TSTP Solution File: GRP704-12 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP704-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n017.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 10:58:01 EDT 2022
% Result : Unsatisfiable 5.41s 5.43s
% Output : Proof 5.41s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP704-12 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 01:09:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 5.41/5.43 % SZS status Unsatisfiable
% 5.41/5.43 % SZS output start Proof
% 5.41/5.43 The input problem is unsatisfiable because
% 5.41/5.43
% 5.41/5.43 [1] the following set of Horn clauses is unsatisfiable:
% 5.41/5.43
% 5.41/5.43 mult(A, ld(A, B)) = B
% 5.41/5.43 ld(A, mult(A, B)) = B
% 5.41/5.43 mult(rd(A, B), B) = A
% 5.41/5.43 rd(mult(A, B), B) = A
% 5.41/5.43 mult(A, unit) = A
% 5.41/5.43 mult(unit, A) = A
% 5.41/5.43 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 5.41/5.43 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)
% 5.41/5.43 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)
% 5.41/5.43 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)
% 5.41/5.43 op_d = ld(A, mult(op_c, A))
% 5.41/5.43 op_e = mult(mult(rd(op_c, mult(A, B)), B), A)
% 5.41/5.43 op_f = mult(A, mult(B, ld(mult(A, B), op_c)))
% 5.41/5.43 mult(x4, mult(op_f, x5)) = mult(mult(x4, op_f), x5) ==> \bottom
% 5.41/5.43
% 5.41/5.43 This holds because
% 5.41/5.43
% 5.41/5.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.41/5.43
% 5.41/5.43 E:
% 5.41/5.43 f1(mult(mult(x4, op_f), x5)) = false__
% 5.41/5.43 f1(mult(x4, mult(op_f, x5))) = true__
% 5.41/5.43 ld(A, mult(A, B)) = B
% 5.41/5.43 mult(A, ld(A, B)) = B
% 5.41/5.43 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 5.41/5.43 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)
% 5.41/5.43 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)
% 5.41/5.43 mult(A, unit) = A
% 5.41/5.43 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)
% 5.41/5.43 mult(rd(A, B), B) = A
% 5.41/5.43 mult(unit, A) = A
% 5.41/5.43 op_d = ld(A, mult(op_c, A))
% 5.41/5.43 op_e = mult(mult(rd(op_c, mult(A, B)), B), A)
% 5.41/5.43 op_f = mult(A, mult(B, ld(mult(A, B), op_c)))
% 5.41/5.43 rd(mult(A, B), B) = A
% 5.41/5.43 G:
% 5.41/5.43 true__ = false__
% 5.41/5.43
% 5.41/5.43 This holds because
% 5.41/5.43
% 5.41/5.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.41/5.43
% 5.41/5.43 mult(Y0, mult(op_c, Y1)) = mult(op_c, mult(Y0, Y1))
% 5.41/5.43 mult(Y0, op_c) = mult(op_c, Y0)
% 5.41/5.43 mult(Y1, mult(op_c, Y1)) = mult(op_c, mult(Y1, Y1))
% 5.41/5.43 mult(op_c, X1) = mult(Y0, mult(ld(Y0, X1), op_c))
% 5.41/5.43 mult(op_c, mult(Y0, Y1)) = mult(Y0, mult(Y1, op_c))
% 5.41/5.43 mult(op_c, mult(op_c, Y0)) = mult(Y0, mult(op_c, op_c))
% 5.41/5.43 f1(mult(op_c, mult(x4, x5))) -> false__
% 5.41/5.43 f1(mult(x4, mult(op_c, x5))) -> false__
% 5.41/5.43 f1(mult(x4, mult(op_e, x5))) -> true__
% 5.41/5.43 f1(mult(x4, mult(op_f, x5))) -> true__
% 5.41/5.43 ld(A, mult(A, B)) -> B
% 5.41/5.43 ld(A, mult(op_c, A)) -> op_c
% 5.41/5.43 ld(Y0, Y0) -> unit
% 5.41/5.43 ld(ld(op_c, X1), X1) -> op_c
% 5.41/5.43 ld(op_c, mult(X0, mult(X1, op_c))) -> mult(X0, X1)
% 5.41/5.43 ld(op_c, mult(Y0, op_c)) -> Y0
% 5.41/5.43 ld(rd(X0, Y1), X0) -> Y1
% 5.41/5.43 ld(unit, Y1) -> Y1
% 5.41/5.43 mult(A, ld(A, B)) -> B
% 5.41/5.43 mult(A, mult(B, ld(mult(A, B), op_c))) -> op_c
% 5.41/5.43 mult(A, unit) -> A
% 5.41/5.43 mult(Y0, mult(ld(Y0, X1), ld(Y0, X1))) -> mult(X1, ld(Y0, X1))
% 5.41/5.43 mult(mult(A, B), op_c) -> mult(A, mult(B, op_c))
% 5.41/5.43 mult(mult(A, op_c), B) -> mult(A, mult(op_c, B))
% 5.41/5.43 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1))
% 5.41/5.43 mult(mult(Y1, Y1), Y2) -> mult(Y1, mult(Y1, Y2))
% 5.41/5.43 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C)))
% 5.41/5.43 mult(mult(op_c, A), B) -> mult(op_c, mult(A, B))
% 5.41/5.43 mult(mult(rd(op_c, mult(A, B)), B), A) -> op_c
% 5.41/5.43 mult(op_c, mult(Y0, ld(mult(op_c, Y0), X1))) -> X1
% 5.41/5.43 mult(rd(A, B), B) -> A
% 5.41/5.43 mult(unit, A) -> A
% 5.41/5.43 op_d -> op_c
% 5.41/5.43 op_e -> op_c
% 5.41/5.43 op_f -> op_c
% 5.41/5.43 rd(X1, ld(Y0, X1)) -> Y0
% 5.41/5.43 rd(Y0, op_c) -> ld(op_c, Y0)
% 5.41/5.43 rd(Y0, unit) -> Y0
% 5.41/5.43 rd(Y1, Y1) -> unit
% 5.41/5.43 rd(mult(A, B), B) -> A
% 5.41/5.43 rd(mult(Y0, op_c), Y0) -> op_c
% 5.41/5.43 true__ -> false__
% 5.41/5.43 with the LPO induced by
% 5.41/5.43 x5 > x4 > f1 > mult > op_d > op_f > op_e > op_c > rd > ld > unit > true__ > false__
% 5.41/5.43
% 5.41/5.43 % SZS output end Proof
% 5.41/5.43
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