%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL802-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n026.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 03:00:54 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.51s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 54 ( 26 ~; 22 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-5 aty)
% Number of variables : 39 ( 36 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_List_Olistsp_type,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
tff(v_as_____type,type,
v_as____: $i ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
tff(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i ).
tff(c_Type_Oshift_type,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $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(c_Ex_type,type,
c_Ex: $i > $i ).
tff(c_Type_Otypings_type,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(v_Ts_____type,type,
v_Ts____: $i ).
tff(1,plain,
( ~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB)
<=> ~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____)
<=> c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).
tff(6,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_ts: $i,V_e: $i,V_Ts: $i] :
refl(( ( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) )
<=> ( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) )
<=> ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) )
<=> ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists__typings_0) ).
tff(11,plain,
! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ( ~ ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) )
| c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB)
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) )
<=> ( ~ ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) )
| c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB)
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) )
| c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB)
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_ts: $i,V_e: $i,V_Ts: $i] :
( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts) )
| c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB)
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
$false,
inference(unit_resolution,[status(thm)],[16,13,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL802-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n026.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 19:24:13 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.23/0.51 % SZS status Unsatisfiable
% 0.23/0.51 % SZS output start Proof
% See solution above
% 0.23/0.54 % E exiting
%------------------------------------------------------------------------------