%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL821-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n010.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 03:00:59 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 114 ( 53 ~; 49 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 3 ( 3 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 : 13 ( 13 usr; 9 con; 0-5 aty)
% Number of variables : 81 ( 72 !; 0 ?; 81 :)
% 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_rs_____type,type,
v_rs____: $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_n_____type,type,
v_n____: $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(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $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_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
tff(v_thesis_____type,type,
v_thesis____: $o ).
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,c_Lambda_OdB_OVar(v_n____),v_rs____,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,c_Lambda_OdB_OVar(v_n____),v_rs____,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,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nT_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,c_Lambda_OdB_OVar(v_n____),v_rs____,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(( ( ~ 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)) )
<=> ( ~ 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] :
( ~ 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] :
( ~ 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] :
( ~ 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] :
( ~ 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))
| ~ 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_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))
| ~ 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] :
( ~ 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))
| ~ 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] :
( ~ 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] :
( ~ 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] :
( ~ 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] :
( ~ 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] :
( ~ 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)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,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_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) )
<=> ( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ 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)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,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_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ 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)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,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_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_T: $i,V_ts: $i,V_t: $i,V_e: $i] :
( ~ 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)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,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_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) ),
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_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ~ v_thesis____
<=> ~ v_thesis____ ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(20,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_Ts: $i] :
refl(( ( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) )
<=> ( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) )
<=> ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) )
<=> ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
tff(25,plain,
! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) )
| v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) )
<=> ( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) )
| v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) )
| v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_Ts: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,V_Ts) )
| v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27,20,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL821-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n010.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 20:48:55 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.43 % SZS status Unsatisfiable
% 0.13/0.43 % SZS output start Proof
% See solution above
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------