TSTP Solution File: MGT023-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : MGT023-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:17:13 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 98 ( 40 unt; 12 typ; 0 def)
% Number of atoms : 644 ( 197 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 1351 ( 135 ~; 238 |; 0 &; 978 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 119 ( 0 ^ 119 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_critical_point,type,
critical_point: $i > $i ).
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_growth_rate,type,
growth_rate: $i > $i > $i ).
thf(tp_in_environment,type,
in_environment: $i > $i > $o ).
thf(tp_sk1,type,
sk1: $i > $i > $i ).
thf(tp_sk2,type,
sk2: $i > $i ).
thf(tp_sk3,type,
sk3: $i ).
thf(tp_stable,type,
stable: $i > $o ).
thf(tp_subpopulations,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater @ B @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_22) ).
thf(2,axiom,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_21) ).
thf(3,axiom,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( sk2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_20) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_19) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( greater @ ( sk1 @ B @ A ) @ B )
| ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_18) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_17) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
~ ( in_environment @ sk3 @ ( critical_point @ sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_25) ).
thf(10,negated_conjecture,
stable @ sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_24) ).
thf(11,negated_conjecture,
environment @ sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_23) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater @ B @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( sk2 @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( B
= ( critical_point @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( greater @ ( sk1 @ B @ A ) @ B )
| ( B
= ( critical_point @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ( B
= ( critical_point @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ~ ( in_environment @ sk3 @ ( critical_point @ sk3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(20,plain,
( ( stable @ sk3 )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(21,plain,
( ( environment @ sk3 )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater @ B @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(24,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( B
= ( critical_point @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(25,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( B
= ( critical_point @ A ) )
| ( greater @ ( sk1 @ B @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(26,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( B
= ( critical_point @ A ) )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(27,plain,
( ( environment @ sk3 )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( stable @ sk3 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ~ ( in_environment @ sk3 @ ( critical_point @ sk3 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( B
= ( critical_point @ A ) )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( B
= ( critical_point @ A ) )
| ( greater @ ( sk1 @ B @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ! [B: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( B
= ( critical_point @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( sk2 @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( ! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ! [B: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater @ B @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(36,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
( ( in_environment @ sk3 @ ( critical_point @ sk3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV1: $i] :
( ( ~ ( environment @ SV1 )
| ! [SY10: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY10 ) @ ( growth_rate @ first_movers @ SY10 ) )
| ~ ( in_environment @ SV1 @ SY10 )
| ( SY10
= ( critical_point @ SV1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SY10 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV2: $i] :
( ( ~ ( environment @ SV2 )
| ! [SY11: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY11 ) @ ( growth_rate @ first_movers @ SY11 ) )
| ~ ( in_environment @ SV2 @ SY11 )
| ( SY11
= ( critical_point @ SV2 ) )
| ( greater @ ( sk1 @ SY11 @ SV2 ) @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV3: $i] :
( ( ~ ( environment @ SV3 )
| ! [SY12: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY12 ) @ ( growth_rate @ first_movers @ SY12 ) )
| ~ ( in_environment @ SV3 @ SY12 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SY12 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SY12 @ SV3 ) ) )
| ( SY12
= ( critical_point @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV4: $i] :
( ( ~ ( environment @ SV4 )
| ~ ( stable @ SV4 )
| ( in_environment @ SV4 @ ( sk2 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV5: $i] :
( ( ~ ( environment @ SV5 )
| ~ ( stable @ SV5 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ SV5 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV6: $i] :
( ( ~ ( environment @ SV6 )
| ~ ( stable @ SV6 )
| ! [SY13: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY13 )
| ~ ( greater @ SY13 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY13 ) @ ( growth_rate @ first_movers @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV1: $i] :
( ( ( ~ ( environment @ SV1 ) )
= $true )
| ( ( ! [SY10: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY10 ) @ ( growth_rate @ first_movers @ SY10 ) )
| ~ ( in_environment @ SV1 @ SY10 )
| ( SY10
