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 v2.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n024.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 : Theorem 0.21s 0.42s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 84 ( 24 unt; 12 typ; 0 def)
% Number of atoms : 712 ( 216 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 1657 ( 223 ~; 232 |; 28 &;1162 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 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 : 115 ( 0 ^ 113 !; 2 ?; 115 :)
% 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_E,type,
sK1_E: $i ).
thf(tp_sK2_To,type,
sK2_To: $i > $i ).
thf(tp_sK3_T,type,
sK3_T: $i > $i > $i ).
thf(tp_stable,type,
stable: $i > $o ).
thf(tp_subpopulations,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(1,axiom,
! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ~ ( greater @ ( growth_rate @ efficient_producers @ To ) @ ( growth_rate @ first_movers @ To ) )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
thf(2,axiom,
! [E: $i,To: $i] :
( ( ( environment @ E )
& ~ ( greater @ ( growth_rate @ efficient_producers @ To ) @ ( growth_rate @ first_movers @ To ) )
& ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) )
=> ( To
= ( critical_point @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(3,conjecture,
! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ( in_environment @ E @ ( critical_point @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
thf(4,negated_conjecture,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ( in_environment @ E @ ( critical_point @ E ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ( in_environment @ E @ ( critical_point @ E ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ~ ( greater @ ( growth_rate @ efficient_producers @ To ) @ ( growth_rate @ first_movers @ To ) )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [E: $i,To: $i] :
( ( ( environment @ E )
& ~ ( greater @ ( growth_rate @ efficient_producers @ To ) @ ( growth_rate @ first_movers @ To ) )
& ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) )
=> ( To
= ( critical_point @ E ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ( ( environment @ sK1_E )
& ( stable @ sK1_E ) )
=> ( in_environment @ sK1_E @ ( critical_point @ sK1_E ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( environment @ sK1_E )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(10,plain,
( ( stable @ sK1_E )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(11,plain,
( ( in_environment @ sK1_E @ ( critical_point @ sK1_E ) )
= $false ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( in_environment @ sK1_E @ ( critical_point @ sK1_E ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ! [SY7: $i] :
( ~ ( greater @ SY7 @ ( sK2_To @ E ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ SY7 )
| ( greater @ ( growth_rate @ efficient_producers @ SY7 ) @ ( growth_rate @ first_movers @ SY7 ) ) )
& ( in_environment @ E @ ( sK2_To @ E ) )
& ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ E ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ E ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [E: $i,To: $i] :
( ( ( greater @ ( sK3_T @ To @ E ) @ To )
& ( subpopulations @ first_movers @ efficient_producers @ E @ ( sK3_T @ To @ E ) )
& ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ To @ E ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ To @ E ) ) ) )
| ~ ( environment @ E )
| ( greater @ ( growth_rate @ efficient_producers @ To ) @ ( growth_rate @ first_movers @ To ) )
| ~ ( in_environment @ E @ To )
| ( To
= ( critical_point @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [E: $i,To: $i] :
( ( ( greater @ ( sK3_T @ To @ E ) @ To )
& ( subpopulations @ first_movers @ efficient_producers @ E @ ( sK3_T @ To @ E ) )
& ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ To @ E ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ To @ E ) ) ) )
| ~ ( environment @ E )
| ( greater @ ( growth_rate @ efficient_producers @ To ) @ ( growth_rate @ first_movers @ To ) )
| ~ ( in_environment @ E @ To )
| ( To
= ( critical_point @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ! [SY7: $i] :
( ~ ( greater @ SY7 @ ( sK2_To @ E ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ SY7 )
| ( greater @ ( growth_rate @ efficient_producers @ SY7 ) @ ( growth_rate @ first_movers @ SY7 ) ) )
& ( in_environment @ E @ ( sK2_To @ E ) )
& ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ E ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ E ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( stable @ sK1_E )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(18,plain,
( ( environment @ sK1_E )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(19,plain,
( ( ~ ( in_environment @ sK1_E @ ( critical_point @ sK1_E ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( greater @ ( sK3_T @ SX1 @ SX0 ) @ SX1 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ ( sK3_T @ SX1 @ SX0 ) ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SX1 @ SX0 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SX1 @ SX0 ) ) ) )
| ~ ( environment @ SX0 )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ ( growth_rate @ first_movers @ SX1 ) )
| ~ ( in_environment @ SX0 @ SX1 )
| ( SX1
= ( critical_point @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(21,plain,
( ( ! [SX0: $i] :
( ~ ( environment @ SX0 )
| ~ ( stable @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( greater @ SX1 @ ( sK2_To @ SX0 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ ( growth_rate @ first_movers @ SX1 ) ) )
| ~ ~ ( ~ ( in_environment @ SX0 @ ( sK2_To @ SX0 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SX0 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(22,plain,
( ( in_environment @ sK1_E @ ( critical_point @ sK1_E ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY8: $i] :
( ~ ( ~ ~ ( ~ ( greater @ ( sK3_T @ SY8 @ SV1 ) @ SY8 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SY8 @ SV1 ) ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SY8 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SY8 @ SV1 ) ) ) )
| ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SY8 ) @ ( growth_rate @ first_movers @ SY8 ) )
| ~ ( in_environment @ SV1 @ SY8 )
| ( SY8
= ( critical_point @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i] :
( ( ~ ( environment @ SV2 )
| ~ ( stable @ SV2 )
