%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL796-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n016.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 03:00:53 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.58s
% Output : Proof 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 2 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $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_H_H_____type,type,
v_T_H_H____: $i ).
tff(v_e_____type,type,
v_e____: $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(1,plain,
^ [V_x: $i,V_T: $i,T_a: $i,V_e: $i] :
refl(( ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
<=> ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
<=> ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
<=> ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
tff(5,plain,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
| ( hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat)) = v_T_H_H____ ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat)) = v_T_H_H____,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat)))
<=> c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____)
<=> c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____)
<=> ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____)
<=> ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(15,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
^ [V_x: $i,V_env: $i] :
refl(( c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x))
<=> c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x))
<=> ! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x))
<=> ! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
tff(21,plain,
! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [V_x: $i,V_env: $i] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x))
| c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL796-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n016.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 : Sat Sep 5 08:29:16 UTC 2026
% 0.07/0.34 % CPUTime :
% 1.27/1.58 % SZS status Unsatisfiable
% 1.27/1.58 % SZS output start Proof
% See solution above
% 1.36/1.67 % E exiting
%------------------------------------------------------------------------------