TSTP Solution File: GRP657-10 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP657-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 5.23s 5.36s
% Output : Proof 5.23s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP657-10 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n020.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 12:16:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 5.23/5.36 % SZS status Unsatisfiable
% 5.23/5.36 % SZS output start Proof
% 5.23/5.36 The input problem is unsatisfiable because
% 5.23/5.36
% 5.23/5.36 [1] the following set of Horn clauses is unsatisfiable:
% 5.23/5.36
% 5.23/5.36 mult(A, ld(A, B)) = B
% 5.23/5.36 ld(A, mult(A, B)) = B
% 5.23/5.36 mult(rd(A, B), B) = A
% 5.23/5.36 rd(mult(A, B), B) = A
% 5.23/5.36 mult(mult(A, B), mult(C, A)) = mult(A, mult(mult(B, C), A))
% 5.23/5.36 tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)) = tuple(x1(X0), x1_2(X0)) ==> \bottom
% 5.23/5.36
% 5.23/5.36 This holds because
% 5.23/5.36
% 5.23/5.36 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.23/5.36
% 5.23/5.36 E:
% 5.23/5.36 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) = true__
% 5.23/5.36 f1(tuple(x1(X0), x1_2(X0)), X0) = false__
% 5.23/5.36 ld(A, mult(A, B)) = B
% 5.23/5.36 mult(A, ld(A, B)) = B
% 5.23/5.36 mult(mult(A, B), mult(C, A)) = mult(A, mult(mult(B, C), A))
% 5.23/5.36 mult(rd(A, B), B) = A
% 5.23/5.36 rd(mult(A, B), B) = A
% 5.23/5.36 G:
% 5.23/5.36 true__ = false__
% 5.23/5.36
% 5.23/5.36 This holds because
% 5.23/5.36
% 5.23/5.36 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.23/5.36
% 5.23/5.36 mult(mult(A, B), mult(C, A)) = mult(A, mult(mult(B, C), A))
% 5.23/5.36 mult(mult(ld(X0, rd(X0, Y1)), rd(mult(Y2, rd(X0, Y1)), X0)), X0) = mult(ld(Y1, Y2), rd(X0, Y1))
% 5.23/5.36 mult(mult(ld(Y1, g1), rd(Y2, Y1)), Y1) = ld(Y1, Y2)
% 5.23/5.36 mult(mult(ld(Y2, X1), Y1), X1) = mult(ld(Y2, X1), mult(mult(Y1, Y2), ld(Y2, X1)))
% 5.23/5.36 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) -> true__
% 5.23/5.36 f1(tuple(x1(X0), x1_2(X0)), X0) -> false__
% 5.23/5.36 f1(tuple(x1(ld(X0, X0)), mult(x1_2(ld(X0, X0)), ld(X0, X0))), ld(X0, X0)) -> true__
% 5.23/5.36 ld(X0, X0) -> g1
% 5.23/5.36 ld(Y0, mult(Y1, X0)) -> mult(mult(ld(Y0, Y1), rd(X0, Y0)), Y0)
% 5.23/5.36 ld(g1, Y1) -> Y1
% 5.23/5.36 ld(ld(Y0, Y0), X1) -> X1
% 5.23/5.36 ld(mult(Y0, Y1), X1) -> mult(ld(Y1, rd(ld(Y0, X1), Y0)), Y0)
% 5.23/5.36 ld(mult(Y0, Y1), mult(Y0, X0)) -> mult(ld(Y1, rd(X0, Y0)), Y0)
% 5.23/5.36 ld(mult(ld(Y1, Y1), X1), mult(X1, Y1)) -> Y1
% 5.23/5.36 ld(rd(X0, Y1), X0) -> Y1
% 5.23/5.36 mult(A, ld(A, B)) -> B
% 5.23/5.36 mult(X1, mult(ld(ld(Y0, X1), Y2), Y0)) -> mult(Y0, mult(Y2, Y0))
% 5.23/5.36 mult(Y1, g1) -> Y1
% 5.23/5.36 mult(Y1, mult(ld(Y1, Y0), Y1)) -> mult(Y0, Y1)
% 5.23/5.36 mult(g1, Y1) -> Y1
% 5.23/5.36 mult(ld(Y1, Y1), X1) -> X1
% 5.23/5.36 mult(ld(Y2, rd(Y2, Y0)), Y0) -> g1
% 5.23/5.36 mult(ld(ld(Y0, X1), Y2), Y0) -> mult(mult(ld(X1, Y0), rd(mult(Y2, Y0), X1)), X1)
% 5.23/5.36 mult(mult(Y0, Y1), Y0) -> mult(Y0, mult(Y1, Y0))
% 5.23/5.36 mult(mult(Y0, Y1), mult(ld(Y1, X1), Y0)) -> mult(Y0, mult(X1, Y0))
% 5.23/5.36 mult(mult(Y0, rd(X0, Y2)), mult(Y2, Y0)) -> mult(Y0, mult(X0, Y0))
% 5.23/5.36 mult(mult(Y0, rd(g1, Y1)), Y1) -> Y0
% 5.23/5.36 mult(mult(Y1, Y2), ld(X0, X0)) -> mult(Y1, mult(Y2, ld(X0, X0)))
% 5.23/5.36 mult(mult(ld(Y0, rd(X0, mult(Y2, Y0))), Y2), Y0) -> ld(Y0, X0)
% 5.23/5.36 mult(mult(mult(ld(Y0, rd(Y0, X1)), rd(mult(X1, rd(Y0, X1)), Y0)), Y0), X1) -> Y0
% 5.23/5.36 mult(rd(A, B), B) -> A
% 5.23/5.36 mult(rd(X0, Y1), mult(mult(Y1, Y2), rd(X0, Y1))) -> mult(X0, mult(Y2, rd(X0, Y1)))
% 5.23/5.36 rd(X1, X1) -> g1
% 5.23/5.36 rd(X1, ld(Y0, X1)) -> Y0
% 5.23/5.36 rd(Y0, g1) -> Y0
% 5.23/5.36 rd(mult(A, B), B) -> A
% 5.23/5.36 rd(mult(Y0, X0), mult(ld(Y2, rd(X0, Y0)), Y0)) -> mult(Y0, Y2)
% 5.23/5.36 rd(mult(Y0, mult(X0, Y0)), mult(Y2, Y0)) -> mult(Y0, rd(X0, Y2))
% 5.23/5.36 rd(mult(ld(Y1, X1), X1), mult(ld(Y2, Y1), ld(Y1, X1))) -> mult(ld(Y1, X1), Y2)
% 5.23/5.36 rd(mult(ld(Y2, X1), mult(mult(Y1, Y2), ld(Y2, X1))), X1) -> mult(ld(Y2, X1), Y1)
% 5.23/5.36 rd(mult(mult(Y0, X1), mult(X2, Y0)), mult(mult(X1, X2), Y0)) -> Y0
% 5.23/5.36 rd(mult(mult(Y0, Y1), Y0), mult(Y1, Y0)) -> Y0
% 5.23/5.36 true__ -> false__
% 5.23/5.36 with the LPO induced by
% 5.23/5.36 x1_2 > x1 > tuple > f1 > ld > rd > mult > g1 > true__ > false__
% 5.23/5.36
% 5.23/5.36 % SZS output end Proof
% 5.23/5.36
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