%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT092+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 : n018.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 08:00:54 AM UTC 2026
% Result : Theorem 7.13s 3.87s
% Output : Refutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 446 ( 16 ~; 7 |; 63 &; 322 @)
% ( 6 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 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 : 107 ( 0 ^; 104 !; 3 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(completion_conflict_decl,type,
completion_conflict: $i > $i > $i > $i > $o ).
thf(v400_decl,type,
v400: $i ).
thf(v800_decl,type,
v800: $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(less_decl,type,
less: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(completion_compatible_decl,type,
completion_compatible: $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(val_decl,type,
val: $i > $o ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ less ) )
& ( D @ ( B @ leq ) )
& ( B @ ( C @ leq ) )
& ( D @ ( A @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( D @ ( C @ ( B @ ( A @ completion_conflict ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',completion_conflict) ).
thf(101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ less ) )
& ( D @ ( B @ leq ) )
& ( B @ ( C @ leq ) )
& ( D @ ( A @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( D @ ( C @ ( B @ ( A @ completion_conflict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_implies_leq) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
v1200 @ ( v0 @ ( v800 @ ( v400 @ completion_conflict ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odrl633) ).
thf(2,negated_conjecture,
~ ( v1200 @ ( v0 @ ( v800 @ ( v400 @ completion_conflict ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ( v1200 @ ( v0 @ ( v800 @ ( v400 @ completion_conflict ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,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(45,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(11,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(54,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(15,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(80,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_def) ).
thf(63,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)],[13]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ completion_compatible ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',completion_compat) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( C @ ( B @ ( A @ completion_compatible ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
v1200 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v1200) ).
thf(104,plain,
v1200 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,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(82,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(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/sandbox2/benchmark/theBenchmark.p',axis_compatible_def) ).
thf(30,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(26,axiom,
( ( v800 != v1200 )
& ( v400 != v1200 )
& ( v400 != v800 )
& ( v0 != v1200 )
& ( v0 != v800 )
& ( v0 != v400 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
thf(107,plain,
( ( v800 != v1200 )
& ( v400 != v1200 )
& ( v400 != v800 )
& ( v0 != v1200 )
& ( v0 != v800 )
& ( v0 != v400 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trichotomy) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_antisym) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,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(37,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
v800 @ ( v400 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v400_v800) ).
thf(106,plain,
v800 @ ( v400 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
v400 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v400) ).
thf(121,plain,
v400 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( A @ less ) )
& ( D @ ( A @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( D @ ( C @ ( A @ completion_compatible ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sharpness_compat) ).
thf(61,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( A @ less ) )
& ( D @ ( A @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( D @ ( C @ ( A @ completion_compatible ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,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(89,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,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(73,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)],[14]) ).
thf(24,axiom,
v1200 @ ( v800 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v800_v1200) ).
thf(105,plain,
v1200 @ ( v800 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive) ).
thf(39,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( A @ less ) )
& ( D @ ( A @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( D @ ( C @ ( B @ ( A @ completion_conflict ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sharpness_conflict) ).
thf(98,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( A @ less ) )
& ( D @ ( A @ leq ) )
& ( A @ ( C @ leq ) ) )
=> ( D @ ( C @ ( B @ ( A @ completion_conflict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
v800 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v800) ).
thf(103,plain,
v800 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
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(91,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(28,axiom,
v0 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v0) ).
thf(122,plain,
v0 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
v400 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v400) ).
thf(100,plain,
v400 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(123,plain,
$false,
inference(e,[status(thm)],[101,52,29,45,54,80,63,50,104,82,30,107,47,42,37,106,121,61,89,73,105,39,98,103,91,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT092+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.11 % 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
% 0.24/0.50 % Computer : n018.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.50 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Sat Sep 26 00:14:37 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 1.43/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.69 % [INFO] Parsing done (354ms).
% 2.35/1.71 % [INFO] Running in sequential loop mode.
% 3.48/2.31 % [INFO] eprover registered as external prover.
% 3.48/2.32 % [INFO] Scanning for conjecture ...
% 3.69/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 41 axioms. Running axiom selection ...
% 3.86/2.55 % [INFO] Axiom selection finished. Selected 26 axioms (removed 15 axioms).
% 4.08/2.64 % [INFO] Problem is first-order (TPTP FOF).
% 4.08/2.66 % [INFO] Type checking passed.
% 4.08/2.66 % [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 ...
% 7.13/3.87 % External prover 'e' found a proof!
% 7.13/3.87 % [INFO] Killing All external provers ...
% 7.13/3.87 % Time passed: 3158ms (effective reasoning time: 2147ms)
% 7.13/3.87 % 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)>
% 7.13/3.87 % Axioms used in derivation (26): ord_v0_v400, val_v1200, leq_antisym, ord_v400_v800, val_v0, irreflexive, transitive, ord_v800_v1200, less_implies_leq, in_ropen, completion_compat, sharpness_compat, leq_trans, leq_less_trans, val_v400, in_closed, in_lopen, distinct, less_leq_trans, completion_conflict, axis_compatible_def, trichotomy, in_open, sharpness_conflict, val_v800, leq_def
% 7.13/3.87 % No. of inferences in proof: 56
% 7.13/3.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3158 ms resp. 2147 ms w/o parsing
% 7.47/3.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.47/3.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------