%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL786-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:51 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 45 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 220 ( 103 ~; 99 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-5 aty)
% Number of variables : 137 ( 123 !; 0 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Type_Otypings_type,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(c_Type_Osko__Type__Xlist__app__typeD__1__1_type,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(v_as_____type,type,
v_as____: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_n_____type,type,
v_n____: $i ).
tff(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
tff(c_Type_Oshift_type,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
tff(v_T_____type,type,
v_T____: $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(v_e_____type,type,
v_e____: $i ).
tff(v_T_H_____type,type,
v_T_H____: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_List_Ofoldl_type,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
tff(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i ).
tff(c_List_Ofoldr_type,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Type_Otype_OFun_type,type,
c_Type_Otype_OFun: $i ).
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(1,plain,
( hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____))
<=> hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(3,plain,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) )
<=> ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) )
<=> ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
rewrite(( ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
<=> ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
tff(10,plain,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) )
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____))
| c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) )
<=> ( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) )
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____))
| c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) )
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____))
| c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T))
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) )
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____))
| c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
refl(( ( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
<=> ( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
<=> ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
<=> ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
tff(22,plain,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
| hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) )
<=> ( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
| hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
| hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) )
| hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(unit_resolution,[status(thm)],[27,24,3]) ).
tff(29,plain,
( ~ v_thesis____
<=> ~ v_thesis____ ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(31,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [V_Ts: $i] :
refl(( ( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) )
<=> ( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) )
<=> ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) )
<=> ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [V_Ts: $i] :
rewrite(( ( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts)
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype))) )
<=> ( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts)
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype))) )
<=> ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts)
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
tff(38,plain,
! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) )
| v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) )
<=> ( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) )
| v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) )
| v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,V_Ts) )
| v_thesis____
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,41,31,28,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL786-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.01 % Command : run_E %s %d THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 4 23:29:29 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.09/0.42 % SZS status Unsatisfiable
% 0.09/0.42 % SZS output start Proof
% See solution above
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------