TPTP Problem File: SWW877+1.p
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%------------------------------------------------------------------------------
% File : SWW877+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : wordProps__112__every_var_exp_mono__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : wordProps__112__every_var_exp_mono__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 : 16 ( 3 unt; 0 def)
% Number of atoms : 87 ( 19 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 75 ( 4 ~; 1 |; 29 &)
% ( 19 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 70 ( 70 !; 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.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.AND_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,cF__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.IMP_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cF__00)) )
<=> ~ 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.bool.AND_IMP_INTRO',axiom,
! [V_27t1_27,V_27t2_27,V_27t3_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_27t3_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_27t3_27)) ) ) ).
fof('thm.bool.IMP_CONG',axiom,
! [V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27x_27) = s__02(cbool__00,V_27x_7c39_7c_27)
& ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> s__02(cbool__00,V_27y_27) = s__02(cbool__00,V_27y_7c39_7c_27) ) )
=> ( ( p__01(s__02(cbool__00,V_27x_27))
=> p__01(s__02(cbool__00,V_27y_27)) )
<=> ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> p__01(s__02(cbool__00,V_27y_7c39_7c_27)) ) ) ) ).
fof('thm.list.EVERY_MEM',axiom,
! [V_27A_27,V_27P_27,V_27l_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))))
<=> ! [V_27e_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27e_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_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_27e_27)))) ) ) ).
fof('thm.wordLang.every_var_exp_ind',axiom,
! [V_27A_27,V_27P_7c39_7c_27] :
( ( ! [V_27P_27,V_27num_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eVar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27num_27))))))
& ! [V_27P_27,V_27exp_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eLoad_27__01(s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27)))))) )
& ! [V_27P_27,V_27wop_27,V_27ls_27] :
( ! [V_27a_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27a_27),s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordLang_2eexp_27__01(V_27A_27)),V_27ls_27))))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27a_27)))) )
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eOp_27__02(s__02(c_27type_2easm_2ebinop_27__00,V_27wop_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordLang_2eexp_27__01(V_27A_27)),V_27ls_27)))))) )
& ! [V_27P_27,V_27sh_27,V_27exp_27,V_27nexp_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eShift_27__03(s__02(c_27type_2east_2eshift_27__00,V_27sh_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27),s__02(c_27type_2ewordLang_2enum__exp_27__01(V_27A_27),V_27nexp_27)))))) )
& ! [V_27P_27,V_27v2_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eConst_27__01(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v2_27))))))
& ! [V_27P_27,V_27v4_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eLookup_27__01(s__02(c_27type_2estackLang_2estore__name_27__00,V_27v4_27)))))) )
=> ! [V_27v_27,V_27v1_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V_27P_7c39_7c_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27v_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27v1_27)))) ) ).
fof('thm.wordLang.every_var_exp_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27P_27,V_27a_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V__0),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27a_27))) = s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27a_27)))
=> ( ! [V_27num_27,V_27P_27] : s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eVar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27num_27))))) = 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_27num_27)))
& ! [V_27exp_27,V_27P_27] : s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eLoad_27__01(s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27))))) = s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27)))
& ! [V_27wop_27,V_27ls_27,V_27P_27] : s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eOp_27__02(s__02(c_27type_2easm_2ebinop_27__00,V_27wop_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordLang_2eexp_27__01(V_27A_27)),V_27ls_27))))) = s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),cbool__00)),V__0),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordLang_2eexp_27__01(V_27A_27)),V_27ls_27)))
& ! [V_27sh_27,V_27nexp_27,V_27exp_27,V_27P_27] : s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eShift_27__03(s__02(c_27type_2east_2eshift_27__00,V_27sh_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27),s__02(c_27type_2ewordLang_2enum__exp_27__01(V_27A_27),V_27nexp_27))))) = s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27)))
& ! [V_27v2_27,V_27P_27] : s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eConst_27__01(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v2_27))))) = s__02(cbool__00,cT__00)
& ! [V_27v4_27,V_27P_27] : s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),c_27const_2ewordLang_2eLookup_27__01(s__02(c_27type_2estackLang_2estore__name_27__00,V_27v4_27))))) = s__02(cbool__00,cT__00) ) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27P_27,V_27exp_27,V_27Q_27] :
( ( ! [V_27x_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_27x_27))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27Q_27),s__02(c_27type_2enum_2enum_27__00,V_27x_27)))) )
& p__01(s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27)))) )
=> p__01(s__02(cbool__00,c_27const_2ewordLang_2eevery__var__exp_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27Q_27),s__02(c_27type_2ewordLang_2eexp_27__01(V_27A_27),V_27exp_27)))) ) ).
%------------------------------------------------------------------------------