TSTP Solution File: REL001-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : REL001-1 : 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 19:46:31 EDT 2022
% Result : Unsatisfiable 9.67s 9.66s
% Output : Proof 9.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : REL001-1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n021.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 : Fri Jul 8 08:53:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.67/9.66 % SZS status Unsatisfiable
% 9.67/9.66 % SZS output start Proof
% 9.67/9.66 The input problem is unsatisfiable because
% 9.67/9.66
% 9.67/9.66 [1] the following set of Horn clauses is unsatisfiable:
% 9.67/9.66
% 9.67/9.66 join(A, B) = join(B, A)
% 9.67/9.66 join(A, join(B, C)) = join(join(A, B), C)
% 9.67/9.66 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B)))
% 9.67/9.66 meet(A, B) = complement(join(complement(A), complement(B)))
% 9.67/9.66 composition(A, composition(B, C)) = composition(composition(A, B), C)
% 9.67/9.66 composition(A, one) = A
% 9.67/9.66 composition(join(A, B), C) = join(composition(A, C), composition(B, C))
% 9.67/9.66 converse(converse(A)) = A
% 9.67/9.66 converse(join(A, B)) = join(converse(A), converse(B))
% 9.67/9.66 converse(composition(A, B)) = composition(converse(B), converse(A))
% 9.67/9.66 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B)
% 9.67/9.66 top = join(A, complement(A))
% 9.67/9.66 zero = meet(A, complement(A))
% 9.67/9.66 join(zero, sk1) = sk1 ==> \bottom
% 9.67/9.66
% 9.67/9.66 This holds because
% 9.67/9.66
% 9.67/9.66 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.67/9.66
% 9.67/9.66 E:
% 9.67/9.66 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B)))
% 9.67/9.66 composition(A, composition(B, C)) = composition(composition(A, B), C)
% 9.67/9.66 composition(A, one) = A
% 9.67/9.66 composition(join(A, B), C) = join(composition(A, C), composition(B, C))
% 9.67/9.66 converse(composition(A, B)) = composition(converse(B), converse(A))
% 9.67/9.66 converse(converse(A)) = A
% 9.67/9.66 converse(join(A, B)) = join(converse(A), converse(B))
% 9.67/9.66 f1(join(zero, sk1)) = true__
% 9.67/9.66 f1(sk1) = false__
% 9.67/9.66 join(A, B) = join(B, A)
% 9.67/9.66 join(A, join(B, C)) = join(join(A, B), C)
% 9.67/9.66 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B)
% 9.67/9.66 meet(A, B) = complement(join(complement(A), complement(B)))
% 9.67/9.66 top = join(A, complement(A))
% 9.67/9.66 zero = meet(A, complement(A))
% 9.67/9.66 G:
% 9.67/9.66 true__ = false__
% 9.67/9.66
% 9.67/9.66 This holds because
% 9.67/9.66
% 9.67/9.66 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.67/9.66
% 9.67/9.66 join(A, B) = join(B, A)
% 9.67/9.66 join(Y0, complement(one)) = join(complement(one), join(complement(one), Y0))
% 9.67/9.66 join(Y0, join(Y1, complement(Y0))) = join(top, Y1)
% 9.67/9.66 join(Y0, top) = join(top, complement(complement(Y0)))
% 9.67/9.66 join(Y0, top) = join(top, top)
% 9.67/9.66 join(Y1, join(Y0, Y2)) = join(Y0, join(Y1, Y2))
% 9.67/9.66 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2))
% 9.67/9.66 join(converse(top), converse(top)) = join(converse(Y0), converse(top))
% 9.67/9.66 complement(complement(Y0)) -> Y0
% 9.67/9.66 complement(top) -> zero
% 9.67/9.66 complement(zero) -> top
% 9.67/9.66 composition(A, one) -> A
% 9.67/9.66 composition(Y0, composition(one, Y2)) -> composition(Y0, Y2)
% 9.67/9.66 composition(composition(A, B), C) -> composition(A, composition(B, C))
% 9.67/9.66 composition(converse(one), X0) -> X0
% 9.67/9.66 composition(converse(one), converse(Y0)) -> converse(Y0)
% 9.67/9.66 composition(join(A, B), C) -> join(composition(A, C), composition(B, C))
% 9.67/9.66 composition(one, Y1) -> Y1
% 9.67/9.66 composition(top, complement(composition(top, top))) -> zero
% 9.67/9.66 converse(complement(converse(zero))) -> top
% 9.67/9.66 converse(composition(A, B)) -> composition(converse(B), converse(A))
% 9.67/9.66 converse(converse(A)) -> A
% 9.67/9.66 converse(join(A, B)) -> join(converse(A), converse(B))
% 9.67/9.66 converse(one) -> one
% 9.67/9.66 converse(top) -> top
% 9.67/9.66 f1(join(zero, sk1)) -> true__
% 9.67/9.66 f1(sk1) -> false__
% 9.67/9.66 join(A, complement(A)) -> top
% 9.67/9.66 join(X0, complement(complement(join(zero, complement(X0))))) -> top
% 9.67/9.66 join(X0, converse(complement(converse(X0)))) -> converse(top)
% 9.67/9.66 join(Y0, complement(join(Y0, zero))) -> top
% 9.67/9.66 join(Y0, join(Y1, complement(join(Y0, Y1)))) -> top
% 9.67/9.66 join(Y0, join(Y1, complement(join(Y1, Y0)))) -> top
% 9.67/9.66 join(Y0, join(complement(Y0), Y2)) -> join(top, Y2)
% 9.67/9.66 join(Y0, top) -> top
