TSTP Solution File: MGT028+1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : MGT028+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 : 300s
% DateTime : Tue May 7 10:42:30 EDT 2024
% Result : Theorem 36.85s 6.70s
% Output : Refutation 37.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 19
% Syntax : Number of formulae : 110 ( 11 unt; 16 typ; 0 def)
% Number of atoms : 417 ( 23 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 1836 ( 223 ~; 232 |; 29 &;1336 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 117 ( 0 ^ 108 !; 9 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(stable_type,type,
stable: $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(appear_type,type,
appear: $i > $i > $i ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(first_movers_type,type,
first_movers: $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(zero_type,type,
zero: $i ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( greater @ B @ ( appear @ efficient_producers @ A ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( greater @ B @ ( appear @ efficient_producers @ A ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( greater @ B @ ( appear @ efficient_producers @ A ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
environment @ sk1,
inference(cnf,[status(esa)],[5]) ).
thf(4,axiom,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ C ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11) ).
thf(18,plain,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ C ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(72,plain,
! [A: $i] :
( ~ ( stable @ A )
| ( in_environment @ A @ ( sk5 @ A ) )
| ( ( environment @ sk1 )
!= ( environment @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,19]) ).
thf(73,plain,
( ~ ( stable @ sk1 )
| ( in_environment @ sk1 @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( sk1 ))]]) ).
thf(9,plain,
stable @ sk1,
inference(cnf,[status(esa)],[5]) ).
thf(85,plain,
( ~ $true
| ( in_environment @ sk1 @ ( sk5 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[73,9]) ).
thf(86,plain,
in_environment @ sk1 @ ( sk5 @ sk1 ),
inference(simp,[status(thm)],[85]) ).
thf(3,axiom,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A )
& ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) )
=> ? [B: $i] :
( ( greater @ B @ ( appear @ efficient_producers @ A ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
thf(11,plain,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A )
& ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) )
=> ? [B: $i] :
( ( greater @ B @ ( appear @ efficient_producers @ A ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk3 @ B @ A ) @ B )
| ( greater @ ( sk4 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( greater_or_equal @ ( sk3 @ B @ A ) @ B )
| ( greater @ ( sk4 @ A ) @ ( appear @ efficient_producers @ A ) )
| ( ( in_environment @ sk1 @ ( sk5 @ sk1 ) )
!= ( in_environment @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86,17]) ).
thf(193,plain,
( ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(203,plain,
( ~ $true
| ~ $true
| ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(rewrite,[status(thm)],[193,6,9]) ).
thf(204,plain,
( ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk3 @ B @ A ) )
| ( greater @ ( sk4 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk3 @ B @ A ) )
| ( greater @ ( sk4 @ A ) @ ( appear @ efficient_producers @ A ) )
| ( ( in_environment @ sk1 @ ( sk5 @ sk1 ) )
!= ( in_environment @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86,14]) ).
thf(241,plain,
( ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(270,plain,
( ~ $true
| ~ $true
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(rewrite,[status(thm)],[241,6,9]) ).
thf(271,plain,
( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater_or_equal @ B @ ( sk5 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater_or_equal @ B @ ( sk5 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) )
| ( ( environment @ sk1 )
!= ( environment @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,20]) ).
thf(524,plain,
! [A: $i] :
( ~ ( stable @ sk1 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(pattern_uni,[status(thm)],[523:[bind(A,$thf( sk1 ))]]) ).
thf(545,plain,
! [A: $i] :
( ~ ( stable @ sk1 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(simp,[status(thm)],[524]) ).
thf(665,plain,
! [A: $i] :
( ~ $true
| ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(rewrite,[status(thm)],[545,9]) ).
thf(666,plain,
! [A: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(686,plain,
! [A: $i] :
( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater_or_equal @ A @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) )
| ( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) )
!= ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[271,666]) ).
thf(687,plain,
( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[686:[bind(A,$thf( sk3 @ ( sk5 @ sk1 ) @ sk1 ))]]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ B @ A ) ) )
| ( greater @ ( sk4 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ B @ A ) ) )
| ( greater @ ( sk4 @ A ) @ ( appear @ efficient_producers @ A ) )
| ( ( in_environment @ sk1 @ ( sk5 @ sk1 ) )
!= ( in_environment @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86,15]) ).
