TPTP Problem File: ALG002-1.p
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% File : ALG002-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : General Algebra
% Problem : In an ordered field, if X > 0 then X^-1 > 0
% Version : [FL+74] axioms.
% 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 5 [FL+74]
% : EX5-T? [WM76]
% : ex5.lop [SETHEO]
% : FEX5 [SPRFN]
% Status : Unsatisfiable
% Rating : 0.00 v8.1.0, 0.17 v7.0.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0
% Syntax : Number of clauses : 14 ( 4 unt; 2 nHn; 11 RR)
% Number of literals : 28 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 2 usr; 0 prp; 1-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 23 ( 1 sgn)
% SPC : CNF_UNS_RFO_NEQ_NHN
% Comments :
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cnf(right_identity,axiom,
product(X,multiplicative_identity,X) ).
cnf(not_abelian,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity) ).
cnf(product_of_inverses1,axiom,
( ~ product(X,Y,Z)
| product(additive_inverse(X),additive_inverse(Y),Z) ) ).
cnf(product_of_inverses2,axiom,
( product(X,Y,Z)
| ~ product(additive_inverse(X),additive_inverse(Y),Z) ) ).
cnf(product_to_inverse,axiom,
( ~ product(X,Y,Z)
| product(X,additive_inverse(Y),additive_inverse(Z)) ) ).
cnf(inverse_and_identity,axiom,
( product(X,multiplicative_inverse(X),multiplicative_identity)
| product(X,X,additive_identity) ) ).
cnf(inverse_greater_than_0,axiom,
( ~ greater_than_0(X)
| ~ greater_than_0(additive_inverse(X)) ) ).
cnf(greater_than_0_square,axiom,
( ~ greater_than_0(X)
| ~ product(X,X,additive_identity) ) ).
cnf(commutativity_of_product,axiom,
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ).
cnf(product_and_inverse,axiom,
( greater_than_0(X)
| product(X,X,additive_identity)
| greater_than_0(additive_inverse(X)) ) ).
cnf(square_to_0,axiom,
( ~ product(Y,Z,X)
| ~ product(Y,Y,additive_identity)
| product(X,X,additive_identity) ) ).
cnf(product_and_greater_than_0,axiom,
( ~ product(Y,Z,X)
| ~ greater_than_0(Y)
| ~ greater_than_0(Z)
| greater_than_0(X) ) ).
cnf(a_greater_than_0,hypothesis,
greater_than_0(a) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)) ).
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