TSTP Solution File: GRP174-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n007.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 : Sat Jul 16 10:53:43 EDT 2022
% Result : Unsatisfiable 10.30s 10.30s
% Output : Proof 10.30s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 07:51:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.30/10.30 % SZS status Unsatisfiable
% 10.30/10.30 % SZS output start Proof
% 10.30/10.30 The input problem is unsatisfiable because
% 10.30/10.30
% 10.30/10.30 [1] the following set of Horn clauses is unsatisfiable:
% 10.30/10.30
% 10.30/10.30 multiply(identity, X) = X
% 10.30/10.30 multiply(inverse(X), X) = identity
% 10.30/10.30 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 10.30/10.30 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 10.30/10.30 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 10.30/10.30 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 10.30/10.30 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 10.30/10.30 least_upper_bound(X, X) = X
% 10.30/10.30 greatest_lower_bound(X, X) = X
% 10.30/10.30 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 10.30/10.30 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 10.30/10.30 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 10.30/10.30 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 10.30/10.30 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 10.30/10.30 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 10.30/10.30 greatest_lower_bound(identity, a) = a
% 10.30/10.30 greatest_lower_bound(identity, inverse(a)) = inverse(a)
% 10.30/10.30 identity = a ==> \bottom
% 10.30/10.30
% 10.30/10.30 This holds because
% 10.30/10.30
% 10.30/10.30 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 10.30/10.30
% 10.30/10.30 E:
% 10.30/10.30 f1(a) = false__
% 10.30/10.30 f1(identity) = true__
% 10.30/10.30 greatest_lower_bound(X, X) = X
% 10.30/10.30 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 10.30/10.30 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 10.30/10.30 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 10.30/10.30 greatest_lower_bound(identity, a) = a
% 10.30/10.30 greatest_lower_bound(identity, inverse(a)) = inverse(a)
% 10.30/10.30 least_upper_bound(X, X) = X
% 10.30/10.30 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 10.30/10.30 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 10.30/10.30 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 10.30/10.30 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 10.30/10.30 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 10.30/10.30 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 10.30/10.30 multiply(identity, X) = X
% 10.30/10.30 multiply(inverse(X), X) = identity
% 10.30/10.30 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 10.30/10.30 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 10.30/10.30 G:
% 10.30/10.30 true__ = false__
% 10.30/10.30
% 10.30/10.30 This holds because
% 10.30/10.30
% 10.30/10.30 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 10.30/10.30
% 10.30/10.30 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 10.30/10.30 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1)
% 10.30/10.30 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1)
% 10.30/10.30 greatest_lower_bound(identity, greatest_lower_bound(Y0, a)) = greatest_lower_bound(a, Y0)
% 10.30/10.30 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 10.30/10.30 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1)
% 10.30/10.30 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1)
% 10.30/10.30 a -> identity
% 10.30/10.30 f1(a) -> false__
% 10.30/10.30 f1(identity) -> true__
% 10.30/10.30 greatest_lower_bound(X, X) -> X
% 10.30/10.30 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 10.30/10.30 greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y0)) -> greatest_lower_bound(Y0, Y1)
% 10.30/10.30 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1)
% 10.30/10.30 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 10.30/10.30 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0
% 10.30/10.30 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 10.30/10.30 greatest_lower_bound(Y1, multiply(a, Y1)) -> multiply(a, Y1)
% 10.30/10.30 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 10.30/10.30 greatest_lower_bound(identity, a) -> a
% 10.30/10.30 greatest_lower_bound(identity, greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a)
% 10.30/10.30 greatest_lower_bound(identity, greatest_lower_bound(a, Y2)) -> greatest_lower_bound(a, Y2)
% 10.30/10.30 greatest_lower_bound(identity, inverse(a)) -> inverse(a)
% 10.30/10.30 greatest_lower_bound(least_upper_bound(X0, identity), least_upper_bound(identity, X0)) -> least_upper_bound(X0, identity)
% 10.30/10.30 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z))
% 10.30/10.30 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X)
% 10.30/10.30 inverse(a) -> identity
% 10.30/10.30 inverse(identity) -> identity
% 10.30/10.30 inverse(inverse(Y0)) -> Y0
% 10.30/10.30 inverse(inverse(identity)) -> identity
% 10.30/10.30 least_upper_bound(X, X) -> X
% 10.30/10.30 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 10.30/10.30 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 10.30/10.30 least_upper_bound(Y0, least_upper_bound(Y1, Y0)) -> least_upper_bound(Y0, Y1)
% 10.30/10.30 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1)
% 10.30/10.30 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 10.30/10.30 least_upper_bound(Y1, multiply(a, Y1)) -> Y1
% 10.30/10.30 least_upper_bound(Y1, multiply(inverse(a), Y1)) -> Y1
% 10.30/10.30 least_upper_bound(a, greatest_lower_bound(identity, greatest_lower_bound(Y1, a))) -> a
% 10.30/10.30 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(a, X0)) -> greatest_lower_bound(X0, a)
% 10.30/10.30 least_upper_bound(greatest_lower_bound(Y0, identity), greatest_lower_bound(identity, Y0)) -> greatest_lower_bound(Y0, identity)
% 10.30/10.30 least_upper_bound(identity, a) -> identity
% 10.30/10.30 least_upper_bound(identity, greatest_lower_bound(Y0, a)) -> identity
% 10.30/10.30 least_upper_bound(identity, greatest_lower_bound(a, X0)) -> identity
% 10.30/10.30 least_upper_bound(identity, inverse(X0)) -> multiply(least_upper_bound(identity, X0), inverse(X0))
% 10.30/10.30 least_upper_bound(identity, inverse(a)) -> identity
% 10.30/10.30 least_upper_bound(identity, least_upper_bound(Y0, a)) -> least_upper_bound(identity, Y0)
% 10.30/10.30 least_upper_bound(identity, least_upper_bound(Y0, inverse(a))) -> least_upper_bound(identity, Y0)
% 10.30/10.30 least_upper_bound(identity, least_upper_bound(a, Y2)) -> least_upper_bound(identity, Y2)
% 10.30/10.30 least_upper_bound(identity, least_upper_bound(inverse(a), Y2)) -> least_upper_bound(identity, Y2)
% 10.30/10.30 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 10.30/10.30 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z))
% 10.30/10.30 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X)
% 10.30/10.30 multiply(X0, multiply(inverse(X0), Y1)) -> Y1
% 10.30/10.30 multiply(Y0, inverse(Y0)) -> identity
% 10.30/10.30 multiply(Y0, inverse(inverse(inverse(Y0)))) -> identity
% 10.30/10.30 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 10.30/10.30 multiply(Y1, identity) -> Y1
% 10.30/10.30 multiply(identity, X) -> X
% 10.30/10.30 multiply(inverse(X), X) -> identity
% 10.30/10.30 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 10.30/10.30 multiply(inverse(identity), Y1) -> Y1
% 10.30/10.30 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 10.30/10.30 multiply(inverse(inverse(Y1)), identity) -> Y1
% 10.30/10.30 multiply(least_upper_bound(identity, inverse(Y0)), Y0) -> least_upper_bound(Y0, identity)
% 10.30/10.30 multiply(least_upper_bound(identity, inverse(identity)), Y0) -> Y0
% 10.30/10.30 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 10.30/10.30 true__ -> false__
% 10.30/10.30 with the LPO induced by
% 10.30/10.30 f1 > a > inverse > identity > least_upper_bound > greatest_lower_bound > multiply > true__ > false__
% 10.30/10.30
% 10.30/10.30 % SZS output end Proof
% 10.30/10.30
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