= ( critical_point @ SV1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SY10 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( ~ ( environment @ SV2 ) )
= $true )
| ( ( ! [SY11: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY11 ) @ ( growth_rate @ first_movers @ SY11 ) )
| ~ ( in_environment @ SV2 @ SY11 )
| ( SY11
= ( critical_point @ SV2 ) )
| ( greater @ ( sk1 @ SY11 @ SV2 ) @ SY11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: $i] :
( ( ( ~ ( environment @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY12 ) @ ( growth_rate @ first_movers @ SY12 ) )
| ~ ( in_environment @ SV3 @ SY12 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SY12 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SY12 @ SV3 ) ) )
| ( SY12
= ( critical_point @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV4: $i] :
( ( ( ~ ( environment @ SV4 ) )
= $true )
| ( ( ~ ( stable @ SV4 )
| ( in_environment @ SV4 @ ( sk2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV5: $i] :
( ( ( ~ ( environment @ SV5 ) )
= $true )
| ( ( ~ ( stable @ SV5 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ SV5 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( ~ ( environment @ SV6 ) )
= $true )
| ( ( ~ ( stable @ SV6 )
| ! [SY13: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY13 )
| ~ ( greater @ SY13 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY13 ) @ ( growth_rate @ first_movers @ SY13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV1: $i] :
( ( ( environment @ SV1 )
= $false )
| ( ( ! [SY10: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY10 ) @ ( growth_rate @ first_movers @ SY10 ) )
| ~ ( in_environment @ SV1 @ SY10 )
| ( SY10
= ( critical_point @ SV1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SY10 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: $i] :
( ( ( environment @ SV2 )
= $false )
| ( ( ! [SY11: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY11 ) @ ( growth_rate @ first_movers @ SY11 ) )
| ~ ( in_environment @ SV2 @ SY11 )
| ( SY11
= ( critical_point @ SV2 ) )
| ( greater @ ( sk1 @ SY11 @ SV2 ) @ SY11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV3: $i] :
( ( ( environment @ SV3 )
= $false )
| ( ( ! [SY12: $i] :
( ( greater @ ( growth_rate @ efficient_producers @ SY12 ) @ ( growth_rate @ first_movers @ SY12 ) )
| ~ ( in_environment @ SV3 @ SY12 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SY12 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SY12 @ SV3 ) ) )
| ( SY12
= ( critical_point @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( environment @ SV4 )
= $false )
| ( ( ~ ( stable @ SV4 )
| ( in_environment @ SV4 @ ( sk2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( environment @ SV5 )
= $false )
| ( ( ~ ( stable @ SV5 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ SV5 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( environment @ SV6 )
= $false )
| ( ( ~ ( stable @ SV6 )
| ! [SY13: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY13 )
| ~ ( greater @ SY13 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY13 ) @ ( growth_rate @ first_movers @ SY13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV1: $i,SV7: $i] :
( ( ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
| ~ ( in_environment @ SV1 @ SV7 )
| ( SV7
= ( critical_point @ SV1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SV7 @ SV1 ) ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( greater @ ( growth_rate @ efficient_producers @ SV8 ) @ ( growth_rate @ first_movers @ SV8 ) )
| ~ ( in_environment @ SV2 @ SV8 )
| ( SV8
= ( critical_point @ SV2 ) )
| ( greater @ ( sk1 @ SV8 @ SV2 ) @ SV8 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV3: $i,SV9: $i] :
( ( ( ( greater @ ( growth_rate @ efficient_producers @ SV9 ) @ ( growth_rate @ first_movers @ SV9 ) )
| ~ ( in_environment @ SV3 @ SV9 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SV9 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SV9 @ SV3 ) ) )
| ( SV9
= ( critical_point @ SV3 ) ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV4: $i] :
( ( ( ~ ( stable @ SV4 ) )
= $true )
| ( ( in_environment @ SV4 @ ( sk2 @ SV4 ) )
= $true )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV5: $i] :
( ( ( ~ ( stable @ SV5 ) )
= $true )
| ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ SV5 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ SV5 ) ) ) )
= $true )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV6: $i] :
( ( ( ~ ( stable @ SV6 ) )
= $true )
| ( ( ! [SY13: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY13 )
| ~ ( greater @ SY13 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY13 ) @ ( growth_rate @ first_movers @ SY13 ) ) ) )
= $true )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV1: $i,SV7: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV7 )
| ( SV7
= ( critical_point @ SV1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SV7 @ SV1 ) ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV2: $i,SV8: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ SV8 ) @ ( growth_rate @ first_movers @ SV8 ) )
= $true )
| ( ( ~ ( in_environment @ SV2 @ SV8 )
| ( SV8
= ( critical_point @ SV2 ) )
| ( greater @ ( sk1 @ SV8 @ SV2 ) @ SV8 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV3: $i,SV9: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ SV9 ) @ ( growth_rate @ first_movers @ SV9 ) )
= $true )
| ( ( ~ ( in_environment @ SV3 @ SV9 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SV9 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SV9 @ SV3 ) ) )
| ( SV9
= ( critical_point @ SV3 ) ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV4: $i] :
( ( ( stable @ SV4 )
= $false )
| ( ( in_environment @ SV4 @ ( sk2 @ SV4 ) )
= $true )
| ( ( environment @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( stable @ SV5 )
= $false )
| ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ SV5 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ SV5 ) ) ) )
= $true )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV6: $i] :
( ( ( stable @ SV6 )
= $false )
| ( ( ! [SY13: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SY13 )
| ~ ( greater @ SY13 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY13 ) @ ( growth_rate @ first_movers @ SY13 ) ) ) )
= $true )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( in_environment @ SV1 @ SV7 ) )
= $true )
| ( ( ( SV7
= ( critical_point @ SV1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SV7 @ SV1 ) ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( in_environment @ SV2 @ SV8 ) )
= $true )
| ( ( ( SV8
= ( critical_point @ SV2 ) )
| ( greater @ ( sk1 @ SV8 @ SV2 ) @ SV8 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV8 ) @ ( growth_rate @ first_movers @ SV8 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( in_environment @ SV3 @ SV9 ) )
= $true )
| ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SV9 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SV9 @ SV3 ) ) )
| ( SV9
= ( critical_point @ SV3 ) ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV9 ) @ ( growth_rate @ first_movers @ SV9 ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ SV5 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ SV5 ) ) )
= $false )
| ( ( stable @ SV5 )
= $false )
| ( ( environment @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV10 )
| ~ ( greater @ SV10 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SV10 ) @ ( growth_rate @ first_movers @ SV10 ) ) )
= $true )
| ( ( stable @ SV6 )
= $false )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV7: $i,SV1: $i] :
( ( ( in_environment @ SV1 @ SV7 )
= $false )
| ( ( ( SV7
= ( critical_point @ SV1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SV7 @ SV1 ) ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV8: $i,SV2: $i] :
( ( ( in_environment @ SV2 @ SV8 )
= $false )
| ( ( ( SV8
= ( critical_point @ SV2 ) )
| ( greater @ ( sk1 @ SV8 @ SV2 ) @ SV8 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV8 ) @ ( growth_rate @ first_movers @ SV8 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV9: $i,SV3: $i] :
( ( ( in_environment @ SV3 @ SV9 )
= $false )
| ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SV9 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SV9 @ SV3 ) ) )
| ( SV9
= ( critical_point @ SV3 ) ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV9 ) @ ( growth_rate @ first_movers @ SV9 ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( greater @ SV10 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SV10 ) @ ( growth_rate @ first_movers @ SV10 ) ) )
= $true )
| ( ( stable @ SV6 )
= $false )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV1: $i,SV7: $i] :
( ( ( SV7
= ( critical_point @ SV1 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sk1 @ SV7 @ SV1 ) )
= $true )
| ( ( in_environment @ SV1 @ SV7 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( environment @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV2: $i,SV8: $i] :
( ( ( SV8
= ( critical_point @ SV2 ) )
= $true )
| ( ( greater @ ( sk1 @ SV8 @ SV2 ) @ SV8 )
= $true )
| ( ( in_environment @ SV2 @ SV8 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV8 ) @ ( growth_rate @ first_movers @ SV8 ) )
= $true )
| ( ( environment @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SV9 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SV9 @ SV3 ) ) ) )
= $true )
| ( ( SV9
= ( critical_point @ SV3 ) )
= $true )
| ( ( in_environment @ SV3 @ SV9 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV9 ) @ ( growth_rate @ first_movers @ SV9 ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV10: $i,SV6: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV10 )
= $false )
| ( ( ~ ( greater @ SV10 @ ( sk2 @ SV6 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SV10 ) @ ( growth_rate @ first_movers @ SV10 ) ) )
= $true )
| ( ( stable @ SV6 )
= $false )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV3: $i,SV9: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ SV9 @ SV3 ) ) @ ( growth_rate @ first_movers @ ( sk1 @ SV9 @ SV3 ) ) )
= $false )
| ( ( SV9
= ( critical_point @ SV3 ) )
= $true )
| ( ( in_environment @ SV3 @ SV9 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV9 ) @ ( growth_rate @ first_movers @ SV9 ) )
= $true )
| ( ( environment @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( greater @ SV10 @ ( sk2 @ SV6 ) ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV10 ) @ ( growth_rate @ first_movers @ SV10 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV10 )
= $false )
| ( ( stable @ SV6 )
= $false )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(84,plain,
! [SV6: $i,SV10: $i] :
( ( ( greater @ SV10 @ ( sk2 @ SV6 ) )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV10 ) @ ( growth_rate @ first_movers @ SV10 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV6 @ SV10 )
= $false )
| ( ( stable @ SV6 )
= $false )
| ( ( environment @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(85,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,84,82,79,78,72,66,44,37,28]) ).
thf(86,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : MGT023-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 9 10:20:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 9
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:9,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:11,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.44
% 0.20/0.44 %**** Beginning of derivation protocol ****
% 0.20/0.44 % SZS output start CNFRefutation
% See solution above
% 0.20/0.44
% 0.20/0.44 %**** End of derivation protocol ****
% 0.20/0.44 %**** no. of clauses in derivation: 86 ****
% 0.20/0.44 %**** clause counter: 85 ****
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------