TPTP Problem File: SWW889+1.p
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%------------------------------------------------------------------------------
% File : SWW889+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : clos_relationProps__13__exp_rel_rtc_semantics__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : clos_relationProps__13__exp_rel_rtc_semantics__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.60 v7.4.0, 0.33 v7.3.0
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 197 ( 28 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 201 ( 48 ~; 31 |; 44 &)
% ( 37 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 17 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 32 ( 32 usr; 10 con; 0-4 aty)
% Number of variables : 140 ( 140 !; 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.EXISTS_DEF',axiom,
! [V_27A_27,Vx] : s__02(cbool__00,c_24exists__01(s__02(cfun__02(V_27A_27,cbool__00),Vx))) = s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),Vx),s__02(V_27A_27,c_27const_2emin_2e_40_27__01(s__02(cfun__02(V_27A_27,cbool__00),Vx))))) ).
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.SELECT_AX',axiom,
! [V_27A_27,V_27P_27,V_27x_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,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,c_27const_2emin_2e_40_27__01(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27)))))) ) ).
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.EXCLUDED_MIDDLE',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,V_27t_27))
| ~ p__01(s__02(cbool__00,V_27t_27)) ) ).
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.NOT_CLAUSES',axiom,
( ! [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,cF__00)) )
& ( ~ p__01(s__02(cbool__00,cF__00))
<=> p__01(s__02(cbool__00,cT__00)) ) ) ).
fof('thm.bool.EQ_REFL',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,V_27x_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_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.LEFT_AND_FORALL_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ( ! [V_27x_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,V_27Q_27)) )
<=> ! [V_27x_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,V_27Q_27)) ) ) ).
fof('thm.bool.RIGHT_AND_FORALL_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ( p__01(s__02(cbool__00,V_27P_27))
& ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) )
<=> ! [V_27x_27] :
( p__01(s__02(cbool__00,V_27P_27))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) ) ) ).
fof('thm.bool.LEFT_FORALL_OR_THM',axiom,
! [V_27A_27,V_27Q_27,V_27P_27] :
( ! [V_27x_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,V_27Q_27)) )
<=> ( ! [V_27x_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,V_27Q_27)) ) ) ).
fof('thm.combin.C_DEF',axiom,
! [V_27C_27,V_27A_27,V_27B_27,Vx,Vx0,Vx1] : s__02(V_27C_27,c_27const_2ecombin_2eC_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),Vx),s__02(V_27B_27,Vx0),s__02(V_27A_27,Vx1))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27B_27,V_27C_27),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),Vx),s__02(V_27A_27,Vx1))),s__02(V_27B_27,Vx0))) ).
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,c_27const_2ecombin_2eo_27__03(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.sat.NOT_NOT',axiom,
! [V_27t_27] :
( ~ ~ p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.sat.AND_INV_IMP',axiom,
! [V_27A_270] :
( p__01(s__02(cbool__00,V_27A_270))
=> ( ~ p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) ) ) ).
fof('thm.sat.OR_DUAL2',axiom,
! [V_27B_270,V_27A_270] :
( ( ~ ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
=> p__01(s__02(cbool__00,cF__00)) )
<=> ( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> ( ~ p__01(s__02(cbool__00,V_27B_270))
=> p__01(s__02(cbool__00,cF__00)) ) ) ) ).
fof('thm.sat.OR_DUAL3',axiom,
! [V_27B_270,V_27A_270] :
( ( ~ ( ~ p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
=> p__01(s__02(cbool__00,cF__00)) )
<=> ( p__01(s__02(cbool__00,V_27A_270))
=> ( ~ p__01(s__02(cbool__00,V_27B_270))
=> p__01(s__02(cbool__00,cF__00)) ) ) ) ).
fof('thm.sat.AND_INV2',axiom,
! [V_27A_270] :
( ( ~ p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> ( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> p__01(s__02(cbool__00,cF__00)) ) ) ).
fof('thm.sat.dc_eq',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> s__02(cbool__00,V_27q_27) = s__02(cbool__00,V_27r_27) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27q_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) )
& ( p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_conj',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ( p__01(s__02(cbool__00,V_27q_27))
& p__01(s__02(cbool__00,V_27r_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) )
& ( p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_disj',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ( p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27q_27)) )
& ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_imp',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ( p__01(s__02(cbool__00,V_27q_27))
=> p__01(s__02(cbool__00,V_27r_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27)) )
& ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27r_27)) )
& ( ~ p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_neg',axiom,
! [V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ~ p__01(s__02(cbool__00,V_27q_27)) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27)) )
& ( ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.pth_ni1',axiom,
! [V_27q_27,V_27p_27] :
( ~ ( p__01(s__02(cbool__00,V_27p_27))
=> p__01(s__02(cbool__00,V_27q_27)) )
=> p__01(s__02(cbool__00,V_27p_27)) ) ).
fof('thm.sat.pth_ni2',axiom,
! [V_27q_27,V_27p_27] :
( ~ ( p__01(s__02(cbool__00,V_27p_27))
=> p__01(s__02(cbool__00,V_27q_27)) )
=> ~ p__01(s__02(cbool__00,V_27q_27)) ) ).
fof('thm.sat.pth_no1',axiom,
! [V_27q_27,V_27p_27] :
( ~ ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27)) )
=> ~ p__01(s__02(cbool__00,V_27p_27)) ) ).
