%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL835-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.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 03:01:03 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.57s
% Output : Proof 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 187 ( 88 ~; 84 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-5 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(v_T_H_____type,type,
v_T_H____: $i ).
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(v_as_____type,type,
v_as____: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(v_r_____type,type,
v_r____: $i ).
tff(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $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(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i ).
tff(1,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
<=> ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)))
<=> hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(6,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
<=> 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).
tff(9,plain,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
refl(( ( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
<=> ( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
<=> ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
<=> ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
trans(monotonicity(rewrite(( ( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
<=> ( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ) )),
( ( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) )),
rewrite(( ( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ) )),
( ( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
tff(16,plain,
! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_t_H: $i,V_T: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) )
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL835-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.33 % Computer : n028.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 5 21:18:17 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.32/0.57 % SZS status Unsatisfiable
% 0.32/0.57 % SZS output start Proof
% See solution above
% 0.32/0.62 % E exiting
%------------------------------------------------------------------------------