%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW318+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:36:49 AM UTC 2025
% Result : Theorem 15.39s 15.59s
% Output : Proof 15.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% 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 : 130 ( 55 ~; 50 |; 0 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 8 ( 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 : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 98 ( 87 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_G_type,type,
v_G: $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(t_a_type,type,
t_a: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_HOL_Obool_type,type,
tc_HOL_Obool: $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,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(3,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool)))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(6,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool)))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
refl(( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) )
<=> ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) )
<=> ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) )
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
| c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
| c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) )),
rewrite(( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
| c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) )
<=> ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_thin) ).
tff(13,plain,
! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G))) )
<=> ( ~ ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_Ga_2: $i,V_ts_2: $i,V_G_H_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G))),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [V_a_2: $i,V_B_2: $i,T_b: $i] :
refl(( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))
<=> ! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))
<=> ! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).
tff(25,plain,
! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [V_a_2: $i,V_B_2: $i,T_b: $i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,27,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW318+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 11:26:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 15.39/15.59 % SZS status Theorem
% 15.39/15.59 % SZS output start Proof
% See solution above
% 15.88/16.04 % E exiting
%------------------------------------------------------------------------------