%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV834-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:11 AM UTC 2025
% Result : Unsatisfiable 0.63s 0.84s
% Output : Proof 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 60 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 42 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 77 ( 25 ~; 31 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-4 aty)
% Number of variables : 158 ( 141 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2: ( $i * $i * $i * $i ) > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_b_type,type,
v_b: $i ).
tff(c_Not_type,type,
c_Not: $i ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i ) > $i ).
tff(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_COMBC_type,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(c_and_type,type,
c_and: $i ).
tff(c_COMBS_type,type,
c_COMBS: ( $i * $i * $i ) > $i ).
tff(c_COMBK_type,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(c_False_type,type,
c_False: $i ).
tff(v_G_type,type,
v_G: $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Collect_type,type,
c_Collect: ( $i * $i ) > $i ).
tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: ( $i * $i * $i * $i ) > $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
tff(1,plain,
^ [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] :
refl(( ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P )
<=> ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P )
<=> ! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P )
<=> ! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
tff(5,plain,
! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_b: $i,V_Q: $i,T_a: $i,V_P: $i] : ( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P )
| ( hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)) = c_COMBK(c_False,tc_bool,tc_Com_Ostate) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)) = c_COMBK(c_False,tc_bool,tc_Com_Ostate),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_COMBK(c_False,tc_bool,tc_Com_Ostate) = hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [T_a: $i,V_P: $i] :
refl(( ( c_Collect(V_P,T_a) = V_P )
<=> ( c_Collect(V_P,T_a) = V_P ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P )
<=> ! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P )
<=> ! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
tff(15,plain,
! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [T_a: $i,V_P: $i] : ( c_Collect(V_P,T_a) = V_P )
| ( c_Collect(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_Com_Ostate) = c_COMBK(c_False,tc_bool,tc_Com_Ostate) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
c_Collect(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_Com_Ostate) = c_COMBK(c_False,tc_bool,tc_Com_Ostate),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [T_a: $i] :
refl(( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) )
<=> ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) )
<=> ! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) )
<=> ! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__def_0) ).
tff(24,plain,
! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [T_a: $i] : ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,T_a),T_a) )
| ( c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_Com_Ostate) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_Com_Ostate),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)) = hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),
inference(transitivity,[status(thm)],[28,19,10]) ).
tff(30,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)) = hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)))
<=> hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)))
<=> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(35,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
refl(( ( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
rewrite(( ( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c))) )
<=> ( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c))) )
<=> ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
tff(42,plain,
! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ( ~ ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(modus_ponens,[status(thm)],[49,32]) ).
tff(51,plain,
^ [V_x: $i,T_a: $i] :
refl(( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x))
<=> ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x))
<=> ! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x))
<=> ! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
tff(55,plain,
! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [V_x: $i,T_a: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV834-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.18/0.32 % WCLimit : 300
% 0.18/0.32 % DateTime : Fri Jun 20 10:56:32 EDT 2025
% 0.18/0.32 % CPUTime :
% 0.63/0.84 % SZS status Unsatisfiable
% 0.63/0.84 % SZS output start Proof
% See solution above
% 0.71/0.88 % E exiting
%------------------------------------------------------------------------------