%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MSC010+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 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 : Sun Sep 27 08:03:11 AM UTC 2026
% Result : Theorem 9.52s 8.62s
% Output : Refutation 9.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 341 ( 75 equ; 0 cnn)
% Maximal formula atoms : 68 ( 56 avg)
% Number of connectives : 1051 ( 16 ~; 0 |; 255 &; 700 @)
% ( 0 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 23 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 110 ( 0 ^; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(pv63_decl,type,
pv63: $i ).
thf(pv64_decl,type,
pv64: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(pv5_decl,type,
pv5: $i ).
thf(n998_decl,type,
n998: $i ).
thf(n5_decl,type,
n5: $i ).
thf(n2_decl,type,
n2: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(h_ds1_filter_init_decl,type,
h_ds1_filter_init: $i ).
thf(init_decl,type,
init: $i ).
thf(phi_ds1_filter_init_decl,type,
phi_ds1_filter_init: $i ).
thf(dv_ds1_filter_init_decl,type,
dv_ds1_filter_init: $i ).
thf(q_ds1_filter_init_decl,type,
q_ds1_filter_init: $i ).
thf(r_ds1_filter_init_decl,type,
r_ds1_filter_init: $i ).
thf(xhatmin_ds1_filter_init_decl,type,
xhatmin_ds1_filter_init: $i ).
thf(pminus_ds1_filter_init_decl,type,
pminus_ds1_filter_init: $i ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(id_ds1_filter_init_decl,type,
id_ds1_filter_init: $i ).
thf(pred_decl,type,
pred: $i > $i ).
thf(1,conjecture,
~ ~ ( ( ! [A: $i] :
( ( ( pv63 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv63 @ gt ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( pv64 @ gt ) )
& ( A = pv63 ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( xhatmin_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( dv_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( phi_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( h_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ( n5 @ ( pv64 @ leq ) )
& ( n5 @ ( pv63 @ leq ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv64 @ ( n0 @ leq ) )
& ( pv63 @ ( n0 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( pv63 != pv64 ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( pv64 @ ( B @ leq ) )
& ( A = pv63 )
& ( pv64 != B ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n91) ).
thf(2,negated_conjecture,
~ ~ ~ ( ( ! [A: $i] :
( ( ( pv63 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv63 @ gt ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( pv64 @ gt ) )
& ( A = pv63 ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( xhatmin_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( dv_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( phi_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( h_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ( n5 @ ( pv64 @ leq ) )
& ( n5 @ ( pv63 @ leq ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv64 @ ( n0 @ leq ) )
& ( pv63 @ ( n0 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( pv63 != pv64 ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( pv64 @ ( B @ leq ) )
& ( A = pv63 )
& ( pv64 != B ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ( ! [A: $i] :
( ( ( pv63 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv63 @ gt ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( pv64 @ gt ) )
& ( A = pv63 ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( xhatmin_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( dv_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( phi_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( h_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ( n5 @ ( pv64 @ leq ) )
& ( n5 @ ( pv63 @ leq ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv64 @ ( n0 @ leq ) )
& ( pv63 @ ( n0 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( pv63 != pv64 ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( pv64 @ ( B @ leq ) )
& ( A = pv63 )
& ( pv64 != B ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( ( ! [A: $i] :
( ( ( pv63 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv63 @ gt ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( pv64 @ gt ) )
& ( A = pv63 ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( xhatmin_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( dv_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( phi_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( h_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ( n5 @ ( pv64 @ leq ) )
& ( n5 @ ( pv63 @ leq ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv64 @ ( n0 @ leq ) )
& ( pv63 @ ( n0 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( pv63 != pv64 ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( pv64 @ ( B @ leq ) )
& ( A = pv63 )
& ( pv64 != B ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n1) ).
thf(54,plain,
( ( ! [A: $i] :
( ( ( pv63 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv63 @ gt ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( pv64 @ gt ) )
& ( A = pv63 ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( xhatmin_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n0 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( dv_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( phi_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( h_ds1_filter_init @ a_select3 ) ) )
= init ) )
& ( n5 @ ( pv64 @ leq ) )
& ( n5 @ ( pv63 @ leq ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv64 @ ( n0 @ leq ) )
& ( pv63 @ ( n0 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( pv63 != pv64 ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( pv64 @ ( B @ leq ) )
& ( A = pv63 )
& ( pv64 != B ) )
=> ( ( B @ ( A @ ( id_ds1_filter_init @ a_select3 ) ) )
= init ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(290,plain,
$false,
inference(e,[status(thm)],[4,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MSC010+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.22/5.49 % Computer : n003.cluster.edu
% 0.22/5.49 % Model : x86_64 x86_64
% 0.22/5.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.49 % Memory : 8046.5625MB
% 0.22/5.49 % OS : Linux 6.8.0-71-generic
% 0.22/5.49 % CPULimit : 300
% 0.22/5.49 % WCLimit : 300
% 0.22/5.49 % DateTime : Sat Sep 26 00:16:59 UTC 2026
% 0.26/5.50 % CPUTime :
% 0.26/5.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.26/5.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/6.17 % [INFO] Parsing done (185ms).
% 1.53/6.18 % [INFO] Running in sequential loop mode.
% 2.40/6.52 % [INFO] eprover registered as external prover.
% 2.40/6.53 % [INFO] Scanning for conjecture ...
% 2.66/6.68 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.96/6.74 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.96/6.76 % [INFO] Problem is first-order (TPTP FOF).
% 2.96/6.77 % [INFO] Type checking passed.
% 2.96/6.77 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 9.52/8.61 % External prover 'e' found a proof!
% 9.52/8.61 % [INFO] Killing All external provers ...
% 9.52/8.61 % Time passed: 2977ms (effective reasoning time: 2424ms)
% 9.52/8.61 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.52/8.62 % Axioms used in derivation (1): n1
% 9.52/8.62 % No. of inferences in proof: 6
% 9.52/8.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2977 ms resp. 2424 ms w/o parsing
% 9.93/8.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.93/8.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------