%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 : Wed Oct 7 10:31:29 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 105 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 713 ( 189 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1399 ( 179 ~; 248 |; 0 &; 972 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 169 ( 0 ^; 169 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_constant,type,
constant: $i > $o ).
thf(tp_decreases,type,
decreases: $i > $o ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_disbanding_rate,type,
disbanding_rate: $i > $i > $i ).
thf(tp_efficient_producers,type,
efficient_producers: $i ).
thf(tp_environment,type,
environment: $i > $o ).
thf(tp_equilibrium,type,
equilibrium: $i > $i ).
thf(tp_first_movers,type,
first_movers: $i ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_greater_or_equal,type,
greater_or_equal: $i > $i > $o ).
thf(tp_in_environment,type,
in_environment: $i > $i > $o ).
thf(tp_increases,type,
increases: $i > $o ).
thf(tp_number_of_organizations,type,
number_of_organizations: $i > $i > $i ).
thf(tp_resources,type,
resources: $i > $i > $i ).
thf(tp_sk1,type,
sk1: $i ).
thf(tp_sk2,type,
sk2: $i ).
thf(tp_subpopulations,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( greater @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_30) ).
thf(2,axiom,
! [A: $i] :
( ~ ( increases @ A )
| ~ ( decreases @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_increase_not_decrease_29) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_not_empty_28) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_in_environment_27) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( resources @ A @ B ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_34) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( decreases @ ( resources @ A @ B ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_33) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ( greater @ ( equilibrium @ A ) @ B )
| ( constant @ ( resources @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_32) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ~ ( greater @ ( equilibrium @ A ) @ B )
| ( decreases @ ( resources @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_31) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
decreases @ ( difference @ ( disbanding_rate @ first_movers @ sk2 ) @ ( disbanding_rate @ efficient_producers @ sk2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_37) ).
thf(12,negated_conjecture,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_36) ).
thf(13,negated_conjecture,
environment @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_35) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( greater @ A @ B )
| ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i] :
( ~ ( increases @ A )
| ~ ( decreases @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( resources @ A @ B ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( decreases @ ( resources @ A @ B ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ( greater @ ( equilibrium @ A ) @ B )
| ( constant @ ( resources @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ~ ( greater @ ( equilibrium @ A ) @ B )
| ( decreases @ ( resources @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ sk2 ) @ ( disbanding_rate @ efficient_producers @ sk2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(24,plain,
( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(25,plain,
( ( environment @ sk1 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( A = B )
| ( greater @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(28,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(29,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(30,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( resources @ A @ B ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(31,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( decreases @ ( resources @ A @ B ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(32,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ( constant @ ( resources @ A @ B ) )
| ( greater @ ( equilibrium @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(33,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ~ ( greater @ ( equilibrium @ A ) @ B )
| ( decreases @ ( resources @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(34,plain,
( ( environment @ sk1 )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(35,plain,
( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ sk2 ) @ ( disbanding_rate @ efficient_producers @ sk2 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(37,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ~ ( greater @ ( equilibrium @ A ) @ B )
| ( decreases @ ( resources @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(38,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ( constant @ ( resources @ A @ B ) )
| ( greater @ ( equilibrium @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(39,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( decreases @ ( resources @ A @ B ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(40,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( resources @ A @ B ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(41,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(42,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ! [A: $i] :
( ~ ( increases @ A )
| ~ ( decreases @ A ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( A = B )
| ( greater @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(45,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[26]) ).
