TPTP Problem File: RNG040-2.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : RNG040-2 : TPTP v8.2.0. Released v1.0.0.
% Domain : Ring Theory
% Problem : Ring property 4
% Version : [Wos65] axioms : Incomplete.
% English :
% Refs : [Wos65] Wos (1965), Unpublished Note
% : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [SPRFN]
% Names : Problem 29 [Wos65]
% : wos29 [WM76]
% Status : Unsatisfiable
% Rating : 0.00 v8.2.0, 0.05 v7.5.0, 0.00 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.07 v6.3.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.10 v5.5.0, 0.35 v5.3.0, 0.39 v5.2.0, 0.25 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0, 0.15 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.10 v3.5.0, 0.09 v3.4.0, 0.17 v3.3.0, 0.21 v3.2.0, 0.15 v3.1.0, 0.18 v2.7.0, 0.33 v2.6.0, 0.30 v2.5.0, 0.33 v2.4.0, 0.33 v2.3.0, 0.22 v2.2.1, 0.33 v2.2.0, 0.11 v2.1.0, 0.22 v2.0.0
% Syntax : Number of clauses : 25 ( 13 unt; 2 nHn; 15 RR)
% Number of literals : 53 ( 4 equ; 27 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : These are the same axioms as in [MOW76].
%--------------------------------------------------------------------------
%----Include ring theory axioms
%include('Axioms/RNG001-0.ax').
%--------------------------------------------------------------------------
cnf(additive_identity1,axiom,
sum(additive_identity,X,X) ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)) ).
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)) ).
cnf(additive_inverse1,axiom,
sum(additive_inverse(X),X,additive_identity) ).
cnf(additive_inverse2,axiom,
sum(X,additive_inverse(X),additive_identity) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) ) ).
cnf(associativity_of_addition2,axiom,
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W)
| sum(U,Z,W) ) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ).
cnf(associativity_of_multiplication1,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ) ).
cnf(associativity_of_multiplication2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(distributivity1,axiom,
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ) ).
cnf(distributivity2,axiom,
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ) ).
%input_clause(distributivity3,axiom,
% [--product(Y,X,V1),
% --product(Z,X,V2),
% --sum(Y,Z,V3),
% --product(V3,X,V4),
% ++sum(V1,V2,V4)]).
%input_clause(distributivity4,axiom,
% [--product(Y,X,V1),
% --product(Z,X,V2),
% --sum(Y,Z,V3),
% --sum(V1,V2,V4),
% ++product(V3,X,V4)]).
%-----Equality axioms for operators
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ) ).
cnf(right_multiplicative_identity,hypothesis,
product(A,multiplicative_identity,A) ).
cnf(left_multiplicative_identity,hypothesis,
product(multiplicative_identity,A,A) ).
cnf(clause30,hypothesis,
( product(A,h(A),multiplicative_identity)
| A = additive_identity ) ).
cnf(clause31,hypothesis,
( product(h(A),A,multiplicative_identity)
| A = additive_identity ) ).
cnf(product_symmetry,hypothesis,
( ~ product(A,B,C)
| product(B,A,C) ) ).
cnf(b_plus_c,negated_conjecture,
sum(b,c,d) ).
cnf(d_plus_a,negated_conjecture,
product(d,a,additive_identity) ).
cnf(b_plus_a,negated_conjecture,
product(b,a,l) ).
cnf(c_plus_a,negated_conjecture,
product(c,a,n) ).
cnf(prove_equation,negated_conjecture,
~ sum(l,n,additive_identity) ).
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