%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL756-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n003.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 03:00:46 PM UTC 2026
% Result : Unsatisfiable 0.47s 0.71s
% Output : Proof 0.47s
% 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 : 5 ( 3 avg)
% Maximal term depth : 4 ( 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
tff(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(v_ja_type,type,
v_ja: $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_ia_type,type,
v_ia: $i ).
tff(v_ra_type,type,
v_ra: $i ).
tff(1,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))
<=> ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_i: $i,V_j: $i] :
refl(( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j))
<=> c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j))
<=> ! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j))
<=> ! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(8,plain,
! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [V_i: $i,V_j: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j))
| c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL756-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n003.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 11:54:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.47/0.71 % SZS status Unsatisfiable
% 0.47/0.71 % SZS output start Proof
% See solution above
% 0.47/0.72 % E exiting
%------------------------------------------------------------------------------