TSTP Solution File: SYN050-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SYN050-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n011.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 : Thu Jul 21 09:13:21 EDT 2022
% Result : Unsatisfiable 0.72s 0.87s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN050-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n011.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
% 0.12/0.33 % DateTime : Mon Jul 11 13:15:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.72/0.87 % SZS status Unsatisfiable
% 0.72/0.87 % SZS output start Proof
% 0.72/0.87 The input problem is unsatisfiable because
% 0.72/0.87
% 0.72/0.87 [1] the following set of Horn clauses is unsatisfiable:
% 0.72/0.87
% 0.72/0.87 big_p(Y) & big_q(Z) ==> big_r(f(Y, Z))
% 0.72/0.87 big_p(Y) & big_q(Z) ==> big_s(X)
% 0.72/0.87 big_p(a)
% 0.72/0.87 big_q(b)
% 0.72/0.87 big_r(W) ==> \bottom
% 0.72/0.87
% 0.72/0.87 This holds because
% 0.72/0.87
% 0.72/0.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.72/0.87
% 0.72/0.87 E:
% 0.72/0.87 big_p(a) = true__
% 0.72/0.87 big_q(b) = true__
% 0.72/0.87 f1(true__, Y, Z) = big_r(f(Y, Z))
% 0.72/0.87 f2(big_q(Z), Y, Z) = true__
% 0.72/0.87 f2(true__, Y, Z) = f1(big_p(Y), Y, Z)
% 0.72/0.87 f3(true__, X) = big_s(X)
% 0.72/0.87 f4(big_q(Z), Y, X) = true__
% 0.72/0.87 f4(true__, Y, X) = f3(big_p(Y), X)
% 0.72/0.87 f5(big_r(W)) = true__
% 0.72/0.87 f5(true__) = false__
% 0.72/0.87 G:
% 0.72/0.87 true__ = false__
% 0.72/0.87
% 0.72/0.87 This holds because
% 0.72/0.87
% 0.72/0.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.72/0.87
% 0.72/0.87 f3(true__, Y1) = f4(true__, a, Y1)
% 0.72/0.87 big_p(a) -> true__
% 0.72/0.87 big_q(b) -> true__
% 0.72/0.87 big_r(f(Y, Z)) -> f1(true__, Y, Z)
% 0.72/0.87 big_s(X) -> f3(true__, X)
% 0.72/0.87 f1(big_p(Y), Y, Z) -> f2(true__, Y, Z)
% 0.72/0.87 f1(true__, a, Y1) -> f2(true__, a, Y1)
% 0.72/0.87 f2(big_q(Z), Y, Z) -> true__
% 0.72/0.87 f2(true__, Y1, b) -> true__
% 0.72/0.87 f3(big_p(Y), X) -> f4(true__, Y, X)
% 0.72/0.87 f3(true__, Y1) -> true__
% 0.72/0.87 f4(big_q(Z), Y, X) -> true__
% 0.72/0.87 f4(true__, Y1, Y2) -> true__
% 0.72/0.87 f5(big_r(W)) -> true__
% 0.72/0.87 f5(f1(true__, X0, X1)) -> true__
% 0.72/0.87 f5(f2(true__, a, Y1)) -> true__
% 0.72/0.87 f5(true__) -> false__
% 0.72/0.87 false__ -> true__
% 0.72/0.87 with the LPO induced by
% 0.72/0.87 f5 > b > a > big_s > f3 > f4 > big_p > big_q > big_r > f1 > f > f2 > false__ > true__
% 0.72/0.87
% 0.72/0.87 % SZS output end Proof
% 0.72/0.87
%------------------------------------------------------------------------------