%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT088+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 : n009.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 4.97s 2.77s
% Output : Refutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 159 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 439 ( 19 ~; 7 |; 51 &; 321 @)
% ( 8 <=>; 33 =>; 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 : 16 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 108 ( 0 ^; 97 !; 11 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_decl,type,
less: $i > $i > $o ).
thf(v200_decl,type,
v200: $i ).
thf(in_lopen_decl,type,
in_lopen: $i > $i > $i > $o ).
thf(v0_decl,type,
v0: $i ).
thf(v400_decl,type,
v400: $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(val_decl,type,
val: $i > $o ).
thf(v600_decl,type,
v600: $i ).
thf(leq_decl,type,
leq: $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(6,axiom,
v600 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v600) ).
thf(56,plain,
v600 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,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(60,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,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(97,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)],[19]) ).
thf(30,axiom,
v0 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v0) ).
thf(140,plain,
v0 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(26,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(130,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)],[26]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ? [C: $i] :
( ( B @ ( C @ less ) )
& ( C @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dense) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ? [C: $i] :
( ( B @ ( C @ less ) )
& ( C @ ( A @ less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
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(48,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(11,axiom,
v400 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v400) ).
thf(72,plain,
v400 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_def) ).
thf(104,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)],[20]) ).
thf(17,axiom,
v200 @ val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',val_v200) ).
thf(82,plain,
v200 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,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(62,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)],[9]) ).
thf(18,axiom,
( ( v400 != v600 )
& ( v200 != v600 )
& ( v200 != v400 )
& ( v0 != v600 )
& ( v0 != v400 )
& ( v0 != v200 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct) ).
thf(83,plain,
( ( v400 != v600 )
& ( v200 != v600 )
& ( v200 != v400 )
& ( v0 != v600 )
& ( v0 != v400 )
& ( v0 != v200 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trichotomy) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
v200 @ ( v0 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v200) ).
thf(138,plain,
v200 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_antisym) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive) ).
thf(78,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,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(116,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)],[22]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_implies_leq) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
v600 @ ( v400 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v400_v600) ).
thf(137,plain,
v600 @ ( v400 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
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(33,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(12,axiom,
v400 @ ( v200 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v200_v400) ).
thf(73,plain,
v400 @ ( v200 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,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(128,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(16,axiom,
v600 @ ( v0 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v600) ).
thf(81,plain,
v600 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,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(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
v600 @ ( v200 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v200_v600) ).
thf(127,plain,
v600 @ ( v200 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
? [A: $i] :
( ( v400 @ ( v0 @ ( A @ in_lopen ) ) )
& ( A @ ( v200 @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odrl509) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( v400 @ ( v0 @ ( A @ in_lopen ) ) )
& ( A @ ( v200 @ less ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ? [A: $i] :
( ( v400 @ ( v0 @ ( A @ in_lopen ) ) )
& ( A @ ( v200 @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(40,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,
! [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(114,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
v400 @ ( v0 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v400) ).
thf(139,plain,
v400 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(141,plain,
$false,
inference(e,[status(thm)],[56,60,97,140,130,123,48,72,104,82,62,83,69,138,57,78,116,74,137,33,73,128,81,76,127,31,40,114,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT088+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
% 0.14/0.40 % Computer : n009.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 00:12:44 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.23 % [INFO] Parsing done (233ms).
% 1.43/1.24 % [INFO] Running in sequential loop mode.
% 2.24/1.65 % [INFO] eprover registered as external prover.
% 2.24/1.65 % [INFO] Scanning for conjecture ...
% 2.48/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 39 axioms. Running axiom selection ...
% 2.68/1.83 % [INFO] Axiom selection finished. Selected 28 axioms (removed 11 axioms).
% 2.68/1.88 % [INFO] Problem is first-order (TPTP FOF).
% 2.68/1.89 % [INFO] Type checking passed.
% 2.92/1.90 % [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 ...
% 4.97/2.77 % External prover 'e' found a proof!
% 4.97/2.77 % [INFO] Killing All external provers ...
% 4.97/2.77 % Time passed: 2215ms (effective reasoning time: 1519ms)
% 4.97/2.77 % 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)>
% 4.97/2.77 % Axioms used in derivation (28): ord_v0_v400, ord_v200_v600, leq_antisym, val_v600, dense, val_v0, ord_v200_v400, axis_conflict_def, irreflexive, ord_v0_v200, leq_def, axis_subsumes_def, less_implies_leq, in_ropen, leq_trans, leq_less_trans, val_v400, in_closed, in_lopen, distinct, less_leq_trans, axis_compatible_def, val_v200, trichotomy, ord_v400_v600, transitive, in_open, ord_v0_v600
% 4.97/2.77 % No. of inferences in proof: 60
% 4.97/2.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2215 ms resp. 1519 ms w/o parsing
% 5.33/2.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.33/2.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------