%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT062+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 : 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 08:00:49 AM UTC 2026
% Result : Theorem 3.92s 1.80s
% Output : Refutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 161 ( 31 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 485 ( 27 ~; 10 |; 67 &; 327 @)
% ( 7 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 67 ( 0 ^; 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(organization_decl,type,
organization: $i > $o ).
thf(robust_position_decl,type,
robust_position: $i > $o ).
thf(has_endowment_decl,type,
has_endowment: $i > $o ).
thf(age_decl,type,
age: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(sigma_decl,type,
sigma: $i ).
thf(tau_decl,type,
tau: $i ).
thf(smaller_or_equal_decl,type,
smaller_or_equal: $i > $i > $o ).
thf(smaller_decl,type,
smaller: $i > $i > $o ).
thf(hazard_of_mortality_decl,type,
hazard_of_mortality: $i > $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(has_immunity_decl,type,
has_immunity: $i > $i > $o ).
thf(dissimilar_decl,type,
dissimilar: $i > $i > $i > $o ).
thf(is_aligned_decl,type,
is_aligned: $i > $i > $o ).
thf(positional_advantage_decl,type,
positional_advantage: $i > $i > $o ).
thf(very_low_decl,type,
very_low: $i ).
thf(low_decl,type,
low: $i ).
thf(mod1_decl,type,
mod1: $i ).
thf(mod2_decl,type,
mod2: $i ).
thf(high_decl,type,
high: $i ).
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(57,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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(60,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(9,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ has_endowment )
& ( A @ organization ) )
=> ~ ( B @ ( A @ has_immunity ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_1) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ has_endowment )
& ( A @ organization ) )
=> ~ ( B @ ( A @ has_immunity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(41,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(14,axiom,
! [A: $i,B: $i] :
( ( A @ organization )
=> ( ( ~ ( B @ ( A @ has_immunity ) )
=> ( ( ( ~ ( B @ ( A @ positional_advantage ) )
& ~ ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= high ) )
& ( ( ~ ( B @ ( A @ positional_advantage ) )
& ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= mod2 ) )
& ( ( ( B @ ( A @ positional_advantage ) )
& ~ ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= mod1 ) )
& ( ( ( B @ ( A @ positional_advantage ) )
& ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= low ) ) ) )
& ( ( B @ ( A @ has_immunity ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= very_low ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_17) ).
thf(105,plain,
! [A: $i,B: $i] :
( ( A @ organization )
=> ( ( ~ ( B @ ( A @ has_immunity ) )
=> ( ( ( ~ ( B @ ( A @ positional_advantage ) )
& ~ ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= high ) )
& ( ( ~ ( B @ ( A @ positional_advantage ) )
& ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= mod2 ) )
& ( ( ( B @ ( A @ positional_advantage ) )
& ~ ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= mod1 ) )
& ( ( ( B @ ( A @ positional_advantage ) )
& ( B @ ( A @ is_aligned ) ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= low ) ) ) )
& ( ( B @ ( A @ has_immunity ) )
=> ( ( B @ ( A @ hazard_of_mortality ) )
= very_low ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,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(91,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)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ( B @ ( A @ is_aligned ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_13) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ( B @ ( A @ is_aligned ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ smaller ) )
<=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller) ).
