TSTP Solution File: PUZ003-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : PUZ003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 : Mon Jul 18 18:21:05 EDT 2022
% Result : Unsatisfiable 5.66s 5.64s
% Output : Proof 5.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n026.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 : Sun May 29 00:26:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.66/5.64 % SZS status Unsatisfiable
% 5.66/5.64 % SZS output start Proof
% 5.66/5.64 The input problem is unsatisfiable because
% 5.66/5.64
% 5.66/5.64 [1] the following set of Horn clauses is unsatisfiable:
% 5.66/5.64
% 5.66/5.64 member(X) & member(Y) & shaved(X, Y) ==> shaved(members, X)
% 5.66/5.64 shaved(members, X) & member(Y) ==> shaved(Y, X)
% 5.66/5.64 member(guido)
% 5.66/5.64 member(lorenzo)
% 5.66/5.64 member(petruchio)
% 5.66/5.64 member(cesare)
% 5.66/5.64 shaved(guido, cesare)
% 5.66/5.64 shaved(petruchio, lorenzo) ==> \bottom
% 5.66/5.64
% 5.66/5.64 This holds because
% 5.66/5.64
% 5.66/5.64 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.66/5.64
% 5.66/5.64 E:
% 5.66/5.64 f1(true__, X) = shaved(members, X)
% 5.66/5.64 f2(true__, X) = f1(member(X), X)
% 5.66/5.64 f3(shaved(X, Y), Y, X) = true__
% 5.66/5.64 f3(true__, Y, X) = f2(member(Y), X)
% 5.66/5.64 f4(true__, Y, X) = shaved(Y, X)
% 5.66/5.64 f5(member(Y), X, Y) = true__
% 5.66/5.64 f5(true__, X, Y) = f4(shaved(members, X), Y, X)
% 5.66/5.64 f6(shaved(petruchio, lorenzo)) = true__
% 5.66/5.64 f6(true__) = false__
% 5.66/5.64 member(cesare) = true__
% 5.66/5.64 member(guido) = true__
% 5.66/5.64 member(lorenzo) = true__
% 5.66/5.64 member(petruchio) = true__
% 5.66/5.64 shaved(guido, cesare) = true__
% 5.66/5.64 G:
% 5.66/5.64 true__ = false__
% 5.66/5.64
% 5.66/5.64 This holds because
% 5.66/5.64
% 5.66/5.64 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.66/5.64
% 5.66/5.64
% 5.66/5.64 f1(member(X), X) -> f3(true__, lorenzo, X)
% 5.66/5.64 f1(true__, X) -> f4(true__, members, X)
% 5.66/5.64 f2(member(Y), X) -> f3(true__, Y, X)
% 5.66/5.64 f2(true__, Y1) -> f3(true__, lorenzo, Y1)
% 5.66/5.64 f3(f3(true__, cesare, lorenzo), lorenzo, members) -> true__
% 5.66/5.64 f3(f4(true__, Y0, Y1), Y1, Y0) -> true__
% 5.66/5.64 f3(true__, cesare, Y1) -> f3(true__, lorenzo, Y1)
% 5.66/5.64 f3(true__, cesare, cesare) -> true__
% 5.66/5.64 f3(true__, cesare, guido) -> true__
% 5.66/5.64 f3(true__, cesare, lorenzo) -> true__
% 5.66/5.64 f3(true__, cesare, members) -> true__
% 5.66/5.64 f3(true__, cesare, petruchio) -> true__
% 5.66/5.64 f3(true__, guido, Y1) -> f3(true__, lorenzo, Y1)
% 5.66/5.64 f3(true__, lorenzo, cesare) -> true__
% 5.66/5.64 f3(true__, lorenzo, guido) -> true__
% 5.66/5.64 f3(true__, lorenzo, lorenzo) -> true__
% 5.66/5.64 f3(true__, lorenzo, members) -> true__
% 5.66/5.64 f3(true__, lorenzo, petruchio) -> true__
% 5.66/5.64 f3(true__, petruchio, Y1) -> f3(true__, lorenzo, Y1)
% 5.66/5.64 f4(f3(true__, lorenzo, guido), guido, guido) -> true__
% 5.66/5.64 f4(f3(true__, petruchio, guido), guido, guido) -> true__
% 5.66/5.64 f4(f3(true__, petruchio, guido), lorenzo, guido) -> true__
% 5.66/5.64 f4(f3(true__, petruchio, guido), petruchio, guido) -> true__
% 5.66/5.64 f4(f3(true__, petruchio, lorenzo), guido, lorenzo) -> true__
% 5.66/5.64 f4(f3(true__, petruchio, lorenzo), lorenzo, lorenzo) -> true__
% 5.66/5.64 f4(f4(true__, members, Y1), cesare, Y1) -> true__
% 5.66/5.64 f4(f4(true__, members, Y1), guido, Y1) -> true__
% 5.66/5.64 f4(f4(true__, members, Y1), lorenzo, Y1) -> true__
% 5.66/5.64 f4(f4(true__, members, Y1), petruchio, Y1) -> true__
% 5.66/5.64 f4(true__, cesare, guido) -> true__
% 5.66/5.64 f4(true__, cesare, lorenzo) -> true__
% 5.66/5.64 f4(true__, guido, cesare) -> true__
% 5.66/5.64 f4(true__, guido, guido) -> true__
% 5.66/5.64 f4(true__, guido, lorenzo) -> true__
% 5.66/5.64 f4(true__, guido, petruchio) -> true__
% 5.66/5.64 f4(true__, lorenzo, guido) -> true__
% 5.66/5.64 f4(true__, lorenzo, lorenzo) -> true__
% 5.66/5.64 f4(true__, lorenzo, petruchio) -> true__
% 5.66/5.64 f4(true__, members, cesare) -> f3(true__, lorenzo, cesare)
% 5.66/5.64 f4(true__, members, guido) -> f3(true__, lorenzo, guido)
% 5.66/5.64 f4(true__, members, lorenzo) -> f3(true__, lorenzo, lorenzo)
% 5.66/5.64 f4(true__, members, petruchio) -> f3(true__, lorenzo, petruchio)
% 5.66/5.64 f4(true__, petruchio, guido) -> true__
% 5.66/5.64 f4(true__, petruchio, lorenzo) -> true__
% 5.66/5.64 f4(true__, petruchio, petruchio) -> true__
% 5.66/5.64 f5(member(Y), X, Y) -> true__
% 5.66/5.64 f5(true__, X, Y) -> f4(f4(true__, members, X), Y, X)
% 5.66/5.64 f6(f4(true__, petruchio, lorenzo)) -> true__
% 5.66/5.64 f6(true__) -> false__
% 5.66/5.64 false__ -> true__
% 5.66/5.64 member(cesare) -> true__
% 5.66/5.64 member(guido) -> true__
% 5.66/5.64 member(lorenzo) -> true__
% 5.66/5.64 member(petruchio) -> true__
% 5.66/5.64 shaved(Y, X) -> f4(true__, Y, X)
% 5.66/5.64 with the LPO induced by
% 5.66/5.64 f5 > f1 > member > members > f2 > f3 > shaved > f4 > cesare > petruchio > guido > lorenzo > f6 > false__ > true__
% 5.66/5.64
% 5.66/5.64 % SZS output end Proof
% 5.66/5.64
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