%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL770-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n020.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 03:00:48 PM UTC 2026
% Result : Unsatisfiable 0.39s 0.65s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 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 : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_i_type,type,
v_i: $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(1,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_i)))
<=> ~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_i))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_i))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_n: $i] :
refl(( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n)))
<=> hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n)))
<=> ! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n)))
<=> ! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
tff(8,plain,
! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [V_n: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n)))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_i))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL770-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 19:13:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.39/0.65 % SZS status Unsatisfiable
% 0.39/0.65 % SZS output start Proof
% See solution above
% 0.39/0.66 % E exiting
%------------------------------------------------------------------------------