TPTP Problem File: RNG001-3.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : RNG001-3 : TPTP v9.0.0. Released v1.0.0.
% Domain : Ring Theory
% Problem : X.additive_identity = additive_identity for any X
% Version : [FL+74] axioms : Incomplete.
% English :
% Refs : [FL+74] Fleisig et al. (1974), An Implementation of the Model
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [SPRFN]
% Names : Example 6a [FL+74]
% : EX6-T? [WM76]
% : ex6.lop [SETHEO]
% : FEX6T1 [SPRFN]
% : FEX6T2 [SPRFN]
% Status : Unsatisfiable
% Rating : 0.13 v9.0.0, 0.18 v8.2.0, 0.14 v8.1.0, 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.17 v5.3.0, 0.25 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.07 v4.0.1, 0.14 v4.0.0, 0.29 v3.4.0, 0.40 v3.3.0, 0.00 v2.7.0, 0.12 v2.6.0, 0.14 v2.5.0, 0.00 v2.4.0, 0.14 v2.3.0, 0.14 v2.2.1, 0.22 v2.1.0, 0.14 v2.0.0
% Syntax : Number of clauses : 8 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 22 ( 0 equ; 15 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 2 usr; 0 prp; 3-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% SPC : CNF_UNS_RFO_NEQ_HRN
% Comments :
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cnf(additive_identity1,axiom,
sum(additive_identity,X,X) ).
cnf(additive_inverse1,axiom,
sum(additive_inverse(X),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(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)) ).
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(prove_a_times_additive_id_is_additive_id,negated_conjecture,
~ product(a,additive_identity,additive_identity) ).
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