%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV921-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:36:20 AM UTC 2025
% Result : Unsatisfiable 0.52s 0.74s
% Output : Proof 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 171 ( 22 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 235 ( 110 ~; 106 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 9 ( 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 : 8 ( 6 usr; 1 prp; 0-5 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-5 aty)
% Number of variables : 191 ( 174 !; 0 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Objects_Ohext_type,type,
c_Objects_Ohext: ( $i * $i ) > $o ).
tff(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_Value_Oval_type,type,
tc_Value_Oval: $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_v_______type,type,
v_v______: $i ).
tff(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
tff(v_D_______type,type,
v_D______: $i ).
tff(v_F_______type,type,
v_F______: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i ) > $i ).
tff(v_fs_______type,type,
v_fs______: $i ).
tff(v_C_______type,type,
v_C______: $i ).
tff(v_a_______type,type,
v_a______: $i ).
tff(v_ha_______type,type,
v_ha______: $i ).
tff(c_Conform_Olconf_type,type,
c_Conform_Olconf: ( $i * $i * $i * $i * $i ) > $o ).
tff(tc_Expr_Oexp_type,type,
tc_Expr_Oexp: $i > $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(v_la_______type,type,
v_la______: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(1,plain,
( ( hAPP(v_ha______,v_a______) = hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)) )
<=> ( hAPP(v_ha______,v_a______) = hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hAPP(v_ha______,v_a______) = hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RedFAss_Ohyps_0) ).
tff(3,plain,
hAPP(v_ha______,v_a______) = hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
refl(( ( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
<=> ( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
<=> ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
<=> ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__upd__obj_0) ).
tff(8,plain,
! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
| ( hAPP(v_ha______,v_a______) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)) )
| c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
<=> ( ~ ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
| ( hAPP(v_ha______,v_a______) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)) )
| c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
| ( hAPP(v_ha______,v_a______) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)) )
| c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_fs_H: $i,V_a: $i,V_h: $i,V_C: $i,V_fs: $i] :
( ( hAPP(V_h,V_a) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs)) )
| c_Objects_Ohext(V_h,c_Fun_Ofun__upd(V_h,V_a,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),V_C),V_fs_H)),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) )
| ( hAPP(v_ha______,v_a______) != hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),v_fs______)) )
| c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
<=> ~ c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(17,plain,
~ c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
<=> c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RedFAss_I3_J_0) ).
tff(20,plain,
c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
refl(( ( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
<=> ( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
<=> ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
<=> ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
trans(monotonicity(rewrite(( ( c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
| ~ c_Objects_Ohext(V_h,V_h_H) )
<=> ( ~ c_Objects_Ohext(V_h,V_h_H)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ) )),
( ( c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
| ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) )
<=> ( ~ c_Objects_Ohext(V_h,V_h_H)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) ) )),
rewrite(( ( ~ c_Objects_Ohext(V_h,V_h_H)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) )
<=> ( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ) )),
( ( c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
| ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) )
<=> ( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
| ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) )
<=> ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
| ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lconf__hext_0) ).
tff(27,plain,
! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) )
<=> ( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) )
<=> ( c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) )
<=> ( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) )
<=> ( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_E: $i,V_h_H: $i,V_l: $i,T_a: $i,V_h: $i,V_P: $i] :
( ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
| c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a) )
| c_Conform_Olconf(v_P,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_Objects_Ohext(v_ha______,c_Fun_Ofun__upd(v_ha______,v_a______,hAPP(c_Option_Ooption_OSome(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))),v_C______),c_Fun_Ofun__upd(v_fs______,hAPP(hAPP(c_Pair(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),v_F______),v_D______),hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v______),tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval)))),tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))))
| ~ c_Conform_Olconf(v_P,v_ha______,v_la______,v_E____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,30,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV921-1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 11:04:12 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.52/0.74 % SZS status Unsatisfiable
% 0.52/0.74 % SZS output start Proof
% See solution above
% 0.65/0.83 % E exiting
%------------------------------------------------------------------------------