TSTP Solution File: MGT032+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : MGT032+2 : 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 : n028.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 22:17:19 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 27 unt; 13 typ; 0 def)
% Number of atoms : 504 ( 125 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1100 ( 154 ~; 141 |; 32 &; 757 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 130 ( 0 ^ 122 !; 8 ?; 130 :)
% 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_in_environment,type,
in_environment: $i > $i > $o ).
thf(tp_sK1_E,type,
sK1_E: $i ).
thf(tp_sK2_SY11,type,
sK2_SY11: $i > $i ).
thf(tp_sK3_To,type,
sK3_To: $i > $i ).
thf(tp_selection_favors,type,
selection_favors: $i > $i > $i > $o ).
thf(tp_stable,type,
stable: $i > $o ).
thf(tp_subpopulations,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(1,axiom,
! [E: $i,S1: $i,S2: $i,T: $i] :
( ( ( environment @ E )
& ( subpopulations @ S1 @ S2 @ E @ T )
& ( greater @ ( growth_rate @ S2 @ T ) @ ( growth_rate @ S1 @ T ) ) )
=> ( selection_favors @ S2 @ S1 @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
thf(2,axiom,
! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
thf(3,conjecture,
! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( selection_favors @ efficient_producers @ first_movers @ T ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1) ).
thf(4,negated_conjecture,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( selection_favors @ efficient_producers @ first_movers @ T ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( selection_favors @ efficient_producers @ first_movers @ T ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [E: $i,S1: $i,S2: $i,T: $i] :
( ( ( environment @ E )
& ( subpopulations @ S1 @ S2 @ E @ T )
& ( greater @ ( growth_rate @ S2 @ T ) @ ( growth_rate @ S1 @ T ) ) )
=> ( selection_favors @ S2 @ S1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ( ( environment @ sK1_E )
& ( stable @ sK1_E ) )
=> ? [SY10: $i] :
( ( in_environment @ sK1_E @ SY10 )
& ! [SY11: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ SY11 )
& ( greater_or_equal @ SY11 @ SY10 ) )
=> ( selection_favors @ efficient_producers @ first_movers @ SY11 ) ) ) )
= $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,
( ( ? [SY10: $i] :
( ( in_environment @ sK1_E @ SY10 )
& ! [SY11: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ SY11 )
& ( greater_or_equal @ SY11 @ SY10 ) )
=> ( selection_favors @ efficient_producers @ first_movers @ SY11 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ? [SY10: $i] :
( ( in_environment @ sK1_E @ SY10 )
& ! [SY11: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ SY11 )
& ( greater_or_equal @ SY11 @ SY10 ) )
=> ( selection_favors @ efficient_producers @ first_movers @ SY11 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY10: $i] :
( ( ( greater_or_equal @ ( sK2_SY11 @ SY10 ) @ SY10 )
& ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SY10 ) )
& ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SY10 ) ) )
| ~ ( in_environment @ sK1_E @ SY10 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(14,plain,
( ( ! [E: $i,S1: $i,S2: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ S1 @ S2 @ E @ T )
| ~ ( greater @ ( growth_rate @ S2 @ T ) @ ( growth_rate @ S1 @ T ) )
| ( selection_favors @ S2 @ S1 @ T ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(15,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ! [SY12: $i] :
( ~ ( greater_or_equal @ SY12 @ ( sK3_To @ E ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ SY12 )
| ( greater @ ( growth_rate @ efficient_producers @ SY12 ) @ ( growth_rate @ first_movers @ SY12 ) ) )
& ( in_environment @ E @ ( sK3_To @ E ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(16,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ! [SY12: $i] :
( ~ ( greater_or_equal @ SY12 @ ( sK3_To @ E ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ SY12 )
| ( greater @ ( growth_rate @ efficient_producers @ SY12 ) @ ( growth_rate @ first_movers @ SY12 ) ) )
& ( in_environment @ E @ ( sK3_To @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [E: $i,S1: $i,S2: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ S1 @ S2 @ E @ T )
| ~ ( greater @ ( growth_rate @ S2 @ T ) @ ( growth_rate @ S1 @ T ) )
| ( selection_favors @ S2 @ S1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( stable @ sK1_E )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( environment @ sK1_E )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ! [SY10: $i] :
