%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL806-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n003.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 03:00:56 PM UTC 2026
% Result : Unsatisfiable 0.30s 0.60s
% Output : Proof 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 266 ( 127 ~; 123 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 8 ( 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_xc_type,type,
v_xc: $i ).
tff(v_xb_type,type,
v_xb: $i ).
tff(v_b_____type,type,
v_b____: $i ).
tff(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(v_T_____type,type,
v_T____: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Type_Otyping_type,type,
c_Type_Otyping: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(c_Type_Oshift_type,type,
c_Type_Oshift: $i > $i ).
tff(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
tff(1,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
<=> ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(3,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(6,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_xb))
<=> hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(9,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(12,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
<=> ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
<=> ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
<=> ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ) )),
( ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)) ) )),
rewrite(( ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)) )
<=> ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ) )),
( ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)) )
<=> ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)) )
<=> ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).
tff(19,plain,
! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) )
<=> ( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))) )
<=> ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))) )
<=> ( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))) )
<=> ( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V_T_H: $i,V_ia: $i,V_u: $i,V_ea: $i] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia))) )
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,12,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL806-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.38 % Computer : n003.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Fri Sep 4 12:47:08 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.30/0.60 % SZS status Unsatisfiable
% 0.30/0.60 % SZS output start Proof
% See solution above
% 0.37/0.65 % E exiting
%------------------------------------------------------------------------------