TSTP Solution File: GRP656-10 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 10:57:28 EDT 2022
% Result : Unsatisfiable 5.85s 5.99s
% Output : Proof 5.85s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.14 % Command : moca.sh %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 08:32:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 5.85/5.99 % SZS status Unsatisfiable
% 5.85/5.99 % SZS output start Proof
% 5.85/5.99 The input problem is unsatisfiable because
% 5.85/5.99
% 5.85/5.99 [1] the following set of Horn clauses is unsatisfiable:
% 5.85/5.99
% 5.85/5.99 mult(A, ld(A, B)) = B
% 5.85/5.99 ld(A, mult(A, B)) = B
% 5.85/5.99 mult(rd(A, B), B) = A
% 5.85/5.99 rd(mult(A, B), B) = A
% 5.85/5.99 mult(mult(A, B), mult(C, A)) = mult(mult(A, mult(B, C)), A)
% 5.85/5.99 tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)) = tuple(x1(X0), x1_2(X0)) ==> \bottom
% 5.85/5.99
% 5.85/5.99 This holds because
% 5.85/5.99
% 5.85/5.99 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.85/5.99
% 5.85/5.99 E:
% 5.85/5.99 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) = true__
% 5.85/5.99 f1(tuple(x1(X0), x1_2(X0)), X0) = false__
% 5.85/5.99 ld(A, mult(A, B)) = B
% 5.85/5.99 mult(A, ld(A, B)) = B
% 5.85/5.99 mult(mult(A, B), mult(C, A)) = mult(mult(A, mult(B, C)), A)
% 5.85/5.99 mult(rd(A, B), B) = A
% 5.85/5.99 rd(mult(A, B), B) = A
% 5.85/5.99 G:
% 5.85/5.99 true__ = false__
% 5.85/5.99
% 5.85/5.99 This holds because
% 5.85/5.99
% 5.85/5.99 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.85/5.99
% 5.85/5.99 mult(X0, mult(ld(Y1, Y2), rd(X0, Y1))) = mult(mult(rd(X0, Y1), Y2), rd(X0, Y1))
% 5.85/5.99 mult(mult(Y0, X1), Y0) = mult(mult(Y0, Y1), mult(ld(Y1, X1), Y0))
% 5.85/5.99 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) -> true__
% 5.85/5.99 f1(tuple(x1(X0), x1_2(X0)), X0) -> false__
% 5.85/5.99 f1(tuple(x1(ld(X0, X0)), mult(x1_2(ld(X0, X0)), ld(X0, X0))), ld(X0, X0)) -> true__
% 5.85/5.99 ld(A, mult(A, B)) -> B
% 5.85/5.99 ld(X0, mult(rd(X0, Y1), mult(Y1, rd(X0, Y1)))) -> rd(X0, Y1)
% 5.85/5.99 ld(X1, X1) -> g1
% 5.85/5.99 ld(X1, mult(Y0, mult(ld(Y0, X1), Y0))) -> Y0
% 5.85/5.99 ld(g1, Y1) -> Y1
% 5.85/5.99 ld(mult(Y0, Y1), mult(X1, Y0)) -> mult(ld(Y1, ld(Y0, X1)), Y0)
% 5.85/5.99 ld(mult(Y0, mult(Y1, rd(X0, Y0))), mult(mult(Y0, Y1), X0)) -> Y0
