TPTP Problem File: HEN011-2.p
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%--------------------------------------------------------------------------
% File : HEN011-2 : TPTP v8.2.0. Released v1.0.0.
% Domain : Henkin Models
% Problem : This operation is commutative
% Version : [MOW76] axioms : Augmented.
% English : Define & on the set of Z', where Z' = identity/Z,
% by X' & Y' = X'/(identity/Y'). The operation is commutative.
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source : [MOW76]
% Names : H11 [MOW76]
% : hp11.ver1.in [ANL]
% Status : Unsatisfiable
% Rating : 0.25 v8.2.0, 0.33 v8.1.0, 0.22 v7.5.0, 0.20 v7.4.0, 0.11 v7.3.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.29 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.20 v6.0.0, 0.44 v5.5.0, 0.69 v5.4.0, 0.73 v5.3.0, 0.58 v5.2.0, 0.50 v5.1.0, 0.43 v5.0.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.17 v3.5.0, 0.00 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.80 v2.0.0
% Syntax : Number of clauses : 26 ( 14 unt; 0 nHn; 19 RR)
% Number of literals : 55 ( 5 equ; 30 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 : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 55 ( 7 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments :
%--------------------------------------------------------------------------
%----Include Henkin model axioms
include('Axioms/HEN001-0.ax').
%--------------------------------------------------------------------------
%----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(xLEy_implies_xQzLEyQz,axiom,
( ~ less_equal(X,Y)
| ~ quotient(X,Z,W1)
| ~ quotient(Y,Z,W2)
| less_equal(W1,W2) ) ).
cnf(one_inversion_equals_three,axiom,
( ~ quotient(identity,X,Y1)
| ~ quotient(identity,Y1,Y2)
| ~ quotient(identity,Y2,Y3)
| Y1 = Y3 ) ).
cnf(inversion_lemma,axiom,
( ~ quotient(identity,X,Y1)
| ~ quotient(identity,Y1,Y2)
| ~ quotient(Y1,Y2,Y3)
| Y1 = Y3 ) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa) ).
cnf(identity_divide_b,hypothesis,
quotient(identity,b,idQb) ).
cnf(identity_divide_idQb,hypothesis,
quotient(identity,idQb,idQ_idQb) ).
cnf(idQa_divide_idQ_idQb,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa) ).
cnf(idQb_divide_idQ_idQa,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa) ).
cnf(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa ).
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