thf(46,plain,
! [SV1: $i] :
( ( ~ ( environment @ SV1 )
| ! [SY15: $i] :
( ~ ( in_environment @ SV1 @ SY15 )
| ~ ( greater @ ( number_of_organizations @ SV1 @ SY15 ) @ zero )
| ~ ( greater @ ( equilibrium @ SV1 ) @ SY15 )
| ( decreases @ ( resources @ SV1 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(47,plain,
! [SV2: $i] :
( ( ~ ( environment @ SV2 )
| ! [SY16: $i] :
( ~ ( in_environment @ SV2 @ SY16 )
| ~ ( greater @ ( number_of_organizations @ SV2 @ SY16 ) @ zero )
| ( constant @ ( resources @ SV2 @ SY16 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(48,plain,
! [SV3: $i] :
( ( ~ ( environment @ SV3 )
| ! [SY17: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY17 )
| ~ ( decreases @ ( resources @ SV3 @ SY17 ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SY17 ) @ ( disbanding_rate @ efficient_producers @ SY17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV4: $i] :
( ( ~ ( environment @ SV4 )
| ! [SY18: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SY18 )
| ~ ( constant @ ( resources @ SV4 @ SY18 ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SY18 ) @ ( disbanding_rate @ efficient_producers @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV5: $i] :
( ( ~ ( environment @ SV5 )
| ! [SY19: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV5 @ SY19 )
| ( in_environment @ SV5 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV6: $i] :
( ( ~ ( environment @ SV6 )
| ! [SY20: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY20 )
| ( greater @ ( number_of_organizations @ SV6 @ SY20 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV7: $i] :
( ( ~ ( increases @ SV7 )
| ~ ( decreases @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV8: $i] :
( ( ! [SY21: $i] :
( ~ ( greater_or_equal @ SV8 @ SY21 )
| ( SV8 = SY21 )
| ( greater @ SV8 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(54,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV1: $i] :
( ( ( ~ ( environment @ SV1 ) )
= $true )
| ( ( ! [SY15: $i] :
( ~ ( in_environment @ SV1 @ SY15 )
| ~ ( greater @ ( number_of_organizations @ SV1 @ SY15 ) @ zero )
| ~ ( greater @ ( equilibrium @ SV1 ) @ SY15 )
| ( decreases @ ( resources @ SV1 @ SY15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( ~ ( environment @ SV2 ) )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( in_environment @ SV2 @ SY16 )
| ~ ( greater @ ( number_of_organizations @ SV2 @ SY16 ) @ zero )
| ( constant @ ( resources @ SV2 @ SY16 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV3: $i] :
( ( ( ~ ( environment @ SV3 ) )
= $true )
| ( ( ! [SY17: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY17 )
| ~ ( decreases @ ( resources @ SV3 @ SY17 ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SY17 ) @ ( disbanding_rate @ efficient_producers @ SY17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( ~ ( environment @ SV4 ) )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SY18 )
| ~ ( constant @ ( resources @ SV4 @ SY18 ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SY18 ) @ ( disbanding_rate @ efficient_producers @ SY18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( ~ ( environment @ SV5 ) )
= $true )
| ( ( ! [SY19: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV5 @ SY19 )
| ( in_environment @ SV5 @ SY19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( ~ ( environment @ SV6 ) )
= $true )
| ( ( ! [SY20: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY20 )
| ( greater @ ( number_of_organizations @ SV6 @ SY20 ) @ zero ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV7: $i] :
( ( ( ~ ( increases @ SV7 ) )
= $true )
| ( ( ~ ( decreases @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV9: $i,SV8: $i] :
( ( ~ ( greater_or_equal @ SV8 @ SV9 )
| ( SV8 = SV9 )
| ( greater @ SV8 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV1: $i] :
( ( ( environment @ SV1 )
= $false )
| ( ( ! [SY15: $i] :
( ~ ( in_environment @ SV1 @ SY15 )
| ~ ( greater @ ( number_of_organizations @ SV1 @ SY15 ) @ zero )
| ~ ( greater @ ( equilibrium @ SV1 ) @ SY15 )
| ( decreases @ ( resources @ SV1 @ SY15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( environment @ SV2 )
= $false )
| ( ( ! [SY16: $i] :
( ~ ( in_environment @ SV2 @ SY16 )
| ~ ( greater @ ( number_of_organizations @ SV2 @ SY16 ) @ zero )
| ( constant @ ( resources @ SV2 @ SY16 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV3: $i] :
( ( ( environment @ SV3 )
= $false )
| ( ( ! [SY17: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY17 )
| ~ ( decreases @ ( resources @ SV3 @ SY17 ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SY17 ) @ ( disbanding_rate @ efficient_producers @ SY17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV4: $i] :
( ( ( environment @ SV4 )
= $false )
| ( ( ! [SY18: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SY18 )
| ~ ( constant @ ( resources @ SV4 @ SY18 ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SY18 ) @ ( disbanding_rate @ efficient_producers @ SY18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( environment @ SV5 )
