TPTP Problem File: SWW856+1.p
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%------------------------------------------------------------------------------
% File : SWW856+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : mlvector__3__length_toList__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : mlvector__3__length_toList__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 1 ~; 1 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% 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.ETA_AX',axiom,
! [V_27B_27,V_27A_27,V_27t_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
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.regexp_compiler.vector_induction',axiom,
! [V_27A_27,V_27P_27] :
( ! [V_27l_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),c_27const_2eregexp__compiler_2eVector_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))))))
=> ! [V_27v_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),V_27v_27)))) ) ).
fof('thm.mlvector.length_def',axiom,
! [V_27A_27,V_27l_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eregexp__compiler_2elength_27__01(s__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),c_27const_2eregexp__compiler_2eVector_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) ).
fof('thm.mlvector.toList_thm',axiom,
! [V_27A_27,V_27ls_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2emlvector_2etoList_27__01(s__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),c_27const_2eregexp__compiler_2eVector_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27ls_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27ls_27) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27vec_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2emlvector_2etoList_27__01(s__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),V_27vec_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2eregexp__compiler_2elength_27__01(s__02(c_27type_2eregexp__compiler_2evector_27__01(V_27A_27),V_27vec_27))) ).
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