%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Thu Sep 24 08:50:40 AM UTC 2026
% Result : Theorem 193.16s 193.48s
% Output : Proof 195.34s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mp1_high_growth_rates,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('theBenchmark.p',mp1_high_growth_rates) ).
fof(l3,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('theBenchmark.p',l3) ).
fof(mp_critical_point_means_FM_and_EP,axiom,
! [E] :
( ( in_environment(E,critical_point(E))
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,critical_point(E)) ),
file('theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(mp_FM_and_EP_when_EP_appears,axiom,
! [E] :
( ( in_environment(E,appear(efficient_producers,E))
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E)) ),
file('theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(mp_difference_between_founding_rates,axiom,
! [T] :
( ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) )
=> decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) ),
file('theBenchmark.p',mp_difference_between_founding_rates) ).
fof(mp_decreasing_function,axiom,
! [E,T,To] :
( ( greater(To,T)
& greater_or_equal(T,appear(efficient_producers,E))
& greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero)
& in_environment(E,To)
& environment(E) )
=> ( decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
=> greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ) ),
file('theBenchmark.p',mp_decreasing_function) ).
fof(mp_negative_growth_rate_difference,axiom,
! [T] :
( greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
<=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
file('theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(mp_positive_growth_rate_difference,axiom,
! [T] :
( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
<=> greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T)) ),
file('theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(mp_durations_are_time_intervals,axiom,
! [E,T1,T2,T] :
( ( greater_or_equal(T,T1)
& greater_or_equal(T2,T)
& in_environment(E,T2)
& in_environment(E,T1)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_durations_are_time_intervals) ).
fof(mp_opening_time_in_duration,axiom,
! [E] :
( environment(E)
=> in_environment(E,start_time(E)) ),
file('theBenchmark.p',mp_opening_time_in_duration) ).
fof(mp_no_FM_before_opening,axiom,
! [E] :
( environment(E)
=> greater_or_equal(appear(first_movers,E),start_time(E)) ),
file('theBenchmark.p',mp_no_FM_before_opening) ).
fof(mp_critical_time_points,axiom,
! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_critical_time_points) ).
fof(mp_contains_FM_and_EP,axiom,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero)
& in_environment(E,T)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('theBenchmark.p',mp_contains_FM_and_EP) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> subpopulations(efficient_producers,first_movers,E,T) ),
file('theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(mp_FM_and_EP_members_EP_appeared,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater_or_equal(T,appear(efficient_producers,E)) ),
file('theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(mp_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('theBenchmark.p',mp_greater_or_equal) ).
fof(mp_relationship_of_growth_rates,axiom,
! [E,T] :
( ( ~ greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ),
file('theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(d1,hypothesis,
! [E,Tc] :
( ( Tc = critical_point(E)
& environment(E) )
=> ( ! [T] :
( ( greater(T,Tc)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) ) ),
file('theBenchmark.p',d1) ).
fof(a10,hypothesis,
! [E,T1,T2,T] :
( ( greater_or_equal(T2,T)
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T2)
& subpopulations(first_movers,efficient_producers,E,T1)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('theBenchmark.p',a10) ).
fof(a12,hypothesis,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) ),
file('theBenchmark.p',a12) ).
fof(prove_t3,conjecture,
! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> selection_favors(first_movers,efficient_producers,T) ),
file('theBenchmark.p',prove_t3) ).
fof(f_1_1,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp1_high_growth_rates]) ).
fof(f_1_2,plain,
! [U_3,U_2,U_1,U_0] :
( selection_favors(U_1,U_2,U_0)
| ~ greater(growth_rate(U_1,U_0),growth_rate(U_2,U_0))
| ~ subpopulations(U_2,U_1,U_3,U_0)
| ~ environment(U_3) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( selection_favors(U_1,U_2,U_0)
| ~ greater(growth_rate(U_1,U_0),growth_rate(U_2,U_0))
| ~ subpopulations(U_2,U_1,U_3,U_0)
| ~ environment(U_3) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [E,T] :
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[l3]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ~ decreases(difference(disbanding_rate(first_movers,U_4),disbanding_rate(efficient_producers,U_4)))
| ~ subpopulations(first_movers,efficient_producers,U_5,U_4)
| ~ environment(U_5) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ decreases(difference(disbanding_rate(first_movers,U_4),disbanding_rate(efficient_producers,U_4)))
| ~ subpopulations(first_movers,efficient_producers,U_5,U_4)
| ~ environment(U_5) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [E] :
( subpopulations(first_movers,efficient_producers,E,critical_point(E))
| ~ in_environment(E,critical_point(E))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_critical_point_means_FM_and_EP]) ).
