%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL839-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n013.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 03:01:04 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : Proof 0.22s
% 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 : 4 ( 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 : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 81 ( 72 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(c_Type_Osko__Type__Xtyping__elims__2__1_type,type,
c_Type_Osko__Type__Xtyping__elims__2__1: ( $i * $i * $i * $i ) > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(v_r_____type,type,
v_r____: $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_Ua_____type,type,
v_Ua____: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $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),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____)
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(3,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
refl(( ( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) )
<=> ( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) )
<=> ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) )
<=> ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
rewrite(( ( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))
| ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) )
<=> ( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))
| ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) )
<=> ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))
| ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
tff(10,plain,
! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) )
<=> ( ~ ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_T: $i,V_u: $i,V_t: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____)
| c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)),
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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(20,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_T_H_H: $i] :
refl(( ( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) )
<=> ( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) )
<=> ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) )
<=> ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
tff(25,plain,
! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) )
| v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) )
<=> ( ~ ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) )
| v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) )
| v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_T_H_H: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H) )
| v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27,20,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL839-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.33 % Computer : n013.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 : Fri Sep 4 20:49:38 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.45 % SZS status Unsatisfiable
% 0.13/0.45 % SZS output start Proof
% See solution above
% 0.22/0.46 % E exiting
%------------------------------------------------------------------------------