TPTP Problem File: SWW916+1.p
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%------------------------------------------------------------------------------
% File : SWW916+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : clos_knownProof__48__ksrel_ssgc_free__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : clos_knownProof__48__ksrel_ssgc_free__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 55 ( 7 unt; 0 def)
% Number of atoms : 271 ( 47 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 262 ( 46 ~; 43 |; 67 &)
% ( 57 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 52 ( 52 usr; 12 con; 0-3 aty)
% Number of variables : 176 ( 163 !; 13 ?)
% SPC : FOF_THM_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.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.FALSITY',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,cF__00))
=> 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.OR_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,cT__00)) )
& ( ( 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,V_27t_27)) )
& ( ( 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,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.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_FORALL_OR_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_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)))) )
<=> ( 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)))) ) ) ).
fof('thm.bool.LEFT_OR_OVER_AND',axiom,
! [V_27A_270,V_27B_270,V_27C_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,V_27C_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,V_27A_270))
| p__01(s__02(cbool__00,V_27C_270)) ) ) ) ).
fof('thm.bool.RIGHT_OR_OVER_AND',axiom,
! [V_27A_270,V_27B_270,V_27C_270] :
( ( ( p__01(s__02(cbool__00,V_27B_270))
& p__01(s__02(cbool__00,V_27C_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,V_27A_270)) )
& ( p__01(s__02(cbool__00,V_27C_270))
| p__01(s__02(cbool__00,V_27A_270)) ) ) ) ).
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.bool.UNWIND_THM2',axiom,
! [V_27A_27,V_27P_27,V_27a_27] :
( ? [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_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,V_27a_27)))) ) ).
fof('thm.bool.PULL_EXISTS',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)) ) )
& ( ( ? [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)) ) )
& ( ( 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)))) )
<=> ? [V_27x_27] :
( p__01(s__02(cbool__00,V_27Q_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)))) ) ) ) ).
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.option.SOME_11',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27)))
<=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) ).
fof('thm.option.NOT_NONE_SOME',axiom,
! [V_27A_27,V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00) != s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ).
fof('thm.option.OPTREL_def',axiom,
! [V_27A_27,V_27B_27,V_27R_27,V_27x_27,V_27y_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cfun__02(c_27type_2eoption_2eoption_27__01(V_27B_27),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27x_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),V_27y_27))))
<=> ( ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27x_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
& s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),V_27y_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eNONE_27__00) )
| ? [V_27x0_27,V_27y0_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27x_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x0_27)))
& s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),V_27y_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27B_27,V_27y0_27)))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27x0_27))),s__02(V_27B_27,V_27y0_27)))) ) ) ) ).
fof('thm.list.LIST_REL_EL_EQN',axiom,
! [V_27A_27,V_27B_27,V_27R_27,V_27l1_27,V_27l2_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_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_27l1_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_27)))
& ! [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_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_27l1_27))))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(V_27A_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27))))),s__02(V_27B_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_27)))))) ) ) ) ).
fof('thm.list.MEM_EL',axiom,
! [V_27A_27,V_27l_27,V_27x_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_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))))))
<=> ? [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_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))))))
& s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) ) ) ).
fof('thm.finite_map.FLOOKUP_EMPTY',axiom,
! [V_27B_27,V_27A_27,V_27k_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2efinite__map_2eFLOOKUP_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(V_27B_27,V_27A_27),c_27const_2efinite__map_2eFEMPTY_27__00),s__02(V_27B_27,V_27k_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00) ).
fof('thm.finite_map.fmap_rel_OPTREL_FLOOKUP',axiom,
! [V_27A_27,V_27B_27,V_27C_27,V_27f2_27,V_27f1_27,V_27R_27] :
( p__01(s__02(cbool__00,c_27const_2efinite__map_2efmap__rel_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(c_27type_2efinite__map_2efmap_27__02(V_27C_27,V_27A_27),V_27f1_27),s__02(c_27type_2efinite__map_2efmap_27__02(V_27C_27,V_27B_27),V_27f2_27))))
<=> ! [V_27k_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cfun__02(c_27type_2eoption_2eoption_27__01(V_27B_27),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2efinite__map_2eFLOOKUP_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(V_27C_27,V_27A_27),V_27f1_27),s__02(V_27C_27,V_27k_27))))),s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2efinite__map_2eFLOOKUP_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(V_27C_27,V_27B_27),V_27f2_27),s__02(V_27C_27,V_27k_27)))))) ) ).
fof('thm.closSem.ref_nchotomy',axiom,
! [V_27A_27,V_27rr_27] :
( ? [V_27l_27] : s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),V_27rr_27) = s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))
| ? [V_27b_27,V_27l_27] : s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),V_27rr_27) = s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27b_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27l_27))) ) ).
fof('thm.closProps.ref_rel_def',axiom,
! [V_27A_27,V_27B_27,V_27ws_27,V_27vs_27,V_27v8_27,V_27v7_27,V_27v6_27,V_27v18_27,V_27v14_27,V_27v13_27,V_27v0_27,V_27g_27,V_27f_27,V_27bs_27,V_27as_27,V_27R_27] :
( s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00)),c_27const_2eclosProps_2eref__rel_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))),s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27vs_27))))),s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27ws_27))))) = s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27vs_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27ws_27)))
& ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00)),c_27const_2eclosProps_2eref__rel_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))),s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27f_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27as_27))))),s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27g_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27))))))
<=> ( s__02(cbool__00,V_27f_27) = s__02(cbool__00,V_27g_27)
& s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27as_27) = s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27) ) )
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00)),c_27const_2eclosProps_2eref__rel_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27v0_27))),s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27v6_27))))),s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27v13_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27v14_27))))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00)),c_27const_2eclosProps_2eref__rel_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27v0_27))),s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27v7_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27v8_27))))),s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27v18_27))))) = s__02(cbool__00,cF__00) ) ).
