8.78 multiply(multiply(b, a), add(Y1, add(b, a))) -> multiply(multiply(b, a), Y1)
% 8.83/8.78 multiply(multiply(b, a), multiply(b, a)) -> multiply(b, a)
% 8.83/8.78 true__ -> false__
% 8.83/8.78 with the LPO induced by
% 8.83/8.78 f1 > inverse > additive_identity > multiplicative_identity > add > multiply > a > b > true__ > false__
% 8.83/8.78
% 8.83/8.78 % SZS output end Proof
% 8.83/8.78
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