thf(314,plain,
( ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(365,plain,
( ~ $true
| ~ $true
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(rewrite,[status(thm)],[314,6,9]) ).
thf(366,plain,
( ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) )
| ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(7,plain,
! [A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ( greater_or_equal @ ( sk2 @ A ) @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(10,plain,
! [A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ B @ A ) ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater_or_equal @ C @ ( sk4 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( environment @ B )
| ~ ( stable @ B )
| ~ ( in_environment @ B @ C )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ C @ B ) ) )
| ~ ( greater_or_equal @ D @ ( sk4 @ B ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ D ) )
| ( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ A ) )
!= ( subpopulations @ first_movers @ efficient_producers @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,12]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk2 @ E ))]]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ $true
| ~ $true
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(rewrite,[status(thm)],[39,6,9]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(8,plain,
! [A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(22,plain,
! [A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) )
!= ( greater @ A @ ( appear @ efficient_producers @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(23,plain,
! [A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) )
!= ( greater @ A @ ( appear @ efficient_producers @ sk1 ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ~ ( greater @ C @ ( appear @ efficient_producers @ sk1 ) )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) )
!= ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,23]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater @ C @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ B )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ B @ sk1 ) ) )
| ( ( greater_or_equal @ ( sk2 @ A ) @ A )
!= ( greater_or_equal @ ( sk2 @ C ) @ ( sk4 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,160]) ).
thf(165,plain,
! [A: $i] :
( ~ ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( sk4 @ sk1 )),bind(B,$thf( B )),bind(C,$thf( sk4 @ sk1 ))]]) ).
thf(173,plain,
! [A: $i] :
( ~ ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(221,plain,
! [A: $i] :
( ~ ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ A @ sk1 ) ) )
| ( ( in_environment @ sk1 @ ( sk5 @ sk1 ) )
!= ( in_environment @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[86,173]) ).
thf(222,plain,
( ~ ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( sk5 @ sk1 ))]]) ).
thf(403,plain,
( ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) )
| ( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
!= ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,222]) ).
thf(404,plain,
~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[403:[]]) ).
thf(798,plain,
( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| $false ),
inference(rewrite,[status(thm)],[687,404]) ).
thf(799,plain,
( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) ) ),
inference(simp,[status(thm)],[798]) ).
thf(805,plain,
( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ( ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
!= ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[204,799]) ).
thf(806,plain,
greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ),
inference(pattern_uni,[status(thm)],[805:[]]) ).
thf(823,plain,
! [A: $i] :
( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ A ) )
| ( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
!= ( greater @ A @ ( appear @ efficient_producers @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[806,10]) ).
thf(824,plain,
subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[823:[bind(A,$thf( sk4 @ sk1 ))]]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk3 @ B @ A ) @ B )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater_or_equal @ C @ ( sk4 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( greater_or_equal @ ( sk3 @ B @ A ) @ B )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater_or_equal @ C @ ( sk4 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ C ) )
| ( ( in_environment @ sk1 @ ( sk5 @ sk1 ) )
!= ( in_environment @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86,16]) ).
thf(466,plain,
! [A: $i] :
( ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(pattern_uni,[status(thm)],[465:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 @ sk1 )),bind(C,$thf( C ))]]) ).
thf(482,plain,
! [A: $i] :
( ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(simp,[status(thm)],[466]) ).
thf(826,plain,
! [A: $i] :
( ( greater_or_equal @ ( sk2 @ A ) @ A )
| ( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
!= ( greater @ A @ ( appear @ efficient_producers @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[806,7]) ).
thf(827,plain,
greater_or_equal @ ( sk2 @ ( sk4 @ sk1 ) ) @ ( sk4 @ sk1 ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( sk4 @ sk1 ))]]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk3 @ B @ A ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater_or_equal @ C @ ( sk4 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( environment @ B )
| ~ ( stable @ B )
| ~ ( in_environment @ B @ C )
| ( subpopulations @ first_movers @ efficient_producers @ B @ ( sk3 @ C @ B ) )
| ~ ( greater_or_equal @ D @ ( sk4 @ B ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ D ) )
| ( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ A ) )
!= ( subpopulations @ first_movers @ efficient_producers @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,13]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk2 @ E ))]]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ $true
| ~ $true
| ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(rewrite,[status(thm)],[66,6,9]) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| ~ ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[1045]) ).