= $false )
| ( ( ! [SY19: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV5 @ SY19 )
| ( in_environment @ SV5 @ SY19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV6: $i] :
( ( ( environment @ SV6 )
= $false )
| ( ( ! [SY20: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY20 )
| ( greater @ ( number_of_organizations @ SV6 @ SY20 ) @ zero ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV7: $i] :
( ( ( increases @ SV7 )
= $false )
| ( ( ~ ( decreases @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV9: $i,SV8: $i] :
( ( ( ~ ( greater_or_equal @ SV8 @ SV9 ) )
= $true )
| ( ( ( SV8 = SV9 )
| ( greater @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV10: $i,SV1: $i] :
( ( ( ~ ( in_environment @ SV1 @ SV10 )
| ~ ( greater @ ( number_of_organizations @ SV1 @ SV10 ) @ zero )
| ~ ( greater @ ( equilibrium @ SV1 ) @ SV10 )
| ( decreases @ ( resources @ SV1 @ SV10 ) ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV11: $i,SV2: $i] :
( ( ( ~ ( in_environment @ SV2 @ SV11 )
| ~ ( greater @ ( number_of_organizations @ SV2 @ SV11 ) @ zero )
| ( constant @ ( resources @ SV2 @ SV11 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SV11 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV12 )
| ~ ( decreases @ ( resources @ SV3 @ SV12 ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SV12 ) @ ( disbanding_rate @ efficient_producers @ SV12 ) ) ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SV13 )
| ~ ( constant @ ( resources @ SV4 @ SV13 ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SV13 ) @ ( disbanding_rate @ efficient_producers @ SV13 ) ) ) )
= $true )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV5 @ SV14 )
| ( in_environment @ SV5 @ SV14 ) )
= $true )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV15 )
| ( greater @ ( number_of_organizations @ SV6 @ SV15 ) @ zero ) )
= $true )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV7: $i] :
( ( ( decreases @ SV7 )
= $false )
| ( ( increases @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV9: $i,SV8: $i] :
( ( ( greater_or_equal @ SV8 @ SV9 )
= $false )
| ( ( ( SV8 = SV9 )
| ( greater @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV10: $i,SV1: $i] :
( ( ( ~ ( in_environment @ SV1 @ SV10 ) )
= $true )
| ( ( ~ ( greater @ ( number_of_organizations @ SV1 @ SV10 ) @ zero )
| ~ ( greater @ ( equilibrium @ SV1 ) @ SV10 )
| ( decreases @ ( resources @ SV1 @ SV10 ) ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV11: $i,SV2: $i] :
( ( ( ~ ( in_environment @ SV2 @ SV11 ) )
= $true )
| ( ( ~ ( greater @ ( number_of_organizations @ SV2 @ SV11 ) @ zero )
| ( constant @ ( resources @ SV2 @ SV11 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SV11 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV12 ) )
= $true )
| ( ( ~ ( decreases @ ( resources @ SV3 @ SV12 ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SV12 ) @ ( disbanding_rate @ efficient_producers @ SV12 ) ) ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( constant @ ( resources @ SV4 @ SV13 ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SV13 ) @ ( disbanding_rate @ efficient_producers @ SV13 ) ) ) )
= $true )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV5 @ SV14 ) )
= $true )
| ( ( in_environment @ SV5 @ SV14 )
= $true )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV15 ) )
= $true )
| ( ( greater @ ( number_of_organizations @ SV6 @ SV15 ) @ zero )
= $true )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV9: $i,SV8: $i] :
( ( ( SV8 = SV9 )
= $true )
| ( ( greater @ SV8 @ SV9 )
= $true )
| ( ( greater_or_equal @ SV8 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV10: $i,SV1: $i] :
( ( ( in_environment @ SV1 @ SV10 )
= $false )
| ( ( ~ ( greater @ ( number_of_organizations @ SV1 @ SV10 ) @ zero )
| ~ ( greater @ ( equilibrium @ SV1 ) @ SV10 )
| ( decreases @ ( resources @ SV1 @ SV10 ) ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV11: $i,SV2: $i] :
( ( ( in_environment @ SV2 @ SV11 )
= $false )
| ( ( ~ ( greater @ ( number_of_organizations @ SV2 @ SV11 ) @ zero )
| ( constant @ ( resources @ SV2 @ SV11 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SV11 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV12: $i,SV3: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV12 )
= $false )
| ( ( ~ ( decreases @ ( resources @ SV3 @ SV12 ) )
| ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SV12 ) @ ( disbanding_rate @ efficient_producers @ SV12 ) ) ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV13: $i,SV4: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SV13 )
= $false )
| ( ( ~ ( constant @ ( resources @ SV4 @ SV13 ) )
| ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SV13 ) @ ( disbanding_rate @ efficient_producers @ SV13 ) ) ) )
= $true )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV14: $i,SV5: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV5 @ SV14 )
