TPTP Problem File: LAT259-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : LAT259-1 : TPTP v8.2.0. Released v3.2.0.
% Domain : Analysis
% Problem : Problem about Tarski's fixed point theorem
% Version : [Pau06] axioms : Especial.
% English :
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names : Tarski__antisymE [Pau06]
% Status : Unsatisfiable
% Rating : 0.15 v8.2.0, 0.19 v8.1.0, 0.16 v7.5.0, 0.26 v7.4.0, 0.24 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.33 v6.4.0, 0.27 v6.3.0, 0.09 v6.2.0, 0.30 v6.1.0, 0.43 v6.0.0, 0.30 v5.5.0, 0.50 v5.3.0, 0.56 v5.2.0, 0.50 v5.1.0, 0.59 v5.0.0, 0.50 v4.1.0, 0.54 v4.0.1, 0.55 v4.0.0, 0.45 v3.7.0, 0.40 v3.5.0, 0.27 v3.4.0, 0.42 v3.3.0, 0.43 v3.2.0
% Syntax : Number of clauses : 2750 ( 656 unt; 250 nHn;1973 RR)
% Number of literals : 6026 (1294 equ;3085 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 89 ( 88 usr; 0 prp; 1-3 aty)
% Number of functors : 249 ( 249 usr; 51 con; 0-18 aty)
% Number of variables : 5745 (1174 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : The problems in the [Pau06] collection each have very many axioms,
% of which only a small selection are required for the refutation.
% The mission is to find those few axioms, after which a refutation
% can be quite easily found.
%------------------------------------------------------------------------------
include('Axioms/LAT006-0.ax').
include('Axioms/MSC001-1.ax').
include('Axioms/MSC001-0.ax').
%------------------------------------------------------------------------------
cnf(cls_Relation_Oantisym__def_0,axiom,
( ~ c_Relation_Oantisym(V_r,T_a)
| ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_U = V_V ) ).
cnf(cls_Relation_Oantisym__def_1,axiom,
( c_Relation_Oantisym(V_r,T_a)
| c_in(c_Pair(c_Main_Oantisym__def__1(V_r,T_a),c_Main_Oantisym__def__2(V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_Relation_Oantisym__def_2,axiom,
( c_Relation_Oantisym(V_r,T_a)
| c_in(c_Pair(c_Main_Oantisym__def__2(V_r,T_a),c_Main_Oantisym__def__1(V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_Relation_Oantisym__def_3,axiom,
( c_Main_Oantisym__def__1(V_r,T_a) != c_Main_Oantisym__def__2(V_r,T_a)
| c_Relation_Oantisym(V_r,T_a) ) ).
cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ).
cnf(cls_Tarski_OPartialOrder__iff_0,axiom,
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ).
cnf(cls_Tarski_OPartialOrder__iff_1,axiom,
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ).
cnf(cls_Tarski_OPartialOrder__iff_2,axiom,
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ).
cnf(cls_Tarski_OPartialOrder__iff_3,axiom,
( ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) ).
cnf(cls_Tarski_Ocl_A_58_APartialOrder_0,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ).
cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
v_a != v_b ).
%------------------------------------------------------------------------------