%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT104+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 : n026.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 08:00:55 AM UTC 2026
% Result : Unsatisfiable 7.26s 3.45s
% Output : Refutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 58
% Syntax : Number of formulae : 117 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 302 ( 85 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 762 ( 43 ~; 27 |; 82 &; 534 @)
% ( 13 <=>; 63 =>; 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 : 27 ( 25 usr; 11 con; 0-4 aty)
% Number of variables : 179 ( 0 ^; 173 !; 6 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_decl,type,
less: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(in_closed_decl,type,
in_closed: $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(in_open_decl,type,
in_open: $i > $i > $i > $o ).
thf(axis_conflict_decl,type,
axis_conflict: $i > $i > $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(is_verdict_decl,type,
is_verdict: $i > $o ).
thf(conflict_decl,type,
conflict: $i ).
thf(compatible_decl,type,
compatible: $i ).
thf(unknown_decl,type,
unknown: $i ).
thf(box_verdict_decl,type,
box_verdict: $i > $i > $i ).
thf(wf_decl,type,
wf: $i > $i > $i > $i > $o ).
thf(eq_decl,type,
eq: $i ).
thf(lteq_decl,type,
lteq: $i ).
thf(gteq_decl,type,
gteq: $i ).
thf(lt_decl,type,
lt: $i ).
thf(gt_decl,type,
gt: $i ).
thf(sem_nonempty_decl,type,
sem_nonempty: $i > $i > $i > $i > $o ).
thf(is_op_decl,type,
is_op: $i > $o ).
thf(val_decl,type,
val: $i > $o ).
thf(v0_decl,type,
v0: $i ).
thf(v1200_decl,type,
v1200: $i ).
thf(20,axiom,
conflict != compatible,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verdicts_distinct_cf_cp) ).
thf(142,plain,
conflict != compatible,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( ( B @ ( A @ box_verdict ) )
= unknown )
| ( ( B @ ( A @ box_verdict ) )
= compatible )
| ( ( B @ ( A @ box_verdict ) )
= conflict ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',box_verdict_total) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( ( B @ ( A @ box_verdict ) )
= unknown )
| ( ( B @ ( A @ box_verdict ) )
= compatible )
| ( ( B @ ( A @ box_verdict ) )
= conflict ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,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(184,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)],[29]) ).
thf(37,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(228,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)],[37]) ).
thf(35,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(224,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)],[35]) ).
thf(19,axiom,
unknown @ is_verdict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown_is_verdict) ).
thf(141,plain,
unknown @ is_verdict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,axiom,
eq != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_4) ).
thf(244,plain,
eq != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(9,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(86,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,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(95,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)],[11]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( ( B = conflict )
| ( A = conflict ) )
& ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( B @ ( A @ box_verdict ) )
= conflict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',box_conflict) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ( ( B = conflict )
| ( A = conflict ) )
& ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( B @ ( A @ box_verdict ) )
= conflict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,axiom,
conflict @ is_verdict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conflict_is_verdict) ).
thf(139,plain,
conflict @ is_verdict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,axiom,
v0 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v0) ).
thf(268,plain,
v0 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(42,axiom,
gteq @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_gteq_is_op) ).
thf(234,plain,
gteq @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(10,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(88,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)],[10]) ).
thf(47,axiom,
lt != lteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_5) ).
thf(247,plain,
lt != lteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(55,axiom,
v1200 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v1200) ).
thf(269,plain,
v1200 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(49,axiom,
lt != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_7) ).
thf(253,plain,
lt != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(44,axiom,
eq != lteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_2) ).
thf(238,plain,
eq != lteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(8,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(84,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,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(116,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)],[14]) ).
thf(53,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(265,plain,
! [A: $i] :
( ( A @ is_op )
=> ( ( A = gteq )
| ( A = gt )
| ( A = lteq )
| ( A = lt )
| ( A = eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(41,axiom,
gt @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_gt_is_op) ).
thf(233,plain,
gt @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(56,axiom,
v1200 @ ( v0 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v1200) ).
thf(270,plain,
v1200 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(33,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(220,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)],[33]) ).
thf(12,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(102,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)],[12]) ).
thf(15,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(124,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)],[15]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_antisym) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,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(109,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)],[13]) ).
thf(50,axiom,
lteq != gt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_8) ).
thf(256,plain,
lteq != gt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( B != conflict )
& ( A != conflict )
& ( ( B = unknown )
| ( A = unknown ) )
& ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( B @ ( A @ box_verdict ) )
= unknown ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',box_unknown) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( ( B != conflict )
& ( A != conflict )
& ( ( B = unknown )
| ( A = unknown ) )
& ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( B @ ( A @ box_verdict ) )
= unknown ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,axiom,
compatible != unknown,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verdicts_distinct_cp_un) ).
thf(148,plain,
compatible != unknown,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trichotomy) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,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(191,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)],[30]) ).
thf(1,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive) ).
thf(59,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(51,axiom,
lteq != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_9) ).
