TSTP Solution File: SYN033-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SYN033-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 09:13:09 EDT 2022
% Result : Unsatisfiable 0.68s 0.91s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN033-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 15:54:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.68/0.91 % SZS status Unsatisfiable
% 0.68/0.91 % SZS output start Proof
% 0.68/0.91 The input problem is unsatisfiable because
% 0.68/0.91
% 0.68/0.91 [1] the following set of Horn clauses is unsatisfiable:
% 0.68/0.91
% 0.68/0.91 p(g(A, B), A, B)
% 0.68/0.91 p(A, h(A, B), B)
% 0.68/0.91 p(A, B, C) & p(D, E, B) & p(A, D, F) ==> p(F, E, C)
% 0.68/0.91 p(k(A), A, k(A)) ==> \bottom
% 0.68/0.91
% 0.68/0.91 This holds because
% 0.68/0.91
% 0.68/0.91 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.68/0.91
% 0.68/0.91 E:
% 0.68/0.91 f1(true__, F, E, C) = p(F, E, C)
% 0.68/0.91 f2(true__, A, B, C, F, E) = f1(p(A, B, C), F, E, C)
% 0.68/0.91 f3(p(A, D, F), D, E, B, A, C, F) = true__
% 0.68/0.91 f3(true__, D, E, B, A, C, F) = f2(p(D, E, B), A, B, C, F, E)
% 0.68/0.91 f4(p(k(A), A, k(A))) = true__
% 0.68/0.91 f4(true__) = false__
% 0.68/0.91 p(A, h(A, B), B) = true__
% 0.68/0.91 p(g(A, B), A, B) = true__
% 0.68/0.91 G:
% 0.68/0.91 true__ = false__
% 0.68/0.91
% 0.68/0.91 This holds because
% 0.68/0.91
% 0.68/0.91 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.68/0.91
% 0.68/0.91
% 0.68/0.91 f1(f1(true__, Y0, Y3, Y4), Y1, h(h(Y0, Y1), Y3), Y4) -> true__
% 0.68/0.91 f1(f1(true__, Y0, h(Y0, Y1), Y4), Y1, h(X1, X1), Y4) -> true__
% 0.68/0.91 f1(f1(true__, g(Y0, Y3), Y2, Y4), Y3, h(Y0, Y2), Y4) -> true__
% 0.68/0.91 f1(f1(true__, g(Y2, Y3), Y2, Y4), Y3, h(X1, X1), Y4) -> true__
% 0.68/0.91 f1(f1(true__, g(g(Y1, Y2), Y3), Y2, Y4), Y3, Y1, Y4) -> true__
% 0.68/0.91 f1(true__, Y0, h(Y0, Y2), Y2) -> true__
% 0.68/0.91 f1(true__, Y1, h(Y0, h(X1, X1)), g(Y0, Y1)) -> true__
% 0.68/0.91 f1(true__, Y1, h(Y0, h(g(Y0, Y1), Y3)), Y3) -> true__
% 0.68/0.91 f1(true__, Y2, Y0, g(g(Y0, h(X1, X1)), Y2)) -> true__
% 0.68/0.91 f1(true__, Y3, h(Y2, Y2), Y3) -> true__
% 0.68/0.91 f1(true__, Y3, h(h(Y0, Y3), h(Y0, Y2)), Y2) -> true__
% 0.68/0.91 f1(true__, Y3, h(h(g(Y1, Y2), Y3), Y1), Y2) -> true__
% 0.68/0.91 f1(true__, g(Y1, Y2), Y1, Y2) -> true__
% 0.68/0.91 f2(f1(true__, Y1, Y3, Y4), g(Y1, Y2), Y4, Y5, Y2, Y3) -> true__
% 0.68/0.91 f2(f1(true__, h(X1, X1), Y3, Y4), Y2, Y4, Y5, Y2, Y3) -> true__
% 0.68/0.91 f2(f1(true__, h(Y0, Y2), Y3, Y4), Y0, Y4, Y5, Y2, Y3) -> true__
% 0.68/0.91 f2(f1(true__, h(h(g(X1, Y2), Y0), X1), Y3, Y4), Y0, Y4, Y5, Y2, Y3) -> true__
% 0.68/0.91 f2(true__, A, B, C, F, E) -> f1(p(A, B, C), F, E, C)
% 0.68/0.91 f3(f1(true__, Y0, Y1, Y2), Y1, Y3, Y4, Y0, Y5, Y2) -> true__
% 0.68/0.91 f3(p(A, D, F), D, E, B, A, C, F) -> true__
% 0.68/0.91 f3(true__, D, E, B, A, C, F) -> f2(p(D, E, B), A, B, C, F, E)
% 0.68/0.91 f4(f1(true__, k(Y0), Y0, k(Y0))) -> true__
% 0.68/0.91 f4(p(k(A), A, k(A))) -> true__
% 0.68/0.91 f4(true__) -> false__
% 0.68/0.91 false__ -> true__
% 0.68/0.91 p(A, h(A, B), B) -> true__
% 0.68/0.91 p(F, E, C) -> f1(true__, F, E, C)
% 0.68/0.91 p(g(A, B), A, B) -> true__
% 0.68/0.91 with the LPO induced by
% 0.68/0.91 k > f4 > f3 > f2 > p > f1 > h > g > false__ > true__
% 0.68/0.91
% 0.68/0.91 % SZS output end Proof
% 0.68/0.91
%------------------------------------------------------------------------------