%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n003.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 08:00:48 AM UTC 2026
% Result : Theorem 4.27s 2.55s
% Output : Refutation 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 11 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 251 ( 13 ~; 10 |; 27 &; 169 @)
% ( 5 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 39 !; 3 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(organization_decl,type,
organization: $i > $o ).
thf(age_decl,type,
age: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(sigma_decl,type,
sigma: $i ).
thf(tau_decl,type,
tau: $i ).
thf(fragile_position_decl,type,
fragile_position: $i > $o ).
thf(robust_position_decl,type,
robust_position: $i > $o ).
thf(smaller_or_equal_decl,type,
smaller_or_equal: $i > $i > $o ).
thf(smaller_decl,type,
smaller: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(positional_advantage_decl,type,
positional_advantage: $i > $i > $o ).
thf(1,conjecture,
! [A: $i] :
( ( ( zero @ ( tau @ greater_or_equal ) )
& ( zero @ ( sigma @ greater_or_equal ) )
& ? [B: $i] :
( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ~ ( ( A @ robust_position )
& ( A @ fragile_position ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( zero @ ( tau @ greater_or_equal ) )
& ( zero @ ( sigma @ greater_or_equal ) )
& ? [B: $i] :
( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ~ ( ( A @ robust_position )
& ( A @ fragile_position ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i] :
( ( ( zero @ ( tau @ greater_or_equal ) )
& ( zero @ ( sigma @ greater_or_equal ) )
& ? [B: $i] :
( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ~ ( ( A @ robust_position )
& ( A @ fragile_position ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ smaller ) )
<=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ greater ) )
=> ( B @ ( A @ smaller ) ) )
& ( ( B @ ( A @ smaller ) )
=> ( A @ ( B @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ robust_position )
<=> ! [B: $i] :
( ( ( tau @ ( B @ ( A @ age ) @ greater ) )
=> ( B @ ( A @ positional_advantage ) ) )
& ( ( tau @ ( B @ ( A @ age ) @ smaller_or_equal ) )
=> ~ ( B @ ( A @ positional_advantage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_4) ).
thf(68,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( ( tau @ ( B @ ( A @ age ) @ greater ) )
=> ( B @ ( A @ positional_advantage ) ) )
& ( ( tau @ ( B @ ( A @ age ) @ smaller_or_equal ) )
=> ~ ( B @ ( A @ positional_advantage ) ) ) )
=> ( A @ robust_position ) )
& ( ( A @ robust_position )
=> ! [B: $i] :
( ( ( tau @ ( B @ ( A @ age ) @ greater ) )
=> ( B @ ( A @ positional_advantage ) ) )
& ( ( tau @ ( B @ ( A @ age ) @ smaller_or_equal ) )
=> ~ ( B @ ( A @ positional_advantage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ smaller_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ smaller ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller_or_equal) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ smaller ) ) )
=> ( B @ ( A @ smaller_or_equal ) ) )
& ( ( B @ ( A @ smaller_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ smaller ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meaning_postulate_greater_strict) ).
thf(46,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ fragile_position )
<=> ! [B: $i] :
( ( ( sigma @ ( B @ ( A @ age ) @ greater ) )
=> ~ ( B @ ( A @ positional_advantage ) ) )
& ( ( sigma @ ( B @ ( A @ age ) @ smaller_or_equal ) )
=> ( B @ ( A @ positional_advantage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_3) ).
thf(54,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( ( sigma @ ( B @ ( A @ age ) @ greater ) )
=> ~ ( B @ ( A @ positional_advantage ) ) )
& ( ( sigma @ ( B @ ( A @ age ) @ smaller_or_equal ) )
=> ( B @ ( A @ positional_advantage ) ) ) )
=> ( A @ fragile_position ) )
& ( ( A @ fragile_position )
=> ! [B: $i] :
( ( ( sigma @ ( B @ ( A @ age ) @ greater ) )
=> ~ ( B @ ( A @ positional_advantage ) ) )
& ( ( sigma @ ( B @ ( A @ age ) @ smaller_or_equal ) )
=> ( B @ ( A @ positional_advantage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meaning_postulate_greater_transitive) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_greater_or_equal) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ greater ) ) )
=> ( B @ ( A @ greater_or_equal ) ) )
& ( ( B @ ( A @ greater_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
| ( A = B )
| ( B @ ( A @ smaller ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meaning_postulate_greater_comparable) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
| ( A = B )
| ( B @ ( A @ smaller ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(82,plain,
$false,
inference(e,[status(thm)],[11,40,68,20,46,54,49,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % 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
% 0.14/0.39 % Computer : n003.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 00:12:08 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.19 % [INFO] Parsing done (198ms).
% 1.47/1.20 % [INFO] Running in sequential loop mode.
% 2.19/1.61 % [INFO] eprover registered as external prover.
% 2.19/1.62 % [INFO] Scanning for conjecture ...
% 2.37/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.37/1.77 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.37/1.79 % [INFO] Problem is first-order (TPTP FOF).
% 2.56/1.80 % [INFO] Type checking passed.
% 2.56/1.80 % [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 ...
% 4.27/2.55 % External prover 'e' found a proof!
% 4.27/2.55 % [INFO] Killing All external provers ...
% 4.27/2.55 % Time passed: 2007ms (effective reasoning time: 1340ms)
% 4.27/2.55 % 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)>
% 4.27/2.55 % Axioms used in derivation (8): definition_4, definition_smaller_or_equal, definition_smaller, definition_3, meaning_postulate_greater_comparable, meaning_postulate_greater_transitive, meaning_postulate_greater_strict, definition_greater_or_equal
% 4.27/2.55 % No. of inferences in proof: 20
% 4.27/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2007 ms resp. 1340 ms w/o parsing
% 4.56/2.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.56/2.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------