%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT084+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 : n012.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 2.33s 11.46s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 58 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 468 ( 22 ~; 7 |; 61 &; 339 @)
% ( 8 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 ^; 93 !; 15 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_lopen_decl,type,
in_lopen: $i > $i > $i > $o ).
thf(v0_decl,type,
v0: $i ).
thf(v600_decl,type,
v600: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(v400_decl,type,
v400: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(v200_decl,type,
v200: $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(in_ropen_decl,type,
in_ropen: $i > $i > $i > $o ).
thf(in_open_decl,type,
in_open: $i > $i > $i > $o ).
thf(16,axiom,
v600 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v600) ).
thf(88,plain,
v600 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
v400 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v400) ).
thf(142,plain,
v400 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,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(78,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,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(70,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(27,axiom,
v200 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v200) ).
thf(141,plain,
v200 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
v600 @ ( v200 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v200_v600) ).
thf(129,plain,
v600 @ ( v200 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(20,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(105,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)],[20]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_def) ).
thf(112,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)],[21]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trichotomy) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
| ( A = B )
| ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
v400 @ ( v200 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v200_v400) ).
thf(67,plain,
v400 @ ( v200 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
v600 @ ( v400 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v400_v600) ).
thf(87,plain,
v600 @ ( v400 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_antisym) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
~ ? [A: $i,B: $i,C: $i] :
( ( C @ ( v200 @ leq ) )
& ( v200 @ ( v0 @ ( C @ in_lopen ) ) )
& ( B @ ( v400 @ less ) )
& ( v400 @ ( v0 @ ( B @ in_lopen ) ) )
& ( A @ ( v600 @ leq ) )
& ( v600 @ ( v0 @ ( A @ in_lopen ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odrl432) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i,B: $i,C: $i] :
( ( C @ ( v200 @ leq ) )
& ( v200 @ ( v0 @ ( C @ in_lopen ) ) )
& ( B @ ( v400 @ less ) )
& ( v400 @ ( v0 @ ( B @ in_lopen ) ) )
& ( A @ ( v600 @ leq ) )
& ( v600 @ ( v0 @ ( A @ in_lopen ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ~ ? [A: $i,B: $i,C: $i] :
( ( C @ ( v200 @ leq ) )
& ( v200 @ ( v0 @ ( C @ in_lopen ) ) )
& ( B @ ( v400 @ less ) )
& ( v400 @ ( v0 @ ( B @ in_lopen ) ) )
& ( A @ ( v600 @ leq ) )
& ( v600 @ ( v0 @ ( A @ in_lopen ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,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(132,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)],[25]) ).
thf(17,axiom,
v600 @ ( v0 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v600) ).
thf(89,plain,
v600 @ ( v0 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
( ( v400 != v600 )
& ( v200 != v600 )
& ( v200 != v400 )
& ( v0 != v600 )
& ( v0 != v400 )
& ( v0 != v200 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
thf(91,plain,
( ( v400 != v600 )
& ( v200 != v600 )
& ( v200 != v400 )
& ( v0 != v600 )
& ( v0 != v400 )
& ( v0 != v200 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
v400 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v400) ).
thf(66,plain,
v400 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,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(130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less ) )
& ( B @ ( A @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,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(80,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)],[14]) ).
thf(11,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive) ).
thf(72,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,axiom,
v0 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v0) ).
thf(143,plain,
v0 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
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(40,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(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/sandbox2/benchmark/theBenchmark.p',axis_conflict_def) ).
thf(55,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(26,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(139,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
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/sandbox2/benchmark/theBenchmark.p',axis_subsumes_def) ).
thf(47,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(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_implies_leq) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
v200 @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v200) ).
thf(90,plain,
v200 @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,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(122,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(144,plain,
$false,
inference(e,[status(thm)],[88,142,78,70,141,129,105,112,63,67,87,75,30,132,89,91,66,130,80,72,143,40,55,139,47,68,90,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT084+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % 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
% 0.07/10.34 % Computer : n012.cluster.edu
% 0.07/10.34 % Model : x86_64 x86_64
% 0.07/10.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.34 % Memory : 8046.5625MB
% 0.07/10.34 % OS : Linux 6.8.0-71-generic
% 0.07/10.34 % CPULimit : 300
% 0.07/10.34 % WCLimit : 300
% 0.07/10.34 % DateTime : Sat Sep 26 00:12:46 UTC 2026
% 0.07/10.34 % CPUTime :
% 0.07/10.34 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
% 0.10/10.62 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.10/10.72 % [INFO] Parsing done (102ms).
% 0.10/10.73 % [INFO] Running in sequential loop mode.
% 0.10/10.91 % [INFO] eprover registered as external prover.
% 0.10/10.92 % [INFO] Scanning for conjecture ...
% 0.10/10.97 % [INFO] Found a conjecture (or negated_conjecture) and 38 axioms. Running axiom selection ...
% 0.10/11.01 % [INFO] Axiom selection finished. Selected 27 axioms (removed 11 axioms).
% 1.34/11.03 % [INFO] Problem is first-order (TPTP FOF).
% 1.34/11.04 % [INFO] Type checking passed.
% 1.34/11.04 % [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 ...
% 2.33/11.45 % External prover 'e' found a proof!
% 2.33/11.46 % [INFO] Killing All external provers ...
% 2.33/11.46 % Time passed: 1033ms (effective reasoning time: 722ms)
% 2.33/11.46 % 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)>
% 2.33/11.46 % Axioms used in derivation (27): ord_v0_v400, ord_v200_v600, leq_antisym, val_v600, 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
% 2.33/11.46 % No. of inferences in proof: 58
% 2.33/11.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1033 ms resp. 722 ms w/o parsing
% 2.33/11.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.33/11.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------