TPTP Problem File: SWW851+1.p
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%------------------------------------------------------------------------------
% File : SWW851+1 : TPTP v9.0.0. Released v7.3.0.
% Domain : Software Verification
% Problem : misc__198__REVERSE_REPLICATE__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : misc__198__REVERSE_REPLICATE__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 31 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 19 ( 3 ~; 1 |; 6 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 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.FORALL_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.EQ_SYM_EQ',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
<=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27x_27) ) ).
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.num.INDUCTION',axiom,
! [V_27P_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))))
& ! [V_27n_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_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)))))) ) )
=> ! [V_27n_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,V_27n_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.list.SNOC_APPEND',axiom,
! [V_27A_27,V_27x_27,V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eSNOC_27__02(s__02(V_27A_27,V_27x_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_2elist_2eAPPEND_27__02(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_2elist_2eCONS_27__02(s__02(V_27A_27,V_27x_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))) ).
fof('thm.rich_list.REPLICATE',axiom,
! [V_27A_27] :
( ! [V_27x_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2erich__list_2eREPLICATE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27n_27,V_27x_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2erich__list_2eREPLICATE_27__02(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,V_27x_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27x_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2erich__list_2eREPLICATE_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(V_27A_27,V_27x_27))))) ) ).
fof('thm.misc.SNOC_REPLICATE',axiom,
! [V_27A_27,V_27n_27,V_27x_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eSNOC_27__02(s__02(V_27A_27,V_27x_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2erich__list_2eREPLICATE_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(V_27A_27,V_27x_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2erich__list_2eREPLICATE_27__02(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,V_27x_27))) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27n_27,V_27x_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_2erich__list_2eREPLICATE_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(V_27A_27,V_27x_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2erich__list_2eREPLICATE_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(V_27A_27,V_27x_27))) ).
%------------------------------------------------------------------------------