%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 08:02:10 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 23
% Syntax : Number of formulae : 156 ( 24 unt; 0 def)
% Number of atoms : 486 ( 66 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 533 ( 203 ~; 330 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 163 ( 8 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l7_47,axiom,
environment(sk1),
file('theBenchmark.p',prove_l7_47) ).
cnf(c_1,plain,
environment(sk1),
inference(clausify,[status(thm)],[prove_l7_47]) ).
fof(mp_time_point_occur_45,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,VAR_1)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_time_point_occur_45) ).
cnf(c_3,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occur_45]) ).
fof(mp_non_zero_producers_44,axiom,
! [VAR_0,VAR_1] :
( greater(cardinality_at_time(efficient_producers,VAR_1),zero)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_non_zero_producers_44) ).
cnf(c_4,plain,
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_non_zero_producers_44]) ).
fof(mp_non_zero_producers_43,axiom,
! [VAR_0,VAR_1] :
( greater(cardinality_at_time(first_movers,VAR_1),zero)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_non_zero_producers_43) ).
cnf(c_5,plain,
( greater(cardinality_at_time(first_movers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_non_zero_producers_43]) ).
fof(mp_growth_rate_42,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(zero,growth_rate(VAR_2,VAR_1))
| ~ decreases(cardinality_at_time(VAR_2,VAR_1))
| ~ greater(cardinality_at_time(VAR_2,VAR_1),zero)
| ~ subpopulation(VAR_2,VAR_0,VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_growth_rate_42) ).
cnf(c_6,plain,
( greater(zero,growth_rate(C,B))
| ~ decreases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_growth_rate_42]) ).
fof(mp_growth_rate_41,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(growth_rate(VAR_2,VAR_1),zero)
| ~ increases(cardinality_at_time(VAR_2,VAR_1))
| ~ greater(cardinality_at_time(VAR_2,VAR_1),zero)
| ~ subpopulation(VAR_2,VAR_0,VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_growth_rate_41) ).
cnf(c_7,plain,
( greater(growth_rate(C,B),zero)
| ~ increases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_growth_rate_41]) ).
fof(mp_growth_rate_40,axiom,
! [VAR_0,VAR_1,VAR_2] :
( growth_rate(VAR_2,VAR_1) = zero
| ~ constant(cardinality_at_time(VAR_2,VAR_1))
| ~ greater(cardinality_at_time(VAR_2,VAR_1),zero)
| ~ subpopulation(VAR_2,VAR_0,VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_growth_rate_40) ).
cnf(c_8,plain,
( growth_rate(C,B) = zero
| ~ constant(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_growth_rate_40]) ).
fof(mp_subpopulations_31,axiom,
! [VAR_0,VAR_1] :
( subpopulation(efficient_producers,VAR_0,VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_subpopulations_31) ).
cnf(c_9,plain,
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_subpopulations_31]) ).
fof(mp_subpopulations_30,axiom,
! [VAR_0,VAR_1] :
( subpopulation(first_movers,VAR_0,VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_subpopulations_30) ).
cnf(c_10,plain,
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_subpopulations_30]) ).
fof(mp_only_members_28,axiom,
! [VAR_0,VAR_1,VAR_2] :
( number_of_organizations(VAR_0,VAR_2) = sum(cardinality_at_time(first_movers,VAR_2),cardinality_at_time(efficient_producers,VAR_2))
| VAR_1 != efficient_producers
| ~ subpopulation(VAR_1,VAR_0,VAR_2)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_only_members_28) ).
cnf(c_12,plain,
( number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C))
| B != efficient_producers
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_only_members_28]) ).