% 9.67/9.66 join(Y1, join(Y0, complement(Y1))) -> join(Y0, top)
% 9.67/9.66 join(Y1, zero) -> Y1
% 9.67/9.66 join(complement(Y0), composition(converse(X0), complement(composition(X0, Y0)))) -> complement(Y0)
% 9.67/9.66 join(complement(Y0), join(zero, Y0)) -> top
% 9.67/9.66 join(complement(Y1), complement(Y1)) -> complement(Y1)
% 9.67/9.66 join(complement(Y1), composition(X0, complement(composition(converse(X0), Y1)))) -> complement(Y1)
% 9.67/9.66 join(complement(Y1), composition(top, complement(composition(top, Y1)))) -> complement(Y1)
% 9.67/9.66 join(complement(Y1), join(Y1, zero)) -> top
% 9.67/9.66 join(complement(join(X0, zero)), join(zero, X0)) -> top
% 9.67/9.66 join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) -> A
% 9.67/9.66 join(complement(join(top, complement(Y0))), complement(join(zero, complement(Y0)))) -> Y0
% 9.67/9.66 join(complement(join(zero, Y1)), complement(join(zero, complement(Y1)))) -> top
% 9.67/9.66 join(complement(one), complement(one)) -> complement(one)
% 9.67/9.66 join(complement(one), composition(X0, complement(converse(X0)))) -> complement(one)
% 9.67/9.66 join(complement(one), composition(converse(Y0), complement(Y0))) -> complement(one)
% 9.67/9.66 join(complement(one), composition(converse(top), zero)) -> complement(one)
% 9.67/9.66 join(complement(one), composition(top, zero)) -> complement(one)
% 9.67/9.66 join(composition(Y0, Y2), composition(top, Y2)) -> composition(top, Y2)
% 9.67/9.66 join(composition(converse(A), complement(composition(A, B))), complement(B)) -> complement(B)
% 9.67/9.66 join(composition(top, Y2), composition(top, Y2)) -> composition(top, Y2)
% 9.67/9.66 join(composition(top, Y2), composition(zero, Y2)) -> composition(top, Y2)
% 9.67/9.66 join(composition(zero, Y2), composition(zero, Y2)) -> composition(zero, Y2)
% 9.67/9.66 join(converse(X0), join(converse(zero), converse(complement(X0)))) -> top
% 9.67/9.66 join(converse(Y0), converse(complement(Y0))) -> converse(top)
% 9.67/9.66 join(converse(Y0), converse(top)) -> converse(top)
% 9.67/9.66 join(converse(complement(X0)), converse(complement(X0))) -> converse(complement(X0))
% 9.67/9.66 join(converse(complement(one)), converse(complement(one))) -> converse(complement(one))
% 9.67/9.66 join(converse(top), converse(Y1)) -> converse(top)
% 9.67/9.66 join(converse(top), converse(complement(X0))) -> converse(top)
% 9.67/9.66 join(converse(top), converse(complement(one))) -> converse(top)
% 9.67/9.66 join(converse(top), converse(complement(zero))) -> join(converse(top), converse(top))
% 9.67/9.66 join(converse(top), converse(top)) -> converse(top)
% 9.67/9.66 join(converse(top), converse(zero)) -> converse(top)
% 9.67/9.66 join(converse(zero), converse(Y1)) -> converse(Y1)
% 9.67/9.66 join(converse(zero), converse(zero)) -> converse(zero)
% 9.67/9.66 join(join(A, B), C) -> join(A, join(B, C))
% 9.67/9.66 join(one, converse(complement(one))) -> converse(top)
% 9.67/9.66 join(one, join(Y0, converse(complement(one)))) -> top
% 9.67/9.66 join(one, join(converse(complement(one)), Y0)) -> top
% 9.67/9.66 join(one, join(zero, converse(complement(one)))) -> top
% 9.67/9.66 join(top, Y0) -> top
% 9.67/9.66 join(top, complement(Y0)) -> top
% 9.67/9.66 join(top, complement(complement(Y0))) -> join(top, Y0)
% 9.67/9.66 join(top, complement(one)) -> top
% 9.67/9.66 join(top, complement(zero)) -> join(top, top)
% 9.67/9.66 join(top, converse(zero)) -> top
% 9.67/9.66 join(top, join(Y0, zero)) -> join(top, Y0)
% 9.67/9.66 join(top, join(zero, Y1)) -> join(top, Y1)
% 9.67/9.66 join(top, one) -> join(top, top)
% 9.67/9.66 join(top, top) -> top
% 9.67/9.66 join(top, zero) -> top
% 9.67/9.66 join(zero, X0) -> X0
% 9.67/9.66 join(zero, complement(join(zero, complement(Y0)))) -> Y0
% 9.67/9.66 join(zero, composition(X0, complement(composition(converse(X0), top)))) -> zero
% 9.67/9.66 join(zero, composition(converse(Y0), complement(composition(Y0, top)))) -> zero
% 9.67/9.66 join(zero, composition(top, complement(composition(top, top)))) -> zero
% 9.67/9.66 join(zero, converse(top)) -> converse(top)
% 9.67/9.66 join(zero, join(Y0, zero)) -> join(zero, Y0)
% 9.67/9.66 join(zero, join(top, top)) -> join(top, top)
% 9.67/9.66 join(zero, join(zero, Y2)) -> join(zero, Y2)
% 9.67/9.66 join(zero, zero) -> zero
% 9.67/9.66 meet(A, B) -> complement(join(complement(A), complement(B)))
% 9.67/9.66 meet(A, complement(A)) -> zero
% 9.67/9.66 true__ -> false__
% 9.67/9.66 with the LPO induced by
% 9.67/9.66 sk1 > f1 > converse > composition > one > meet > join > complement > zero > top > true__ > false__
% 9.67/9.66
% 9.67/9.66 % SZS output end Proof
% 9.67/9.66
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