TSTP Solution File: ROB013-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n022.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 : Mon Jul 18 20:54:46 EDT 2022
% Result : Unsatisfiable 1.52s 1.69s
% Output : Proof 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : moca.sh %s
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Thu Jun 9 13:41:49 EDT 2022
% 0.14/0.33 % CPUTime :
% 1.52/1.69 % SZS status Unsatisfiable
% 1.52/1.69 % SZS output start Proof
% 1.52/1.69 The input problem is unsatisfiable because
% 1.52/1.69
% 1.52/1.69 [1] the following set of Horn clauses is unsatisfiable:
% 1.52/1.69
% 1.52/1.69 add(X, Y) = add(Y, X)
% 1.52/1.69 add(add(X, Y), Z) = add(X, add(Y, Z))
% 1.52/1.69 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X
% 1.52/1.69 negate(add(a, b)) = c
% 1.52/1.69 negate(add(c, negate(add(negate(b), a)))) = a ==> \bottom
% 1.52/1.69
% 1.52/1.69 This holds because
% 1.52/1.69
% 1.52/1.69 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.52/1.69
% 1.52/1.69 E:
% 1.52/1.69 add(X, Y) = add(Y, X)
% 1.52/1.69 add(add(X, Y), Z) = add(X, add(Y, Z))
% 1.52/1.69 f1(a) = false__
% 1.52/1.69 f1(negate(add(c, negate(add(negate(b), a))))) = true__
% 1.52/1.69 negate(add(a, b)) = c
% 1.52/1.69 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X
% 1.52/1.69 G:
% 1.52/1.69 true__ = false__
% 1.52/1.69
% 1.52/1.69 This holds because
% 1.52/1.69
% 1.52/1.69 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.52/1.69
% 1.52/1.69 add(X, Y) = add(Y, X)
% 1.52/1.69 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2))
% 1.52/1.69 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2))
% 1.52/1.69 add(add(X, Y), Z) -> add(X, add(Y, Z))
% 1.52/1.69 f1(a) -> false__
% 1.52/1.69 f1(negate(add(c, negate(add(a, negate(b)))))) -> true__
% 1.52/1.69 f1(negate(add(c, negate(add(negate(b), a))))) -> true__
% 1.52/1.69 negate(add(a, b)) -> c
% 1.52/1.69 negate(add(a, negate(add(a, add(c, negate(b)))))) -> c
% 1.52/1.69 negate(add(a, negate(add(c, negate(negate(add(a, negate(b)))))))) -> c
% 1.52/1.69 negate(add(c, negate(add(a, negate(b))))) -> a
% 1.52/1.69 negate(add(c, negate(add(negate(a), b)))) -> b
% 1.52/1.69 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) -> X
% 1.52/1.69 negate(add(negate(add(Y0, Y1)), negate(add(negate(Y0), Y1)))) -> Y1
% 1.52/1.69 negate(add(negate(add(Y0, Y1)), negate(add(negate(Y1), Y0)))) -> Y0
% 1.52/1.69 negate(add(negate(add(Y0, add(a, b))), negate(add(c, Y0)))) -> Y0
% 1.52/1.69 negate(add(negate(add(Y0, c)), negate(add(Y0, add(a, b))))) -> Y0
% 1.52/1.69 negate(add(negate(add(Y1, Y0)), negate(add(Y0, negate(Y1))))) -> Y0
% 1.52/1.69 negate(add(negate(add(a, add(b, Y1))), negate(add(Y1, c)))) -> Y1
% 1.52/1.69 true__ -> false__
% 1.52/1.69 with the LPO induced by
% 1.52/1.69 f1 > b > c > add > a > negate > true__ > false__
% 1.52/1.69
% 1.52/1.69 % SZS output end Proof
% 1.52/1.69
%------------------------------------------------------------------------------