TPTP Problem File: SCT029-1.p
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%------------------------------------------------------------------------------
% File : SCT029-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Social Choice Theory
% Problem : Arrow Order 156_1
% 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-156_1 [Nip10]
% Status : Satisfiable
% Rating : 0.00 v7.4.0, 0.09 v7.3.0, 0.00 v6.2.0, 0.20 v6.1.0, 0.11 v6.0.0, 0.14 v5.5.0, 0.12 v5.4.0, 0.30 v5.3.0, 0.33 v5.2.0, 0.30 v5.0.0, 0.22 v4.1.0
% Syntax : Number of clauses : 13 ( 4 unt; 4 nHn; 7 RR)
% Number of literals : 23 ( 3 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 5 sgn)
% SPC : CNF_SAT_RFO_EQU_NUE
% Comments :
%------------------------------------------------------------------------------
cnf(cls_IIA__def_4,axiom,
( c_Arrow__Order__Mirabelle_OIIA(V_F)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(V_F),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ) ).
cnf(cls_unanimity__def_1,axiom,
( c_Arrow__Order__Mirabelle_Ounanimity(V_F)
| c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(V_F),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ) ).
cnf(cls_dictator__def_0,axiom,
( hAPP(V_F,V_x) = hAPP(V_x,V_i)
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Odictator(V_F,V_i) ) ).
cnf(cls_mem__def_1,axiom,
( c_in(V_x,V_S,T_a)
| ~ hBOOL(hAPP(V_S,V_x)) ) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(V_S,V_x))
| ~ c_in(V_x,V_S,T_a) ) ).
cnf(cls_IIA__def_5,axiom,
( c_Arrow__Order__Mirabelle_OIIA(V_F)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(V_F),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ) ).
cnf(cls_dictator__def_1,axiom,
( c_Arrow__Order__Mirabelle_Odictator(V_F,V_i)
| c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(V_F,V_i),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ) ).
cnf(cls_assms_I3_J_0,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F) ).
cnf(cls_dictator__def_2,axiom,
( hAPP(V_F,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(V_F,V_i)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(V_F,V_i),V_i)
| c_Arrow__Order__Mirabelle_Odictator(V_F,V_i) ) ).
cnf(cls_u_0,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_Arrow__Order__Mirabelle_Odictator(v_F,V_x) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ c_fequal(V_X,V_Y,T_a) ) ).
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