( ( ( greater_or_equal @ ( sK2_SY11 @ SY10 ) @ SY10 )
& ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SY10 ) )
& ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SY10 ) ) )
| ~ ( in_environment @ sK1_E @ SY10 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY11 @ SX0 ) @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SX0 ) ) )
| ~ ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SX0 ) ) )
| ~ ( in_environment @ sK1_E @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ~ ( environment @ SX0 )
| ~ ( stable @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( greater_or_equal @ SX1 @ ( sK3_To @ SX0 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ ( growth_rate @ first_movers @ SX1 ) ) )
| ~ ( in_environment @ SX0 @ ( sK3_To @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY13: $i,SY14: $i,SY15: $i] :
( ~ ( environment @ SV1 )
| ~ ( subpopulations @ SY13 @ SY14 @ SV1 @ SY15 )
| ~ ( greater @ ( growth_rate @ SY14 @ SY15 ) @ ( growth_rate @ SY13 @ SY15 ) )
| ( selection_favors @ SY14 @ SY13 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV2: $i] :
( ( ~ ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) ) )
| ~ ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SV2 ) ) )
| ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i] :
( ( ~ ( environment @ SV3 )
| ~ ( stable @ SV3 )
| ~ ( ~ ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) )
| ~ ( in_environment @ SV3 @ ( sK3_To @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( environment @ SV1 )
| ~ ( subpopulations @ SV4 @ SY17 @ SV1 @ SY18 )
| ~ ( greater @ ( growth_rate @ SY17 @ SY18 ) @ ( growth_rate @ SV4 @ SY18 ) )
| ( selection_favors @ SY17 @ SV4 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) ) )
| ~ ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: $i] :
( ( ( ~ ( environment @ SV3 )
| ~ ( stable @ SV3 ) )
= $true )
| ( ( ~ ( ~ ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) )
| ~ ( in_environment @ SV3 @ ( sK3_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: $i,SV4: $i,SV1: $i] :
( ( ! [SY19: $i] :
( ~ ( environment @ SV1 )
| ~ ( subpopulations @ SV4 @ SV5 @ SV1 @ SY19 )
| ~ ( greater @ ( growth_rate @ SV5 @ SY19 ) @ ( growth_rate @ SV4 @ SY19 ) )
| ( selection_favors @ SV5 @ SV4 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) ) )
| ~ ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SV2 ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV3: $i] :
( ( ( ~ ( environment @ SV3 ) )
= $true )
| ( ( ~ ( stable @ SV3 ) )
= $true )
| ( ( ~ ( ~ ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) )
| ~ ( in_environment @ SV3 @ ( sK3_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV1: $i] :
( ( ~ ( environment @ SV1 )
| ~ ( subpopulations @ SV4 @ SV5 @ SV1 @ SV6 )
| ~ ( greater @ ( growth_rate @ SV5 @ SV6 ) @ ( growth_rate @ SV4 @ SV6 ) )
| ( selection_favors @ SV5 @ SV4 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( ~ ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SV2 ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( environment @ SV3 )
= $false )
| ( ( ~ ( stable @ SV3 ) )
= $true )
| ( ( ~ ( ~ ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) )
| ~ ( in_environment @ SV3 @ ( sK3_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 )
| ~ ( subpopulations @ SV4 @ SV5 @ SV1 @ SV6 )
| ~ ( greater @ ( growth_rate @ SV5 @ SV6 ) @ ( growth_rate @ SV4 @ SV6 ) ) )
= $true )
| ( ( selection_favors @ SV5 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( ~ ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SV2 ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV3: $i] :
( ( ( stable @ SV3 )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( ~ ( ~ ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) )
| ~ ( in_environment @ SV3 @ ( sK3_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 )
| ~ ( subpopulations @ SV4 @ SV5 @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( greater @ ( growth_rate @ SV5 @ SV6 ) @ ( growth_rate @ SV4 @ SV6 ) ) )
= $true )
| ( ( selection_favors @ SV5 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( ~ ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SV2 ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( ~ ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) )
| ~ ( in_environment @ SV3 @ ( sK3_To @ SV3 ) ) )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( environment @ SV1 ) )
