%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : MGT036-3 : 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 : n019.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 10:31:35 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.22s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 82 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 520 ( 129 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1097 ( 147 ~; 180 |; 0 &; 770 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 228 ( 0 ^; 228 !; 0 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_efficient_producers,type,
efficient_producers: $i ).
thf(tp_environment,type,
environment: $i > $o ).
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_growth_rate,type,
growth_rate: $i > $i > $i ).
thf(tp_outcompetes,type,
outcompetes: $i > $i > $i > $o ).
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,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ( subpopulations @ C @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
thf(2,axiom,
greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_8) ).
thf(3,axiom,
greater_or_equal @ ( growth_rate @ first_movers @ sk2 ) @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_7) ).
thf(4,axiom,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_6) ).
thf(5,axiom,
environment @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_5) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater @ zero @ ( growth_rate @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_4) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_3) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
| ( outcompetes @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_2) ).
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,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star_9) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ( subpopulations @ C @ B @ A @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( greater_or_equal @ ( growth_rate @ first_movers @ sk2 ) @ zero )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( environment @ sk1 )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater @ zero @ ( growth_rate @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
| ( outcompetes @ C @ B @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
| ( outcompetes @ C @ B @ D ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater @ zero @ ( growth_rate @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( environment @ sk1 )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2 )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( greater_or_equal @ ( growth_rate @ first_movers @ sk2 ) @ zero )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(30,plain,
( ( greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ( subpopulations @ C @ B @ A @ D ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[22]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ~ ( environment @ SV1 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ SY18 )
| ~ ( outcompetes @ first_movers @ efficient_producers @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY19: $i,SY20: $i,SY21: $i] :
( ~ ( environment @ SV2 )
| ~ ( subpopulations @ SY19 @ SY20 @ SV2 @ SY21 )
| ~ ( greater_or_equal @ ( growth_rate @ SY20 @ SY21 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SY19 @ SY21 ) )
| ( outcompetes @ SY20 @ SY19 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV3: $i] :
( ( ! [SY22: $i,SY23: $i,SY24: $i] :
( ~ ( environment @ SV3 )
| ~ ( subpopulations @ SY22 @ SY23 @ SV3 @ SY24 )
| ~ ( outcompetes @ SY23 @ SY22 @ SY24 )
| ( greater_or_equal @ ( growth_rate @ SY23 @ SY24 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV4: $i] :
( ( ! [SY25: $i,SY26: $i,SY27: $i] :
( ~ ( environment @ SV4 )
| ~ ( subpopulations @ SY25 @ SY26 @ SV4 @ SY27 )
| ~ ( outcompetes @ SY26 @ SY25 @ SY27 )
| ( greater @ zero @ ( growth_rate @ SY25 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV5: $i] :
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
( ~ ( environment @ SV5 )
| ~ ( subpopulations @ SY28 @ SY29 @ SV5 @ SY30 )
| ( subpopulations @ SY29 @ SY28 @ SV5 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( environment @ SV1 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ SV6 )
| ~ ( outcompetes @ first_movers @ efficient_producers @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( environment @ SV2 )
| ~ ( subpopulations @ SV7 @ SY31 @ SV2 @ SY32 )
| ~ ( greater_or_equal @ ( growth_rate @ SY31 @ SY32 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SV7 @ SY32 ) )
| ( outcompetes @ SY31 @ SV7 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( environment @ SV3 )
| ~ ( subpopulations @ SV8 @ SY33 @ SV3 @ SY34 )
| ~ ( outcompetes @ SY33 @ SV8 @ SY34 )
| ( greater_or_equal @ ( growth_rate @ SY33 @ SY34 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ( environment @ SV4 )
| ~ ( subpopulations @ SV9 @ SY35 @ SV4 @ SY36 )
| ~ ( outcompetes @ SY35 @ SV9 @ SY36 )
| ( greater @ zero @ ( growth_rate @ SV9 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ( environment @ SV5 )