fof(f_3_2,plain,
! [U_6] :
( subpopulations(first_movers,efficient_producers,U_6,critical_point(U_6))
| ~ in_environment(U_6,critical_point(U_6))
| ~ environment(U_6) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( subpopulations(first_movers,efficient_producers,U_6,critical_point(U_6))
| ~ in_environment(U_6,critical_point(U_6))
| ~ environment(U_6) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [E] :
( subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E))
| ~ in_environment(E,appear(efficient_producers,E))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_FM_and_EP_when_EP_appears]) ).
fof(f_4_2,plain,
! [U_7] :
( subpopulations(first_movers,efficient_producers,U_7,appear(efficient_producers,U_7))
| ~ in_environment(U_7,appear(efficient_producers,U_7))
| ~ environment(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( subpopulations(first_movers,efficient_producers,U_7,appear(efficient_producers,U_7))
| ~ in_environment(U_7,appear(efficient_producers,U_7))
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [T] :
( decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) ),
inference(fof_nnf,[status(thm)],[mp_difference_between_founding_rates]) ).
fof(f_5_2,plain,
! [U_8] :
( decreases(difference(growth_rate(first_movers,U_8),growth_rate(efficient_producers,U_8)))
| decreases(difference(disbanding_rate(first_movers,U_8),disbanding_rate(efficient_producers,U_8)))
| ~ decreases(difference(founding_rate(first_movers,U_8),founding_rate(efficient_producers,U_8))) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( decreases(difference(growth_rate(first_movers,U_8),growth_rate(efficient_producers,U_8)))
| decreases(difference(disbanding_rate(first_movers,U_8),disbanding_rate(efficient_producers,U_8)))
| ~ decreases(difference(founding_rate(first_movers,U_8),founding_rate(efficient_producers,U_8))) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [E,T,To] :
( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
| ~ decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| ~ greater(To,T)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero)
| ~ in_environment(E,To)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_decreasing_function]) ).
fof(f_6_2,plain,
! [U_11,U_10,U_9] :
( greater(difference(growth_rate(first_movers,U_10),growth_rate(efficient_producers,U_10)),zero)
| ~ decreases(difference(growth_rate(first_movers,U_10),growth_rate(efficient_producers,U_10)))
| ~ greater(U_9,U_10)
| ~ greater_or_equal(U_10,appear(efficient_producers,U_11))
| ~ greater_or_equal(difference(growth_rate(first_movers,U_9),growth_rate(efficient_producers,U_9)),zero)
| ~ in_environment(U_11,U_9)
| ~ environment(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_11,U_10] :
( ! [U_9] :
( ~ greater(U_9,U_10)
| ~ greater_or_equal(difference(growth_rate(first_movers,U_9),growth_rate(efficient_producers,U_9)),zero)
| ~ in_environment(U_11,U_9) )
| ~ greater_or_equal(U_10,appear(efficient_producers,U_11))
| ~ environment(U_11)
| greater(difference(growth_rate(first_movers,U_10),growth_rate(efficient_producers,U_10)),zero)
| ~ decreases(difference(growth_rate(first_movers,U_10),growth_rate(efficient_producers,U_10))) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( ~ greater(U_9,U_10)
| ~ greater_or_equal(difference(growth_rate(first_movers,U_9),growth_rate(efficient_producers,U_9)),zero)
| ~ in_environment(U_11,U_9)
| ~ greater_or_equal(U_10,appear(efficient_producers,U_11))
| ~ environment(U_11)
| greater(difference(growth_rate(first_movers,U_10),growth_rate(efficient_producers,U_10)),zero)
| ~ decreases(difference(growth_rate(first_movers,U_10),growth_rate(efficient_producers,U_10))) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [T] :
( ( greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) ) ),
inference(fof_nnf,[status(thm)],[mp_negative_growth_rate_difference]) ).