thf(1058,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ B ) ) )
| ( ( greater_or_equal @ ( sk2 @ ( sk4 @ sk1 ) ) @ ( sk4 @ sk1 ) )
!= ( greater_or_equal @ ( sk2 @ B ) @ ( sk4 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[827,1046]) ).
thf(1059,plain,
! [A: $i] :
( ~ ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
| ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ ( sk4 @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( A )),bind(B,$thf( sk4 @ sk1 ))]]) ).
thf(833,plain,
! [A: $i] :
( ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) )
| ( ( greater @ ( sk4 @ sk1 ) @ ( appear @ efficient_producers @ sk1 ) )
!= ( greater @ A @ ( appear @ efficient_producers @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[806,8]) ).
thf(834,plain,
~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ ( sk4 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[833:[bind(A,$thf( sk4 @ sk1 ))]]) ).
thf(1165,plain,
! [A: $i] :
( ~ $true
| ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| $false ),
inference(rewrite,[status(thm)],[1059,834,806]) ).
thf(1166,plain,
! [A: $i] :
( ~ ( in_environment @ sk1 @ A )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[1165]) ).
thf(1181,plain,
! [A: $i] :
( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ A @ sk1 ) )
| ( ( in_environment @ sk1 @ ( sk5 @ sk1 ) )
!= ( in_environment @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[86,1166]) ).
thf(1182,plain,
subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ),
inference(pattern_uni,[status(thm)],[1181:[bind(A,$thf( sk5 @ sk1 ))]]) ).
thf(1195,plain,
! [A: $i] :
( ~ ( greater_or_equal @ A @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) )
| ( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) )
!= ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1182,666]) ).
thf(1196,plain,
( ~ ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1195:[bind(A,$thf( sk3 @ ( sk5 @ sk1 ) @ sk1 ))]]) ).
thf(1220,plain,
( ~ ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) )
| $false ),
inference(rewrite,[status(thm)],[1196,404]) ).
thf(1221,plain,
~ ( greater_or_equal @ ( sk3 @ ( sk5 @ sk1 ) @ sk1 ) @ ( sk5 @ sk1 ) ),
inference(simp,[status(thm)],[1220]) ).
thf(2585,plain,
! [A: $i] :
( ~ $true
| ~ $true
| $false
| ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(rewrite,[status(thm)],[482,1221,6,9]) ).
thf(2586,plain,
! [A: $i] :
( ~ ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A )
| ~ ( greater_or_equal @ A @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) ) ),
inference(simp,[status(thm)],[2585]) ).
thf(2605,plain,
! [A: $i] :
( ~ ( greater_or_equal @ A @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ A ) )
| ( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ ( sk4 @ sk1 ) ) )
!= ( subpopulations @ first_movers @ efficient_producers @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[824,2586]) ).
thf(2606,plain,
( ~ ( greater_or_equal @ ( sk2 @ ( sk4 @ sk1 ) ) @ ( sk4 @ sk1 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ ( sk2 @ ( sk4 @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2605:[bind(A,$thf( sk2 @ ( sk4 @ sk1 ) ))]]) ).
thf(2624,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[2606,834,827]) ).
thf(2625,plain,
$false,
inference(simp,[status(thm)],[2624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : MGT028+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n002.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 23:10:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.01 % [INFO] Parsing done (117ms).
% 1.29/1.02 % [INFO] Running in sequential loop mode.
% 1.74/1.25 % [INFO] nitpick registered as external prover.
% 1.74/1.25 % [INFO] Scanning for conjecture ...
% 1.74/1.32 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.95/1.35 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.95/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 1.95/1.37 % [INFO] Type checking passed.
% 1.95/1.37 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 36.85/6.65 % [INFO] Killing All external provers ...
% 36.85/6.67 % Time passed: 6127ms (effective reasoning time: 5640ms)
% 36.85/6.69 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 36.85/6.70 % Axioms used in derivation (2): l11, mp_first_movers_negative_growth
% 36.85/6.70 % No. of inferences in proof: 94
% 36.85/6.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6127 ms resp. 5640 ms w/o parsing
% 37.12/6.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.12/6.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------