%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT090+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 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 : 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 08:00:53 AM UTC 2026
% Result : Theorem 5.79s 12.95s
% Output : Refutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 100 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 49 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 686 ( 39 ~; 15 |; 66 &; 500 @)
% ( 13 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 9 con; 0-4 aty)
% Number of variables : 161 ( 0 ^; 155 !; 6 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(wf_decl,type,
wf: $i > $i > $i > $i > $o ).
thf(lt_decl,type,
lt: $i ).
thf(v600_decl,type,
v600: $i ).
thf(v0_decl,type,
v0: $i ).
thf(v1200_decl,type,
v1200: $i ).
thf(axis_compatible_decl,type,
axis_compatible: $i > $i > $i > $i > $o ).
thf(in_closed_decl,type,
in_closed: $i > $i > $i > $o ).
thf(axis_subsumes_decl,type,
axis_subsumes: $i > $i > $i > $i > $o ).
thf(axis_conflict_decl,type,
axis_conflict: $i > $i > $i > $i > $o ).
thf(eq_decl,type,
eq: $i ).
thf(gteq_decl,type,
gteq: $i ).
thf(is_op_decl,type,
is_op: $i > $o ).
thf(lteq_decl,type,
lteq: $i ).
thf(gt_decl,type,
gt: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(in_open_decl,type,
in_open: $i > $i > $i > $o ).
thf(in_lopen_decl,type,
in_lopen: $i > $i > $i > $o ).
thf(in_ropen_decl,type,
in_ropen: $i > $i > $i > $o ).
thf(sem_nonempty_decl,type,
sem_nonempty: $i > $i > $i > $i > $o ).
thf(val_decl,type,
val: $i > $o ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( gt @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( gt @ sem_nonempty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_gt) ).
thf(174,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( gt @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( gt @ sem_nonempty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( lteq @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( lteq @ sem_nonempty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_lteq) ).
thf(165,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( lteq @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( lteq @ sem_nonempty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_implies_leq) ).
thf(124,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
eq != lteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_2) ).
thf(86,plain,
eq != lteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive) ).
thf(150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(17,axiom,
lteq != gt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_8) ).
thf(104,plain,
lteq != gt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
v1200 @ ( v0 @ ( v600 @ ( lt @ wf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odrl613) ).
thf(2,negated_conjecture,
~ ( v1200 @ ( v0 @ ( v600 @ ( lt @ wf ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(51,plain,
~ ( v1200 @ ( v0 @ ( v600 @ ( lt @ wf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',axis_compatible_def) ).
thf(52,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)],[3]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_closed ) ) )
<=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_closed) ).
thf(110,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)],[19]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( gteq @ wf ) ) ) )
<=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wf_gteq) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ ( gteq @ wf ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( gteq @ wf ) ) ) )
=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_trans) ).
thf(152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
lteq @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_lteq_is_op) ).
thf(78,plain,
lteq @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
lt @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_lt_is_op) ).
thf(164,plain,
lt @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trichotomy) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(41,axiom,
v600 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v600) ).
thf(206,plain,
v600 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_antisym) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_def) ).
thf(133,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)],[25]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( lt @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( lt @ sem_nonempty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_lt) ).
thf(233,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( lt @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( lt @ sem_nonempty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(20,axiom,
eq @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_eq_is_op) ).
thf(117,plain,
eq @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_less_trans) ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_open ) ) )
<=> ( ( C @ ( A @ less ) )
& ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_open) ).
thf(97,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)],[16]) ).
thf(46,axiom,
lt != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_7) ).
thf(224,plain,
lt != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
v1200 @ ( v600 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v600_v1200) ).
thf(156,plain,
v1200 @ ( v600 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
lt != gt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_6) ).
thf(188,plain,
lt != gt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( gt @ wf ) ) ) )
<=> ( ( A != C )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wf_gt) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != C )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ ( gt @ wf ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( gt @ wf ) ) ) )
=> ( ( A != C )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(39,axiom,
( ( v600 != v1200 )
& ( v0 != v1200 )
& ( v0 != v600 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct) ).
thf(191,plain,
( ( v600 != v1200 )
& ( v0 != v1200 )
& ( v0 != v600 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',axis_subsumes_def) ).
thf(59,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)],[4]) ).
thf(21,axiom,
lteq != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_9) ).
thf(118,plain,
lteq != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
v1200 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v1200) ).
thf(187,plain,
v1200 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(44,axiom,
eq != lt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_1) ).
thf(219,plain,
eq != lt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_leq_trans) ).
thf(81,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
lt != lteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_5) ).
thf(230,plain,
lt != lteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( lt @ wf ) ) ) )
<=> ( ( A != B )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wf_lt) ).
thf(208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != B )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ ( lt @ wf ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( lt @ wf ) ) ) )
=> ( ( A != B )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9,axiom,
gt @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_gt_is_op) ).
