TPTP Problem File: SWW884+1.p
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%------------------------------------------------------------------------------
% File : SWW884+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : ml_translator__39__Eval_FUN_FORALL__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : ml_translator__39__Eval_FUN_FORALL__dep [Kum18]
% Status : Theorem
% Rating : 0.83 v8.2.0, 0.86 v8.1.0, 0.78 v7.5.0, 0.84 v7.4.0, 0.80 v7.3.0
% Syntax : Number of formulae : 33 ( 4 unt; 0 def)
% Number of atoms : 157 ( 17 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 169 ( 45 ~; 28 |; 23 &)
% ( 30 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-5 aty)
% Number of variables : 87 ( 85 !; 2 ?)
% 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.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_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.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.ml_translator.Eval_def',axiom,
! [V_27env_27,V_27exp_27,V_27P_27] :
( p__01(s__02(cbool__00,c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27env_27),s__02(c_27type_2east_2eexp_27__00,V_27exp_27),s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00),V_27P_27))))
<=> ! [V_27refs_27] :
? [V_27res_27,V_27refs_7c39_7c_27] :
( p__01(s__02(cbool__00,c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00,cF__00),s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27env_27),s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00),c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),V_27refs_27))),s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00),c_27const_2eml__translator_2eempty__state_27__00))),s__02(c_27type_2east_2eexp_27__00,V_27exp_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00),c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27type_2esemanticPrimitives_2ev_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00),c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),V_27refs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),V_27refs_7c39_7c_27))))),s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00),c_27const_2eml__translator_2eempty__state_27__00))),s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00,V_27res_27))))))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2esemanticPrimitives_2ev_27__00,V_27res_27)))) ) ) ).
fof('thm.ml_translator.evaluate_11_Rval',axiom,
! [V_27A_27,V_27s2_27,V_27s1_27,V_27s_27,V_27res2_27,V_27res1_27,V_27exp_27,V_27env_27,V_27b_27] :
( p__01(s__02(cbool__00,c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00,V_27b_27),s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27env_27),s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27),V_27s_27),s__02(c_27type_2east_2eexp_27__00,V_27exp_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27),c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27type_2esemanticPrimitives_2ev_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27),V_27s1_27),s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00,V_27res1_27))))))))
=> ( p__01(s__02(cbool__00,c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00,V_27b_27),s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27env_27),s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27),V_27s_27),s__02(c_27type_2east_2eexp_27__00,V_27exp_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27),c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27type_2esemanticPrimitives_2ev_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27),V_27s2_27),s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00,V_27res2_27))))))))
=> s__02(c_27type_2esemanticPrimitives_2ev_27__00,V_27res1_27) = s__02(c_27type_2esemanticPrimitives_2ev_27__00,V_27res2_27) ) ) ).
fof('thm.ml_translator.FUN_FORALL',axiom,
! [V_27A_27,V_27B_27,Vx,Vx0,Vx1] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00),c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),Vx),s__02(V_27B_27,Vx0))),s__02(c_27type_2esemanticPrimitives_2ev_27__00,Vx1))))
<=> ! [V_27y_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),Vx),s__02(V_27A_27,V_27y_27))),s__02(V_27B_27,Vx0))),s__02(c_27type_2esemanticPrimitives_2ev_27__00,Vx1)))) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27B_27,V__0] :
( ! [V_27p_27,V_27x_27] : s__02(cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00)))),V__0),s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),V_27p_27))),s__02(V_27A_27,V_27x_27))) = s__02(cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),V_27p_27),s__02(V_27A_27,V_27x_27)))
=> ! [V_27env_27,V_27exp_27,V_27p_27,V_27f_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27env_27),s__02(c_27type_2east_2eexp_27__00,V_27exp_27),s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),V_27p_27),s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27f_27))))))
=> p__01(s__02(cbool__00,c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27env_27),s__02(c_27type_2east_2eexp_27__00,V_27exp_27),s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00),c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00)))),V__0),s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2ev_27__00,cbool__00))),V_27p_27))),s__02(V_27B_27,V_27f_27)))))) ) ) ).
%------------------------------------------------------------------------------