TSTP Solution File: GRP704-10 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP704-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n010.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 10:58:00 EDT 2022
% Result : Unsatisfiable 5.29s 5.43s
% Output : Proof 5.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP704-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Mon Jun 13 13:54:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 5.29/5.43 % SZS status Unsatisfiable
% 5.29/5.43 % SZS output start Proof
% 5.29/5.43 The input problem is unsatisfiable because
% 5.29/5.43
% 5.29/5.43 [1] the following set of Horn clauses is unsatisfiable:
% 5.29/5.43
% 5.29/5.43 mult(A, ld(A, B)) = B
% 5.29/5.43 ld(A, mult(A, B)) = B
% 5.29/5.43 mult(rd(A, B), B) = A
% 5.29/5.43 rd(mult(A, B), B) = A
% 5.29/5.43 mult(A, unit) = A
% 5.29/5.43 mult(unit, A) = A
% 5.29/5.43 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 5.29/5.43 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)
% 5.29/5.43 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)
% 5.29/5.43 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)
% 5.29/5.43 op_d = ld(A, mult(op_c, A))
% 5.29/5.43 op_e = mult(mult(rd(op_c, mult(A, B)), B), A)
% 5.29/5.43 op_f = mult(A, mult(B, ld(mult(A, B), op_c)))
% 5.29/5.43 mult(op_f, mult(x4, x5)) = mult(mult(op_f, x4), x5) ==> \bottom
% 5.29/5.43
% 5.29/5.43 This holds because
% 5.29/5.43
% 5.29/5.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.29/5.43
% 5.29/5.43 E:
% 5.29/5.43 f1(mult(mult(op_f, x4), x5)) = false__
% 5.29/5.43 f1(mult(op_f, mult(x4, x5))) = true__
% 5.29/5.43 ld(A, mult(A, B)) = B
% 5.29/5.43 mult(A, ld(A, B)) = B
% 5.29/5.43 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 5.29/5.43 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)
% 5.29/5.43 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)
% 5.29/5.43 mult(A, unit) = A
% 5.29/5.43 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)
% 5.29/5.43 mult(rd(A, B), B) = A
% 5.29/5.43 mult(unit, A) = A
% 5.29/5.43 op_d = ld(A, mult(op_c, A))
% 5.29/5.43 op_e = mult(mult(rd(op_c, mult(A, B)), B), A)
% 5.29/5.43 op_f = mult(A, mult(B, ld(mult(A, B), op_c)))
% 5.29/5.43 rd(mult(A, B), B) = A
% 5.29/5.43 G:
% 5.29/5.43 true__ = false__
% 5.29/5.43
% 5.29/5.43 This holds because
% 5.29/5.43
% 5.29/5.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.29/5.43
% 5.29/5.43 ld(op_e, mult(X0, mult(op_e, op_e))) = mult(op_e, X0)
% 5.29/5.43 mult(Y0, mult(op_e, Y1)) = mult(op_e, mult(Y0, Y1))
% 5.29/5.43 mult(Y0, op_e) = mult(op_e, Y0)
% 5.29/5.43 mult(Y1, mult(op_e, Y1)) = mult(op_e, mult(Y1, Y1))
% 5.29/5.43 mult(op_e, mult(Y0, Y1)) = mult(Y0, mult(Y1, op_e))
% 5.29/5.43 mult(op_e, mult(op_e, Y0)) = mult(Y0, mult(op_e, op_e))
% 5.29/5.43 f1(mult(mult(op_e, x4), x5)) -> false__
% 5.29/5.43 f1(mult(mult(op_f, x4), x5)) -> false__
% 5.29/5.43 f1(mult(op_c, mult(x4, x5))) -> false__
% 5.29/5.43 f1(mult(op_c, mult(x4, x5))) -> true__
% 5.29/5.43 f1(mult(op_e, mult(x4, x5))) -> true__
% 5.29/5.43 ld(A, mult(A, B)) -> B
% 5.29/5.43 ld(Y0, Y0) -> unit
% 5.29/5.43 ld(Y0, mult(op_e, Y0)) -> op_e
% 5.29/5.43 ld(Y0, mult(op_e, mult(Y0, X1))) -> mult(op_e, X1)
% 5.29/5.43 ld(ld(op_e, Y0), Y0) -> op_e
% 5.29/5.43 ld(op_c, mult(X0, mult(X1, op_c))) -> mult(X0, X1)
% 5.29/5.43 ld(op_e, mult(X0, mult(X1, op_e))) -> mult(X0, X1)
% 5.29/5.43 ld(op_e, mult(Y0, op_e)) -> Y0
% 5.29/5.43 ld(rd(X0, Y1), X0) -> Y1
% 5.29/5.43 ld(unit, Y1) -> Y1
% 5.29/5.43 mult(A, ld(A, B)) -> B
% 5.29/5.43 mult(A, unit) -> A
% 5.29/5.43 mult(Y0, mult(Y1, ld(mult(Y0, Y1), op_e))) -> op_e
% 5.29/5.43 mult(Y0, mult(ld(Y0, X1), op_c)) -> mult(op_e, X1)
% 5.29/5.43 mult(mult(A, B), op_c) -> mult(A, mult(B, op_e))
% 5.29/5.43 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1))
% 5.29/5.43 mult(mult(Y0, op_e), Y1) -> mult(Y0, mult(op_e, Y1))
% 5.29/5.43 mult(mult(Y1, Y1), Y2) -> mult(Y1, mult(Y1, Y2))
% 5.29/5.43 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C)))
% 5.29/5.43 mult(mult(op_e, Y0), Y1) -> mult(op_e, mult(Y0, Y1))
% 5.29/5.43 mult(mult(rd(op_e, mult(Y0, Y1)), Y1), Y0) -> op_e
% 5.29/5.43 mult(op_c, mult(Y0, ld(mult(op_c, Y0), X1))) -> X1
% 5.29/5.43 mult(op_e, mult(Y0, ld(op_e, X1))) -> mult(Y0, X1)
% 5.29/5.43 mult(op_e, mult(ld(op_e, X1), ld(op_e, X1))) -> mult(ld(op_e, X1), X1)
% 5.29/5.43 mult(rd(A, B), B) -> A
% 5.29/5.43 mult(rd(X0, Y1), mult(Y1, op_c)) -> mult(op_e, X0)
% 5.29/5.43 mult(unit, A) -> A
% 5.29/5.43 op_c -> op_e
% 5.29/5.43 op_d -> op_e
% 5.29/5.43 op_f -> op_e
% 5.29/5.43 rd(X0, op_e) -> ld(op_e, X0)
% 5.29/5.43 rd(X1, ld(Y0, X1)) -> Y0
% 5.29/5.43 rd(Y0, unit) -> Y0
% 5.29/5.43 rd(Y1, Y1) -> unit
% 5.29/5.43 rd(mult(A, B), B) -> A
% 5.29/5.43 rd(mult(X0, mult(X1, op_c)), mult(X0, X1)) -> op_e
% 5.29/5.43 rd(mult(X0, mult(X1, op_e)), mult(X0, X1)) -> op_e
% 5.29/5.43 rd(mult(Y1, op_e), Y1) -> op_e
% 5.29/5.43 true__ -> false__
% 5.29/5.43 with the LPO induced by
% 5.29/5.43 x5 > x4 > f1 > mult > op_d > rd > ld > op_f > op_c > op_e > unit > true__ > false__
% 5.29/5.43
% 5.29/5.43 % SZS output end Proof
% 5.29/5.43
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