TPTP Problem File: SWW853+1.p
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%------------------------------------------------------------------------------
% File : SWW853+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : mllist__12__tabulate_GENLIST__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : mllist__12__tabulate_GENLIST__dep [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 ( 10 unt; 0 def)
% Number of atoms : 32 ( 24 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 17 ( 3 ~; 1 |; 6 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-4 aty)
% Number of variables : 52 ( 52 !; 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.LET_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27x_27] : s__02(V_27B_27,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_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.combin.o_DEF',axiom,
! [V_27B_27,V_27C_27,V_27A_27,V_27f_27,V_27g_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2ecombin_2eo_27__02(s__02(cfun__02(V_27C_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,V_27C_27),V_27g_27))),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27C_27,V_27B_27),V_27f_27),s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27A_27,V_27C_27),V_27g_27),s__02(V_27A_27,Vx))))) ).
fof('thm.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,c_27const_2ecombin_2eI_27__01(s__02(V_27A_27,V_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.arithmetic.SUB_0',axiom,
! [V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(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))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_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.FUNPOW_0',axiom,
! [V_27A_27,V_27x_27,V_27f_27] : s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27A_27,V_27A_27),c_27const_2earithmetic_2eFUNPOW_27__02(s__02(cfun__02(V_27A_27,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_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.list.APPEND',axiom,
! [V_27A_27] :
( ! [V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_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)
& ! [V_27l1_27,V_27l2_27,V_27h_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))))) ) ).
fof('thm.list.REVERSE_DEF',axiom,
! [V_27A_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eREVERSE_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eREVERSE_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eREVERSE_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))) ) ).
fof('thm.mllist.tabulate_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27n_27,V_27f_27,V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27))),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),c_27const_2emllist_2etabulate__aux_27__04(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))
=> ! [V_27n_27,V_27f_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2emllist_2etabulate_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) ) ).
fof('thm.mllist.tabulate_aux_GENLIST',axiom,
! [V_27A_27,V_27n_27,V_27m_27,V_27f_27,V_27acc_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2emllist_2etabulate__aux_27__04(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27acc_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eREVERSE_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27acc_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eGENLIST_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),c_27const_2ecombin_2eo_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2eFUNPOW_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2enum_2eSUC_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27f_27,V_27n_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2emllist_2etabulate_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eGENLIST_27__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))) ).
%------------------------------------------------------------------------------