fof('thm.closProps.ref_rel_simp',axiom,
! [V_27A_27,V_27B_27,V_27y_27,V_27vs_27,V_27f_27,V_27bs_27,V_27R_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00)),c_27const_2eclosProps_2eref__rel_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))),s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27vs_27))))),s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),V_27y_27))))
<=> ? [V_27ws_27] :
( s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),V_27y_27) = s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27ws_27)))
& p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27vs_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27ws_27)))) ) )
& ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),cfun__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),cbool__00)),c_27const_2eclosProps_2eref__rel_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))),s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27f_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27))))),s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),V_27y_27))))
<=> s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),V_27y_27) = s__02(c_27type_2eclosSem_2eref_27__01(V_27B_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27f_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27))) ) ) ).
fof('thm.closProps.ssgc_free_def',axiom,
! [V_27A_27,V_27s_27] :
( p__01(s__02(cbool__00,c_27const_2eclosProps_2essgc__free_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s_27))))
<=> ( ! [V_27n_27,V_27m_27,V_27e_27] :
( s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2efinite__map_2eFLOOKUP_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2eclosSem_2estate__code_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27)))))
=> s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2eclosProps_2eset__globals_27__01(s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2ebag_2eEMPTY__BAG_27__00) )
& ! [V_27n_27,V_27vl_27] :
( s__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2efinite__map_2eFLOOKUP_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__refs_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vl_27)))))
=> p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclosProps_2evsgc__free_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vl_27)))) )
& ! [V_27v_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2eclosSem_2ev_27__00,V_27v_27))),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00),cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__globals_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s_27))))))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclosProps_2evsgc__free_27__00),s__02(c_27type_2eclosSem_2ev_27__00,V_27v_27)))) ) ) ) ).
fof('thm.clos_knownProof.kvrel_vsgc_free',axiom,
! [V_27g_27,V_27v1_27,V_27v2_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),c_27const_2eclos__knownProof_2eval__rel_27__01(s__02(c_27type_2esptree_2espt_27__01(c_27type_2eclos__known_2eval__approx_27__00),V_27g_27))),s__02(c_27type_2eclosSem_2ev_27__00,V_27v1_27))),s__02(c_27type_2eclosSem_2ev_27__00,V_27v2_27))))
=> s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclosProps_2evsgc__free_27__00),s__02(c_27type_2eclosSem_2ev_27__00,V_27v1_27))) = s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclosProps_2evsgc__free_27__00),s__02(c_27type_2eclosSem_2ev_27__00,V_27v2_27))) ) ).
fof('thm.clos_knownProof.kvrel_EVERY_vsgc_free',axiom,
! [V_27g_27,V_27vs1_27,V_27vs2_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),c_27const_2eclos__knownProof_2eval__rel_27__01(s__02(c_27type_2esptree_2espt_27__01(c_27type_2eclos__known_2eval__approx_27__00),V_27g_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs2_27))))
=> s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclosProps_2evsgc__free_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs1_27))) = s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclosProps_2evsgc__free_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs2_27))) ) ).
fof('thm.clos_knownProof.state_rel_def',axiom,
! [V_27A_27,V_27g_27,V_27s1_27,V_27s2_27] :
( p__01(s__02(cbool__00,c_27const_2eclos__knownProof_2estate__rel_27__03(s__02(c_27type_2esptree_2espt_27__01(c_27type_2eclos__known_2eval__approx_27__00),V_27g_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))))
<=> ( s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2estate__clock_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2estate__clock_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27)))
& s__02(c_27type_2effi_2effi__state_27__01(V_27A_27),c_27const_2eclosSem_2estate__ffi_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))) = s__02(c_27type_2effi_2effi__state_27__01(V_27A_27),c_27const_2eclosSem_2estate__ffi_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_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_27s2_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_27s1_27)))
& p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),c_27const_2eclos__knownProof_2eval__rel_27__01(s__02(c_27type_2esptree_2espt_27__01(c_27type_2eclos__known_2eval__approx_27__00),V_27g_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__globals_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__globals_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))))))
& p__01(s__02(cbool__00,c_27const_2efinite__map_2efmap__rel_27__03(s__02(cfun__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),cbool__00)),c_27const_2eclosProps_2eref__rel_27__01(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),c_27const_2eclos__knownProof_2eval__rel_27__01(s__02(c_27type_2esptree_2espt_27__01(c_27type_2eclos__known_2eval__approx_27__00),V_27g_27))))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__refs_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__refs_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))))))
& s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2eclosSem_2estate__code_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27))) = s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2efinite__map_2eFEMPTY_27__00)
& s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2eclosSem_2estate__code_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))) = s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2efinite__map_2eFEMPTY_27__00) ) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27g_27,V_27s1_27,V_27s2_27] :
( p__01(s__02(cbool__00,c_27const_2eclos__knownProof_2estate__rel_27__03(s__02(c_27type_2esptree_2espt_27__01(c_27type_2eclos__known_2eval__approx_27__00),V_27g_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))))
=> s__02(cbool__00,c_27const_2eclosProps_2essgc__free_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27))) = s__02(cbool__00,c_27const_2eclosProps_2essgc__free_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))) ) ).
%------------------------------------------------------------------------------