TPTP Problem File: ROB015-1.p
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%--------------------------------------------------------------------------
% File : ROB015-1 : TPTP v8.2.0. Released v1.0.0.
% Domain : Robbins Algebra
% Problem : If -(-e + -(d + -e)) = d then -(e + k(d + -(d + -e))) = -e
% Version : [Win90] (equality) axioms.
% English : This is the induction step of an induction proof.
% Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% Source : [Win90]
% Names : Lemma 3.6 [Win90]
% Status : Satisfiable
% Rating : 0.50 v8.2.0, 0.70 v8.1.0, 0.62 v7.5.0, 0.67 v7.4.0, 0.64 v7.3.0, 0.67 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.29 v6.3.0, 0.25 v6.2.0, 0.40 v6.1.0, 0.44 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0, 0.78 v5.2.0, 0.80 v5.0.0, 0.78 v4.1.0, 0.71 v4.0.1, 1.00 v4.0.0, 0.50 v3.7.0, 0.33 v3.4.0, 0.50 v3.3.0, 0.33 v3.2.0, 0.80 v3.1.0, 0.67 v2.7.0, 0.33 v2.6.0, 0.86 v2.5.0, 0.50 v2.4.0, 0.67 v2.2.1, 0.75 v2.2.0, 0.67 v2.1.0, 1.00 v2.0.0
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 6 RR)
% Number of literals : 13 ( 8 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% SPC : CNF_SAT_RFO_EQU_NUE
% Comments :
%--------------------------------------------------------------------------
%----Include axioms for Robbins algebra
include('Axioms/ROB001-0.ax').
%----Include axioms for numbers in Robbins algebras
include('Axioms/ROB001-1.ax').
%--------------------------------------------------------------------------
cnf(condition,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d ).
cnf(k_positive,axiom,
positive_integer(k) ).
cnf(base_step,axiom,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e) ).
cnf(prove_induction_step,negated_conjecture,
negate(add(e,multiply(successor(k),add(d,negate(add(d,negate(e))))))) != negate(e) ).
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