TPTP Problem File: RNG039-2.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : RNG039-2 : TPTP v8.2.0. Released v1.0.0.
% Domain : Ring Theory
% Problem : Ring property 2
% Version : [Wos65] axioms : Reduced > Incomplete.
% English :
% Refs : [Wos65] Wos (1965), Unpublished Note
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [SPRFN]
% Names : Problem 28 [Wos65]
% : wos28 [WM76]
% Status : Unsatisfiable
% Rating : 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v5.5.0, 0.06 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.1.0, 0.06 v5.0.0, 0.07 v4.0.1, 0.00 v2.7.0, 0.12 v2.6.0, 0.43 v2.5.0, 0.14 v2.4.0, 0.00 v2.3.0, 0.14 v2.2.1, 0.44 v2.1.0, 0.29 v2.0.0
% Syntax : Number of clauses : 74 ( 50 unt; 0 nHn; 49 RR)
% Number of literals : 129 ( 0 equ; 56 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 3 usr; 0 prp; 2-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 139 ( 3 sgn)
% SPC : CNF_UNS_RFO_NEQ_HRN
% Comments : There is no additive inverse in this problem.
%--------------------------------------------------------------------------
%----Include ring theory axioms
%include('Axioms/RNG001-0.ax').
%--------------------------------------------------------------------------
%input_clause(additive_inverse_substitution,axiom,
% [--equalish(X,Y),
% ++equalish(additive_inverse(X),additive_inverse(Y))]).
cnf(add_substitution1,axiom,
( ~ equalish(X,Y)
| equalish(add(X,W),add(Y,W)) ) ).
cnf(add_substitution2,axiom,
( ~ equalish(X,Y)
| equalish(add(W,X),add(W,Y)) ) ).
cnf(sum_substitution1,axiom,
( ~ equalish(X,Y)
| ~ sum(X,W,Z)
| sum(Y,W,Z) ) ).
cnf(sum_substitution2,axiom,
( ~ equalish(X,Y)
| ~ sum(W,X,Z)
| sum(W,Y,Z) ) ).
cnf(sum_substitution3,axiom,
( ~ equalish(X,Y)
| ~ sum(W,Z,X)
| sum(W,Z,Y) ) ).
cnf(multiply_substitution1,axiom,
( ~ equalish(X,Y)
| equalish(multiply(X,W),multiply(Y,W)) ) ).
cnf(multiply_substitution2,axiom,
( ~ equalish(X,Y)
| equalish(multiply(W,X),multiply(W,Y)) ) ).
cnf(product_substitution1,axiom,
( ~ equalish(X,Y)
| ~ product(X,W,Z)
| product(Y,W,Z) ) ).
cnf(product_substitution2,axiom,
( ~ equalish(X,Y)
| ~ product(W,X,Z)
| product(W,Y,Z) ) ).
cnf(product_substitution3,axiom,
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ) ).
cnf(reflexivity,axiom,
equalish(X,X) ).
%input_clause(symmetry,axiom,
% [--equalish(X,Y),
% ++equalish(Y,X)]).
cnf(transitivity,axiom,
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) ) ).
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)) ).
%input_clause(additive_inverse1,axiom,
% [++sum(additive_inverse(X),X,additive_identity)]).
%input_clause(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) ) ).
cnf(distributivity3,axiom,
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) ) ).
cnf(distributivity4,axiom,
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) ) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X,additive_identity) ).
cnf(multiplicative_identity2,axiom,
product(X,additive_identity,additive_identity) ).
%-----Equality axioms for operators
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| equalish(U,V) ) ).
cnf(sum_left_cancellation,axiom,
( ~ sum(A,B,C)
| ~ sum(D,B,C)
| equalish(D,A) ) ).
cnf(sum_right_concellation,axiom,
( ~ sum(A,B,C)
| ~ sum(A,D,C)
| equalish(D,B) ) ).
cnf(absorbtion1,axiom,
sum(A,add(A,B),B) ).
cnf(absorbtion2,axiom,
sum(add(A,B),B,A) ).
cnf(clause32,axiom,
sum(A,A,additive_identity) ).
cnf(clause33,axiom,
equalish(add(A,additive_identity),A) ).
cnf(clause34,axiom,
equalish(add(A,A),additive_identity) ).
cnf(clause35,axiom,
equalish(multiply(A,A),A) ).
cnf(clause36,axiom,
equalish(multiply(a,b),c) ).
cnf(clause37,axiom,
equalish(multiply(b,a),d) ).
cnf(clause38,axiom,
sum(A,B,add(B,A)) ).
cnf(clause39,axiom,
product(a,c,c) ).
cnf(clause40,axiom,
product(b,d,d) ).
cnf(clause41,axiom,
product(c,b,c) ).
cnf(clause42,axiom,
product(d,a,d) ).
cnf(clause43,axiom,
product(A,multiply(A,B),multiply(A,B)) ).
cnf(clause44,axiom,
product(a,multiply(b,A),multiply(B,A)) ).
cnf(clause45,axiom,
product(a,b,multiply(c,b)) ).
cnf(clause46,axiom,
product(a,multiply(b,c),c) ).
cnf(clause47,axiom,
product(b,multiply(a,A),multiply(d,A)) ).
cnf(clause48,axiom,
product(b,a,multiply(d,a)) ).
cnf(clause49,axiom,
product(b,multiply(a,d),d) ).
cnf(clause50,axiom,
product(b,c,multiply(d,b)) ).
cnf(clause51,axiom,
product(a,d,multiply(c,a)) ).
cnf(clause52,axiom,
product(multiply(A,B),B,multiply(A,B)) ).
cnf(clause53,axiom,
product(multiply(A,a),b,multiply(A,c)) ).
cnf(clause54,axiom,
product(a,b,multiply(a,c)) ).
cnf(clause55,axiom,
product(multiply(c,a),b,c) ).
cnf(clause56,axiom,
product(d,b,multiply(b,c)) ).
cnf(clause57,axiom,
product(multiply(A,b),a,multiply(A,d)) ).
cnf(clause58,axiom,
product(b,a,multiply(b,d)) ).
cnf(clause59,axiom,
product(multiply(d,b),a,d) ).
cnf(clause60,axiom,
product(c,a,multiply(a,d)) ).
cnf(clause63,axiom,
product(a,add(b,a),add(c,a)) ).
cnf(clause64,axiom,
product(a,add(a,b),add(a,c)) ).
cnf(clause65,axiom,
product(b,add(a,b),add(d,b)) ).
cnf(clause66,axiom,
product(b,add(b,a),add(b,d)) ).
cnf(clause67,axiom,
product(add(a,b),b,add(c,b)) ).
cnf(clause68,axiom,
product(add(b,a),b,add(b,c)) ).
cnf(clause69,axiom,
product(add(b,a),a,add(d,a)) ).
cnf(clause70,axiom,
product(add(a,b),a,add(a,d)) ).
cnf(clause71,axiom,
product(A,A,A) ).
cnf(a_times_b,negated_conjecture,
product(a,b,c) ).
cnf(b_times_a,negated_conjecture,
product(b,a,d) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equalish(c,d) ).
%--------------------------------------------------------------------------