= $false )
| ( ( in_environment @ SV5 @ SV14 )
= $true )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV15: $i,SV6: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV15 )
= $false )
| ( ( greater @ ( number_of_organizations @ SV6 @ SV15 ) @ zero )
= $true )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV10: $i,SV1: $i] :
( ( ( ~ ( greater @ ( number_of_organizations @ SV1 @ SV10 ) @ zero ) )
= $true )
| ( ( ~ ( greater @ ( equilibrium @ SV1 ) @ SV10 )
| ( decreases @ ( resources @ SV1 @ SV10 ) ) )
= $true )
| ( ( in_environment @ SV1 @ SV10 )
= $false )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV11: $i,SV2: $i] :
( ( ( ~ ( greater @ ( number_of_organizations @ SV2 @ SV11 ) @ zero ) )
= $true )
| ( ( ( constant @ ( resources @ SV2 @ SV11 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SV11 ) )
= $true )
| ( ( in_environment @ SV2 @ SV11 )
= $false )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( decreases @ ( resources @ SV3 @ SV12 ) ) )
= $true )
| ( ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SV12 ) @ ( disbanding_rate @ efficient_producers @ SV12 ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV12 )
= $false )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( constant @ ( resources @ SV4 @ SV13 ) ) )
= $true )
| ( ( ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SV13 ) @ ( disbanding_rate @ efficient_producers @ SV13 ) ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SV13 )
= $false )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV10: $i,SV1: $i] :
( ( ( greater @ ( number_of_organizations @ SV1 @ SV10 ) @ zero )
= $false )
| ( ( ~ ( greater @ ( equilibrium @ SV1 ) @ SV10 )
| ( decreases @ ( resources @ SV1 @ SV10 ) ) )
= $true )
| ( ( in_environment @ SV1 @ SV10 )
= $false )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV11: $i,SV2: $i] :
( ( ( greater @ ( number_of_organizations @ SV2 @ SV11 ) @ zero )
= $false )
| ( ( ( constant @ ( resources @ SV2 @ SV11 ) )
| ( greater @ ( equilibrium @ SV2 ) @ SV11 ) )
= $true )
| ( ( in_environment @ SV2 @ SV11 )
= $false )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV12: $i,SV3: $i] :
( ( ( decreases @ ( resources @ SV3 @ SV12 ) )
= $false )
| ( ( increases @ ( difference @ ( disbanding_rate @ first_movers @ SV12 ) @ ( disbanding_rate @ efficient_producers @ SV12 ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV12 )
= $false )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV13: $i,SV4: $i] :
( ( ( constant @ ( resources @ SV4 @ SV13 ) )
= $false )
| ( ( ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SV13 ) @ ( disbanding_rate @ efficient_producers @ SV13 ) ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SV13 )
= $false )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV10: $i,SV1: $i] :
( ( ( ~ ( greater @ ( equilibrium @ SV1 ) @ SV10 ) )
= $true )
| ( ( decreases @ ( resources @ SV1 @ SV10 ) )
= $true )
| ( ( greater @ ( number_of_organizations @ SV1 @ SV10 ) @ zero )
= $false )
| ( ( in_environment @ SV1 @ SV10 )
= $false )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV11: $i,SV2: $i] :
( ( ( constant @ ( resources @ SV2 @ SV11 ) )
= $true )
| ( ( greater @ ( equilibrium @ SV2 ) @ SV11 )
= $true )
| ( ( greater @ ( number_of_organizations @ SV2 @ SV11 ) @ zero )
= $false )
| ( ( in_environment @ SV2 @ SV11 )
= $false )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV4: $i,SV13: $i] :
( ( ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ SV13 ) @ ( disbanding_rate @ efficient_producers @ SV13 ) ) )
= $false )
| ( ( constant @ ( resources @ SV4 @ SV13 ) )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV4 @ SV13 )
= $false )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV10: $i,SV1: $i] :
( ( ( greater @ ( equilibrium @ SV1 ) @ SV10 )
= $false )
| ( ( decreases @ ( resources @ SV1 @ SV10 ) )
= $true )
| ( ( greater @ ( number_of_organizations @ SV1 @ SV10 ) @ zero )
= $false )
| ( ( in_environment @ SV1 @ SV10 )
= $false )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,103,102,101,98,91,90,85,77,54,36,35]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 12:42:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.27
% 0.07/0.27 No.of.Axioms: 11
% 0.07/0.27
% 0.07/0.27 Length.of.Defs: 0
% 0.07/0.27
% 0.07/0.27 Contains.Choice.Funs: false
% 0.07/0.27 ..
% 0.07/0.27
% 0.07/0.27 ********************************
% 0.07/0.27 * All subproblems solved! *
% 0.07/0.27 ********************************
% 0.07/0.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.27
% 0.07/0.27 %**** Beginning of derivation protocol ****
% 0.07/0.27 % SZS output start CNFRefutation
% See solution above
% 0.07/0.27
% 0.07/0.27 %**** End of derivation protocol ****
% 0.07/0.27 %**** no. of clauses in derivation: 105 ****
% 0.07/0.27 %**** clause counter: 104 ****
% 0.07/0.27
% 0.07/0.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------