%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT021-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:23:59 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 49
% Syntax : Number of formulae : 111 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 825 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 1303 ( 639 ~; 598 |; 0 &)
% ( 66 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 50 ( 50 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 229 ( 203 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
tff(greater_type,type,
greater: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(equilibrium_type,type,
equilibrium: $i > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(zero_type,type,
zero: $i ).
tff(number_of_organizations_type,type,
number_of_organizations: ( $i * $i ) > $i ).
tff(subpopulations_type,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(efficient_producers_type,type,
efficient_producers: $i ).
tff(first_movers_type,type,
first_movers: $i ).
tff(environment_type,type,
environment: $i > $o ).
tff(in_environment_type,type,
in_environment: ( $i * $i ) > $o ).
tff(decreases_type,type,
decreases: $i > $o ).
tff(resources_type,type,
resources: ( $i * $i ) > $i ).
tff(increases_type,type,
increases: $i > $o ).
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(disbanding_rate_type,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(constant_type,type,
constant: $i > $o ).
tff(1,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
<=> subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3_36) ).
tff(3,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( environment(sk1)
<=> environment(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3_35) ).
tff(6,plain,
environment(sk1),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [B: $i,A: $i] :
refl(( ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [B: $i,A: $i] :
rewrite(( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(number_of_organizations(A,B),zero) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(number_of_organizations(A,B),zero) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(number_of_organizations(A,B),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty_28) ).
tff(13,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| greater(number_of_organizations(sk1,sk2),zero) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| greater(number_of_organizations(sk1,sk2),zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| greater(number_of_organizations(sk1,sk2),zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| greater(number_of_organizations(A,B),zero) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| greater(number_of_organizations(sk1,sk2),zero) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
greater(number_of_organizations(sk1,sk2),zero),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [B: $i,A: $i] :
refl(( ( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [B: $i,A: $i] :
rewrite(( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) )
<=> ( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment_27) ).
tff(27,plain,
! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
in_environment(sk1,sk2),
inference(unit_resolution,[status(thm)],[36,30,6,3]) ).
tff(38,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
<=> decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3_37) ).
tff(40,plain,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [A: $i] :
refl(( ( ~ decreases(A)
| ~ increases(A) )
<=> ( ~ decreases(A)
| ~ increases(A) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) )
<=> ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) )
<=> ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [A: $i] :
rewrite(( ( ~ increases(A)
| ~ decreases(A) )
<=> ( ~ decreases(A)
| ~ increases(A) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [A: $i] :
( ~ increases(A)
| ~ decreases(A) )
<=> ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [A: $i] :
( ~ increases(A)
| ~ decreases(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_increase_not_decrease_29) ).
tff(47,plain,
! [A: $i] :
( ~ decreases(A)
| ~ increases(A) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [A: $i] :
( ~ decreases(A)
| ~ increases(A) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [A: $i] :
( ~ decreases(A)
| ~ increases(A) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [A: $i] :
( ~ decreases(A)
| ~ increases(A) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) )
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) )
<=> ( ~ ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) )
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) )
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [A: $i] :
( ~ decreases(A)
| ~ increases(A) )
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(unit_resolution,[status(thm)],[53,50,40]) ).
tff(55,plain,
^ [B: $i,A: $i] :
refl(( ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
^ [B: $i,A: $i] :
trans(monotonicity(rewrite(( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(resources(A,B)) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(resources(A,B)) ) )),
( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(resources(A,B))
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(resources(A,B))
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ) )),
rewrite(( ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(resources(A,B))
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ) )),
( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(resources(A,B))
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(resources(A,B))
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(resources(A,B))
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_33) ).
tff(61,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2)) ),
inference(unit_resolution,[status(thm)],[67,64,6,3]) ).
tff(69,plain,
~ decreases(resources(sk1,sk2)),
inference(unit_resolution,[status(thm)],[68,54]) ).
tff(70,plain,
^ [B: $i,A: $i] :
refl(( ( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
<=> ( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
^ [B: $i,A: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero) )
<=> ( ~ environment(A)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B) )
<=> ( ~ environment(A)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ greater(equilibrium(A),B) ) )),
rewrite(( ( ~ environment(A)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ greater(equilibrium(A),B) )
<=> ( ~ environment(A)
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B) )
<=> ( ~ environment(A)
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B)
| decreases(resources(A,B)) )
<=> ( ~ environment(A)
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| decreases(resources(A,B)) ) )),
rewrite(( ( ~ environment(A)
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| decreases(resources(A,B)) )
<=> ( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B)
| decreases(resources(A,B)) )
<=> ( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B)
| decreases(resources(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B)
| decreases(resources(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_31) ).
tff(76,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ greater(equilibrium(sk1),sk2),
inference(unit_resolution,[status(thm)],[82,79,6,69,37,20]) ).
tff(84,plain,
^ [B: $i,A: $i] :
refl(( ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
^ [B: $i,A: $i] :
trans(monotonicity(rewrite(( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(resources(A,B)) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ constant(resources(A,B)) ) )),
( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(resources(A,B))
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ constant(resources(A,B))
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ) )),
rewrite(( ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ constant(resources(A,B))
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ) )),
( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(resources(A,B))
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(resources(A,B))
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(resources(A,B))
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_34) ).
tff(90,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B)) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
~ constant(resources(sk1,sk2)),
inference(unit_resolution,[status(thm)],[96,93,6,3,40]) ).
tff(98,plain,
^ [B: $i,A: $i] :
refl(( ( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
<=> ( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
^ [B: $i,A: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero) )
<=> ( ~ environment(A)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B) )
<=> ( ~ environment(A)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| greater(equilibrium(A),B) ) )),
rewrite(( ( ~ environment(A)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| greater(equilibrium(A),B) )
<=> ( ~ environment(A)
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B) )
<=> ( ~ environment(A)
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B)
| constant(resources(A,B)) )
<=> ( ~ environment(A)
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| constant(resources(A,B)) ) )),
rewrite(( ( ~ environment(A)
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| constant(resources(A,B)) )
<=> ( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B)
| constant(resources(A,B)) )
<=> ( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B)
| constant(resources(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B)
| constant(resources(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_32) ).
tff(104,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i] :
( ~ environment(A)
| constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B) )
| ~ environment(sk1)
| constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,107,6,97,37,20,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 12:04:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.41 % SZS status Unsatisfiable
% 0.12/0.41 % SZS output start Proof
% See solution above
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------