fof(f_7_2,plain,
! [U_12] :
( ( greater(zero,difference(growth_rate(first_movers,U_12),growth_rate(efficient_producers,U_12)))
| ~ greater(growth_rate(efficient_producers,U_12),growth_rate(first_movers,U_12)) )
& ( greater(growth_rate(efficient_producers,U_12),growth_rate(first_movers,U_12))
| ~ greater(zero,difference(growth_rate(first_movers,U_12),growth_rate(efficient_producers,U_12))) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_14] :
( greater(zero,difference(growth_rate(first_movers,U_14),growth_rate(efficient_producers,U_14)))
| ~ greater(growth_rate(efficient_producers,U_14),growth_rate(first_movers,U_14)) )
& ! [U_13] :
( greater(growth_rate(efficient_producers,U_13),growth_rate(first_movers,U_13))
| ~ greater(zero,difference(growth_rate(first_movers,U_13),growth_rate(efficient_producers,U_13))) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( greater(growth_rate(efficient_producers,U_13),growth_rate(first_movers,U_13))
| ~ greater(zero,difference(growth_rate(first_movers,U_13),growth_rate(efficient_producers,U_13))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( greater(zero,difference(growth_rate(first_movers,U_14),growth_rate(efficient_producers,U_14)))
| ~ greater(growth_rate(efficient_producers,U_14),growth_rate(first_movers,U_14)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [T] :
( ( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
| ~ greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T)) )
& ( greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T))
| ~ greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ) ),
inference(fof_nnf,[status(thm)],[mp_positive_growth_rate_difference]) ).
fof(f_8_2,plain,
! [U_15] :
( ( greater(difference(growth_rate(first_movers,U_15),growth_rate(efficient_producers,U_15)),zero)
| ~ greater(growth_rate(first_movers,U_15),growth_rate(efficient_producers,U_15)) )
& ( greater(growth_rate(first_movers,U_15),growth_rate(efficient_producers,U_15))
| ~ greater(difference(growth_rate(first_movers,U_15),growth_rate(efficient_producers,U_15)),zero) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_17] :
( greater(difference(growth_rate(first_movers,U_17),growth_rate(efficient_producers,U_17)),zero)
| ~ greater(growth_rate(first_movers,U_17),growth_rate(efficient_producers,U_17)) )
& ! [U_16] :
( greater(growth_rate(first_movers,U_16),growth_rate(efficient_producers,U_16))
| ~ greater(difference(growth_rate(first_movers,U_16),growth_rate(efficient_producers,U_16)),zero) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( greater(growth_rate(first_movers,U_16),growth_rate(efficient_producers,U_16))
| ~ greater(difference(growth_rate(first_movers,U_16),growth_rate(efficient_producers,U_16)),zero) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( greater(difference(growth_rate(first_movers,U_17),growth_rate(efficient_producers,U_17)),zero)
| ~ greater(growth_rate(first_movers,U_17),growth_rate(efficient_producers,U_17)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [E,T1,T2,T] :
( in_environment(E,T)
| ~ greater_or_equal(T,T1)
| ~ greater_or_equal(T2,T)
| ~ in_environment(E,T2)
| ~ in_environment(E,T1)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_durations_are_time_intervals]) ).
fof(f_9_2,plain,
! [U_21,U_20,U_19,U_18] :
( in_environment(U_21,U_18)
| ~ greater_or_equal(U_18,U_20)
| ~ greater_or_equal(U_19,U_18)
| ~ in_environment(U_21,U_19)
| ~ in_environment(U_21,U_20)
| ~ environment(U_21) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( in_environment(U_21,U_18)
| ~ greater_or_equal(U_18,U_20)
| ~ greater_or_equal(U_19,U_18)
| ~ in_environment(U_21,U_19)
| ~ in_environment(U_21,U_20)
| ~ environment(U_21) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [E] :
( in_environment(E,start_time(E))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_opening_time_in_duration]) ).
fof(f_10_2,plain,
! [U_22] :
( in_environment(U_22,start_time(U_22))
| ~ environment(U_22) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( in_environment(U_22,start_time(U_22))
| ~ environment(U_22) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [E] :
( greater_or_equal(appear(first_movers,E),start_time(E))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_no_FM_before_opening]) ).
fof(f_11_2,plain,
! [U_23] :
( greater_or_equal(appear(first_movers,U_23),start_time(U_23))
| ~ environment(U_23) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( greater_or_equal(appear(first_movers,U_23),start_time(U_23))
| ~ environment(U_23) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [E,T] :
( in_environment(E,T)
| ~ greater(critical_point(E),T)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,critical_point(E))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_critical_time_points]) ).
fof(f_12_2,plain,
! [U_25,U_24] :
( in_environment(U_25,U_24)
| ~ greater(critical_point(U_25),U_24)
| ~ greater_or_equal(U_24,appear(efficient_producers,U_25))
| ~ in_environment(U_25,critical_point(U_25))
| ~ environment(U_25) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( in_environment(U_25,U_24)
| ~ greater(critical_point(U_25),U_24)
| ~ greater_or_equal(U_24,appear(efficient_producers,U_25))
| ~ in_environment(U_25,critical_point(U_25))
| ~ environment(U_25) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [E,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_contains_FM_and_EP]) ).