| ~ ( subpopulations @ SV10 @ SY37 @ SV5 @ SY38 )
| ( subpopulations @ SY37 @ SV10 @ SV5 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ SV6 )
| ~ ( outcompetes @ first_movers @ efficient_producers @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV11: $i,SV7: $i,SV2: $i] :
( ( ! [SY39: $i] :
( ~ ( environment @ SV2 )
| ~ ( subpopulations @ SV7 @ SV11 @ SV2 @ SY39 )
| ~ ( greater_or_equal @ ( growth_rate @ SV11 @ SY39 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SV7 @ SY39 ) )
| ( outcompetes @ SV11 @ SV7 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY40: $i] :
( ~ ( environment @ SV3 )
| ~ ( subpopulations @ SV8 @ SV12 @ SV3 @ SY40 )
| ~ ( outcompetes @ SV12 @ SV8 @ SY40 )
| ( greater_or_equal @ ( growth_rate @ SV12 @ SY40 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY41: $i] :
( ~ ( environment @ SV4 )
| ~ ( subpopulations @ SV9 @ SV13 @ SV4 @ SY41 )
| ~ ( outcompetes @ SV13 @ SV9 @ SY41 )
| ( greater @ zero @ ( growth_rate @ SV9 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ! [SY42: $i] :
( ~ ( environment @ SV5 )
| ~ ( subpopulations @ SV10 @ SV14 @ SV5 @ SY42 )
| ( subpopulations @ SV14 @ SV10 @ SV5 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV6: $i,SV1: $i] :
( ( ( environment @ SV1 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ SV6 )
| ~ ( outcompetes @ first_movers @ efficient_producers @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ~ ( environment @ SV2 )
| ~ ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
| ~ ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
| ( outcompetes @ SV11 @ SV7 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ~ ( environment @ SV3 )
| ~ ( subpopulations @ SV8 @ SV12 @ SV3 @ SV16 )
| ~ ( outcompetes @ SV12 @ SV8 @ SV16 )
| ( greater_or_equal @ ( growth_rate @ SV12 @ SV16 ) @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( environment @ SV4 )
| ~ ( subpopulations @ SV9 @ SV13 @ SV4 @ SV17 )
| ~ ( outcompetes @ SV13 @ SV9 @ SV17 )
| ( greater @ zero @ ( growth_rate @ SV9 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV18: $i,SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( environment @ SV5 )
| ~ ( subpopulations @ SV10 @ SV14 @ SV5 @ SV18 )
| ( subpopulations @ SV14 @ SV10 @ SV5 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( outcompetes @ first_movers @ efficient_producers @ SV6 ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( environment @ SV2 ) )
= $true )
| ( ( ~ ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
| ~ ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
| ( outcompetes @ SV11 @ SV7 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( environment @ SV3 ) )
= $true )
| ( ( ~ ( subpopulations @ SV8 @ SV12 @ SV3 @ SV16 )
| ~ ( outcompetes @ SV12 @ SV8 @ SV16 )
| ( greater_or_equal @ ( growth_rate @ SV12 @ SV16 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( environment @ SV4 ) )
= $true )
| ( ( ~ ( subpopulations @ SV9 @ SV13 @ SV4 @ SV17 )
| ~ ( outcompetes @ SV13 @ SV9 @ SV17 )
| ( greater @ zero @ ( growth_rate @ SV9 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV18: $i,SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( environment @ SV5 ) )
= $true )
| ( ( ~ ( subpopulations @ SV10 @ SV14 @ SV5 @ SV18 )
| ( subpopulations @ SV14 @ SV10 @ SV5 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV6: $i,SV1: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ SV6 )
= $false )
| ( ( ~ ( outcompetes @ first_movers @ efficient_producers @ SV6 ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ( environment @ SV2 )
= $false )
| ( ( ~ ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
| ~ ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
| ( outcompetes @ SV11 @ SV7 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( environment @ SV3 )
= $false )
| ( ( ~ ( subpopulations @ SV8 @ SV12 @ SV3 @ SV16 )
| ~ ( outcompetes @ SV12 @ SV8 @ SV16 )
| ( greater_or_equal @ ( growth_rate @ SV12 @ SV16 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( environment @ SV4 )
= $false )
| ( ( ~ ( subpopulations @ SV9 @ SV13 @ SV4 @ SV17 )
| ~ ( outcompetes @ SV13 @ SV9 @ SV17 )
| ( greater @ zero @ ( growth_rate @ SV9 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV18: $i,SV14: $i,SV10: $i,SV5: $i] :
( ( ( environment @ SV5 )
= $false )
| ( ( ~ ( subpopulations @ SV10 @ SV14 @ SV5 @ SV18 )
| ( subpopulations @ SV14 @ SV10 @ SV5 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV1: $i,SV6: $i] :
( ( ( outcompetes @ first_movers @ efficient_producers @ SV6 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ SV6 )
= $false )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV15: $i,SV2: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 ) )
= $true )
| ( ( ~ ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
| ( outcompetes @ SV11 @ SV7 @ SV15 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV16: $i,SV3: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( subpopulations @ SV8 @ SV12 @ SV3 @ SV16 ) )
= $true )
| ( ( ~ ( outcompetes @ SV12 @ SV8 @ SV16 )
