%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL773-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n019.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 03:00:49 PM UTC 2026
% Result : Unsatisfiable 0.57s 0.80s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 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; 3 con; 0-3 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% 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_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_i_type,type,
v_i: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(1,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat)))
<=> ~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_InductTermi_OIT(v_r)
<=> c_InductTermi_OIT(v_r) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_InductTermi_OIT(v_r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(6,plain,
c_InductTermi_OIT(v_r),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_i: $i,V_r: $i,V_j: $i] :
refl(( ( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) )
<=> ( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) )
<=> ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) )
<=> ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_i: $i,V_r: $i,V_j: $i] :
rewrite(( ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
| ~ c_InductTermi_OIT(V_r) )
<=> ( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_i: $i,V_r: $i,V_j: $i] :
( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
| ~ c_InductTermi_OIT(V_r) )
<=> ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_i: $i,V_r: $i,V_j: $i] :
( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
| ~ c_InductTermi_OIT(V_r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
tff(13,plain,
! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) )
| ~ c_InductTermi_OIT(v_r)
| c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))) )
<=> ( ~ ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) )
| ~ c_InductTermi_OIT(v_r)
| c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) )
| ~ c_InductTermi_OIT(v_r)
| c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_i: $i,V_r: $i,V_j: $i] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) )
| ~ c_InductTermi_OIT(v_r)
| c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL773-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 08:28:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.57/0.80 % SZS status Unsatisfiable
% 0.57/0.80 % SZS output start Proof
% See solution above
% 0.57/0.88 % E exiting
%------------------------------------------------------------------------------