%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL793-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n004.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 03:00:52 PM UTC 2026
% Result : Unsatisfiable 0.56s 0.80s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 97 ( 45 ~; 41 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
tff(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: ( $i * $i ) > $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $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_Lambda_Olift_type,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(v_u_____type,type,
v_u____: $i ).
tff(1,plain,
( ~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))))
<=> ~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)))
<=> c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(6,plain,
c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_i: $i,V_t: $i] :
refl(( ( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
<=> ( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
<=> ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
<=> ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_i: $i,V_t: $i] :
rewrite(( ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))
| ~ c_InductTermi_OIT(V_t) )
<=> ( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_i: $i,V_t: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))
| ~ c_InductTermi_OIT(V_t) )
<=> ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_i: $i,V_t: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))
| ~ c_InductTermi_OIT(V_t) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
tff(13,plain,
! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) )
<=> ( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))) )
<=> ( c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))) )
<=> ( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))) )
<=> ( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_i: $i,V_t: $i] :
( ~ c_InductTermi_OIT(V_t)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) )
| c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL793-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n004.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 00:05:46 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.56/0.80 % SZS status Unsatisfiable
% 0.56/0.80 % SZS output start Proof
% See solution above
% 0.56/0.88 % E exiting
%------------------------------------------------------------------------------