%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV840-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:36:12 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.51s
% Output : Proof 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 140 ( 65 ~; 61 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 98 ( 87 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
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(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_Q_type,type,
v_Q: $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(c_Option_Othe_type,type,
c_Option_Othe: $i > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(1,plain,
^ [V_a: $i,T_a: $i,V_B: $i] :
refl(( c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool))
<=> c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool))
<=> ! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool))
<=> ! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
tff(5,plain,
! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_a: $i,T_a: $i,V_B: $i] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool))
| c_lessequals(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_lessequals(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(12,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(15,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
refl(( ( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) )
<=> ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) )
<=> ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
^ [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
trans(monotonicity(rewrite(( ( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
<=> ( ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) )
<=> ( ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) ) )),
rewrite(( ( ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) )
<=> ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_thin_0) ).
tff(22,plain,
! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_lessequals(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) )
<=> ( ~ ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_lessequals(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_lessequals(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V_G_H: $i,V_ts: $i,T_a: $i,V_G: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_lessequals(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,25,15,12,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV840-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 10:55:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51 % SZS output start Proof
% See solution above
% 0.37/0.54 % E exiting
%------------------------------------------------------------------------------