%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT061+1 : TPTP v9.3.1. Released v2.4.0.
% 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 08:00:48 AM UTC 2026
% Result : Theorem 2.61s 1.57s
% Output : Refutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 38 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 28 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 489 ( 27 ~; 10 |; 61 &; 337 @)
% ( 7 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 67 ( 0 ^; 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(organization_decl,type,
organization: $i > $o ).
thf(fragile_position_decl,type,
fragile_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(smaller_or_equal_decl,type,
smaller_or_equal: $i > $i > $o ).
thf(hazard_of_mortality_decl,type,
hazard_of_mortality: $i > $i > $i ).
thf(has_immunity_decl,type,
has_immunity: $i > $i > $o ).
thf(very_low_decl,type,
very_low: $i ).
thf(is_aligned_decl,type,
is_aligned: $i > $i > $o ).
thf(positional_advantage_decl,type,
positional_advantage: $i > $i > $o ).
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(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(dissimilar_decl,type,
dissimilar: $i > $i > $i > $o ).
thf(smaller_decl,type,
smaller: $i > $i > $o ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',definition_3) ).
thf(69,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)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_greater_or_equal) ).
thf(56,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)],[8]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( sigma @ ( D @ ( A @ age ) @ greater ) )
& ( sigma @ ( C @ ( A @ age ) @ smaller_or_equal ) )
& ( zero @ ( sigma @ greater ) )
& ( ( B @ ( A @ age ) )
= zero )
& ~ ( A @ has_endowment )
& ( A @ fragile_position )
& ( A @ organization ) )
=> ( ( ( C @ ( A @ hazard_of_mortality ) )
= ( B @ ( A @ hazard_of_mortality ) ) )
& ( C @ ( A @ hazard_of_mortality ) @ ( D @ ( A @ hazard_of_mortality ) @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_7) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( sigma @ ( D @ ( A @ age ) @ greater ) )
& ( sigma @ ( C @ ( A @ age ) @ smaller_or_equal ) )
& ( zero @ ( sigma @ greater ) )
& ( ( B @ ( A @ age ) )
= zero )
& ~ ( A @ has_endowment )
& ( A @ fragile_position )
& ( A @ organization ) )
=> ( ( ( C @ ( A @ hazard_of_mortality ) )
= ( B @ ( A @ hazard_of_mortality ) ) )
& ( C @ ( A @ hazard_of_mortality ) @ ( D @ ( A @ hazard_of_mortality ) @ greater ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( sigma @ ( D @ ( A @ age ) @ greater ) )
& ( sigma @ ( C @ ( A @ age ) @ smaller_or_equal ) )
& ( zero @ ( sigma @ greater ) )
& ( ( B @ ( A @ age ) )
= zero )
& ~ ( A @ has_endowment )
& ( A @ fragile_position )
& ( A @ organization ) )
=> ( ( ( C @ ( A @ hazard_of_mortality ) )
= ( B @ ( A @ hazard_of_mortality ) ) )
& ( C @ ( A @ hazard_of_mortality ) @ ( D @ ( A @ hazard_of_mortality ) @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ smaller ) )
<=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller) ).
thf(117,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)],[16]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ has_endowment )
& ( A @ organization ) )
=> ~ ( B @ ( A @ has_immunity ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_1) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ has_endowment )
& ( A @ organization ) )
=> ~ ( B @ ( A @ has_immunity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',assumption_17) ).
thf(32,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)],[3]) ).
thf(4,axiom,
low @ ( mod2 @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_18e) ).
thf(49,plain,
low @ ( mod2 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
low @ ( mod1 @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_18b) ).
thf(98,plain,
low @ ( mod1 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_strict) ).
thf(66,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
| ( A = B )
| ( B @ ( A @ smaller ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_comparable) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
| ( A = B )
| ( B @ ( A @ smaller ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ( B @ ( A @ is_aligned ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_13) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ age ) )
= zero )
& ( A @ organization ) )
=> ( B @ ( A @ is_aligned ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',assumption_15) ).
thf(99,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)],[14]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_transitive) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ dissimilar ) ) )
<=> ( ~ ( ( B @ ( A @ is_aligned ) )
<=> ( C @ ( A @ is_aligned ) ) )
& ( A @ organization ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_2) ).
thf(83,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)],[11]) ).
thf(5,axiom,
very_low @ ( low @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_18c) ).
thf(50,plain,
very_low @ ( low @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
mod2 @ ( high @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_18d) ).
thf(127,plain,
mod2 @ ( high @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ smaller_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ smaller ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller_or_equal) ).
thf(107,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)],[15]) ).
thf(18,axiom,
mod1 @ ( high @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_18a) ).
thf(126,plain,
mod1 @ ( high @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(137,plain,
$false,
inference(e,[status(thm)],[69,56,20,117,53,32,49,98,66,123,95,99,51,83,50,127,107,126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT061+1 : TPTP v9.3.1. Released v2.4.0.
% 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
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Sat Sep 26 00:10:35 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 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
% 0.50/0.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.74 % [INFO] Parsing done (107ms).
% 0.65/0.75 % [INFO] Running in sequential loop mode.
% 1.07/0.95 % [INFO] eprover registered as external prover.
% 1.07/0.96 % [INFO] Scanning for conjecture ...
% 1.32/1.03 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 1.32/1.07 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.32/1.09 % [INFO] Problem is first-order (TPTP FOF).
% 1.32/1.10 % [INFO] Type checking passed.
% 1.32/1.10 % [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 ...
% 2.61/1.57 % External prover 'e' found a proof!
% 2.61/1.57 % [INFO] Killing All external provers ...
% 2.61/1.57 % Time passed: 1176ms (effective reasoning time: 814ms)
% 2.61/1.57 % 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)>
% 2.61/1.57 % Axioms used in derivation (17): definition_2, assumption_18c, assumption_17, assumption_18b, assumption_13, assumption_18d, definition_smaller, definition_3, meaning_postulate_greater_comparable, meaning_postulate_greater_strict, definition_greater_or_equal, assumption_18a, definition_smaller_or_equal, assumption_18e, assumption_15, meaning_postulate_greater_transitive, assumption_1
% 2.61/1.57 % No. of inferences in proof: 38
% 2.61/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1176 ms resp. 814 ms w/o parsing
% 2.89/1.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.89/1.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------