thf(80,plain,
gt @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( lteq @ wf ) ) ) )
<=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wf_lteq) ).
thf(167,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ ( lteq @ wf ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( lteq @ wf ) ) ) )
=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',axis_conflict_def) ).
thf(67,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)],[5]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( eq @ wf ) ) ) )
<=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wf_eq) ).
thf(199,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ ( eq @ wf ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( eq @ wf ) ) ) )
=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( eq @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( eq @ sem_nonempty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_eq) ).
thf(154,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( eq @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( eq @ sem_nonempty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_ropen ) ) )
<=> ( ( C @ ( A @ less ) )
& ( A @ ( B @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_ropen) ).
thf(143,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)],[26]) ).
thf(6,axiom,
eq != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_4) ).
thf(75,plain,
eq != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(50,axiom,
v0 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v0) ).
thf(235,plain,
v0 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(42,axiom,
v600 @ ( v0 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v600) ).
thf(207,plain,
v600 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(18,axiom,
eq != gt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_3) ).
thf(107,plain,
eq != gt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ in_lopen ) ) )
<=> ( ( C @ ( A @ leq ) )
& ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_lopen) ).
thf(126,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)],[24]) ).
thf(8,axiom,
gteq @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_gteq_is_op) ).
thf(79,plain,
gteq @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
gt != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_10) ).
thf(94,plain,
gt != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ is_op )
=> ( ( A = gteq )
| ( A = gt )
| ( A = lteq )
| ( A = lt )
| ( A = eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_enum) ).
thf(227,plain,
! [A: $i] :
( ( A @ is_op )
=> ( ( A = gteq )
| ( A = gt )
| ( A = lteq )
| ( A = lt )
| ( A = eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(11,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive) ).
thf(83,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( gteq @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( gteq @ sem_nonempty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_gteq) ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( gteq @ wf ) ) ) )
=> ( C @ ( B @ ( A @ ( gteq @ sem_nonempty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(236,plain,
$false,
inference(e,[status(thm)],[174,165,124,86,150,104,51,52,110,157,152,78,164,121,206,89,133,233,117,92,97,224,156,188,176,191,59,118,187,219,81,230,208,80,167,67,199,154,143,75,235,207,107,126,79,94,227,83,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT090+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.08 % 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
% 0.15/10.41 % Computer : n001.cluster.edu
% 0.15/10.41 % Model : x86_64 x86_64
% 0.15/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.41 % Memory : 8046.5625MB
% 0.15/10.41 % OS : Linux 6.8.0-71-generic
% 0.15/10.41 % CPULimit : 300
% 0.15/10.41 % WCLimit : 300
% 0.15/10.41 % DateTime : Sat Sep 26 00:18:21 UTC 2026
% 0.15/10.41 % CPUTime :
% 0.15/10.41 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
% 0.19/11.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/11.26 % [INFO] Parsing done (250ms).
% 1.40/11.27 % [INFO] Running in sequential loop mode.
% 2.27/11.68 % [INFO] eprover registered as external prover.
% 2.27/11.68 % [INFO] Scanning for conjecture ...
% 2.49/11.78 % [INFO] Found a conjecture (or negated_conjecture) and 59 axioms. Running axiom selection ...
% 2.69/11.85 % [INFO] Axiom selection finished. Selected 48 axioms (removed 11 axioms).
% 2.92/11.92 % [INFO] Problem is first-order (TPTP FOF).
% 2.92/11.94 % [INFO] Type checking passed.
% 2.92/11.94 % [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 ...
% 5.79/12.95 % External prover 'e' found a proof!
% 5.79/12.95 % [INFO] Killing All external provers ...
% 5.79/12.95 % Time passed: 2388ms (effective reasoning time: 1669ms)
% 5.79/12.95 % 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)>
% 5.79/12.95 % Axioms used in derivation (48): op_enum, ops_distinct_10, ops_distinct_5, ord_v600_v1200, ops_distinct_6, wf_eq, val_v0, ops_distinct_7, axis_conflict_def, irreflexive, wf_gteq, nonempty_lteq, nonempty_eq, wf_lt, nonempty_gteq, leq_def, op_lteq_is_op, ops_distinct_1, val_v1200, op_lt_is_op, leq_antisym, ops_distinct_9, ops_distinct_8, wf_gt, val_v600, nonempty_lt, ops_distinct_2, axis_subsumes_def, less_implies_leq, in_ropen, leq_trans, leq_less_trans, in_closed, in_lopen, distinct, ops_distinct_3, op_eq_is_op, less_leq_trans, axis_compatible_def, trichotomy, transitive, wf_lteq, op_gt_is_op, in_open, ord_v0_v600, nonempty_gt, ops_distinct_4, op_gteq_is_op
% 5.79/12.95 % No. of inferences in proof: 100
% 5.79/12.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2388 ms resp. 1669 ms w/o parsing
% 5.79/13.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.79/13.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------