cnf(c_15,plain,
( number_of_organizations(sk1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
| A != efficient_producers
| ~ subpopulation(A,sk1,B) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_16,plain,
( number_of_organizations(sk1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
| efficient_producers != A
| ~ subpopulation(A,sk1,B) ),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_19,plain,
( subpopulation(first_movers,sk1,A)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_20,plain,
( subpopulation(efficient_producers,sk1,A)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_21,plain,
( growth_rate(B,A) = zero
| ~ constant(cardinality_at_time(B,A))
| ~ greater(cardinality_at_time(B,A),zero)
| ~ subpopulation(B,sk1,A)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_22,plain,
( greater(growth_rate(B,A),zero)
| ~ increases(cardinality_at_time(B,A))
| ~ greater(cardinality_at_time(B,A),zero)
| ~ subpopulation(B,sk1,A)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_23,plain,
( greater(zero,growth_rate(B,A))
| ~ decreases(cardinality_at_time(B,A))
| ~ greater(cardinality_at_time(B,A),zero)
| ~ subpopulation(B,sk1,A)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_24,plain,
( greater(cardinality_at_time(first_movers,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_25,plain,
( greater(cardinality_at_time(efficient_producers,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_26,plain,
( in_environment(sk1,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(prove_l7_52,axiom,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('theBenchmark.p',prove_l7_52) ).
cnf(c_29,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(clausify,[status(thm)],[prove_l7_52]) ).
fof(prove_l7_51,axiom,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('theBenchmark.p',prove_l7_51) ).
cnf(c_30,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(clausify,[status(thm)],[prove_l7_51]) ).
fof(prove_l7_50,axiom,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
file('theBenchmark.p',prove_l7_50) ).
cnf(c_31,plain,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
inference(clausify,[status(thm)],[prove_l7_50]) ).
fof(prove_l7_49,axiom,
constant(number_of_organizations(sk1,sk2)),
file('theBenchmark.p',prove_l7_49) ).
cnf(c_32,plain,
constant(number_of_organizations(sk1,sk2)),
inference(clausify,[status(thm)],[prove_l7_49]) ).
fof(prove_l7_48,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('theBenchmark.p',prove_l7_48) ).
cnf(c_33,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(clausify,[status(thm)],[prove_l7_48]) ).
fof(mp_abc_sum_increase_39,axiom,
! [VAR_0,VAR_1,VAR_2] :
( increases(VAR_2)
| decreases(VAR_2)
| constant(VAR_2)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_39) ).
cnf(c_34,plain,
( increases(C)
| decreases(C)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_39]) ).
cnf(c_35,plain,
( increases(B)
| decreases(B)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_34]) ).
fof(mp_abc_sum_increase_38,axiom,
! [VAR_0,VAR_1,VAR_2] :
( decreases(VAR_1)
| decreases(VAR_2)
| constant(VAR_2)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_38) ).
cnf(c_36,plain,
( decreases(B)
| decreases(C)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_38]) ).
cnf(c_37,plain,
( decreases(A)
| decreases(B)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_36]) ).
fof(mp_abc_sum_increase_37,axiom,
! [VAR_0,VAR_1,VAR_2] :
( increases(VAR_2)
| increases(VAR_1)
| constant(VAR_2)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_37) ).
cnf(c_38,plain,
( increases(C)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_37]) ).
cnf(c_39,plain,
( increases(B)
| increases(A)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_38]) ).
fof(mp_abc_sum_increase_36,axiom,
! [VAR_0,VAR_1,VAR_2] :
( decreases(VAR_1)
| increases(VAR_1)
| constant(VAR_2)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_36) ).
cnf(c_40,plain,
( decreases(B)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_36]) ).
cnf(c_41,plain,
( decreases(A)
| increases(A)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_40]) ).
fof(mp_abc_sum_increase_35,axiom,
! [VAR_0,VAR_1,VAR_2] :
( increases(VAR_2)
| decreases(VAR_2)
| constant(VAR_1)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_35) ).
cnf(c_42,plain,
( increases(C)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_35]) ).
cnf(c_43,plain,
( increases(B)
| decreases(B)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_42]) ).
fof(mp_abc_sum_increase_34,axiom,
! [VAR_0,VAR_1,VAR_2] :
( decreases(VAR_1)
| decreases(VAR_2)
| constant(VAR_1)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_34) ).
cnf(c_44,plain,
( decreases(B)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_34]) ).
cnf(c_45,plain,
( decreases(A)
| decreases(B)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_44]) ).
fof(mp_abc_sum_increase_33,axiom,
! [VAR_0,VAR_1,VAR_2] :
( increases(VAR_2)
| increases(VAR_1)
| constant(VAR_1)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_33) ).
cnf(c_46,plain,
( increases(C)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_33]) ).
cnf(c_47,plain,
( increases(B)
| increases(A)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_46]) ).