fof(f_13_2,plain,
! [U_27,U_26] :
( subpopulations(first_movers,efficient_producers,U_27,U_26)
| ~ greater(cardinality_at_time(efficient_producers,U_26),zero)
| ~ greater(cardinality_at_time(first_movers,U_26),zero)
| ~ in_environment(U_27,U_26)
| ~ environment(U_27) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( subpopulations(first_movers,efficient_producers,U_27,U_26)
| ~ greater(cardinality_at_time(efficient_producers,U_26),zero)
| ~ greater(cardinality_at_time(first_movers,U_26),zero)
| ~ in_environment(U_27,U_26)
| ~ environment(U_27) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [E,T] :
( subpopulations(efficient_producers,first_movers,E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations]) ).
fof(f_14_2,plain,
! [U_29,U_28] :
( subpopulations(efficient_producers,first_movers,U_29,U_28)
| ~ subpopulations(first_movers,efficient_producers,U_29,U_28)
| ~ environment(U_29) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( subpopulations(efficient_producers,first_movers,U_29,U_28)
| ~ subpopulations(first_movers,efficient_producers,U_29,U_28)
| ~ environment(U_29) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [E,T] :
( greater_or_equal(T,appear(efficient_producers,E))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_FM_and_EP_members_EP_appeared]) ).
fof(f_15_2,plain,
! [U_31,U_30] :
( greater_or_equal(U_30,appear(efficient_producers,U_31))
| ~ subpopulations(first_movers,efficient_producers,U_31,U_30)
| ~ environment(U_31) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( greater_or_equal(U_30,appear(efficient_producers,U_31))
| ~ subpopulations(first_movers,efficient_producers,U_31,U_30)
| ~ environment(U_31) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [X,Y] :
( ( greater_or_equal(X,Y)
| ( X != Y
& ~ greater(X,Y) ) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(fof_nnf,[status(thm)],[mp_greater_or_equal]) ).
fof(f_16_2,plain,
! [U_33,U_32] :
( ( greater_or_equal(U_33,U_32)
| ( U_33 != U_32
& ~ greater(U_33,U_32) ) )
& ( U_33 = U_32
| greater(U_33,U_32)
| ~ greater_or_equal(U_33,U_32) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_37,U_35] :
( greater_or_equal(U_37,U_35)
| ( U_37 != U_35
& ~ greater(U_37,U_35) ) )
& ! [U_36,U_34] :
( U_36 = U_34
| greater(U_36,U_34)
| ~ greater_or_equal(U_36,U_34) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( U_36 = U_34
| greater(U_36,U_34)
| ~ greater_or_equal(U_36,U_34) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( ~ greater(U_37,U_35)
| greater_or_equal(U_37,U_35) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
( U_37 != U_35
| greater_or_equal(U_37,U_35) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [E,T] :
( greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
| greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_relationship_of_growth_rates]) ).
fof(f_17_2,plain,
! [U_39,U_38] :
( greater_or_equal(difference(growth_rate(first_movers,U_38),growth_rate(efficient_producers,U_38)),zero)
| greater(zero,difference(growth_rate(first_movers,U_38),growth_rate(efficient_producers,U_38)))
| ~ subpopulations(first_movers,efficient_producers,U_39,U_38)
| ~ environment(U_39) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( greater_or_equal(difference(growth_rate(first_movers,U_38),growth_rate(efficient_producers,U_38)),zero)
| greater(zero,difference(growth_rate(first_movers,U_38),growth_rate(efficient_producers,U_38)))
| ~ subpopulations(first_movers,efficient_producers,U_39,U_38)
| ~ environment(U_39) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [E,Tc] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) )
| Tc != critical_point(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[d1]) ).
fof(f_18_2,plain,
! [U_42,U_41] :
( ( ! [U_40] :
( greater(growth_rate(efficient_producers,U_40),growth_rate(first_movers,U_40))
| ~ greater(U_40,U_41)
| ~ subpopulations(first_movers,efficient_producers,U_42,U_40) )
& ~ greater(growth_rate(efficient_producers,U_41),growth_rate(first_movers,U_41)) )
| U_41 != critical_point(U_42)
| ~ environment(U_42) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ greater(growth_rate(efficient_producers,U_41),growth_rate(first_movers,U_41))
| U_41 != critical_point(U_42)
| ~ environment(U_42) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( greater(growth_rate(efficient_producers,U_40),growth_rate(first_movers,U_40))
| ~ greater(U_40,U_41)
| ~ subpopulations(first_movers,efficient_producers,U_42,U_40)
| U_41 != critical_point(U_42)
| ~ environment(U_42) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [E,T1,T2,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater_or_equal(T2,T)
| ~ greater_or_equal(T,T1)
| ~ subpopulations(first_movers,efficient_producers,E,T2)
| ~ subpopulations(first_movers,efficient_producers,E,T1)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[a10]) ).