fof('thm.sat.pth_no2',axiom,
! [V_27q_27,V_27p_27] :
( ~ ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27)) )
=> ~ p__01(s__02(cbool__00,V_27q_27)) ) ).
fof('thm.sat.pth_nn',axiom,
! [V_27p_27] :
( ~ ~ p__01(s__02(cbool__00,V_27p_27))
=> p__01(s__02(cbool__00,V_27p_27)) ) ).
fof('thm.relation.RTC_INDUCT',axiom,
! [V_27A_27,V_27R_27,V_27P_27] :
( ( ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27P_27),s__02(V_27A_27,V_27x_27))),s__02(V_27A_27,V_27x_27))))
& ! [V_27x_27,V_27y_27,V_27z_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27x_27))),s__02(V_27A_27,V_27y_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27P_27),s__02(V_27A_27,V_27y_27))),s__02(V_27A_27,V_27z_27)))) )
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27P_27),s__02(V_27A_27,V_27x_27))),s__02(V_27A_27,V_27z_27)))) ) )
=> ! [V_27x_27,V_27y_27] :
( p__01(s__02(cbool__00,c_27const_2erelation_2eRTC_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27x_27),s__02(V_27A_27,V_27y_27))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27P_27),s__02(V_27A_27,V_27x_27))),s__02(V_27A_27,V_27y_27)))) ) ) ).
fof('thm.clos_relation.exp_rel_refl',axiom,
! [V_27FFI_27,V__3] :
( ! [V_27n_27,V_27n_7c39_7c_27,V_27w_27,V_27e_27,V_27e_7c39_7c_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))))),V__3),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_7c39_7c_27))),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27))),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_7c39_7c_27))))
<=> ( s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27n_7c39_7c_27)
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00)),c_27const_2eclos__relation_2eexp__rel_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27const_2ebool_2ethe__value_27__00),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eNIL_27__00))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eNIL_27__00)))))) ) )
=> ! [V__2] :
( ! [V_27n_27,V_27w_27,V_27e_27,V_27n_7c39_7c_27] : s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_7c39_7c_27))) = s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))))),V__3),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_7c39_7c_27))),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27)))
=> ! [V__1] :
( ! [V_27n_27,V_27w_27,V_27e_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cbool__00))))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27)))))
=> ! [V__0] :
( ! [V_27w_27,V_27n_27] : s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27w_27)))
=> ! [V_27w_27] :
( ! [V_27e_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00)),c_27const_2eclos__relation_2eexp__rel_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27const_2ebool_2ethe__value_27__00),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eNIL_27__00))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eNIL_27__00))))))
& ! [V_27es_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00)),c_27const_2eclos__relation_2eexp__rel_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27const_2ebool_2ethe__value_27__00),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27es_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27es_27))))
& ! [V_27ne_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2epair_2eFST_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),V_27ne_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2epair_2eFST_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),V_27ne_27)))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00)),c_27const_2eclos__relation_2eexp__rel_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27const_2ebool_2ethe__value_27__00),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosLang_2eexp_27__00,c_27const_2epair_2eSND_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),V_27ne_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eNIL_27__00))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosLang_2eexp_27__00,c_27const_2epair_2eSND_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),V_27ne_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),c_27const_2elist_2eNIL_27__00)))))) )
& ! [V_27funs_27] : p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),cbool__00)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27w_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27funs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27funs_27)))) ) ) ) ) ) ).
fof('thm.clos_relation.state_rel_refl',axiom,
! [V_27A_27,V_27i_27,V_27s_27] : p__01(s__02(cbool__00,c_27const_2eclos__relation_2estate__rel_27__04(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2estate__max__app_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s_27))),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s_27)))) ).
fof('thm.clos_relationProps.exp_rel_semantics',axiom,
! [V_27FFI_27,V_27w_27,V_27e1_27,V_27e2_27,V_27s1_27,V_27s2_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00)),c_27const_2eclos__relation_2eexp__rel_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27const_2ebool_2ethe__value_27__00),s__02(c_27type_2enum_2enum_27__00,V_27w_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e2_27))))
& ! [V_27i_27] : p__01(s__02(cbool__00,c_27const_2eclos__relation_2estate__rel_27__04(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,V_27w_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s2_27))))
& s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2eclosSem_2esemantics_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e1_27))) != s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2effi_2eFail_27__00) )
=> s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2eclosSem_2esemantics_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e1_27))) = s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2eclosSem_2esemantics_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e2_27))) ) ).
fof(conjecture,conjecture,
! [V_27FFI_27,V_27e1_27,V_27e2_27,V_27s1_27,V_27s2_27] :
( ( p__01(s__02(cbool__00,c_27const_2erelation_2eRTC_27__03(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),cbool__00)),c_27const_2eclos__relation_2eexp__rel_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27const_2ebool_2ethe__value_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2estate__max__app_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e2_27))))
& ! [V_27i_27] : p__01(s__02(cbool__00,c_27const_2eclos__relation_2estate__rel_27__04(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2estate__max__app_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27))),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s2_27))))
& s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2eclosSem_2esemantics_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e1_27))) != s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2effi_2eFail_27__00) )
=> s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2eclosSem_2esemantics_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e1_27))) = s__02(c_27type_2effi_2ebehaviour_27__00,c_27const_2eclosSem_2esemantics_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosLang_2eexp_27__00),V_27e2_27))) ) ).
%------------------------------------------------------------------------------