%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW317+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 14.58s 14.79s
% Output : Proof 15.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: ( $i * $i * $i * $i ) > $i ).
tff(v_P_type,type,
v_P: $i ).
tff(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
tff(v_Ga_type,type,
v_Ga: $i ).
tff(1,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),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,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(3,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),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,
^ [V_P_2: $i,V_G_2: $i,T_b: $i] :
refl(( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
<=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
<=> ! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
<=> ! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OSkip) ).
tff(8,plain,
! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [V_P_2: $i,V_G_2: $i,T_b: $i] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_2,c_Com_Ocom_OSKIP,V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW317+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 11:26:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 14.58/14.79 % SZS status Theorem
% 14.58/14.79 % SZS output start Proof
% See solution above
% 15.04/15.23 % E exiting
%------------------------------------------------------------------------------