fof(mp_abc_sum_increase_32,axiom,
! [VAR_0,VAR_1,VAR_2] :
( decreases(VAR_1)
| increases(VAR_1)
| constant(VAR_1)
| ~ constant(VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',mp_abc_sum_increase_32) ).
cnf(c_48,plain,
( decreases(B)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[mp_abc_sum_increase_32]) ).
cnf(c_49,plain,
( decreases(A)
| increases(A)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_52,plain,
in_environment(sk1,sk2),
inference(resolve,[status(thm)],[c_33,c_26]) ).
cnf(c_53,plain,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(resolve,[status(thm)],[c_33,c_25]) ).
cnf(c_54,plain,
greater(cardinality_at_time(first_movers,sk2),zero),
inference(resolve,[status(thm)],[c_33,c_24]) ).
cnf(c_55,plain,
( increases(B)
| decreases(B)
| constant(B)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_56,plain,
( decreases(A)
| decreases(B)
| constant(B)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_37,c_32]) ).
cnf(c_58,plain,
( increases(B)
| increases(A)
| constant(B)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_39,c_32]) ).
cnf(c_60,plain,
( decreases(A)
| increases(A)
| constant(B)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_41,c_32]) ).
cnf(c_61,plain,
( increases(B)
| decreases(B)
| constant(A)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_43,c_32]) ).
cnf(c_62,plain,
( decreases(A)
| decreases(B)
| constant(A)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_45,c_32]) ).
cnf(c_63,plain,
( increases(B)
| increases(A)
| constant(A)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_47,c_32]) ).
cnf(c_64,plain,
( decreases(A)
| increases(A)
| constant(A)
| sum(A,B) != number_of_organizations(sk1,sk2) ),
inference(resolve,[status(thm)],[c_49,c_32]) ).
cnf(c_65,plain,
subpopulation(efficient_producers,sk1,sk2),
inference(resolve,[status(thm)],[c_52,c_20]) ).
cnf(c_66,plain,
subpopulation(first_movers,sk1,sk2),
inference(resolve,[status(thm)],[c_52,c_19]) ).
cnf(c_153,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(resolve,[status(thm)],[c_65,c_23]) ).
cnf(c_154,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolve,[status(thm)],[c_52,c_153]) ).
cnf(c_67,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_53,c_154]) ).
cnf(c_155,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(resolve,[status(thm)],[c_65,c_22]) ).
cnf(c_156,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolve,[status(thm)],[c_52,c_155]) ).
cnf(c_68,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_53,c_156]) ).
cnf(c_157,plain,
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(resolve,[status(thm)],[c_65,c_21]) ).
cnf(c_158,plain,
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolve,[status(thm)],[c_52,c_157]) ).
cnf(c_69,plain,
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_53,c_158]) ).
cnf(c_159,plain,
( number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
| efficient_producers != efficient_producers ),
inference(resolve,[status(thm)],[c_65,c_16]) ).
cnf(c_71,plain,
number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_160,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(resolve,[status(thm)],[c_66,c_23]) ).
cnf(c_161,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolve,[status(thm)],[c_52,c_160]) ).
cnf(c_72,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_54,c_161]) ).
cnf(c_162,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(resolve,[status(thm)],[c_66,c_22]) ).
cnf(c_163,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolve,[status(thm)],[c_52,c_162]) ).
cnf(c_73,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_54,c_163]) ).
cnf(c_164,plain,
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ in_environment(sk1,sk2) ),
inference(resolve,[status(thm)],[c_66,c_21]) ).
cnf(c_165,plain,
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolve,[status(thm)],[c_52,c_164]) ).
cnf(c_74,plain,
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_54,c_165]) ).
cnf(c_166,plain,
( decreases(A)
| increases(A)
| constant(A)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_75,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_166]) ).
cnf(c_167,plain,
( increases(B)
| increases(A)
| constant(A)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_76,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_167]) ).
cnf(c_168,plain,
( decreases(A)
| decreases(B)
| constant(A)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_77,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_168]) ).
cnf(c_169,plain,
( increases(B)
| decreases(B)
| constant(A)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_78,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_169]) ).
cnf(c_170,plain,
( decreases(A)
| increases(A)
| constant(B)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_79,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_170]) ).
cnf(c_171,plain,
( increases(B)
| increases(A)
| constant(B)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_80,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_171]) ).
