TPTP Problem File: HEN008-2.p
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%--------------------------------------------------------------------------
% File : HEN008-2 : TPTP v8.2.0. Released v1.0.0.
% Domain : Henkin Models
% Problem : X <= Y => X/Z <= Y/Z
% Version : [MOW76] axioms : Augmented.
% English :
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source : [MOW76]
% Names : H8 [MOW76]
% Status : Unsatisfiable
% Rating : 0.12 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.19 v5.4.0, 0.13 v5.3.0, 0.08 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.00 v4.0.0, 0.17 v3.5.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.14 v2.1.0, 0.20 v2.0.0
% Syntax : Number of clauses : 20 ( 11 unt; 0 nHn; 13 RR)
% Number of literals : 40 ( 2 equ; 21 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 5 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments :
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%----Include Henkin model axioms
include('Axioms/HEN001-0.ax').
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%----McCharen uses these earlier results too. I don't
cnf(everything_divide_identity_is_zero,axiom,
quotient(X,identity,zero) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X,zero) ).
cnf(x_divide_x_is_zero,axiom,
quotient(X,X,zero) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X,zero,X) ).
cnf(transitivity_of_less_equal,axiom,
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( ~ less_equal(X,Y)
| ~ quotient(Z,Y,W1)
| ~ quotient(Z,X,W2)
| less_equal(W1,W2) ) ).
cnf(aLEb,hypothesis,
less_equal(a,b) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ less_equal(aQc,bQc) ).
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