%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV858-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:36:14 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 71 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 375 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 507 ( 223 ~; 245 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 177 ( 159 !; 0 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_Ga_type,type,
v_Ga: $i ).
tff(v_n_type,type,
v_n: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_in_type,type,
c_in: $i > $i ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_ts_H_type,type,
v_ts_H: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(v_tsa_type,type,
v_tsa: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: ( $i * $i * $i ) > $o ).
tff(1,plain,
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
<=> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
<=> c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(6,plain,
c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
refl(( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
rewrite(( ( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
tff(13,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H)),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [V_nb: $i,V_na: $i] :
refl(( ( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) )
<=> ( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) )
<=> ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) )
<=> ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [V_nb: $i,V_na: $i] :
trans(monotonicity(rewrite(( ( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ) )),
( ( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a)
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga)) ) )),
rewrite(( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a)
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga)) )
<=> ( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ) )),
( ( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga)) )
<=> ( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_nb: $i,V_na: $i] :
( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga)) )
<=> ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [V_nb: $i,V_na: $i] :
( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(30,plain,
! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
<=> ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(36,plain,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) )
<=> ( ~ ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [V_nb: $i,V_na: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nb,t_a) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga)),
inference(unit_resolution,[status(thm)],[39,36,33,23]) ).
tff(41,plain,
^ [V_nc: $i,V_na: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
<=> ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
<=> ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [V_nc: $i,V_na: $i] :
trans(monotonicity(rewrite(( ( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a) ) )),
( ( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ) )),
rewrite(( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ) )),
( ( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V_nc: $i,V_na: $i] :
( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
<=> ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [V_nc: $i,V_na: $i] :
( c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(47,plain,
! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) )
<=> ( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) )
<=> ( c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) )
<=> ( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) )
<=> ( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [V_nc: $i,V_na: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nc),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(V_na,V_nc,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a) )
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a),
inference(unit_resolution,[status(thm)],[56,36,50,23]) ).
tff(58,plain,
^ [V_xb: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
<=> ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
<=> ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
^ [V_xb: $i] :
rewrite(( ( c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [V_xb: $i] :
( c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga)) )
<=> ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [V_xb: $i] :
( c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(64,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) )
<=> ( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
$false,
inference(unit_resolution,[status(thm)],[70,67,57,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV858-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 10:58:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54 % SZS output start Proof
% See solution above
% 0.19/0.58 % E exiting
%------------------------------------------------------------------------------