TPTP Problem File: SWW854+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW854+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : mlstring__6__explode_11__brokendep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : mlstring__6__explode_11__brokendep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 38 ( 24 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 23 ( 3 ~; 1 |; 4 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 44 ( 43 !; 1 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof('HL_TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('HL_FALSITY',axiom,
~ p__01(s__02(cbool__00,cF__00)) ).
fof('HL_BOOL_CASES',axiom,
! [Vt] :
( s__02(cbool__00,Vt) = s__02(cbool__00,cT__00)
| s__02(cbool__00,Vt) = s__02(cbool__00,cF__00) ) ).
fof('HL_EXT',axiom,
! [V_3f2384,V_3f2380,Vf,Vg] :
( ! [Vx] : s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vf),s__02(V_3f2384,Vx))) = s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vg),s__02(V_3f2384,Vx)))
=> s__02(cfun__02(V_3f2384,V_3f2380),Vf) = s__02(cfun__02(V_3f2384,V_3f2380),Vg) ) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.IMP_ANTISYM_AX',axiom,
! [V_27t1_27,V_27t2_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> p__01(s__02(cbool__00,V_27t2_27)) )
=> ( ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t1_27)) )
=> s__02(cbool__00,V_27t1_27) = s__02(cbool__00,V_27t2_27) ) ) ).
fof('thm.bool.REFL_CLAUSE',axiom,
! [V_27A_27,V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27)
<=> p__01(s__02(cbool__00,cT__00)) ) ).
fof('thm.bool.EQ_CLAUSES',axiom,
! [V_27t_27] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,V_27t_27)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,V_27t_27)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.JRH_INDUCT_UTIL',axiom,
! [V_27A_27,V_27P_27,V_27t_27] :
( ! [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27t_27)
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) )
=> p__01(s__02(cbool__00,c_24exists__01(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27)))) ) ).
fof('thm.arithmetic.ADD_0',axiom,
! [V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) ).
fof('thm.arithmetic.ADD_SYM',axiom,
! [V_27m_27,V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ).
fof('thm.ind_type.CONSTR_REC',axiom,
! [V_27B_27,V_27A_27,V__0] :
( ! [V_27f_27,V_27r_27,V_27n_27] : s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27B_27),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,V_27B_27)),chapp__02(s__02(cfun__02(cfun__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),V_27B_27),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,V_27B_27))),V__0),s__02(cfun__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),V_27B_27),V_27f_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),V_27r_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),V_27B_27),V_27f_27),s__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),V_27r_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
=> ! [V_27Fn_27] :
? [V_27f_27] :
! [V_27c_27,V_27i_27,V_27r_27] : s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),V_27B_27),V_27f_27),s__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),c_27const_2eind__type_2eCONSTR_27__03(s__02(c_27type_2enum_2enum_27__00,V_27c_27),s__02(V_27A_27,V_27i_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),V_27r_27))))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27B_27),V_27B_27),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27B_27),V_27B_27)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27B_27),V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(V_27A_27,cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27B_27),V_27B_27)))),V_27Fn_27),s__02(c_27type_2enum_2enum_27__00,V_27c_27))),s__02(V_27A_27,V_27i_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),V_27r_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27B_27),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,V_27B_27)),chapp__02(s__02(cfun__02(cfun__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),V_27B_27),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,V_27B_27))),V__0),s__02(cfun__02(c_27type_2eind__type_2erecspace_27__01(V_27A_27),V_27B_27),V_27f_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eind__type_2erecspace_27__01(V_27A_27)),V_27r_27))))) ) ).
fof('thm.ind_type.FCONS',axiom,
! [V_27A_27] :
( ! [V_27a_27,V_27f_27] : s__02(V_27A_27,c_27const_2eind__type_2eFCONS_27__03(s__02(V_27A_27,V_27a_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(V_27A_27,V_27a_27)
& ! [V_27a_27,V_27f_27,V_27n_27] : s__02(V_27A_27,c_27const_2eind__type_2eFCONS_27__03(s__02(V_27A_27,V_27a_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ) ).
fof('thm.list.DROP_0',axiom,
! [V_27A_27,V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) ).
fof('thm.mlstring.strlen_def',axiom,
! [V_27s_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2emlstring_2estrlen_27__01(s__02(c_27type_2emlstring_2emlstring_27__00,c_27const_2emlstring_2estrlit_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27s_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27s_27))) ).
fof('thm.mlstring.explode_aux_thm',axiom,
! [V_27max_27,V_27n_27,V_27ls_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27max_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27ls_27)))
=> s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2emlstring_2eexplode__aux_27__03(s__02(c_27type_2emlstring_2emlstring_27__00,c_27const_2emlstring_2estrlit_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27ls_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27max_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27ls_27))) ) ).
fof('thm.mlstring.explode_def',axiom,
! [V_27s_27] : s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2emlstring_2eexplode_27__01(s__02(c_27type_2emlstring_2emlstring_27__00,V_27s_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2emlstring_2eexplode__aux_27__03(s__02(c_27type_2emlstring_2emlstring_27__00,V_27s_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2emlstring_2estrlen_27__01(s__02(c_27type_2emlstring_2emlstring_27__00,V_27s_27))))) ).
fof(conjecture,conjecture,
! [V_27s1_27,V_27s2_27] :
( s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2emlstring_2eexplode_27__01(s__02(c_27type_2emlstring_2emlstring_27__00,V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2emlstring_2eexplode_27__01(s__02(c_27type_2emlstring_2emlstring_27__00,V_27s2_27)))
<=> s__02(c_27type_2emlstring_2emlstring_27__00,V_27s1_27) = s__02(c_27type_2emlstring_2emlstring_27__00,V_27s2_27) ) ).
%------------------------------------------------------------------------------