= $true )
| ( ( ~ ( subpopulations @ SV4 @ SV5 @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( greater @ ( growth_rate @ SV5 @ SV6 ) @ ( growth_rate @ SV4 @ SV6 ) ) )
= $true )
| ( ( selection_favors @ SV5 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( ~ ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV2: $i] :
( ( ( in_environment @ sK1_E @ SV2 )
= $false )
| ( ( selection_favors @ efficient_producers @ first_movers @ ( sK2_SY11 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV3: $i] :
( ( ( ~ ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) ) )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV3: $i] :
( ( ( ~ ( in_environment @ SV3 @ ( sK3_To @ SV3 ) ) )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(50,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV1: $i] :
( ( ( environment @ SV1 )
= $false )
| ( ( ~ ( subpopulations @ SV4 @ SV5 @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( greater @ ( growth_rate @ SV5 @ SV6 ) @ ( growth_rate @ SV4 @ SV6 ) ) )
= $true )
| ( ( selection_favors @ SV5 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV2: $i] :
( ( ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV3: $i] :
( ( ( ! [SY16: $i] :
( ~ ( greater_or_equal @ SY16 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY16 )
| ( greater @ ( growth_rate @ efficient_producers @ SY16 ) @ ( growth_rate @ first_movers @ SY16 ) ) ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV3: $i] :
( ( ( in_environment @ SV3 @ ( sK3_To @ SV3 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV6: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( subpopulations @ SV4 @ SV5 @ SV1 @ SV6 )
= $false )
| ( ( environment @ SV1 )
= $false )
| ( ( ~ ( greater @ ( growth_rate @ SV5 @ SV6 ) @ ( growth_rate @ SV4 @ SV6 ) ) )
= $true )
| ( ( selection_favors @ SV5 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( in_environment @ sK1_E @ SV2 )
= $false )
| ( ( greater_or_equal @ ( sK2_SY11 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV2: $i] :
( ( ( in_environment @ sK1_E @ SV2 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY11 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( greater_or_equal @ SV7 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV7 )
| ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV1: $i,SV4: $i,SV6: $i,SV5: $i] :
( ( ( greater @ ( growth_rate @ SV5 @ SV6 ) @ ( growth_rate @ SV4 @ SV6 ) )
= $false )
| ( ( environment @ SV1 )
= $false )
| ( ( subpopulations @ SV4 @ SV5 @ SV1 @ SV6 )
= $false )
| ( ( selection_favors @ SV5 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( greater_or_equal @ SV7 @ ( sK3_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV7 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( greater_or_equal @ SV7 @ ( sK3_To @ SV3 ) ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV7 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV3: $i,SV7: $i] :
( ( ( greater_or_equal @ SV7 @ ( sK3_To @ SV3 ) )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV7 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(63,plain,
! [SV7: $i,SV3: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV7 )
= $false )
| ( ( greater_or_equal @ SV7 @ ( sK3_To @ SV3 ) )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV7 ) @ ( growth_rate @ first_movers @ SV7 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,63,59,57,56,54,47,19]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:10:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 2
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (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)...
% 0.19/0.40
% 0.19/0.40 ********************************
% 0.19/0.40 * All subproblems solved! *
% 0.19/0.40 ********************************
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox2/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:64,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40
% 0.19/0.40 %**** Beginning of derivation protocol ****
% 0.19/0.40 % SZS output start CNFRefutation
% See solution above
% 0.19/0.40
% 0.19/0.40 %**** End of derivation protocol ****
% 0.19/0.40 %**** no. of clauses in derivation: 65 ****
% 0.19/0.40 %**** clause counter: 64 ****
% 0.19/0.40
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox2/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:64,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------