%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n014.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 0.38s 0.68s
% Output : Proof 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 58 ( 27 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 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 : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 30 !; 0 ?; 33 :)
% 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(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
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)),
inference(modus_ponens,[status(thm)],[4,3]) ).
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)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,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)],[6,2]) ).
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))
| 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(9,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))))
<=> ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(12,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_r: $i] :
refl(( ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
<=> ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
<=> ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
<=> ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
tff(17,plain,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(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))) )
<=> ( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(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(21,plain,
( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(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(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(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(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,12,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 15:46:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.38/0.68 % SZS status Unsatisfiable
% 0.38/0.68 % SZS output start Proof
% See solution above
% 0.44/0.74 % E exiting
%------------------------------------------------------------------------------