%------------------------------------------------------------------------------
% File     : SCT072-1 : TPTP v9.0.0. Released v4.1.0.
% Domain   : Social Choice Theory
% Problem  : Arrow Order 255_4
% Version  : Especial.
% English  : Formalization of two proofs of Arrow's impossibility theorem. One
%            formalization is based on utility functions, the other one on 
%            strict partial orders.

% Refs     : [Nip09] Nipkow (2009), Social Choice Theory in HOL: Arrow and
%          : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : Arrow_Order-255_46 [Nip10]

% Status   : Satisfiable
% Rating   : 0.00 v7.5.0, 0.11 v7.4.0, 0.18 v7.3.0, 0.11 v7.1.0, 0.00 v6.3.0, 0.12 v6.2.0, 0.10 v6.1.0, 0.00 v5.3.0, 0.11 v5.2.0, 0.10 v5.0.0, 0.11 v4.1.0
% Syntax   : Number of clauses     :    4 (   2 unt;   2 nHn;   2 RR)
%            Number of literals    :    6 (   2 equ;   1 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :    4 (   4 sgn)
% SPC      : CNF_SAT_RFO_EQU_NUE

% Comments :
%------------------------------------------------------------------------------
cnf(cls_that_0,axiom,
    ( v_thesis____
    | V_a = V_b ) ).

cnf(cls_CHAINED_0,axiom,
    c_List_Odistinct(c_List_Olist_OCons(v_sko__CHAINED__1,c_List_Olist_OCons(v_sko__CHAINED__2,c_List_Olist_OCons(v_sko__CHAINED__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ v_thesis____ ).

cnf(cls_conjecture_1,negated_conjecture,
    ( v_thesis____
    | V_x = V_xa ) ).

%------------------------------------------------------------------------------