## TPTP Problem File: ROB014-2.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : ROB014-2 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Robbins Algebra
% Problem  : If -(-e + -(d + -e)) = d then -(e + k(d + -(d + -e))) = -e, k=1
% Version  : [Win90] (equality) axioms : Augmented.
% English  : This is the base step of an induction proof.

% Refs     : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% Source   : [Win90]
% Names    : Lemma 3.6 [Win90]

% Status   : Unsatisfiable
% Rating   : 0.33 v7.5.0, 0.20 v7.4.0, 0.11 v7.3.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.00 v6.1.0, 0.20 v6.0.0, 0.44 v5.5.0, 0.69 v5.4.0, 0.60 v5.3.0, 0.67 v5.2.0, 0.25 v5.1.0, 0.00 v5.0.0, 0.29 v4.1.0, 0.22 v4.0.1, 0.00 v3.4.0, 0.17 v3.3.0, 0.14 v3.2.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.17 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.50 v2.3.0, 0.33 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.80 v2.0.0
% Syntax   : Number of clauses     :   11 (   0 non-Horn;   7 unit;   6 RR)
%            Number of atoms       :   16 (  11 equality)
%            Maximal clause size   :    3 (   1 average)
%            Number of predicates  :    2 (   0 propositional; 1-2 arity)
%            Number of functors    :    7 (   3 constant; 0-2 arity)
%            Number of variables   :   18 (   0 singleton)
%            Maximal term depth    :    8 (   3 average)
% SPC      : CNF_UNS_RFO_SEQ_HRN

% Comments : The extra lemmas are suggested by [Win90].
%--------------------------------------------------------------------------
%----Include axioms for Robbins algebra
include('Axioms/ROB001-0.ax').
%----Include axioms for numbers in Robbins algebras
include('Axioms/ROB001-1.ax').
%--------------------------------------------------------------------------
%----These are the extra lemmas
cnf(lemma_3_2,axiom,
| X = Y )).

cnf(lemma_3_4,axiom,
( negate(add(X,negate(Y))) != Z
| ~ positive_integer(Vk)