%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT081+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:00:52 AM UTC 2026
% Result : Theorem 7.52s 3.63s
% Output : Refutation 7.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 36
% Syntax : Number of formulae : 116 ( 63 unt; 0 typ; 3 def)
% Number of atoms : 290 ( 69 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 806 ( 87 ~; 32 |; 94 &; 550 @)
% ( 8 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 179 ( 4 ^; 152 !; 20 ?; 179 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_lopen_decl,type,
in_lopen: $i > $i > $i > $o ).
thf(v0_decl,type,
v0: $i ).
thf(v400_decl,type,
v400: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(v800_decl,type,
v800: $i ).
thf(v600_decl,type,
v600: $i ).
thf(v200_decl,type,
v200: $i ).
thf(axis_conflict_decl,type,
axis_conflict: $i > $i > $i > $i > $o ).
thf(in_closed_decl,type,
in_closed: $i > $i > $i > $o ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(axis_compatible_decl,type,
axis_compatible: $i > $i > $i > $i > $o ).
thf(axis_subsumes_decl,type,
axis_subsumes: $i > $i > $i > $i > $o ).
thf(in_open_decl,type,
in_open: $i > $i > $i > $o ).
thf(val_decl,type,
val: $i > $o ).
thf(in_ropen_decl,type,
in_ropen: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ? [B: $i] :
( ( B @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( B @ in_lopen ) ) ) )
& ( A @ ( v800 @ leq ) )
& ( v400 @ ( v0 @ ( A @ in_lopen ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( A @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( A @ in_lopen ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
( ( A @ ( B @ ( E @ in_closed ) ) )
& ( C @ ( D @ ( E @ in_closed ) ) ) ) ) ) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_def) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ less ) ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30,axiom,
( ( v600 != v800 )
& ( v400 != v800 )
& ( v400 != v600 )
& ( v200 != v800 )
& ( v200 != v600 )
& ( v200 != v400 )
& ( v0 != v800 )
& ( v0 != v600 )
& ( v0 != v400 )
& ( v0 != v200 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
thf(133,plain,
( ( v600 != v800 )
& ( v400 != v800 )
& ( v400 != v600 )
& ( v200 != v800 )
& ( v200 != v600 )
& ( v200 != v400 )
& ( v0 != v800 )
& ( v0 != v600 )
& ( v0 != v400 )
& ( v0 != v200 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(134,plain,
( ( v600 != v800 )
& ( v400 != v800 )
& ( v400 != v600 )
& ( v200 != v800 )
& ( v200 != v600 )
& ( v200 != v400 )
& ( v0 != v800 )
& ( v0 != v600 )
& ( v0 != v400 )
& ( v0 != v200 ) ),
inference(cnf,[status(esa)],[133]) ).
thf(139,plain,
v400 != v600,
inference(cnfConj,[status(thm)],[134]) ).
thf(153,plain,
v600 != v400,
inference(lifteq,[status(thm)],[139]) ).
thf(1,conjecture,
~ ? [A: $i,B: $i] :
( ( B @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( B @ in_lopen ) ) )
& ( A @ ( v800 @ leq ) )
& ( v400 @ ( v0 @ ( A @ in_lopen ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odrl402) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i,B: $i] :
( ( B @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( B @ in_lopen ) ) )
& ( A @ ( v800 @ leq ) )
& ( v400 @ ( v0 @ ( A @ in_lopen ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ~ ? [A: $i,B: $i] :
( ( B @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( B @ in_lopen ) ) )
& ( A @ ( v800 @ leq ) )
& ( v400 @ ( v0 @ ( A @ in_lopen ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,plain,
? [A: $i,B: $i] :
( ( B @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( B @ in_lopen ) ) )
& ( A @ ( v800 @ leq ) )
& ( v400 @ ( v0 @ ( A @ in_lopen ) ) ) ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(37,plain,
? [A: $i] :
( ? [B: $i] :
( ( B @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( B @ in_lopen ) ) ) )
& ( A @ ( v800 @ leq ) )
& ( v400 @ ( v0 @ ( A @ in_lopen ) ) ) ),
inference(miniscope,[status(thm)],[36]) ).
thf(38,plain,
( ( sk2 @ ( v200 @ leq ) )
& ( v600 @ ( v0 @ ( sk2 @ in_lopen ) ) )
& ( sk1 @ ( v800 @ leq ) )
& ( v400 @ ( v0 @ ( sk1 @ in_lopen ) ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(42,plain,
sk2 @ ( v200 @ leq ),
inference(cnfConj,[status(thm)],[38]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_less_trans) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive) ).