% 5.85/5.99 ld(mult(Y0, mult(Y1, rd(ld(mult(Y0, Y1), X1), Y0))), X1) -> Y0
% 5.85/5.99 ld(mult(Y0, mult(ld(Y0, X1), Y2)), mult(X1, mult(Y2, Y0))) -> Y0
% 5.85/5.99 ld(mult(Y0, mult(ld(Y0, rd(X0, mult(Y2, Y0))), Y2)), X0) -> Y0
% 5.85/5.99 ld(mult(Y0, rd(X0, Y0)), mult(Y0, X0)) -> Y0
% 5.85/5.99 ld(mult(Y1, X1), mult(mult(Y1, X2), mult(ld(X2, X1), Y1))) -> Y1
% 5.85/5.99 ld(mult(Y1, Y2), mult(Y1, mult(Y2, Y1))) -> Y1
% 5.85/5.99 ld(mult(Y1, mult(X1, X2)), mult(mult(Y1, X1), mult(X2, Y1))) -> Y1
% 5.85/5.99 ld(mult(ld(Y1, X1), Y1), mult(ld(Y1, X1), X1)) -> ld(Y1, X1)
% 5.85/5.99 ld(mult(ld(Y2, X1), mult(Y1, Y2)), mult(mult(ld(Y2, X1), Y1), X1)) -> ld(Y2, X1)
% 5.85/5.99 ld(mult(ld(Y2, X1), mult(ld(ld(Y2, X1), Y1), Y2)), mult(Y1, X1)) -> ld(Y2, X1)
% 5.85/5.99 ld(mult(rd(X0, Y1), mult(Y1, Y2)), mult(X0, mult(Y2, rd(X0, Y1)))) -> rd(X0, Y1)
% 5.85/5.99 ld(mult(rd(X0, Y2), Y1), mult(X0, mult(ld(Y2, Y1), rd(X0, Y2)))) -> rd(X0, Y2)
% 5.85/5.99 ld(rd(X0, Y1), X0) -> Y1
% 5.85/5.99 mult(A, ld(A, B)) -> B
% 5.85/5.99 mult(X1, mult(ld(X1, Y0), X1)) -> mult(Y0, X1)
% 5.85/5.99 mult(Y1, g1) -> Y1
% 5.85/5.99 mult(Y1, mult(ld(Y1, g1), Y1)) -> Y1
% 5.85/5.99 mult(g1, Y1) -> Y1
% 5.85/5.99 mult(ld(ld(X1, Y0), X2), X1) -> ld(Y0, mult(mult(X1, X2), X1))
% 5.85/5.99 mult(mult(A, mult(B, C)), A) -> mult(mult(A, B), mult(C, A))
% 5.85/5.99 mult(mult(X0, X1), X0) -> mult(X0, mult(X1, X0))
% 5.85/5.99 mult(mult(Y0, Y2), mult(ld(Y2, g1), Y0)) -> mult(Y0, Y0)
% 5.85/5.99 mult(mult(Y0, rd(X0, Y2)), mult(Y2, Y0)) -> mult(mult(Y0, X0), Y0)
% 5.85/5.99 mult(mult(rd(X0, Y1), Y2), mult(ld(Y2, Y1), rd(X0, Y1))) -> mult(X0, rd(X0, Y1))
% 5.85/5.99 mult(rd(A, B), B) -> A
% 5.85/5.99 rd(X1, ld(Y0, X1)) -> Y0
% 5.85/5.99 rd(Y0, g1) -> Y0
% 5.85/5.99 rd(Y1, Y1) -> g1
% 5.85/5.99 rd(mult(A, B), B) -> A
% 5.85/5.99 rd(mult(X1, mult(Y2, Y0)), Y0) -> mult(Y0, mult(ld(Y0, X1), Y2))
% 5.85/5.99 rd(mult(Y0, X1), ld(Y1, X1)) -> mult(ld(Y1, X1), ld(X1, mult(mult(Y1, Y0), Y1)))
% 5.85/5.99 rd(mult(mult(X0, X2), X0), mult(ld(X1, X2), X0)) -> mult(X0, X1)
% 5.85/5.99 true__ -> false__
% 5.85/5.99 with the LPO induced by
% 5.85/5.99 x1_2 > x1 > tuple > f1 > rd > ld > mult > g1 > true__ > false__
% 5.85/5.99
% 5.85/5.99 % SZS output end Proof
% 5.85/5.99
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