TSTP Solution File: REL049-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : REL049-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 19:47:38 EDT 2022
% Result : Unsatisfiable 1.80s 1.93s
% Output : Proof 1.80s
% 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 : REL049-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.12/0.33 % Computer : n021.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 09:57:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.80/1.93 % SZS status Unsatisfiable
% 1.80/1.93 % SZS output start Proof
% 1.80/1.93 The input problem is unsatisfiable because
% 1.80/1.93
% 1.80/1.93 [1] the following set of Horn clauses is unsatisfiable:
% 1.80/1.93
% 1.80/1.93 join(A, B) = join(B, A)
% 1.80/1.93 join(A, join(B, C)) = join(join(A, B), C)
% 1.80/1.93 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B)))
% 1.80/1.93 meet(A, B) = complement(join(complement(A), complement(B)))
% 1.80/1.93 composition(A, composition(B, C)) = composition(composition(A, B), C)
% 1.80/1.93 composition(A, one) = A
% 1.80/1.93 composition(join(A, B), C) = join(composition(A, C), composition(B, C))
% 1.80/1.93 converse(converse(A)) = A
% 1.80/1.93 converse(join(A, B)) = join(converse(A), converse(B))
% 1.80/1.93 converse(composition(A, B)) = composition(converse(B), converse(A))
% 1.80/1.93 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B)
% 1.80/1.93 top = join(A, complement(A))
% 1.80/1.93 zero = meet(A, complement(A))
% 1.80/1.93 join(sk1, sk2) = sk2
% 1.80/1.93 join(sk3, sk2) = sk2
% 1.80/1.93 join(join(sk1, sk3), sk2) = sk2 ==> \bottom
% 1.80/1.93
% 1.80/1.93 This holds because
% 1.80/1.93
% 1.80/1.93 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.80/1.93
% 1.80/1.93 E:
% 1.80/1.93 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B)))
% 1.80/1.93 composition(A, composition(B, C)) = composition(composition(A, B), C)
% 1.80/1.93 composition(A, one) = A
% 1.80/1.93 composition(join(A, B), C) = join(composition(A, C), composition(B, C))
% 1.80/1.93 converse(composition(A, B)) = composition(converse(B), converse(A))
% 1.80/1.93 converse(converse(A)) = A
% 1.80/1.93 converse(join(A, B)) = join(converse(A), converse(B))
% 1.80/1.93 f1(join(join(sk1, sk3), sk2)) = true__
% 1.80/1.93 f1(sk2) = false__
% 1.80/1.93 join(A, B) = join(B, A)
% 1.80/1.93 join(A, join(B, C)) = join(join(A, B), C)
% 1.80/1.93 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B)
% 1.80/1.93 join(sk1, sk2) = sk2
% 1.80/1.93 join(sk3, sk2) = sk2
% 1.80/1.93 meet(A, B) = complement(join(complement(A), complement(B)))
% 1.80/1.93 top = join(A, complement(A))
% 1.80/1.93 zero = meet(A, complement(A))
% 1.80/1.93 G:
% 1.80/1.93 true__ = false__
% 1.80/1.93
% 1.80/1.93 This holds because
% 1.80/1.93
% 1.80/1.93 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.80/1.93
% 1.80/1.93 join(A, B) = join(B, A)
% 1.80/1.93 composition(A, one) -> A
% 1.80/1.93 composition(composition(A, B), C) -> composition(A, composition(B, C))
% 1.80/1.93 composition(join(A, B), C) -> join(composition(A, C), composition(B, C))
% 1.80/1.93 composition(one, Y1) -> Y1
% 1.80/1.93 converse(composition(A, B)) -> composition(converse(B), converse(A))
% 1.80/1.93 converse(converse(A)) -> A
% 1.80/1.93 converse(join(A, B)) -> join(converse(A), converse(B))
% 1.80/1.93 converse(one) -> one
% 1.80/1.93 f1(join(join(sk1, sk3), sk2)) -> true__
% 1.80/1.93 f1(join(sk2, join(sk1, sk3))) -> true__
% 1.80/1.93 f1(join(sk2, join(sk3, sk1))) -> true__
% 1.80/1.93 f1(sk2) -> false__
% 1.80/1.93 join(A, complement(A)) -> top
% 1.80/1.93 join(X0, converse(complement(converse(X0)))) -> converse(top)
% 1.80/1.93 join(complement(Y1), composition(X0, complement(composition(converse(X0), Y1)))) -> complement(Y1)
% 1.80/1.93 join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) -> A
% 1.80/1.93 join(complement(one), complement(one)) -> complement(one)
% 1.80/1.93 join(complement(one), composition(X0, complement(converse(X0)))) -> complement(one)
% 1.80/1.93 join(complement(one), composition(converse(Y0), complement(Y0))) -> complement(one)
% 1.80/1.93 join(composition(converse(A), complement(composition(A, B))), complement(B)) -> complement(B)
% 1.80/1.93 join(composition(converse(Y0), complement(Y0)), complement(one)) -> complement(one)
% 1.80/1.93 join(converse(Y0), converse(complement(Y0))) -> converse(top)
% 1.80/1.93 join(converse(sk1), converse(sk2)) -> converse(sk2)
% 1.80/1.93 join(converse(sk1), converse(top)) -> converse(top)
% 1.80/1.93 join(converse(sk2), converse(sk1)) -> converse(sk2)
% 1.80/1.93 join(converse(sk2), converse(sk3)) -> converse(sk2)
% 1.80/1.93 join(converse(top), converse(sk1)) -> converse(top)
% 1.80/1.93 join(join(A, B), C) -> join(A, join(B, C))
% 1.80/1.93 join(one, converse(complement(one))) -> converse(top)
% 1.80/1.93 join(sk1, join(sk2, Y2)) -> join(sk2, Y2)
% 1.80/1.93 join(sk1, sk2) -> sk2
% 1.80/1.93 join(sk1, top) -> top
% 1.80/1.93 join(sk2, sk1) -> sk2
% 1.80/1.93 join(sk2, sk3) -> sk2
% 1.80/1.93 join(sk3, join(sk2, Y2)) -> join(sk2, Y2)
% 1.80/1.93 join(sk3, sk2) -> sk2
% 1.80/1.93 join(sk3, top) -> top
% 1.80/1.93 join(top, sk1) -> top
% 1.80/1.93 meet(A, B) -> complement(join(complement(A), complement(B)))
% 1.80/1.93 meet(A, complement(A)) -> zero
% 1.80/1.93 true__ -> false__
% 1.80/1.93 with the LPO induced by
% 1.80/1.93 sk1 > meet > complement > zero > converse > composition > join > top > sk3 > one > sk2 > f1 > true__ > false__
% 1.80/1.93
% 1.80/1.93 % SZS output end Proof
% 1.80/1.93
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