%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL808-1 : 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 03:00:57 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.52s
% Output : Proof 0.28s
% 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 : 2 ( 1 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 : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
tff(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(v_u_____type,type,
v_u____: $i ).
tff(v_b_____type,type,
v_b____: $i ).
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(v_T_____type,type,
v_T____: $i ).
tff(v_e_____type,type,
v_e____: $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_Ua_____type,type,
v_Ua____: $i ).
tff(1,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
<=> ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).
tff(6,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
refl(( ( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
<=> ( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
<=> ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
<=> ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
trans(monotonicity(rewrite(( ( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| ~ c_InductTermi_OIT(V_ua) )
<=> ( ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ) )),
( ( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) )
<=> ( ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
| ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) ) )),
rewrite(( ( ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
| ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) )
<=> ( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ) )),
( ( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) )
<=> ( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) )
<=> ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(13,plain,
! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(19,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( c_InductTermi_OIT(v_u____)
<=> c_InductTermi_OIT(v_u____) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
c_InductTermi_OIT(v_u____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
tff(22,plain,
c_InductTermi_OIT(v_u____),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) )
<=> ( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) )
<=> ( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) )
<=> ( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) )
<=> ( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V_ua: $i,V_T_H: $i,V_ia: $i,V_ea: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H)
| ~ c_InductTermi_OIT(V_ua)
| ~ c_Type_Otyping(V_ea,V_ua,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia)) )
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL808-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E %s %d THM
% 0.16/0.41 % Computer : n003.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 5 05:28:22 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.28/0.52 % SZS status Unsatisfiable
% 0.28/0.52 % SZS output start Proof
% See solution above
% 0.28/0.54 % E exiting
%------------------------------------------------------------------------------