thf(51,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(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( sigma @ ( D @ ( A @ age ) @ greater ) )
& ( sigma @ ( C @ ( A @ age ) @ smaller_or_equal ) )
& ( sigma = tau )
& ( zero @ ( tau @ greater ) )
& ( zero @ ( sigma @ greater ) )
& ( ( B @ ( A @ age ) )
= zero )
& ~ ( A @ has_endowment )
& ( A @ robust_position )
& ( A @ organization ) )
=> ( ( ( C @ ( A @ hazard_of_mortality ) )
= ( B @ ( A @ hazard_of_mortality ) ) )
& ( C @ ( A @ hazard_of_mortality ) @ ( D @ ( A @ hazard_of_mortality ) @ smaller ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_8) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( sigma @ ( D @ ( A @ age ) @ greater ) )
& ( sigma @ ( C @ ( A @ age ) @ smaller_or_equal ) )
& ( sigma = tau )
& ( zero @ ( tau @ greater ) )
& ( zero @ ( sigma @ greater ) )
& ( ( B @ ( A @ age ) )
= zero )
& ~ ( A @ has_endowment )
& ( A @ robust_position )
& ( A @ organization ) )
=> ( ( ( C @ ( A @ hazard_of_mortality ) )
= ( B @ ( A @ hazard_of_mortality ) ) )
& ( C @ ( A @ hazard_of_mortality ) @ ( D @ ( A @ hazard_of_mortality ) @ smaller ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( sigma @ ( D @ ( A @ age ) @ greater ) )
& ( sigma @ ( C @ ( A @ age ) @ smaller_or_equal ) )
& ( sigma = tau )
& ( zero @ ( tau @ greater ) )
& ( zero @ ( sigma @ greater ) )
& ( ( B @ ( A @ age ) )
= zero )
& ~ ( A @ has_endowment )
& ( A @ robust_position )
& ( A @ organization ) )
=> ( ( ( C @ ( A @ hazard_of_mortality ) )
= ( B @ ( A @ hazard_of_mortality ) ) )
& ( C @ ( A @ hazard_of_mortality ) @ ( D @ ( A @ hazard_of_mortality ) @ smaller ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(31,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(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ dissimilar ) ) )
<=> ( ~ ( ( B @ ( A @ is_aligned ) )
<=> ( C @ ( A @ is_aligned ) ) )
& ( A @ organization ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_2) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( ( ( C @ ( A @ is_aligned ) )
=> ( B @ ( A @ is_aligned ) ) )
& ( ( B @ ( A @ is_aligned ) )
=> ( C @ ( A @ is_aligned ) ) ) )
& ( A @ organization ) )
=> ( C @ ( B @ ( A @ dissimilar ) ) ) )
& ( ( C @ ( B @ ( A @ dissimilar ) ) )
=> ( ~ ( ( ( C @ ( A @ is_aligned ) )
=> ( B @ ( A @ is_aligned ) ) )
& ( ( B @ ( A @ is_aligned ) )
=> ( C @ ( A @ is_aligned ) ) ) )
& ( A @ organization ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(62,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
| ( A = B )
| ( B @ ( A @ smaller ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
mod1 @ ( mod2 @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_19) ).
thf(122,plain,
mod1 @ ( mod2 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ( ( sigma @ ( C @ ( A @ age ) @ greater ) )
<=> ( C @ ( B @ ( A @ dissimilar ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_15) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ( ( ( C @ ( B @ ( A @ dissimilar ) ) )
=> ( sigma @ ( C @ ( A @ age ) @ greater ) ) )
& ( ( sigma @ ( C @ ( A @ age ) @ greater ) )
=> ( C @ ( B @ ( A @ dissimilar ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(126,plain,
$false,
inference(e,[status(thm)],[57,60,65,41,105,91,80,51,16,31,68,62,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT062+1 : TPTP v9.3.1. Released v2.4.0.
% 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
% 0.14/0.42 % Computer : n009.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 00:10:45 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.84 % [INFO] Parsing done (120ms).
% 0.91/0.85 % [INFO] Running in sequential loop mode.
% 1.51/1.05 % [INFO] eprover registered as external prover.
% 1.51/1.05 % [INFO] Scanning for conjecture ...
% 1.51/1.12 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 1.79/1.17 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.96/1.20 % [INFO] Problem is first-order (TPTP FOF).
% 1.96/1.21 % [INFO] Type checking passed.
% 1.96/1.22 % [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 ...
% 3.92/1.80 % External prover 'e' found a proof!
% 3.92/1.80 % [INFO] Killing All external provers ...
% 3.92/1.80 % Time passed: 1294ms (effective reasoning time: 949ms)
% 3.92/1.80 % 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)>
% 3.92/1.80 % Axioms used in derivation (13): definition_2, assumption_17, assumption_19, assumption_13, definition_4, definition_smaller_or_equal, definition_smaller, assumption_15, meaning_postulate_greater_comparable, meaning_postulate_greater_strict, definition_greater_or_equal, meaning_postulate_greater_transitive, assumption_1
% 3.92/1.80 % No. of inferences in proof: 30
% 3.92/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1294 ms resp. 949 ms w/o parsing
% 4.23/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.23/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------