thf(51,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,plain,
~ ? [A: $i] : ( A @ ( A @ less ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(cnf,[status(esa)],[52]) ).
thf(41,plain,
v600 @ ( v0 @ ( sk2 @ in_lopen ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(140,plain,
v0 != v400,
inference(cnfConj,[status(thm)],[134]) ).
thf(150,plain,
v400 != v0,
inference(lifteq,[status(thm)],[140]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_closed ) ) )
<=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_closed) ).
thf(99,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ in_closed ) ) ) )
& ( ( C @ ( B @ ( A @ in_closed ) ) )
=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
v800 @ ( v200 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v200_v800) ).
thf(82,plain,
v800 @ ( v200 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23,axiom,
v800 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v800) ).
thf(110,plain,
v800 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_ropen ) ) )
<=> ( ( C @ ( A @ less ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_ropen) ).
thf(125,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ less ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ in_ropen ) ) ) )
& ( ( C @ ( B @ ( A @ in_ropen ) ) )
=> ( ( C @ ( A @ less ) )
& ( A @ ( B @ leq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(32,axiom,
v200 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v200) ).
thf(157,plain,
v200 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) )
<=> ~ ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axis_conflict_def) ).
thf(43,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) )
=> ~ ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,plain,
( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) )
=> ~ ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( H @ ( G @ ( F @ axis_conflict ) ) ) )
| ( I @ ( H @ ( F @ ( G @ ( H @ ( I @ sk3 ) ) ) @ in_closed ) ) ) )
& ( ( I @ ( H @ ( G @ ( F @ axis_conflict ) ) ) )
| ( G @ ( F @ ( F @ ( G @ ( H @ ( I @ sk3 ) ) ) @ in_closed ) ) ) )
& ( ~ ( D @ ( C @ ( E @ in_closed ) ) )
| ~ ( B @ ( A @ ( E @ in_closed ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ in_closed ) ) )
| ~ ( B @ ( A @ ( E @ in_closed ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(15,axiom,
v800 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v800) ).
thf(93,plain,
v800 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(143,plain,
v0 != v200,
inference(cnfConj,[status(thm)],[134]) ).
thf(152,plain,
v200 != v0,
inference(lifteq,[status(thm)],[143]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ axis_compatible ) ) ) )
<=> ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axis_compatible_def) ).
thf(57,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ axis_compatible ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ axis_compatible ) ) ) )
=> ? [E: $i] :
( ( D @ ( C @ ( E @ in_closed ) ) )
& ( B @ ( A @ ( E @ in_closed ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
v600 @ ( v400 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v400_v600) ).
thf(106,plain,
v600 @ ( v400 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_implies_leq) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(137,plain,
v200 != v600,
inference(cnfConj,[status(thm)],[134]) ).
thf(147,plain,
v200 != v600,
inference(lifteq,[status(thm)],[137]) ).
thf(29,axiom,
v600 @ ( v200 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v200_v600) ).
thf(132,plain,
v600 @ ( v200 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_open ) ) )
<=> ( ( C @ ( A @ less ) )
& ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_open) ).
thf(74,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ less ) )
& ( A @ ( B @ less ) ) )
=> ( C @ ( B @ ( A @ in_open ) ) ) )
& ( ( C @ ( B @ ( A @ in_open ) ) )
=> ( ( C @ ( A @ less ) )
& ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
v600 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v600) ).
thf(109,plain,
v600 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(116,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
| ( B @ ( A @ less ) ) )
=> ( B @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ) ),
inference(miniscope,[status(thm)],[115]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ leq ) )
| ( C != D ) )
& ( ( D @ ( C @ leq ) )
| ~ ( D @ ( C @ less ) ) )
& ( ( A = B )
| ( B @ ( A @ less ) )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[116]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[117]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(124,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[123]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_antisym) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(141,plain,
v200 != v800,
inference(cnfConj,[status(thm)],[134]) ).
thf(148,plain,
v200 != v800,
inference(lifteq,[status(thm)],[141]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ axis_subsumes ) ) ) )
<=> ! [E: $i] :
( ( B @ ( A @ ( E @ in_closed ) ) )
=> ( D @ ( C @ ( E @ in_closed ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axis_subsumes_def) ).
thf(64,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( A @ ( E @ in_closed ) ) )
=> ( D @ ( C @ ( E @ in_closed ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ axis_subsumes ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ axis_subsumes ) ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ in_closed ) ) )
=> ( D @ ( C @ ( E @ in_closed ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(144,plain,
v600 != v800,
inference(cnfConj,[status(thm)],[134]) ).