| ~ ( ~ ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) )
| ~ ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ~ ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) ) )
| ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 )
| ( SV3
= ( critical_point @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: $i] :
( ( ( ~ ( environment @ SV2 )
| ~ ( stable @ SV2 ) )
= $true )
| ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) )
| ~ ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) ) )
| ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i] :
( ( ( ~ ( environment @ SV2 ) )
= $true )
| ( ( ~ ( stable @ SV2 ) )
= $true )
| ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) )
| ~ ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) ) ) )
= $true )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( environment @ SV2 )
= $false )
| ( ( ~ ( stable @ SV2 ) )
= $true )
| ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) )
| ~ ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( stable @ SV2 )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) )
| ~ ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV2: $i] :
( ( ( ~ ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) )
| ~ ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( ~ ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) ) )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV1: $i,SV3: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( ! [SY9: $i] :
( ~ ( greater @ SY9 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SY9 )
| ( greater @ ( growth_rate @ efficient_producers @ SY9 ) @ ( growth_rate @ first_movers @ SY9 ) ) ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 ) )
= $false )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( greater @ SV4 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SV4 )
| ( greater @ ( growth_rate @ efficient_producers @ SV4 ) @ ( growth_rate @ first_movers @ SV4 ) ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV2: $i] :
( ( ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
| ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV1: $i,SV3: $i] :
( ( ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
= $true )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV3: $i,SV1: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) )
= $true )
| ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
| ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( greater @ SV4 @ ( sK2_To @ SV2 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SV4 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV4 ) @ ( growth_rate @ first_movers @ SV4 ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV2: $i] :
( ( ( ~ ( in_environment @ SV2 @ ( sK2_To @ SV2 ) ) )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV2: $i] :
( ( ( ~ ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 )
| ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV3: $i,SV1: $i] :
( ( ( environment @ SV1 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( greater @ SV4 @ ( sK2_To @ SV2 ) ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SV4 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV4 ) @ ( growth_rate @ first_movers @ SV4 ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV2: $i] :
( ( ( in_environment @ SV2 @ ( sK2_To @ SV2 ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV2: $i] :
( ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV3: $i,SV1: $i] :
( ( ( in_environment @ SV1 @ SV3 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( environment @ SV1 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ ( sK3_T @ SV3 @ SV1 ) ) @ ( growth_rate @ first_movers @ ( sK3_T @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV2: $i,SV4: $i] :
( ( ( greater @ SV4 @ ( sK2_To @ SV2 ) )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SV4 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV4 ) @ ( growth_rate @ first_movers @ SV4 ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV2: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ ( sK2_To @ SV2 ) ) @ ( growth_rate @ first_movers @ ( sK2_To @ SV2 ) ) )
= $false )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV3: $i,SV1: $i] :
( ( ( environment @ SV1 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV3: $i,SV1: $i] :
( ( ( environment @ SV1 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( ~ ( in_environment @ SV1 @ SV3 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV4: $i,SV2: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV2 @ SV4 )
= $false )
| ( ( greater @ SV4 @ ( sK2_To @ SV2 ) )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV4 ) @ ( growth_rate @ first_movers @ SV4 ) )
= $true )
| ( ( environment @ SV2 )
= $false )
| ( ( stable @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV3: $i,SV1: $i] :
( ( ( in_environment @ SV1 @ SV3 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( environment @ SV1 )
= $false )
| ( ( greater @ ( sK3_T @ SV3 @ SV1 ) @ SV3 )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV3: $i,SV1: $i] :
( ( ( in_environment @ SV1 @ SV3 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV3 ) @ ( growth_rate @ first_movers @ SV3 ) )
= $true )
| ( ( environment @ SV1 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV1 @ ( sK3_T @ SV3 @ SV1 ) )
= $true )
| ( ( SV3
= ( critical_point @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,70,69,68,65,63,59,22,18]) ).
thf(72,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 9 09:39:34 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 2
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.36 (rf:0,axioms:2,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:4,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.21/0.42
% 0.21/0.42 ********************************
% 0.21/0.42 * All subproblems solved! *
% 0.21/0.42 ********************************
% 0.21/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:71,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.42
% 0.21/0.42 %**** Beginning of derivation protocol ****
% 0.21/0.42 % SZS output start CNFRefutation
% See solution above
% 0.21/0.42
% 0.21/0.42 %**** End of derivation protocol ****
% 0.21/0.42 %**** no. of clauses in derivation: 72 ****
% 0.21/0.42 %**** clause counter: 71 ****
% 0.21/0.42
% 0.21/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:71,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------