fof(f_19_2,plain,
! [U_46,U_45,U_44,U_43] :
( subpopulations(first_movers,efficient_producers,U_46,U_43)
| ~ greater_or_equal(U_44,U_43)
| ~ greater_or_equal(U_43,U_45)
| ~ subpopulations(first_movers,efficient_producers,U_46,U_44)
| ~ subpopulations(first_movers,efficient_producers,U_46,U_45)
| ~ environment(U_46) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( subpopulations(first_movers,efficient_producers,U_46,U_43)
| ~ greater_or_equal(U_44,U_43)
| ~ greater_or_equal(U_43,U_45)
| ~ subpopulations(first_movers,efficient_producers,U_46,U_44)
| ~ subpopulations(first_movers,efficient_producers,U_46,U_45)
| ~ environment(U_46) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [E,T] :
( decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[a12]) ).
fof(f_20_2,plain,
! [U_48,U_47] :
( decreases(difference(founding_rate(first_movers,U_47),founding_rate(efficient_producers,U_47)))
| ~ subpopulations(first_movers,efficient_producers,U_48,U_47)
| ~ environment(U_48) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( decreases(difference(founding_rate(first_movers,U_47),founding_rate(efficient_producers,U_47)))
| ~ subpopulations(first_movers,efficient_producers,U_48,U_47)
| ~ environment(U_48) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,negated_conjecture,
~ ! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> selection_favors(first_movers,efficient_producers,T) ),
inference(negate,[status(cth)],[prove_t3]) ).
fof(f_21_2,negated_conjecture,
? [E,T] :
( ~ selection_favors(first_movers,efficient_producers,T)
& greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) ),
inference(fof_nnf,[status(thm)],[f_21_1]) ).
fof(f_21_3,negated_conjecture,
? [U_50,U_49] :
( ~ selection_favors(first_movers,efficient_producers,U_49)
& greater(critical_point(U_50),U_49)
& greater_or_equal(U_49,appear(efficient_producers,U_50))
& in_environment(U_50,critical_point(U_50))
& environment(U_50) ),
inference(variable_rename,[status(thm)],[f_21_2]) ).
fof(f_21_4,negated_conjecture,
? [U_49] :
( ~ selection_favors(first_movers,efficient_producers,U_49)
& greater(critical_point(sK1),U_49)
& greater_or_equal(U_49,appear(efficient_producers,sK1))
& in_environment(sK1,critical_point(sK1))
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_50,sK1)],[f_21_3]) ).
fof(f_21_5,negated_conjecture,
( ~ selection_favors(first_movers,efficient_producers,sK2)
& greater(critical_point(sK1),sK2)
& greater_or_equal(sK2,appear(efficient_producers,sK1))
& in_environment(sK1,critical_point(sK1))
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_49,sK2)],[f_21_4]) ).
cnf(f_21_6,negated_conjecture,
environment(sK1),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,negated_conjecture,
in_environment(sK1,critical_point(sK1)),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,negated_conjecture,
greater_or_equal(sK2,appear(efficient_producers,sK1)),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,negated_conjecture,
greater(critical_point(sK1),sK2),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_10,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sK2),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( growth_rate(Eq_x_0,Eq_x_1) = growth_rate(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( disbanding_rate(Eq_x_0,Eq_x_1) = disbanding_rate(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( difference(Eq_x_0,Eq_x_1) = difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( critical_point(Eq_x_0) = critical_point(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( appear(Eq_x_0,Eq_x_1) = appear(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( founding_rate(Eq_x_0,Eq_x_1) = founding_rate(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( start_time(Eq_x_0) = start_time(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( cardinality_at_time(Eq_x_0,Eq_x_1) = cardinality_at_time(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( environment(Eq_y_0)
| ~ environment(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( subpopulations(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ subpopulations(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( greater(Eq_y_0,Eq_y_1)
| ~ greater(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( selection_favors(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ selection_favors(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( decreases(Eq_y_0)
| ~ decreases(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( in_environment(Eq_y_0,Eq_y_1)
| ~ in_environment(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( greater_or_equal(Eq_y_0,Eq_y_1)
| ~ greater_or_equal(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 16:13:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 193.16/193.48 % SZS status Theorem for theBenchmark
% 193.16/193.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------