TSTP Solution File: SWV834-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV834-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Thu Sep 29 15:24:40 EDT 2022
% Result : Unsatisfiable 0.76s 0.80s
% Output : Proof 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 51
% Syntax : Number of formulae : 92 ( 39 unt; 26 typ; 0 def)
% Number of atoms : 119 ( 52 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 78 ( 30 ~; 28 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 15 >; 23 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-4 aty)
% Number of variables : 150 ( 137 !; 0 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_sko__Hoare__Mirabelle__Xescape__2_type,type,
v_sko__Hoare__Mirabelle__Xescape__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(v_sko__Hoare__Mirabelle__Xescape__1_type,type,
v_sko__Hoare__Mirabelle__Xescape__1: ( $i * $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $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_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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4,3]) ).
tff(6,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)],[5]) ).
tff(7,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)],[6,2]) ).
tff(8,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(t_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,t_a),t_a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Collect(c_COMBK(c_False,tc_bool,t_a),t_a) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
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,t_a),t_a) = c_COMBK(c_False,tc_bool,t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
c_Collect(c_COMBK(c_False,tc_bool,t_a),t_a) = c_COMBK(c_False,tc_bool,t_a),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
c_COMBK(c_False,tc_bool,t_a) = c_Collect(c_COMBK(c_False,tc_bool,t_a),t_a),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
c_COMBK(c_False,tc_bool,t_a) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
inference(transitivity,[status(thm)],[20,10]) ).
tff(22,plain,
hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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(27,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)],[26,25]) ).
tff(28,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)],[27]) ).
tff(29,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)],[28,24]) ).
tff(30,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_False,tc_bool,t_a),v_x) = c_False ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = c_False,
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
c_False = hAPP(c_COMBK(c_False,tc_bool,t_a),v_x),
inference(symmetry,[status(thm)],[31]) ).
tff(33,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_False,tc_bool,tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__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_False ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
hAPP(c_COMBK(c_False,tc_bool,tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__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_False,
inference(unit_resolution,[status(thm)],[33,29]) ).
tff(35,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__Xescape__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(36,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__Xescape__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)],[35,29]) ).
tff(37,plain,
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__Xescape__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__Xescape__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(c_COMBK(c_False,tc_bool,tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__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)],[36]) ).
tff(38,plain,
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__Xescape__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__Xescape__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(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x),
inference(transitivity,[status(thm)],[37,34,32,22]) ).
tff(39,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__Xescape__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__Xescape__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(t_a,tc_bool)),v_x)) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x))
<=> 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__Xescape__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__Xescape__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)],[39]) ).
tff(41,plain,
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x))
<=> ~ 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__Xescape__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__Xescape__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)],[40]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,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(46,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)],[45,44]) ).
tff(47,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)],[46]) ).
tff(48,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)],[47,43]) ).
tff(49,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(t_a,tc_bool)),v_x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x)),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,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__Xescape__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__Xescape__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)],[50,41]) ).
tff(52,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(53,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(54,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)],[53,52]) ).
tff(55,plain,
^ [V_c: $i,V_Q: $i,V_G: $i,V_P: $i] :
refl(
( ( 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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ) )),
inference(bind,[status(th)],]) ).
tff(56,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) )
<=> ! [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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) )
<=> ! [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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).
tff(59,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__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(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)
| 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__Xescape__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__Xescape__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))) )
<=> ( ~ ! [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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__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(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)
| 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__Xescape__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__Xescape__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(rewrite,[status(thm)],]) ).
tff(63,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__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(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)
| 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__Xescape__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__Xescape__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(64,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__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__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(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)
| 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__Xescape__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__Xescape__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)],[63,62]) ).
tff(65,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__Xescape__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__Xescape__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)],[64,61,54]) ).
tff(66,plain,
$false,
inference(unit_resolution,[status(thm)],[65,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV834-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 08:37:05 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.76/0.80 % SZS status Unsatisfiable
% 0.76/0.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------