%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV938-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:36:22 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.56s
% Output : Proof 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 46 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 253 ( 118 ~; 112 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 11 ( 11 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; 0-5 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-5 aty)
% Number of variables : 258 ( 231 !; 0 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Map_Omap__le_type,type,
c_Map_Omap__le: ( $i * $i * $i * $i ) > $o ).
tff(tc_Type_Oty_type,type,
tc_Type_Oty: $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(c_COMBK_type,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
tff(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
tff(c_Map_Omap__upds_type,type,
c_Map_Omap__upds: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(v_Ts_____type,type,
v_Ts____: $i ).
tff(c_Type_Oty_OClass_type,type,
c_Type_Oty_OClass: $i > $i ).
tff(v_D_____type,type,
v_D____: $i ).
tff(v_pns_____type,type,
v_pns____: $i ).
tff(c_Type_Othis_type,type,
c_Type_Othis: $i ).
tff(c_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o ).
tff(v_T_H_H_____type,type,
v_T_H_H____: $i ).
tff(v_body_____type,type,
v_body____: $i ).
tff(v_ha_____type,type,
v_ha____: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(1,plain,
( ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
<=> ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
<=> c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(6,plain,
c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
<=> ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
<=> ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
trans(monotonicity(rewrite(( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty) )
<=> ( ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ) )),
( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) )
<=> ( ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) ) )),
rewrite(( ( ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ) )),
( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) )
<=> ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__env__mono_0) ).
tff(13,plain,
! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) )
<=> ( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____) )
<=> ( c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____) )
<=> ( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____) )
<=> ( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_E: $i,V_E_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Map_Omap__le(V_E,V_E_H,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E_H,V_e,V_T) )
| c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),v_body____,v_T_H_H____)
| ~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
refl(( ( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) )
<=> ( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) )
<=> ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) )
<=> ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
rewrite(( ( c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b)
| ~ c_Map_Omap__le(V_f,V_g,T_a,T_b) )
<=> ( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b)
| ~ c_Map_Omap__le(V_f,V_g,T_a,T_b) )
<=> ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b)
| ~ c_Map_Omap__le(V_f,V_g,T_a,T_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__upds_0) ).
tff(30,plain,
! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) )
| ~ c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),v_E____,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) )
<=> ( ~ ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) )
| ~ c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),v_E____,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) )
| ~ c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),v_E____,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [T_b: $i,V_bs: $i,V_f: $i,V_as: $i,T_a: $i,V_g: $i] :
( ~ c_Map_Omap__le(V_f,V_g,T_a,T_b)
| c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b) )
| ~ c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),v_E____,tc_List_Olist(tc_String_Ochar),tc_Type_Oty)
| c_Map_Omap__le(c_Map_Omap__upds(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),c_Map_Omap__upds(v_E____,c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty),tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),v_E____,tc_List_Olist(tc_String_Ochar),tc_Type_Oty),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,plain,
^ [T_b: $i,T_a: $i,V_g: $i] :
refl(( c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b)
<=> c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b)
<=> ! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b)
<=> ! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__empty_0) ).
tff(42,plain,
! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [T_b: $i,T_a: $i,V_g: $i] : c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b)
| c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(tc_Type_Oty),tc_Option_Ooption(tc_Type_Oty),tc_List_Olist(tc_String_Ochar)),v_E____,tc_List_Olist(tc_String_Ochar),tc_Type_Oty) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,44,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SWV938-1 : TPTP v9.0.0. Released v4.1.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 11:05:11 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.56 % SZS status Unsatisfiable
% 0.22/0.56 % SZS output start Proof
% See solution above
% 0.42/0.60 % E exiting
%------------------------------------------------------------------------------