cnf(c_172,plain,
( decreases(A)
| decreases(B)
| constant(B)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_81,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_172]) ).
cnf(c_173,plain,
( increases(B)
| decreases(B)
| constant(B)
| number_of_organizations(sk1,sk2) != sum(A,B) ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_82,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_71,c_173]) ).
cnf(c_94,plain,
( greater(growth_rate(first_movers,sk2),zero)
| decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_75,c_73]) ).
cnf(c_95,plain,
( greater(growth_rate(first_movers,sk2),zero)
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_76,c_73]) ).
cnf(c_96,plain,
( greater(zero,growth_rate(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_77,c_72]) ).
cnf(c_97,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_78,c_68]) ).
cnf(c_98,plain,
( greater(growth_rate(first_movers,sk2),zero)
| decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_79,c_73]) ).
cnf(c_99,plain,
( greater(growth_rate(first_movers,sk2),zero)
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_80,c_73]) ).
cnf(c_100,plain,
( greater(zero,growth_rate(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_81,c_72]) ).
cnf(c_101,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_82,c_68]) ).
cnf(c_102,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_94,c_30]) ).
cnf(c_103,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_95,c_30]) ).
cnf(c_104,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_97,c_29]) ).
cnf(c_105,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_98,c_30]) ).
cnf(c_106,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_99,c_30]) ).
cnf(c_107,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_101,c_29]) ).
cnf(c_174,plain,
( decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_104,c_96]) ).
cnf(c_175,plain,
( decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(copy,[status(thm)],[c_174]) ).
cnf(c_109,plain,
( decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_110,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_109,c_67]) ).
cnf(c_176,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_110,c_103]) ).
cnf(c_111,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(copy,[status(thm)],[c_176]) ).
cnf(c_177,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_110,c_102]) ).
cnf(c_112,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_113,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_111,c_68]) ).
cnf(c_114,plain,
( greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_112,c_72]) ).
cnf(c_115,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_113,c_29]) ).
cnf(c_178,plain,
( constant(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_115,c_114]) ).
cnf(c_116,plain,
constant(cardinality_at_time(first_movers,sk2)),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_117,plain,
growth_rate(first_movers,sk2) = zero,
inference(resolve,[status(thm)],[c_116,c_74]) ).
cnf(c_118,plain,
growth_rate(efficient_producers,sk2) != zero,
inference(resolve,[status(thm)],[c_117,c_31]) ).
cnf(c_119,plain,
~ constant(cardinality_at_time(efficient_producers,sk2)),
inference(resolve,[status(thm)],[c_118,c_69]) ).
cnf(c_120,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_119,c_107]) ).
cnf(c_121,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_119,c_106]) ).
cnf(c_122,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_119,c_105]) ).
cnf(c_124,plain,
( greater(zero,growth_rate(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_119,c_100]) ).
cnf(c_179,plain,
( decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_124,c_120]) ).
cnf(c_143,plain,
decreases(cardinality_at_time(efficient_producers,sk2)),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_144,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(resolve,[status(thm)],[c_143,c_67]) ).
cnf(c_146,plain,
decreases(cardinality_at_time(first_movers,sk2)),
inference(resolve,[status(thm)],[c_144,c_122]) ).
cnf(c_147,plain,
increases(cardinality_at_time(efficient_producers,sk2)),
inference(resolve,[status(thm)],[c_144,c_121]) ).
cnf(c_149,plain,
greater(zero,growth_rate(first_movers,sk2)),
inference(resolve,[status(thm)],[c_146,c_72]) ).
cnf(c_150,plain,
greater(growth_rate(efficient_producers,sk2),zero),
inference(resolve,[status(thm)],[c_147,c_68]) ).
cnf(c_180,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(resolve,[status(thm)],[c_150,c_29]) ).
cnf(c_152,plain,
$false,
inference(resolve,[status(thm)],[c_149,c_180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 23:59:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3511040 was started by sandbox2 on n017,
% 0.08/0.37 % Fri Sep 25 23:59:48 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.40
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.40
% 0.15/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.40 % Length of proof is 105.
% 0.15/0.40 % Level of proof is 22.
% 0.15/0.40 % Maximum clause weight is 33.000.
% 0.15/0.40 % Given clauses 101.
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------