| ( greater_or_equal @ ( growth_rate @ SV12 @ SV16 ) @ zero ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV17: $i,SV4: $i,SV13: $i,SV9: $i] :
( ( ( ~ ( subpopulations @ SV9 @ SV13 @ SV4 @ SV17 ) )
= $true )
| ( ( ~ ( outcompetes @ SV13 @ SV9 @ SV17 )
| ( greater @ zero @ ( growth_rate @ SV9 @ SV17 ) ) )
= $true )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV18: $i,SV5: $i,SV14: $i,SV10: $i] :
( ( ( ~ ( subpopulations @ SV10 @ SV14 @ SV5 @ SV18 ) )
= $true )
| ( ( subpopulations @ SV14 @ SV10 @ SV5 @ SV18 )
= $true )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV15: $i,SV2: $i,SV11: $i,SV7: $i] :
( ( ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
= $false )
| ( ( ~ ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
| ( outcompetes @ SV11 @ SV7 @ SV15 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV16: $i,SV3: $i,SV12: $i,SV8: $i] :
( ( ( subpopulations @ SV8 @ SV12 @ SV3 @ SV16 )
= $false )
| ( ( ~ ( outcompetes @ SV12 @ SV8 @ SV16 )
| ( greater_or_equal @ ( growth_rate @ SV12 @ SV16 ) @ zero ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV17: $i,SV4: $i,SV13: $i,SV9: $i] :
( ( ( subpopulations @ SV9 @ SV13 @ SV4 @ SV17 )
= $false )
| ( ( ~ ( outcompetes @ SV13 @ SV9 @ SV17 )
| ( greater @ zero @ ( growth_rate @ SV9 @ SV17 ) ) )
= $true )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV18: $i,SV5: $i,SV14: $i,SV10: $i] :
( ( ( subpopulations @ SV10 @ SV14 @ SV5 @ SV18 )
= $false )
| ( ( subpopulations @ SV14 @ SV10 @ SV5 @ SV18 )
= $true )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV2: $i,SV7: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero ) )
= $true )
| ( ( ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
| ( outcompetes @ SV11 @ SV7 @ SV15 ) )
= $true )
| ( ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
= $false )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV3: $i,SV16: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( outcompetes @ SV12 @ SV8 @ SV16 ) )
= $true )
| ( ( greater_or_equal @ ( growth_rate @ SV12 @ SV16 ) @ zero )
= $true )
| ( ( subpopulations @ SV8 @ SV12 @ SV3 @ SV16 )
= $false )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV13: $i] :
( ( ( ~ ( outcompetes @ SV13 @ SV9 @ SV17 ) )
= $true )
| ( ( greater @ zero @ ( growth_rate @ SV9 @ SV17 ) )
= $true )
| ( ( subpopulations @ SV9 @ SV13 @ SV4 @ SV17 )
= $false )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV2: $i,SV7: $i,SV15: $i,SV11: $i] :
( ( ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
= $false )
| ( ( ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
| ( outcompetes @ SV11 @ SV7 @ SV15 ) )
= $true )
| ( ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
= $false )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV3: $i,SV16: $i,SV8: $i,SV12: $i] :
( ( ( outcompetes @ SV12 @ SV8 @ SV16 )
= $false )
| ( ( greater_or_equal @ ( growth_rate @ SV12 @ SV16 ) @ zero )
= $true )
| ( ( subpopulations @ SV8 @ SV12 @ SV3 @ SV16 )
= $false )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV13: $i] :
( ( ( outcompetes @ SV13 @ SV9 @ SV17 )
= $false )
| ( ( greater @ zero @ ( growth_rate @ SV9 @ SV17 ) )
= $true )
| ( ( subpopulations @ SV9 @ SV13 @ SV4 @ SV17 )
= $false )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV2: $i,SV11: $i,SV15: $i,SV7: $i] :
( ( ( ~ ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) ) )
= $true )
| ( ( outcompetes @ SV11 @ SV7 @ SV15 )
= $true )
| ( ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
= $false )
| ( ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
= $false )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV2: $i,SV11: $i,SV15: $i,SV7: $i] :
( ( ( greater @ zero @ ( growth_rate @ SV7 @ SV15 ) )
= $false )
| ( ( outcompetes @ SV11 @ SV7 @ SV15 )
= $true )
| ( ( greater_or_equal @ ( growth_rate @ SV11 @ SV15 ) @ zero )
= $false )
| ( ( subpopulations @ SV7 @ SV11 @ SV2 @ SV15 )
= $false )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(81,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,80,78,77,72,64,38,30,29,28]) ).
thf(82,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-3 : 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
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 12:42:46 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.22
% 0.09/0.22 No.of.Axioms: 9
% 0.09/0.22
% 0.09/0.22 Length.of.Defs: 0
% 0.09/0.22
% 0.09/0.22 Contains.Choice.Funs: false
% 0.09/0.22 .
% 0.09/0.22
% 0.09/0.22 ********************************
% 0.09/0.22 * All subproblems solved! *
% 0.09/0.22 ********************************
% 0.09/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:81,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.22
% 0.09/0.22 %**** Beginning of derivation protocol ****
% 0.09/0.22 % SZS output start CNFRefutation
% See solution above
% 0.09/0.22
% 0.09/0.22 %**** End of derivation protocol ****
% 0.09/0.22 %**** no. of clauses in derivation: 82 ****
% 0.09/0.22 %**** clause counter: 81 ****
% 0.09/0.22
% 0.09/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:81,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------