thf(259,plain,
lteq != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(58,axiom,
v0 @ ( v0 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contradiction) ).
thf(274,plain,
v0 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(38,axiom,
eq @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_eq_is_op) ).
thf(230,plain,
eq @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(57,axiom,
v0 != v1200,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct) ).
thf(271,plain,
v0 != v1200,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(18,axiom,
compatible @ is_verdict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible_is_verdict) ).
thf(140,plain,
compatible @ is_verdict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(31,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(198,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)],[31]) ).
thf(36,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(226,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)],[36]) ).
thf(45,axiom,
eq != gt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_3) ).
thf(241,plain,
eq != gt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_implies_leq) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( B = compatible )
& ( A = compatible )
& ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( B @ ( A @ box_verdict ) )
= compatible ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',box_compatible) ).
thf(162,plain,
! [A: $i,B: $i] :
( ( ( B = compatible )
& ( A = compatible )
& ( B @ is_verdict )
& ( A @ is_verdict ) )
=> ( ( B @ ( A @ box_verdict ) )
= compatible ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,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(209,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)],[32]) ).
thf(21,axiom,
conflict != unknown,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verdicts_distinct_cf_un) ).
thf(145,plain,
conflict != unknown,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_def) ).
thf(67,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)],[4]) ).
thf(28,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(177,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)],[28]) ).
thf(48,axiom,
lt != gt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_6) ).
thf(250,plain,
lt != gt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
lt @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_lt_is_op) ).
thf(231,plain,
lt @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(43,axiom,
eq != lt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_1) ).
thf(235,plain,
eq != lt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(7,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(82,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ is_verdict )
=> ( ( A = unknown )
| ( A = compatible )
| ( A = conflict ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verdict_enum) ).
thf(151,plain,
! [A: $i] :
( ( A @ is_verdict )
=> ( ( A = unknown )
| ( A = compatible )
| ( A = conflict ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(52,axiom,
gt != gteq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ops_distinct_10) ).
thf(262,plain,
gt != gteq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(16,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(131,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)],[16]) ).
thf(2,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(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,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(222,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)],[34]) ).
thf(40,axiom,
lteq @ is_op,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_lteq_is_op) ).
thf(232,plain,
lteq @ is_op,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(275,plain,
$false,
inference(e,[status(thm)],[142,174,184,228,224,141,244,86,95,154,139,268,234,88,247,269,253,238,84,116,265,233,270,220,102,124,77,109,256,166,148,64,191,59,259,274,230,271,140,198,226,241,80,162,209,145,67,177,250,231,235,82,151,262,131,62,222,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : MGT104+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.28 % 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
% 0.11/0.59 % Computer : n026.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.60 % CPULimit : 300
% 0.11/0.60 % WCLimit : 300
% 0.11/0.60 % DateTime : Sat Sep 26 00:16:14 UTC 2026
% 0.11/0.60 % CPUTime :
% 0.11/0.60 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
% 0.90/1.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.37 % [INFO] Parsing done (228ms).
% 1.42/1.38 % [INFO] Running in sequential loop mode.
% 2.46/1.74 % [INFO] eprover registered as external prover.
% 2.46/1.75 % [INFO] Scanning for conjecture ...
% 2.75/1.80 % [INFO] 58 axioms and no conjecture found.
% 3.01/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 3.01/1.93 % [INFO] Type checking passed.
% 3.01/1.93 % [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 ...
% 7.26/3.44 % External prover 'e' found a proof!
% 7.26/3.44 % [INFO] Killing All external provers ...
% 7.26/3.44 % Time passed: 2703ms (effective reasoning time: 2052ms)
% 7.26/3.45 % Axioms used in derivation (58): ops_distinct_5, ops_distinct_6, val_v0, ops_distinct_7, axis_conflict_def, irreflexive, wf_gteq, nonempty_eq, nonempty_gteq, op_lteq_is_op, ops_distinct_1, val_v1200, op_lt_is_op, verdicts_distinct_cf_cp, op_enum, leq_antisym, ops_distinct_9, ops_distinct_10, box_conflict, conflict_is_verdict, ops_distinct_8, wf_gt, verdicts_distinct_cp_un, wf_eq, verdicts_distinct_cf_un, nonempty_lt, ops_distinct_2, box_verdict_total, axis_subsumes_def, less_implies_leq, contradiction, in_ropen, unknown_is_verdict, leq_trans, leq_less_trans, in_closed, in_lopen, ord_v0_v1200, nonempty_lteq, compatible_is_verdict, distinct, ops_distinct_3, op_eq_is_op, less_leq_trans, axis_compatible_def, trichotomy, transitive, wf_lteq, op_gt_is_op, in_open, nonempty_gt, wf_lt, box_compatible, ops_distinct_4, op_gteq_is_op, verdict_enum, box_unknown, leq_def
% 7.26/3.45 % No. of inferences in proof: 117
% 7.26/3.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2703 ms resp. 2052 ms w/o parsing
% 8.01/3.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.01/3.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------