%------------------------------------------------------------------------------
% File     : SWV904-1 : TPTP v9.0.0. Released v4.1.0.
% Domain   : Software Verification
% Problem  : Hoare logic with procedures 450_1
% Version  : Especial.
% English  : Completeness is taken relative to completeness of the underlying
%            logic. Two versions of completeness proof: nested single recursion
%            and simultaneous recursion in call rule.

% Refs     : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : Hoare-450_1 [Nip10]

% Status   : Unsatisfiable
% Rating   : 0.00 v5.5.0, 0.05 v5.4.0, 0.10 v5.3.0, 0.06 v5.2.0, 0.00 v5.1.0, 0.06 v5.0.0, 0.07 v4.1.0
% Syntax   : Number of clauses     :   29 (  15 unt;   2 nHn;  27 RR)
%            Number of literals    :   45 (  25 equ;  28 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-2 aty)
%            Number of variables   :   46 (  25 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_option_Osimps_I2_J_0,axiom,
    c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ).

cnf(cls_not__Some__eq_1,axiom,
    c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_y,T_a) ).

cnf(cls_option_Osimps_I3_J_0,axiom,
    c_Option_Ooption_OSome(V_a_H,T_a) != c_Option_Ooption_ONone(T_a) ).

cnf(cls_not__None__eq_1,axiom,
    c_Option_Ooption_OSome(V_xa,T_a) != c_Option_Ooption_ONone(T_a) ).

cnf(cls_WT_OBody_0,axiom,
    ( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
    | c_Com_Obody(V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ).

cnf(cls_com_Osimps_I19_J_0,axiom,
    c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSKIP ).

cnf(cls_com_Osimps_I49_J_0,axiom,
    c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).

cnf(cls_com_Osimps_I48_J_0,axiom,
    c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OBODY(V_pname_H) ).

cnf(cls_com_Osimps_I6_J_0,axiom,
    ( c_Com_Ocom_OBODY(V_pname) != c_Com_Ocom_OBODY(V_pname_H)
    | V_pname = V_pname_H ) ).

cnf(cls_com_Osimps_I18_J_0,axiom,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(V_pname_H) ).

cnf(cls_WTs__elim__cases_I7_J_0,axiom,
    ( c_Com_Obody(V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom)
    | ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P)) ) ).

cnf(cls_com_Osimps_I3_J_1,axiom,
    ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
    | V_com2 = V_com2_H ) ).

cnf(cls_com_Osimps_I3_J_0,axiom,
    ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
    | V_com1 = V_com1_H ) ).

cnf(cls_option_Oinject_0,axiom,
    ( c_Option_Ooption_OSome(V_a,T_a) != c_Option_Ooption_OSome(V_a_H,T_a)
    | V_a = V_a_H ) ).

cnf(cls_com_Osimps_I13_J_0,axiom,
    c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).

cnf(cls_com_Osimps_I12_J_0,axiom,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).

cnf(cls_WT__bodiesD_0,axiom,
    ( c_Com_Obody(V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom)
    | ~ c_Com_OWT__bodies
    | c_Com_OWT(V_b) ) ).

cnf(cls_WT_OSemi_0,axiom,
    ( c_Com_OWT(c_Com_Ocom_OSemi(V_c0,V_c1))
    | ~ c_Com_OWT(V_c1)
    | ~ c_Com_OWT(V_c0) ) ).

cnf(cls_WTs__elim__cases_I4_J_0,axiom,
    ( c_Com_OWT(V_c1)
    | ~ c_Com_OWT(c_Com_Ocom_OSemi(V_c1,V_c2)) ) ).

cnf(cls_WTs__elim__cases_I4_J_1,axiom,
    ( c_Com_OWT(V_c2)
    | ~ c_Com_OWT(c_Com_Ocom_OSemi(V_c1,V_c2)) ) ).

cnf(cls_state__not__singleton__def__raw_0,axiom,
    ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).

cnf(cls_state__not__singleton__def_1,axiom,
    ( c_Hoare__Mirabelle_Ostate__not__singleton
    | V_x = V_xa ) ).

cnf(cls_single__stateE_0,axiom,
    ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).

cnf(cls_WT_OSkip_0,axiom,
    c_Com_OWT(c_Com_Ocom_OSKIP) ).

cnf(cls_state__not__singleton__def_0,axiom,
    ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Hoare__Mirabelle_Ostate__not__singleton ).

cnf(cls_conjecture_1,negated_conjecture,
    c_Com_OWT__bodies ).

cnf(cls_conjecture_2,negated_conjecture,
    c_Com_OWT(v_c) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ostate__not__singleton ).

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