thf(149,plain,
v600 != v800,
inference(lifteq,[status(thm)],[144]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trichotomy) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) )
| ( B @ ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ in_closed ) ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) )
| ( B @ ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ in_closed ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_lopen ) ) )
<=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_lopen) ).
thf(86,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ less ) ) )
=> ( C @ ( B @ ( A @ in_lopen ) ) ) )
& ( ( C @ ( B @ ( A @ in_lopen ) ) )
=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(34,axiom,
v0 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v0) ).
thf(159,plain,
v0 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,axiom,
v200 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v200) ).
thf(81,plain,
v200 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,plain,
v400 @ ( v0 @ ( sk1 @ in_lopen ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_trans) ).
thf(155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
v600 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v600) ).
thf(108,plain,
v600 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(160,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( C @ ( E @ in_closed ) ) )
!= ( B @ ( A @ ( E @ in_closed ) ) ) )
| ~ ( B @ ( A @ ( E @ in_closed ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ axis_conflict ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ in_closed ) ) )
| ~ ( B @ ( A @ ( B @ ( A @ axis_conflict ) ) ) ) ),
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( C )),bind(B,$thf( D ))]]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ in_closed ) ) )
| ~ ( B @ ( A @ ( B @ ( A @ axis_conflict ) ) ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_leq_trans) ).
thf(112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(138,plain,
v0 != v600,
inference(cnfConj,[status(thm)],[134]) ).
thf(145,plain,
v600 != v0,
inference(lifteq,[status(thm)],[138]) ).
thf(136,plain,
v200 != v400,
inference(cnfConj,[status(thm)],[134]) ).
thf(154,plain,
v200 != v400,
inference(lifteq,[status(thm)],[136]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive) ).
thf(72,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
sk1 @ ( v800 @ leq ),
inference(cnfConj,[status(thm)],[38]) ).
thf(33,axiom,
v400 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v400) ).
thf(158,plain,
v400 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
v800 @ ( v400 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v400_v800) ).
thf(114,plain,
v800 @ ( v400 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(135,plain,
v400 != v800,
inference(cnfConj,[status(thm)],[134]) ).
thf(151,plain,
v800 != v400,
inference(lifteq,[status(thm)],[135]) ).
thf(142,plain,
v0 != v800,
inference(cnfConj,[status(thm)],[134]) ).
thf(146,plain,
v800 != v0,
inference(lifteq,[status(thm)],[142]) ).
thf(20,axiom,
v400 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v400) ).
thf(107,plain,
v400 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
v800 @ ( v600 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v600_v800) ).
thf(111,plain,
v800 @ ( v600 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
v400 @ ( v200 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v200_v400) ).
thf(83,plain,
v400 @ ( v200 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(799,plain,
$false,
inference(e,[status(thm)],[115,153,42,97,53,41,35,150,99,82,110,125,157,46,93,152,57,106,84,147,132,133,74,109,124,96,148,64,149,54,49,86,159,81,39,155,108,162,112,145,154,72,43,40,158,114,151,146,51,107,94,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT081+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n001.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 00:17:58 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.22 % [INFO] Parsing done (225ms).
% 1.41/1.23 % [INFO] Running in sequential loop mode.
% 2.06/1.63 % [INFO] eprover registered as external prover.
% 2.06/1.63 % [INFO] Scanning for conjecture ...
% 2.24/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ...
% 2.40/1.82 % [INFO] Axiom selection finished. Selected 32 axioms (removed 11 axioms).
% 2.40/1.87 % [INFO] Problem is first-order (TPTP FOF).
% 2.40/1.88 % [INFO] Type checking passed.
% 2.40/1.89 % [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 ...
% 7.52/3.62 % External prover 'e' found a proof!
% 7.52/3.62 % [INFO] Killing All external provers ...
% 7.52/3.62 % Time passed: 3077ms (effective reasoning time: 2386ms)
% 7.52/3.62 % 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)>
% 7.52/3.63 % Axioms used in derivation (32): ord_v200_v600, leq_antisym, ord_v400_v800, val_v600, ord_v600_v800, val_v0, ord_v200_v400, axis_conflict_def, irreflexive, ord_v0_v200, ord_v0_v800, ord_v0_v400, axis_subsumes_def, less_implies_leq, in_ropen, leq_trans, leq_less_trans, val_v400, in_closed, in_lopen, distinct, ord_v200_v800, less_leq_trans, axis_compatible_def, val_v200, trichotomy, ord_v400_v600, transitive, in_open, ord_v0_v600, val_v800, leq_def
% 7.52/3.63 % No. of inferences in proof: 113
% 7.52/3.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3077 ms resp. 2386 ms w/o parsing
% 7.89/3.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.89/3.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------