%------------------------------------------------------------------------------ % 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 : %------------------------------------------------------------------------------ %----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 %------------------------------------------------------------------------------